^
^Vr
THE LIBRARY
OF
THE UNIVERSITY
OF CALIFORNIA
LOS ANGELES
GIFT
Dr. K. R. Beigelman
'•k.
».
oPTiCKs:
O R, A
TREATISE
O F T H E
Reflections, Refradiqns^
InfieBions and Colours
O F
LIGHT.
ne Fourth Edition, correSied,
By Sir ISAAC NEWTON, Knt.
L O N D 0 N:
Printed for William Innys at the Wefl- End of St. Paul's, Mdccxxx.
©
837
■ ^. 'it
Advertifement L
ART of the en- fui?ig Difeourfe a- bout hight ivas "Written at the De- fire of fame Gen- tlemen of the Royal -Society, in the Tear 1^7^, and then fent to their Seeretary, and read at their Meetings, and the refiivas add- ed about tivehe Tears after to complete, the Theory ; except the third Book, and the lafl Propo- fit ion of the Second, vjhich "were fince put together out of f car- ter d Papers, To a\:oid be- ing engaged in Difputes about
A z thefe
Advertifement.
thefe Matters, I haw hitherto de- layed the printing, and jhould flill ha've delayed it, had not the Importunity of Friends prevailed upon me. If any other Papers nvrit on this SubjeB are got out of my Hands they are imperfeB, and ivere perhaps ^written before I had tried all the Experiments here fet do'von, and fully fatisfi- ed my felf about theLaivs of Re* fraBions and Compofttion of Co- lours. I have here publijUd "vjhat I think proper to eome abroad, mping that it may not be tran- Jlated into another hanguage mthout my Confem.
The Crowns of Colours, ivhieh fometimes appear about the Sun and Moon, I ha'oe endea'voured to gi've an Account of) but for
"want
Advertifement.
^o^ant of fufficient Obfer'vations leave that Matter to be farther examined. The Siibjeti of the Third Book I have alfo left im- perfeBy not having tried all the Experiments "which I intended ivhen Iivas about the fe Matters, nor repeated fome ofthofe ivhich I did try, until I had fatisfied my felf about all their Circum- fiances. To communicate vjhat I have tried, and leave the refl to others for farther Enquiry, is all my Defign in publijhing thefe Papers.
IndLettervjrittento Tlfr.Leib- nitz in the Tear I (!) 7^, and pub- lijhed by Dr, Wallis, / mention d a Method by vohich I had found fome general Theorems about fquaring Curvilinear Figures,
or
Advertifement.
or comparing them mth the Co- nic SeBions, or other the jimplefl Figures mth v)hich they may be compared. And fome Tears ago I lent out a Manuscript contain- ing fuch Theorems, and halving fince met mth fome Things copi- ed out of it, I have on this Occa- fion made it public k, prefixing to it ^//Introdudion, and Subjoin- ing a Scholium concerning that Method, And Ihavejoinedrnth it another fmall TraB concern- ing the Curvilinear Figures of the Second Kind, "which ivas alfo "written many Tears ago, and made knov)n to fome Friends, "who have folic it ed the making it publicL
April r. T M
1704. X. -L^«
dvertifement 11.
this Second Edition [hefeOpticks Iha've oMtted the Mathema- tical ^aBs publipd at the End of the former Edi- tion, as not belonging to the SiibjeB. And at the End of the Third Book I ha%w added fome Queflions. And to fiev) that I do not take Gratuity for an ejfential Property of Bodies, I have added one Queflion con- cerning its Caufe, chiifing to propofe it by "way of a Quefli- on, becaufe I am not yet fatif- fied about it for vjant of Expe- riments.
^^- IN.
Advertisement to this Fourth Edition.
HIS neuo Edition of Sir Ifaac Newtonx Opticks is carefully printed frow> the Third Edition, as it vjas correBed by the Author s oivn Hand, and left before his Death with the Bookfeller, Since Sir Ifaac j* Lediones Opticas, which he public kly read in the Uni'verfity of Cambridge in the Tears l66^, 16^0, and 16'ji, are lately printed, it has been thought proper to make at the bottom of the Pages fencer al Citations from thence, where may be found the Demonfirations, which the Au- thor omitted in thefe Opticks. *
C I]
THE
FIRST BOOK
O F
OPTICKS.
PART I.
", Y Delign in this Book is not to ex- plain the Properties of Light by Hy- pothefes, but to propofe and prove them by Reafon and Experiments : In order to which I ihall premife the following Definitions and Axioms.
B
DEFI-
B
O P T I C K S. DEFINITIONS.
D E F I N. I.
T the Rays of Light I under/land its leafi TartSy and thofe as well Siiccejive in the fame Lines, as Contemporary in feveral Lines. For it is manifeft that Light confifts of Parts, both Succeflive and Contemporary j becaufe in the fame place you may ftop that which comes one moment, and let pafs that which comes pre- fently after; and in the fame time you may Hop it in any one place, and let it pafs in any other. For that part of Light which is ftopp'd cannot be the fame with fhat which is let pafs. The leafl Light or part of Light, which may be flopp'd alone without the reft of the Light, or propagated alone, or do or fuffer any thing alone, which the reft of the Light doth not or fuifers not, I call a Ray of Light.
D E F I N. IL
Refrangibility of the Rays of Light, is their T>ifpofition to be refraBed or turned out of their Way in pafjing out of one tranfparent Body or Medium into another. And a greater or lefs Re- frangibility of Rays, is their Difpofition to be turned more or lefs out of their Way in like^ In- cidences on the fame Medium. Mathematicians ufually confider the Rays of Light to be Lines reaching from the luminous Body to the Body illuminated, and the refradiion of thofe Rays to be the bending or breaking of thofe lines in
their
BOOK! 3
their pafling out of one Medium into another. And thus may Rays and Refradions be confi- dered, if Light be propagated in an inftanr. But by an Argument taken from the i^qua- tions of the times of the Eclipfes of Jupiter i BatelliteSy it feems that Light is propagated in time, fpending in its pafTage from the Sun to us about feven Minutes of time: And therefore I have chofen to define Rays and Pvcfradions in fuch general terms as may agree to Light in both cafes.
D E F I N. in.
Reflexibility of Rays^ is fbeir Difpojitic?! to be rejieSted or turned back into the fame Mediu?n jroni any other Medium upon whoje Surface they fall. And Rays are more or lefs refexible, which are turned back more or lefs eafly. As if Light pafs out of a Glafs into Air, and by being iiiclmed more and more to the common Surface of the Glafs and Air, begins at length to be totally re- fledled by that Surface ; thofe io:::^ of Rays which at like Incidences are refledted moft co- pioully, or by inclining the Rays begin fooneil to be totally refledted, are mofl reflexible.
D E F I N. IV.
I'he A?jgle of Licidence is that Angle, u-hick, the Line defcribed by the incident Ray contains with the Perpendicular to the refeSiing or refracting Sur-- face at the, Point of Incidence,
p2 DEFIN,
4 O P T I C K S.
D E F I N. V.
^ke Afigle of Reflexion or HefraBion^ is the
Angle which the line defcribed by the i'-eJleBed or re-
fraBed Ray coiitaineth with the Perpendicular to
the refleBing or refraSiifig Surface at the Point of
Incidence,
D E F I N. VL
'^he Sines of Incidence^ Reflexion^ and Refra- Bion, are the Si?ies of the Angles of Incidence, Re- fexion, and Refr/^Bio?!.
D E F I N. VII.
^hc Light ivhofe Rays are all alike Refran- gible^ I call Simple, Homogeneal and Similar ; and that whofe Rays are fome more Refrangible than others, I call Compound, Heterogeneal and Diffijnilar. The former Light I call Homoge- neal, not becaufe I would affirm it fo in all re- ipedts, but becaufe the Rays which agree in Re- frangibility, agree at leaft in all thofe their other Properties which I confider in the following Difcourfe,
D E F I N. VIII.
\the Colours of Homogeneal Lights, I call Pri~ wary, Ilofjiogeneal and Simple j ajid thofe of He- teroge??.eal Lights, Heterogeneal ajid Compound. For thefe are always compounded of the colours of Homogeneal Lights j as will appear in the fol- lowing Difcourfe.
'O
AXIOMS.
B O O K I. 5
A X I 0 MS.
A X. I.
npHR Ajigks of RefexioJi and "Refracllon^ lit in one and the fame Flane with the A?igle of In- cidence.
A X. II.
'The Angle of Refexion is equal to the Angle of\ Incidence.
AX. III.
If the ref-aBed Ray be returned direclly back to the Poifit of Incidence^ itJJ:all be rfraBed into the Line before defcribed by the incident Ray.
A X. IV.
RefraBion out of the rarer Medium into the denfer, is made towards the Perpendicular ; that is, Jo that the A?igle of Refraclion be lefs than the Angle of Incidence.
: A X. \.
The Siiie of Incidence is either accurately or 'very nearly in a green Ratio to the Sine of Re- fraBion.
Whence if that Proportion be known in any one Inclination of the incident Ray, 'tis known in all the Inclinations, and thereby the Refra- iftion in all cafes of Incidence on the fame refra- <fting Body may be determined. Thus if the
B 3 R'efra-
6 O P T I C K S.
Refradion be made out of Air into Water, the Sine of Incidence of the red Light is to the Sine of its Refracftion as 4 to 3 . If out of Air into Glafs, the Sines are as 17 to 11. In Light of other Colours the Sines have other Proportions: but the difference is fo little that it need feldom be coniidered.
Suppofe therefore, that RS [ in Fig. i. ] repre- fents the Surface of ftagnating Water, and that C is the point of Incidence in which any Ray coming in the Air from A in the Line A C is refledled or refrad:ed, and I would know whither this Ray fhall go after Reflexion or Refraction: I ereA upon the Surface of the Water from the point of Incidence the Perpendicular CP and produce it downwards to Q^, and conclude by the firft Axiom, that the Ray after Reflexion and Re- fradiion, fliall be found fomewhere in the Plane of the Angle of Incidence ACP produced. I let fall therefore upon the Perpendicular C P jthe Sine of Incidence A D j and if the refiedted Ray be deflred, I produce AD to B fo that D B be equal to A D, and draw C B. For this Line C B fhall be the refiedted Ray j the Angle of Reflexion B C P and its Sine B D being e- qual to the Angle and Sine of Incidence, as they ought to be by the fecond Axiom, But if the refra(5led Ray be defired, I produce A D to H, fo that D H may be to A D as the Sine of Re- fradion to the Sine of Incidence, that is, (if the Light be red) as 3 to 4; and about the Center C and in the Plane A C P with the Radius CA defcribing a Circle ABE, I draw a parallel to the Perpendicular CPQ^, the Line HE cutting tl^e
Circum-
B O O K I. 7
Circumference in E, and joining C E, this Line CE fhall be the Line of the refradied Ray., For if E F be let fiiU perpendicularly on the Line P Q^ this Line E F fliall be the Sine of Re- fra<flion of the Ray C E, the Angle of Refradion being E C Qj^ and this Sine E F is equal to D H, and confequently in Proportion to the Sine of Incidence AD as 3 to 4.
In like manner, if there be a Prifm of Glafs (that is, a Glafs bounded with two Equal and Parallel Triangular ends, and three plain and well polifhed Sides, which meet in three Parallel Lines running from the three Angles of one end to the three Angles of the other end) and if the Refradion of the Light in pafTing crofs this Prifm be defired: Let ACB [inFig,2.] reprefent a Plane cutting this Prifm tranfverlly to its three Parallel lines or edges there where the Light pafleth through it, and let D E be the Ray in- cident upon the firft fide of the Prifm A C where the Light goes into the Glafs ; and by putting the Proportion of the Sine of Incidence to the Sine of Refradion as 1 7 to 11 find E F the firft refraded Ray. Then taking this Ray for the Incident Ray upon the fecond fide of the Glafs B C where the Light goes out, find the next refraded Ray EG by putting the Proportion of the Sine of Incidence to the Sine of Re- fradion as II to 17. For if the Sine of Inci- dence out of Air into Glafs be to the Sine of Refradion as 17 to 11, the Sine of Incidence out of Glafs into Air muil on the contrary be to the Sine of Refradipn as 11 to 15^ by the third; A?«tom»
S O P T I C K S.
Much after the fame manner, if A C B D [in Fig. 2'] reprefent a Glafs fpherically convex on both fides (ufually called aLem^ fuch as is a Burn- ing-glafs, or Speftacle-glafs, or an Objedt-glafs of a Telefcope) and it be required to know how Light faUing upon it from any lucid point Q^ fhall be refra(5led, let Q^JVI reprefent a Ray falling upon any point M of its firfl fpherical Surface A C B, and by ered;ing a Perpendicular to the Glafs at the point M, find the firll re- fracted Ray M N by the Proportion of the Sines 17 to 11. Let that Ray in going out of the Glafs be incident upon N, and then find the fecond refraded Ray N q by the Propor- tion of the Sines 1 1 to 17. And after the fame manner may the Refradion be found when the Lens is convex on one fide and plane or con- cave on the other, or concave on both fides.
A X. VI.
Homogeneal Rays which foiD from feveral Points cf any Objecl^ and fall perpendicularly or almoji perpendicularly on any refieSiing or refraBing Flane or fpherical Surface^ Jhall afterwards diverge from fo many other Points^ or be parallel to Jo tnany other Lines, or converge to fo many other Points^ either accurately or without any fetifble 'E,rror. And the fame thing will happen, if the Rays be refcBed or refracted fucceffively by two or three or more Plane or Spherical Surfaces.
The Point from which Rays diverge or to which they converge may be called their Focus, And the Focus of the incident Rays being gi- I'cn, that of the refleded or refraded ones may
be
B O O K I. 9
be found by finding the Refradtion of any two Rays, as above j or niore readily thus.
Caf. I. Let ACB [in Fig. 4.] be a refleding or refradling Plane, and Q^he Focus of the incident Rays, and Q ^ C a Perpendicular to that Plane. And if this Perpendicular be produced to q^ fo that ^ C be equal to Q^, the Point q fhall be the Focus of the refledted Rays : Or if ^ C be taken on the fame fide of the Plane with Q^, and in proportion to Q^ as the Sine of Incidence to the Sine of Refra6tion, the Point q fliall be the Focus of the refracted Rays.
Caf 2. Let ACB [in Fig. 5.] be the refleding Surface of any Sphere whofe Centre is E. Bi- fed: any Radius thereof, ( fuppofe EC) in T, and if in that Radius on the fame fide the Point T you take the Points Q^nd ^, fo that T Q^ T E, and T q^ be continual Proportionals, and the Point QJ)e the Focus of the incident Rays, the Point q fliall be the Focus of the refiedted ones.
Caf. 3. Let ACB [in Fig. 6.] be the refnidting Surface of any Sphere whofe Centre is E. In any Radius thereof E C produced both ways take E T and C t equal to one another and fe- verally in fuch Proportion to that Radius as the lefi^er of the Sines of Incidence and P^e- fradion hath to the difference of thofe Sines. And then if in the fame Line you find any two Points Q^nd ^, fo that T QJ^e to E T as E /^ to / q^ taking t q the contrary way from / which T QJAeth from T, and if the Point QJ)e the Focus of any incident Rays, the Point q fliall be the Focus of the refracted ones>
2 And
lo O P T I C K S.
And by the fame means the Focus of the Rays after two or more Reflexions or Refradions may be found.
Caf.^. Let ACBD [in Fig. 7.] be any refrad- ing Lens , fpherically Convex or Concave or Plane on either fide, and let C D be its Axis ( that is, the Line which cuts both its Surfaces perpendicularly, and paiTes through the Centres of the Spheres,) and in this Axis produced let F andybe the Foci of the refradled Rays found as above, w^hen the incident Rays on both iides the Lens are parallel to the fame Axis j and upon the Diameter F f bifecCled in E, defcribe a Circle. Suppofe now that any Point QJ>e the Focus of any incident Rsys. Draw QJ^ cutting the faid Circle in T and t^ and therein take t q m fuch proportion to / E as /^ E or T E hath to T Q^ Let / ^ lie the contrary way from t which T Q doth from T, and q fhall be the Focus of the, rcfrafted Rays without any 'fenfible Error, pro- vided the Point QJ)e not fo remote from the Axis, nor the Lens fo broad as to make any of the Rays fall too obliquely on the refracting Surfaces. *
And by the like Operations may the reflecting or refracHiing Surfaces be found when the two Foci are given, and thereby a Lens be formed, which Ihall make the Rays flow towards or from what Place you pleafe. -f-
* In our Author's LeEliones Optica:, Part I. Seft. IV. Prop. 29, 30, there is an elegant Method of determining thefe Foci ; not only in fpherical Surfaces, but likewife in any other curved Figure what- ev«r : And in Prop. 32, 33, the fame thing is done tor any Ray ly- ing out of the Axis.
f Ibid. Prop. ^4.
. Sq
B O O K I. It
So then the Meaning of this Axiom is, that if Rays fall upon any Plane or Spherical Surface or Lens, and before their Incidence flow from or towards any Point Q^ they fhall after Re- flexion or Refra6lion flow from or towards the Point q found by the foregoing Rules. And if the incident Rays flow from or towards feveral points Q^ the refleded or refradled Rays fliall flow from or towards fo many other Points q found by the fame Rules. Whether the refle<5t- ed and refracted Rays flow from or towards the Point q is eafily known by the fltuation of that Point. For if that Point be on the fame flde of the refleding or refracting Surface or Lens with the Point Q^ and the incident Rays flow from the Point Q^ the reflected flow towards the Point q and the refradled from it ; and if the incident Rays flow towards Q, the refleded flow from q, and the refraded towards it. And the contrary happens when q is on the other fide of the Surface.
A X. VIL
Wherever the Rays which come from all the Points of any Object meet again in Jo many Poi?its after they have been made to converge by RefeBion or RefraBion^ there they will make a Pi' Bure of the ObjeB upon any white Body on which they fall.
So if PR [in Fig. 3.] reprefent any Objed with- out Doors, and A B be a Lens placed at a hole in the Window-ihut of a dark Chamber, where- by the Rays that come from any Point Q^of I that
12 O P T I C K S.
that Qbje6t are made to converge and meet a- gain in the Point q j and if a Sheet of white Pa- per be held at q for the Light there to fall up- on it, the Pidlure of that Objed; P R will ap- pear upon the Paper in its proper jQiape and Co- lours. For as the Light which comes from the Point Q^goes to the Point q, fo the Light which comes from other Points P and R of the Objed:, will go to fo many other correfpondent Points p and r ( as is manifell by the fixth Axiom j ) fo that every Point of the Objed: fhall illuminate a correfpondent Point of the Pidure, and there- by make a Pidture like the Objed in Shape and Colour, this only excepted, that the Pidture fhall be inverted. And this is the Reafon of that vul- gar Experiment of cafting the Species of Objeds from abroad upon a Wall or Sheet of white Pa- per in a dark Room.
In like manner, when a Man views any Objed: P QR, [in Fig. 8.] the Light which comes from the feveral Points of the Objed is fo refraded by the tranfparent fkins and humours of the Eye, (that is, by the outward coat E F G, called the "Tunica Corfiea, and by the cryftalline hu- mour A B which is beyond the Pupil ;;z ^ ) as to converge and meet again in fo many Points in the bottom of the Eye, and there to paint the Pidure of the Objed upon that fkin (called the Tunica Retina ) with which the bottom of the Eye is covered. For Anatomifts, when they have taken off from the bottom of the Eye that out- ward and moft thick Coat called the Dura Ma- ter^ can then fee through the thinner Coats, the Pidures of Objeds , lively paint^ there- on^
B O O K I. 13
on. And thefe Pidlures, propagated by Mo- tion along the Fibres of the Optick Nerves in- to the Brain, are the caufe of Vilion. For ac- cordingly as thefe Pidtures are perfed: or im- perfedl, the Objed: is feen perfectly or imperfed:- ly. If the Eye be tinged with any colour (as in the Difeafe of the yawidice) fo as to tinge the Pidures in the bottom of the Eye with that Colour, then all Objeds appear tinged with the fame Colour. If the Humours of the Eye by old Age decay, fo as by (hrinking to make the Cornea and Coat of the Ci'yiialline Humour grow flatter than before, the Light will not be re- frad:ed enough, and for want of a fufficient Re- fraction will not converge to the bottom of the Eye but to fome place beyond it, and by con- fequence paint in the bottom of the Eye a con- fufed Pidlure, and according to the Indifl:in(ft- nefs of this Pidture the Objed: will appear con- fufed. This is the reafon of the decay of fight in old Men, and fhews why their Sight is mend- ed by Spedacles. For thofe Convex glalTes fup- ply the defed of plumpnefs in the Eye, and by increafing the Refradion make the Rays con- verge fooner, fo as to convene diftindly at the bottom of the Eye if the Glafs have a due de- gree of convexity. And the contrary happens in fhort-fighted Men whofe Eyes are too plump. For the Refradion being now too great, the Rays converge and convene in the Eyes before they come at the bottom > and therefore the Pidure made in the bottom and the Vifion caufed thereby will not be diftind, unlefs the Object be brought fo near the Eye as that the ,
place
14 o p T I c k: s.
place where the converging Rays convene may be removed to the bottom, or that the plump- nefs of the Eye be taken off and the Refrad:i- ons diminifhed by a Concave-glafs of a due de- gree of Concavity, or laflly that by Age the Eye grow flatter till it come to a due Figure: For fhort-fighted Men fee remote Objeds beft in Old Age, and therefore they are accounted to have the moft lafling Eyes.
A X. VIII.
An ObjeB fcen by Reflexion or "RefraSiion, ap' pears in that place from whence the Rays after their laji Reflexion or RefraBion diverge in falling on the SpeBators Eye,
If the Object A [in Fig.^!\ be feen by Reflexion of a Looking-glafs m n^ it fliall appear, not in its proper place A, but behind the Glafs at a, from whence any Rays AB, AC, AD, which flow from one and the fame Point of the Objed, do after their Reflexion made in the Points B, C, D, di- verge in going from the Glafs to E, F, G, where they are incident on the Spectator's Eyes. For theJf^ Rays do make the fame Picture in the bottom of the Eyes as if they had come from the Objed: really placed at a without the Inter- pofition of the Looking-glafs; and all Vifion is made according to the place and fliape of that Pidure.
In like manner the Obje6t D [in Fig. 2.] feen through a Prifm, appears not in its proper place D, but is thence tranflated to fome other place d fituated in the laft refraded Ray F G drawn backward from F to d. And
B O O K I. 15
And fo the'Objed: Q^[ in Fig. 10.] feentlirough tlie Lens A B, appears at the place q from whence the Rays diverge in paffing from the Lens to the Eye. Now it is to be noted, that the Image of the Objed; at q is fo much bigger or lelTer than the Objed: it felf at Q^, as the diftance of the Image at q from the Lens A B is bigger or lefs than the diftance of the Objed: at C^rom the fame Lens. And if the Objedl be feen through two or more fuch Convex or Concave-glafl'es, every Glafs fhall make a new Image, and the Object fhall appear in the pkce of the big- nefs of the laft Image. Which confideration un- folds the Theory of Microfcopes and Telefcopcs. For that Theory coniifts in almoll nothing elfe than the defcribing fuch Glafles as fliall make the laft Image of any Objedl as diHind and large and luminous as it can conveniently be made.
I have now given in Axioms and their Ex- plications the fum of what hath hitherto been treated of in Opticks. For what hath been ge- nerally agreed on I content my felf to allume under the notion of Principles, in order to what I have farther to write. And this may fuffice for an Introdu6tion to Readers of quick Wit and good Underftanding not yet verfed in Op- ticks : Although thofe who are already acquaint- ed with this Science, and have handled GlalTes, will more readily apprehend what followeth.
PROPO"
O P T I C K S.
PROPOSITIONS.
P ROP.l T H E O R. I.
T IG HTS which differ in Colour, differ alfo in Degrees of Refrangibility,
The Proof by Experiments.
Exper. I. I took a black oblong ftifF Paper terminated by Parallel Sides, and with a Per- pendicular right Line drawn crofs from one Side to the other, diftinguifhed it into two e- qual Parts. One of thefe parts I painted with a red colour and the other with a blue. The Paper was very black, and the Colours intenfe and thickJy laid on, that the Phaenomenon might be more confpicuous. This Paper I view'd through a Prifm of folid Glafs, wllofe two Sides through which the Light pafled to the Eye were plane and well polifhed, and contained an Angle of about fixty degrees ; which Angle I call the refracting; Angle of the Prifm. And whilft I view'd it, I held it and the Prifm before a Window in fuch manner that the Sides of the Paper were parallel to the Prifm, and both thofe Sides and the Prifm were parallel to the Horizon, and the crofs Line was*alfo parallel to it: and that the Light which fell from the Window upon the Paper made an Angle with the Paper, equal to that Angle which was made with the fame
Paper
B O O K I. J7
Paper by the Light refle6led from It to the Eye. Beyond the Prifm was the Wall of the Chamber under the Window covered over with black Cloth, and the Cloth was involved in Darknefs that no Light might be reflected from thence, which in palTing by the Edges of the Paper to the Eye, might mingle itfelf with the Light of the Paper, and obfcure the Phaenomenon there- of. Thefe things being thus ordered, I found that if the refracting Angle of the Prifm be turned upwards, fo that the Paper may feem to be lifted upwards by the Refraction, its blue half will be lifted higher by the Refradlon ; ban its red half. But if the refrad:ing Angle of the Prifm be turned downward, fo that the Paper may feem to be carried lower by the Refra- d:ion, its blue half will be carried fomethin^ lower thereby than its red half Wherefore in both Cafes the Light which comes from the blue half of the Paper tlirough the Prifm to the Eye, does in like Circumitances fuffer a greater Refradion than the Light which comes from the red half, and by confequence is m.ore refrangible.
Ilhijlration. In the eleventh Figure, M N reprefents the Window, and D E the Paper terminated with parallel Sides D J and H E, and by the tranfverfe Line F G diftinguiilied into two halfs, the one D G of an intenfely blue Colour, the other F E of an intenfely red. And ^ hC c a b reprefents the Prifm whofe refrading Planes KB b a and KC c a meet in the Edge of the refracting Angle *% a. This Edge A a being upward, is paralldftoth to
C the
i8 O P T I C K S.
the Horizon, and to the Parallel-Edges of the Paper D J and HE, and the tranfverfe Line FG is perpendicular to the Plane of the Window. And de reprefents the Image of the Paper {0,^x1 by Refraction upwards in fuch manner, that the blue half DG is carried higher to dg than the red half F E is to fe^ and therefore fuffers a greater Refrad:ion. If the Edge of the refracting Angle be turned downward, the Image of the Paper vv^ill be refraded downward j fuppofe to ^ e, and the blue half will be refracted lower to ^ y, than the red half is to 9 g.
Exper, 2. About the aforeiaid Paper, whofe two halfs were painted over with red and blue, and which was ftifflike thin Pafteboard, I lapped feveral times a llender Thred of very black Silk, in fuch manner that the feveral parts of the Thred might appear upon the Colours like fo many black Lines drawn over them, or like long and {lender dark Shadows caft upon them. I might have drawn black Lines with a Pen, but the Threds were fmaller and better defined. This Paper thus coloured and lined I fet againft a Wall perpendicularly to the Horizon, fo that one of the Colours might ftand to the Right Hand, and the other to the Left. Clofe before the Paper, at the Confine of the Colours below, I placed a Candle to illuminate the Paper ftrong- ly : For the Experiment was tried in the Night. The Flame of the Candle reached up to the lower edge of the Paper, or a very little higher. Then at the diftance of fix Feet, and one or two Inches from the Paper upon the Floor I ereCted a Giafs Lens four Inches ajid a quarter broad,
which
B O O K I. x^
which might colled: the Rays coming from the feveral Points of the Paper, and make them con- verge towards fo many other Points at the fame diftance of fix Feet, and one or two Inches on the other fide of the Lens, and fo form the Image of the coloured Paper upon a white Paper placed there, after the fame manner that a Lens at a Hole in a Window cafts the Images of Objedts abroad upon a Sheet of white Paper in a dark Room. The aforefiid white Paper, ere<5i:ed per- pendicular to the Horizon, and to the Rays which fell upon it from the Lens, I moved fometimes towards the Lens, fometimes from it, to find the Places where the Images of the blue and red Parts of the coloured Paper appear- ed mojft diftindt. Thofe Places I eafily knew by the Images of the black Lines which I had made by winding the Silk about the Paper. For the Images of thofe fine and flender Lines (which by reafon of their Blacknefs were like Shadows on the Colours) were confufed and fcarce vifi- ble, unlefs when the Colours on either fide of each Line were terminated moft diftindlly. No- ting therefore, as diligently as I could, the Places where the Images of the red and blue halfs of the coloured Paper appeared mofl di- flindt, I found that where the red half of the Paper appeared diftindt, the blue half appeared confufed, fo that the black Lines drawn upon it could fcarce be feen ; and on the contrary, where the blue half appeared mofl diftindt, the red half appeared confufed, fo that the black Lines upon it were fcarce vifible. And between the two Places where thefe Images appeared
C 3 diflindt
2® O P T I C K S.
diftind there was the diftance of an Inch atid a half; the diftance of the white Paper from the Lens, when the Image of the red. half of the co- loured Paper appeared moft diftind, being greater by an Inch and an half than the diftance of the fame white Paper from the Lens, when the Image of the blue half appeared moft diftind:. Irv like Incidences therefore of the blue and red upon the Lens, the blue was refradted more by the Lens than the red, fo as to converge fooner by an Inch and a half, and therefore is more refran- gible.
Illiijlration. In the twelfth Figure, D E iig- nifies the coloured Paper, D G the blue half, FE the red half, MN the Lens, HJ the white Paper in that Place where the red half with its black Lines appeared diftind, and h i the fame Paper in that Place where the blue half appeared diftind:. The Place h i was nearer to the Lens M N than the Place H J by an Inch and an half
^ Scholium. The fame Things fucceed, notwith- ftanding that fome of the Circumftances be va- ried y as in the firft Experiment when the Prifm and Paper are any ways inclined to the Hori- zon, and in both when coloured Lines are drawn upon very black Paper. But in the De- fcription of thefe Experiments, I have fet down fuch Circumftances, by which either the Phae- nomenon might be render'd more confpicuous, or a Novice might more eafily try them, or by which I did try them only. The fame Thing, I have often done in the following Experiments : Concerning all which, this one Admonition may
fuffice.
B O O K I. 2£
fuffice. Now from thefe Experiments It follows nor, that all the Light of the blue is more refran- gible than all the Light of the red : For both Lights are mixed of Rays differently refrangible, fo that in the red there are fome Rays not lefs re- frangible than thofe of the blue, and in the blue there are fome Rays not more refrangible than thofe of the red : But thefe Rays, in proportion to the whole Light, are but few, and ferve to dimi- nifh the Event of the Experiment, but are not able to deftroy it. For, if the red and blue Co- lours were more dilute and weak, the diflance of the Images would be lefs than an Inch and a half; and if they were more intenfe and full, that di- ftance would be greater, as will appear hereafter. Thefe Experiments may fuffice for the Colours of Natural Bodies. For in the Colours made by the Refradtion of Prifms, this Propof tion will ap- pear by the Experiments which are now to fol- low in the next Fropolition.
PROP. 11. The OR. II.
lie Light of the Sim confifls of Rajs differently Refrangible,
The Proof by Experiments.
Exper. 3. TN a very dark Chamber, at a round jj Hole, about one third Part of an Inch broaa, made in the Shut of a Window, I placed a Glafs Prifm, whereby the Beam of tlie Sun's Light, which came in at that Hole, might be refraj^ed upwards toward the oppofite \Vail
C 3 of
22 O P T I C K S.
of the Chamber, and there form a colour'd I- mage of the Sun. The Axis of the Prifm ( that is, the Line paffing through the middle of the Prifm. from one end of it to the other end pa- rallel to the edge of the Refracting Angle ) was in this and the following Experiments perpen- dicular to the incident Rays. About this Axis I turned the Prifm flowly, and faw the refradt- ed Light on the Wall, or coloured Image of the Sun, firfl to defcend, and then to afcend. Between the Defcent and Afcent, when the I- mage feemed Stationary, I ftopp'd the Prifm, and fix'd it in that Pofture, that it fhould be moved no more. For in that Pofture the Re- fractions of the Light at the two Sides of the refracting Angle, that is, at the Entrance of the Rays into the Prifm, and at their going out of it, were equal to one another*. So alfo in other Experiments, as often as I would have the Re-' fractions on both fides the Prifm to be equal to one another, I noted the Place where the Image of the Sun formed by the refraCted Light ftood ftill between its two contrary Motions, in the common Period of its Progrefs and Regrefs ; and when the Image fell upon that Place, I made faft the Prifm. And in this Pofture, as the moft convenient, it is to be underftood that all the Prifms are placed in the following Experiments, unlefs where fome other Pofture is defcribed. The Prifm therefore being placed in this Po- fture, I let the refracted Light fall perpendicu- larly upon a Sheet of white Paper at the oppo- fite Wall of the Chamber, and obferved the Fi-
* See eur AuthorV Leftiones Optica, Parti. Se£i. i. § !©• StU, II. § 29. and SeSl. III. frop. 25. gurc
B O O K I. Q3
gure and Dimenrions of the Solar Image form- ed on the Paper by that Light. This Image was Oblong and not Oval, but terminated with two Rectilinear and Parallel Sides, and tv/o Se- micircular Ends. On its Sides it was bounded pretty diftindtly, but on its Ends very confuled- ly and indiftindly, the Light there decaying and vanifl:iing by degrees. The Breadch of this Image anfwered to the Sun's Diam.eter, and was about two Inches and the eighth Part of an Inch, including the Penumbra. For the Image was eighteen Feet and an half dlftant from the Prifm, and at this diftance that Breadth, if di- minifhed by the Diameter of the Hole in the Window-fhut, that is by a quarter of an Inch, fubtended an Angle at the Prifm of about half a Degree, which is the Sun's apparent Diame- ter. But the Length of rhe Image was about ten Inches and a quarter, and the Length oi the Re- d-ilinear Sides about eight Inches ; and the re- fracting Angle of the Prifm, whereby fo great a Length was made, was 64 degrees. With a lefs Angle the Length of the Image was lefs, the Breadth remaining the fame. If the Prifm was turned about its Axis that way which made the Rays emerge more obliquely out of the fecond refracting Surface of the Prifm, the Image foon became an Inch or two longer, or morej and if the Prifm was turned about the contrary way, fo as to make the Rays fall more obliquely on the firft refraCting Surface, the Image fooa became an Inch or two fhorter. And there- fore in trying this Experiment, I was as curi- Qus as I could be in placing the Prifm by xhe
C 4 abo\^*
24 O P T I C K S.
above-mention'd Rule exadtly in fuch a Poflure, that the Refradions of the Rays at their Emer- gence out of the Prifm might be equal to that at their Incidence on it. This Prifm had fome Veins running along within the Glafs from one end to the other, which fcattered fome of the Sun's Light irregularly, but had no fenfible Ef- fect in increafing the Length of the coloured Spedirum. For I tried the fame Experiment with other Prifms with the fame Succefs. And particularly with a Prifm which feemed free from fuch Veins, and whofe refracting Angle was 625 Degrees, I found the Length of the Image 95 or 10 Inches at the diflance of i8| Feet from the Prifm, the Breadth of the Hole in the Window-fhut being J of an Inch, as be- fore. And becaufe it is eaiy to commit aMi- llake in placing the Prifm in its due Pofture, I repeated the Experiment four or five Times, and always found the Length of the Image that which is fet down above. With another Prifm of clearer Glafs and better Polifh, which feem- ed free from Veins, and whofe refracting Angle was 631 Degrees, the Length of this Image at the fam^e diftance of i8i Feet was alfo about 10 Inches, or loi Beyond thefe Meafures for a- bout a : or i of an Inch at either end of the SpeCtrum the Light of the Clouds feemed to be a little tinged with red and violet, but fo very faintly, that I fufpeded that TinCture might ei- ther v/holly, or in great Meafure arife from fome Rays of the Spedtrum fcattered irregularly by fome Inequalities in the Subftance and Polilli of the Glafs, and therefore I did not include it in I tliefe
B O O K I. 25
thefe Meafures. Now the different Magnitude of the hole in the Window-fhut, and different thicknefs of the Prifm where the Rays palled through it, and different inclinations of the Prifm to the Horizon, made no fenfible chan- ges in the length of the Image. Neither did the different matter of the Prifms make any: for in a Veffel made of polifhed Plates of Glafs cemented together in the fhape of a Prifm and filled with Water, there is the like Succefs of the Experiment according to the quantity of the Refradlion. It is farther to be obferved, that the Rays went on in right Lines from the Prifm to the Image, and therefore at their very going out of the Prifm had all that Inclina- tion to one another from which the length of the Image proceeded, that is, the Inclination of more than two degrees and an half. And yet according to the Laws of Opticks vulgarly re- ceived, they could not poffibly be fo much incli- ned to one another *. For let E G [ mFig. 1 3.] re- prefent the Window-fhut, F the hole made there- in through which a beam of the Sun's Light was tranfmitted into the darkned Chamber, and ABC a Triangular Imaginary Plane whereby the Prifm is feigned to be cut tranfverfly through the middle of the Light. Or if you pleafe, let ABC reprefent the Prifm it felf, looking di- redtly towards the Speftator's Eye with its nearer end; And let X Y be the Sun, MN the Pa- per upon which the Solar Image or Spectrum is caff, and P T the Image it felf whofe fides to- wards 1; and w are Redlilinear and Parallel, and ends towards P and T Semicircular. YKHP
and
* See OMx Author's Lenionei Opticcy Part. I. Sect. i. §.5.
^6 d p T I c K a
and X L J T are two Rays, the firft of. which comes from the lower part of the Sun to the higher part of the Image, and is refraded in the Prifm at K and H, and the latter comes from the higher part of the Sun to the lower part of the Image, and is refradted at L and J. Since the Refradions on both fides the Prifm are e- qual to one another, that is, the Refraction at K equal to the Refradion at J, and the Refra- dion at L equal to the Refradion at H, fo that the Refradions of the incident Rays at K and L taken together, are equal to the Refradions of the emergent Rays at H and J taken together : it follows by adding equal things to equal things, that the Refradions at K and H taken together, are equal to the Refradions at J and L taken together, and therefore the two Rays being e- qually refraded, have the fame Inclination to one another after Refradion which they had before ; that is, the Inclination of half a Degree anfwering to the Sun's Diameter. For fo great was the Inclination of the Rays to one another before Refradion. So then, the length of the Image P T would by the Rules of Vulgar Op- ticks fubtend an Angle of half a Degree at the Prifm , and by Confequence be equal to the breadth 'y w -, and therefore the Image would be round. Thus it would be were the two Rays XL JT and YKHP, and all the reft which form the Image P w T 'u, alike refrangible. And therefore feeing by Experience it is found that the Image is not round, but about five times longer than broad, the Rays which going to the upper end P of the Image fuffer the greateft Re- fradion,
BOOK I. a;
fradion, mufl be more refrarxgible than thofe which go to the lower end T, unlefs the Inequa- lity of Refradtion be cafual.
This Image or Spectrum P T was .coloured, being red at its leaft refradled end T, and vio- let at its moil refraded end P , and yellow green and blue in the intermediate Spaces. Which agrees with the firft Proportion, that Lights which differ in Colour, do alio differ in Refrangibility. The length of the Image in the foregoing Experiments, I meafured from the fainteft and outmoft red at one end, to the fainteft and outmoft blue at the other end, ex- cepting only a little Penumbra, whofe breadth fcarce exceeded a (quarter of an Inch, as was faid above.
Exper. 4. In the Sun's Beam which was pro- pagated into the Room through the hole in the Window-fhut , at the diffance of fome Feet from the hole, I held the Prifm in fuch a Po- llure, that its Axis might be perpendicular to that Beam. Then I looked through the Prifm upon the hole, and turning the Prifm to and fro about its Axis, to rhake the Image of the Hole afcend and defcend-, when between its two contrary Motions it feemed Stationary, I ftopp'd the Prifm, that the Refradions of both fides of the refrading Angle might be equal to each other, as in the former Experiment. In this Situation of the Priim viewing through it the faid Hole, I obferved the length of its re- fraded Image to be many times greater than its breadth, and that the moH: refraded part ■ thereof appeared violet, the lead refraded red, 2 the
28 O P T I C K S.
the middle parts blue, green and yellow in or- der. The fame thing happen'd when I remo- ved the Prifm out of the Sun's Light, and look- ed through it upon the hole fliining by the Light of the Clouds beyond it. And yet if the Refradtion were done regularly according to one certain Proportion of the Sines of Inci- dence and Refradion as is vulgarly fuppofed, the refraded Image ought to have appeared round.
So then, by thefe two Experiments it appears, that in equafi Incidences there is a confiderable inequality of Refractions. But whence this in- equality arifes, whether it be that fome of the incident Rays are refradled more, and others lefs, conftantly, or by chance, or that one and the fame Ray is by Refrad;ion difturbed, fliatter'd, dilated , and as it were fplit and fpread into ma- ny diverging Rays, as Grimaldo fuppofes, does not yet appear by thefe Experiments, but will appear by thofe that follow.
Exper. 5. Confidering therefore, that if in the third Experiment the Image of the Sun jfhould be drawn out into an oblong Form, ei- ther by a Dilatation of every Ray, or by any o- ther cafual inequality of the Refradions, the fame oblong Image would by a fecond Refra- dion made fideways be drawn out as much in breadth by the like Dilatation of the Rays, or o- ther cafual inequality of the Refradions fide- ways, I tried what would be the Effeds of fuch a fecond Refradion. For this end I ordered all things as in the third Experiment, and then placed a fecond Prifm immediately after the
firfl
B O O K L 2p
I firfl: in a crofs Pofition to it, that it might again refrad; the beam of the Sun*s Light which came to it through the firfl: Prifm. In the firfl Prifm this beam was refracted upwards, and in the fecond fideways. And I found that by the Re- fraction of the fecond Prifm, the breadth of the Image was not increafed, but its fuperior part, which in the firfl Prifm fuffered the greater Re- fradlion, and appeared violet and blue, did again in the fecond Prifm fuffer a greater Refradlion than its inferior part, which appeared red and yellow, and this without any Dilatation of the Image in breadth.
Illiijiration. Let S [in Fig. 14. ] reprefent the Sun, F the hole in the Window, ABC tlie iirfl Prifm, D H the fecond Prifm, Y the round Image of the Sun made by a diredl beam of Light when the Prifms are taken away, P T the oblong Image of the Sun made by that beam pafling through the firfl Prifm alone, when the fecond Prifm is taken away, and p t the Image made by the crofs Refradions of both Prifms together. Now if the Rays which tend to- wards the feveral Points of the round Image Y were dilated and fpread by the Refraction of the firfl Prifm, fg that they fhould not any lon- ger go in fmgle Lines to fingle Points, but that every Ray being fplit, fliattered, and changed from a Linear Ray to a Superficies of Rays di- verging from the Point of Refraction, and ly- ing in the Plane of the Angles of Incidence and Refraction, they fhould go in thofe Planes to fo many Lines reaching almofl from one end of the Image P T to the other, and if that Image
fhould
50 ' OP T I C K S.
fhould thence become oblong: thofe Rays and their feveral parts tending towards the feveral Points of the Image P T ought to be again di- lated and fpread fide ways by the tranfverfe Refraftion of the fecond Prifm, fo as to com- pofe a four fquare Image, fuch as is reprefented at iH. For the better underftanding of which, let the Image P T be diftinguiflied into five e- qual parts P QK, KQRL, LRSM, MSVN, N VT. And by the fame irregularity that the orbicular Light Y is by the Refraction of the firft Prifm dilated and drawn out into a long Image P T, the Light P QK which takes up a fpace of the fame length and breadth with the Light Y ought to be by the Refraftion of the fecond Prifm dilated and drawn out into the long Image tt q k p, and the Light K QjR. L into the long Image kqrl, and the Lights LRSM, MSVN, N V T, into fo many other long I- mages /r ^?;7, ?nsvny nvtl, and all thefe long Images would compofe the four fquare Image •TT?. Thus it ought to be were every Ray dila- ted by Refraction, and fpread into a triangular Superficies of Rays diverging from the Point of Refradlion. For the fecond Refradion would fpread the Rays one way as much as the firft doth another, and fo dilate the Image in breadth as much as the firft doth in length. And the fame thing ought to happen , were fome Rays cafually refradled more than others. But the Event is other wife. The Image P T was not made broader by the Refraction of the fecond Prifm., but only became oblique, as 'tis reprefented at / ^ , its upper end P being by
the
B O O K I. 31
the Refradion tranflatedto a greater diftance than its lower end T. So then the Light which went towards the upper end P of the Image, was ( at equal Incidences ) more refraded in the fecond Prifm, than the Light which tended towards the lower end T, that is the blue and violet, than the red and yellow j and therefore was more refran- gible. The fame Light was by the Refradion of the iirft Prifm tranflated farther from the place. Y to which it tended before Refraction ; and therefore fuffered as well in the firft Prifm as in the fecond a greater Refradion than the reft of the Light, and by confequence was more refran- gible than the reft, even before its incidence on the firft Prifm.
Sometimes I placed a third Prifm after the fecond, and fometimes alfo a fourth after the third, by all which the Image might be often refraded fideways: but the Rays which were more refradted than the reft in the firft Prifm were alfo more refraded in all the reft, and that without any Dilatation of the Image fideways : and therefore thofe Rays for their conftancy of a greater Refraction are defervedly reputed more refrangible.
But that the meaning of this Experiment may more clearly appear, it is to be confidercd that the Rays which are equally refrangible do fall upon a Circle anfwering to the Sun's Difque. For this was proved in the third Experiment. By a Circle I underftand not here a perfect geo- metrical Circle, but any orbicular Figure whofe length is equal to its breadth,' and which, as to Senfe, may feem circular. Let therefore A G
[in
32 O P T I C K S.
[in Fig. 15.] reprefent the Circle which all the niofl: refrangible Rays propagated from the whole Difque of the Sun, would illuminate and paint upon the oppofite Wall if they were a- lonej E L the Circle which all the leafl refran- gible Rays would in like manner illuminate and paint if they were alone; B H, C J, DK, the Circles which fo many intermediate forts of Rays would fucceffively paint upon the Wall, if they were fmgly propagated from the Sun in fucceflive order, the reft being always inter- cepted ; and conceive that there are other in* termediate Circles without Number , which innumerable other intermediate forts of Rays would fucceffively paint upon the Wall if the Sun fliould fucceffively emit every fort apart. And feeing the Sun emits all thefe forts at once, they muft all together illuminate and paint in- numerable equal Circles, of all which, being according to their degrees of Refrangibility placed in order in a continual Series, that ob- long Spedrum P T is compofed which I defcri- bed in the third Experiment. Now if the Sun's 'circular Image Y [in Fig. 14, 15.] which is made by an unrefradled beam of Light was by any Dilation of the fnigle Rays, or by any other irregularity in the Refra<5lion of the iirft Prifm, converted into the oblong Spedtrum, P T : then ought every Circle AG, B H, C J, ^c. in that Spedtrum, by the crofs Refradion of the fecond Prifm again dilating or other wife fcattering the Rays as before, to be in like man- ner drawn out and transformed into an oblong Figure, and thereby the breadth of the Image
" FT
B O O K I. 3 3
PT would be now as much augmented as tlie length of the Image Y was before by the Refra- dionof the firftPrifmj and thus by the Refra- ctions of both Prifms together would be formed a four fquare Figure p ir t% as I defcribed a- bove. Wherefore fmce the breadth of the Spe- drum PT is not increafed by the Refradion fideways, it is certain that the Rays are nqt fplit or dilated, or otherways irregularly fcatter'd by that Refradtion, but that every Circle is by a regular and uniform Refradion tranflated entire into another Place, as the Circle AG by the greateft Refradion into the place a gy the Circle B H by a lefs Refradioh into the place b h, the Circle C J by a Refradion ftill lefs into the place c i, and fo of the reft) by which means a new Spedrum p t inclined to the former P T is in like manner compofed of Circles lying in a right Line ; and thefe Circles muft be of the fame bignefs with the former, becaufe the breadths of all the Spedrums Y, P T and /> / at equal diftances from the Prifms are equal.
I conlidered farther, tliat by the breadth of the hole F through which the Light enters in- to the dark Chamber , there is a Penumbra made in the Circuit of the Spedrum Y, and that Penumbra remains in the redilinear Sides of the Spedrums P T and pt. I 'placed there- fore at that hole a Lens or Objed-glafs of a Te- lefcope w^hich might caft the Image of the Sun diftindly on Y without any Penumbra at all, and found that the Penumbra of the redilinear Sides of the oblong Spedrums P T and / 1 was
D alfo
34 O P T I C K S.
alfu thereby taken away, fo that thofe Sides ap- peared as diilindily defined as did the Circum- ference of the firft Image Y. Thus it happens if the Glafs of the Prifms be free from Veins, and their Sides be accurately plane and well polifhed without thofe numberlefs Waves or Curies which ufually arife from Sand-holes a little fmoothed in polilliing with Putty. If the Glafs be only well polifhed and free from Veins, and the Sides not accurately plane, but a little Convex or Concave, as it frequently happens; yet may the three Spedtrums Y, P T and p t want Penumbras , but not in equal diftances from the Prifms. Now from this want of Pe- numbras, I knew more certainly that every one of the Circles v/as refracted according to fome inoft regular, uniform and conftant Law. For if there were any irregularity in the Refra(5tion, rhe right Lines A E and G L, which all the Cir- cles in the Spe6lrum P T do touch, could not by that Refraction be tranflated into the Lines a e and ^ / as diflind: and fcraight as they were before, but there would arife in thofe tranflated Lines fome Penumbra or Crookednefs or Un- dulation, or other fenfible Perturbation contrary to what is found by Experience. Whatfoever Penumbra or Perturbation fhould be made in the Circles by the crofs Refraction of the fecond Prifm, all that Penumbra or Perturbation would be confpicuous in the right Lines ae and gl which touch thofe Circles. And therefore fince there is no fuch Penumbra or Perturbation in thofe right Lines, there muft be none in the Cir^ cles. Since the difbance between thofe Tangents
■2 or
B O O K r. 35
or breadth of the Spedrum is not increafed by the Refra<5tions, the Diameters of the Circles are not increafed thereby. Since thofe Tangents continue to be right Lines, every Circle wiiich in the iirft Prifm is more or lefs refraded, is exactly in the fame proportion more or lefs re- fracted in the fecond. And feeing all thefe things continue to fucceed after the lame man- ner when the Rays are again in a third Prifm, and again in a fourth refra6led fideways, it is evident that the Rays of one and the fame Circle, as to their degree of Refrangibility, continue al- ways uniform and homogeneal to one another, and that thole of feveral Circles do differ in de- gree of Refrangibility, and that in fome certain and conflant Proportion. Which is the thing I was to prove.
There is yet another Clrcumflance or two of this Experiment by which it becomes Hill more plain and convincing. Let the fecond Prifm DH [in Fig, i6.] be placed not immedi- ately after the firlt , but at fome diftance from it; fuppofe in the mid-way between it and the Wall on which the oblong Spe<5truni PT is caft, fo that the Light from the firft Prifm may fall upon it in the form of an ob- long Spedrum -r^ parallel to this fecond Prifm, and be refraded tideways to form the oblong Spedrum pt upon the Wall. And you- will find as before, that this Spedirum /> / is inclined to that Spedrum P T, which the firft Prifm forms alone without the fecond; the blue ends P and p being farther diftant from one another than the red ones T and /, and by confequence
D 2 ' that
3^ O P T I C K S.
that the Rays which go to the blue end cr of the Image <t 7, and which therefore fuffer the greateft Refradion in the firft Prifm, are again in the fecond Prifm more refradied than the reft.
The fame thing I try'd alfo by letting the Sun's Light into a dark Room through two lit- tle round holes F and (p [in Fig. 17.] made in the Window , and with two parallel Prifms ABC and a/Sy placed at thofe holes ( one at each ) refra6ting thofe two beams of Light to the oppofite Wall of the Chamber, in fuch man- ner that the tv/o colour'd Images P T and M N which they there painted were joined end to end and lay in one flraight Line, the red end T of the one touching the blue end M of the other. For if thefe two refracfted Beams were again. by a third Prifm DH placed crofs to the two firft , refraded fideways , and the Spedlrums thereby tranilated to fome other part of the Wall of the Chamber, fuppofe the Sped:rum P T to pt and the Spedrum M N to m ;/, thefe tranflated Spedrums p t and. m n would not lie in one ftraight Line with their ends contiguous as before, but be broken oif from one another and become parallel, the blue end m of the I- mage m n bein^ by a greater Refradion tran- flated farther from its former place M T, than the red end t of the other Image p t from the fam.e place M T ; which puts the Propofition pad Difpute. And this happens whether the third Prifm D H be placed immediately after the two firft, or at a great diftance from them, fo that the Light refraded in the two
firfl
B O O K I. ' 37
iirft Prifms be either white and circular, or co- loured and oblong when it falls on the third.
^xper. 6. In the middle of two. thin Boards I made round holes a third part of an Inch in diameter , and iri the Window-fliut a much broader hole being made to let into my dark- ned Chamber a large Beam of the Sun's Light; I placed a Prifm behind the Shut in that beam to refradl it towards the oppofite Wali, and clofe behind the Prifm I fixed one of the Boards, in fuch manner that the middle of the refradled Light might pafs through the hole made in it, and the reft be intercepted by the Board. Then at the diftance of about twelve Feet from the firft Board I fixed the other Board in fuch man- ner, that the middle of the refraded Light which canie through the hole in the firft Board, and fell upon the oppofite Wall, might pafs through the hole in this other Board , and the reft being intercepted by the Board might paint upon it the coloured Spectrum of the Sun. And clofe behind this Board I fixed another Prifm to rc- fra<ft the Light v/hich came through the hole. Then I returned fpeedily to the firft Prifm, and by turning it llowly to and fro about its Axis, I caufed the Image which fell upon the fecond Board to move up and down upon that Board, that all its parts might fucceflively pafs through the hole in that Board and fall upon the Prifm behind it. And in. the mean time, I noted the places on the oppofite Wall to which that Light after its Refraftion in the fecond Prifm did pafs ; and by the difference of the places I found that the Light which being ir.olt refraded in the
JD 3 firft
38 O P T I C K S.
firfl Prifm did go to the blue end of the Image, was again more refraded in the fecond Prifm than the Light which went to the red end of that Image, which proves as well the firfl Pro- portion as the fecond. And this happened whe- ther the Axis of the two Prifms were parallel, or inclined to one another, and to the Horizon in any given Angles.
TUnJlration. Let F \\xs.Fig. i8.] be the wide hole in the Window-ihut, through which the Sun fliines upon the firfl Prifrii ABC, and let the refracted Light fall upon the middle of the Board D E, and the middle part of that Light upon the hole G made in the middle part of that Board. Let this trajed:ed part of that Light fall again upon the middle of the fecond Board d e, and there paint fuch an oblong coloured I- mage of the Sun as was defcribed in the third Experiment. By turning the Prifm ABC flow- iy to and fro about its Axis, this Image will be made to move up and down the Board de, and by this means all its parts from one end to the other may be made to pafs fucceffively through the hole g which is made in the mid- dle of that Board. In the mean while another Prifm abcisto be fixed next after that hole gy to refrad: the trajed:ed Light a fecond time. And thefe things being thus orderea, I marked the places M and N of the oppofite Wall upon which the refracted Light fell, and found that whilft the two Boards and fecond Prifm re- mained unmoved, thofe places by turning the firfl: Prifm about its Axis were changed perpe- tually. For when the lower part of the Light
which
B O O K I. 3p
which fell upon the fecond Board d e \vas call through the hole g, it went to a lower place M on the Wall, and when the higher part of that Light was caft through the fame hole o-, it went to a higher place N on the Wall, and wheii any intermediate part of the Light was caft through that hole, it went to fome place on the Wall be- tween M and N. The unchanged Pofition of the holes in the Boards, made the L^cidence of the Rays upon the fecond Prifm to be the fame in all cafes. And yet in that common In- cidence fome of the Rays were more refra(5tcd, and others lefs. , And thofe were more refraded in this Prifm, which by a greater Refradion in the firft Prifm were more turned out of the way, and therefore for their Conftancy of being more refradied are defervedly called more refran- gible.
Exper. J. At two holes made near one ano- ther in my Window- fliut I placed two Prifms, one at each, which nii?;ht caft upon the oppo- fite Wall (after the manner of the third Expe- riment) two oblong coloured Luages of the Sun. And at a little diftance from the Wall I placed a long (lender Paper with ftraight and pa- rallel edges, and ordered the Prifms and Pa- per fo, that the red Colour of cneiCmage might fall diredly upon one half of the Paper, and the violet Colour of the other Image upon the other half of the fame Paper ; fo that the Pa- per appeared of two Colours, red and violet, much after the manner of the painted Paper in the firft and fecond Experiments. Then with a black Cloth I covered the Wall behind
D 4 thQ
40 O P T I C K S.
the Paper, that no Light might be refledied from it to difliirb the Experiment, and viewing the Paper through a third Prifm held parallel to it, I faw that half of it which was illuminated by the violet Light to be divided from the other half by a greater Refra(5lion, efpecially when I went a good way off from the Paper. For when I viewed it too near at hand, the two halfs of the Paper did not appear fully divided from one another, but feemed contiguous at one of their Angles like the painted Paper in the firft Experiment. Which alfo happened when the Paper was too broad.
Sometimes inftead of the Paper I ufed a white Thred, and this appeared through the Prifm divided into two parallel Threds as is repre- fented in the nineteenth Figure , where D G denotes the Thred illuminated with violet Light from D to E and with red Light from F to G, and d e fg are the parts of the Thred feen by Refradion. If one half of the Thred be con- ftanrly illuminated v/ith red, and the other half be ilkuninated with all the Colours fucceffively, ( which may be done by caufing one of the Prifms to be turned about its Axis whilft the other remains unmoved) this other half in view- ing the Thred through the Prifm, will appear in a continual right Line with the firfl half when illuminated with red, and begin to be a little divided from it when illuminated with Orange, jind remove farther from it when illuminated yvith yellow, and ftill farther when with green, ^nd farther when with blue, and go yet farther pff when illuriiinated with Iiidigo, and fartheft
when
B O O K L 41
when with deep violet. Which plainly fhews, that the Lights of feveral Colours are more and more refrangible one than another, in this Order of their Colours, red, orange, yellow, green, blue, indigo, deep violet j and fo proves as well the firft Proportion as the fecond.
I caufed alfo the coloured Spedrums P T [ in Fig. ij. ] and M N made in a dark Cham- ber by the Refradions of -two Prifms to lie in a Right Line end to end, as was defcribed above in the fifth Experiment, and viewing them through a third Prifm held parallel to their Length, they appeared no longer in a Right Line, but became broken from one another, as they are reprefented at ^ ^ and ;;/ ;/, the violet end m of the Specftrum m n being by a greater Refradion tranllated farther from its former Place M T than the red end t of the other Spedrum pt.
I farther caufed thofe two Spedtrums P T [ in Fig. 20. ] and M N to become co-incident in an inverted Order of their Colours, the red end of each falling on the violet end of the o- ther, as they are reprefented in the oblong Fi- gure PTMN J and then viewing them through a Prifm D H held parallel to their Length, they appeared not co-incident, as when view'd with the naked Eye, but in the form of two diftindt Spedrums p t and m n croffing one another in the middle after the manner of the Letter X. "Which fliews that the red of the one Spedrum and violet of the other, which were co-incident at PN and MT, being parted from one another by a greater Refradipn of the violet to p and m
thau
42 O P T I C K S.
than of the red to n and /, do differ in degrees of Refrangibility.
I illuminated alfo a little Circular fiece of white Paper all over with the Lights of both Prifms intermixed, and when it was illumina- ted with the red of one Speftrum, and deep violet of the other, fo as by the Mixture of thofe Colours to appear all over purple, I view- ed the Paper, firft at a lefs diflance, and then at a greater, through a third Prifmj and as I went from the Paper, the refracted Image there- of became more and more divided by the une- qual Refraction of the two mixed Colours, and at length parted into two diftind: Images, a red one and a violet one, whereof the violet v/as fartheft from the Paper, and therefore fuffered the greateft Refraction. And when that Prifm at the Window, which caft the violet on the Pa- per was taken away, the violet Image difiip- peared ; but when the other Prifm was taken away the red vaniflied ; which fhews, that thefe two Images were nothing elfe than the Lights of the two Prifms, which had been intermixed on the purple Paper, but were parted again by their unequal Refradions made in the third Prifm, through which the Paper was view'd. This alfo was obfervable, that if one of the Prifms at the Window, fuppgfe that which caft the violet on the Paper, v/as turned about its Axis to make all the Colours in this order,- vio- let, indigo, blue, green, yellow, orange, red, fall fucceffively on the Paper from that Prifm, the violet Image changed Colour accordingly, turning fucceffively to indigo, blue, green, yel- low
B O O K ^. 45
low and red, and in changing Colbur came nearer and nearer to the red Image made by the other Prifm, until when it was alfo red both Images be- came fully co-incident.
I placed alfo tv/o Paper Circles very near one another, the one in the red Light of one Prifm, and the other in the violet Light of the other. The Circles were each of tliem an Inch in diame- ter, and behind them the Wall was dark, that- the Experiment might not be diflurbed by any Light coming from thence. Thefe Circles thus illu* minated, I viewed through a Prifm fo held, that the Refradlion might be made towards the red Circle, and as 1 went from them they came nearer and nearer together, and at length became co- incident } and afterwards when I went flill far- ther off, they parted again in a contrary Order, the violet by a greater Refradtion being carried beyond the red.
Exper. 8. In Summer, when the Sun's Light ufes to be ftrongefl, I placed a Prifm at the Hole of the Window-fliut, as in the third Expe- riment, yet fo that its Axis might be parallel to the Axis of the. World, and at the oppofite Wall in the Sun's refrad:ed Light, I placed an open Book. Then going fix Feet and two Inches from the Book, 1 placed there the above- mentioned Lens, by which the Light reflected from the Book might be made to converge and meet again at the diftance of fix Feet and two Inches behind the Lens, and there paint the Species of the Book upon a Sheet of white Pa- per much after the manner of the fecond Ex- periment. The Book and Lens being made fall,
I no-
44 O P T I C K S.
I noted the Place where the Paper was, when the Letters of the Book, illuminated by the fuUeft red Light of the Solar Image falling upon it, did cafl their Species on that Paper moft diftinftly : And then I ftay'd till by the Motion of the Sun, and confequent Motion of his Image on the Book, all the Colours from that red to the middle of the blue pafs'd over thofe Let- ters J and when thofe Letters were illuminated by that blue, I noted again the Place of the Pa- per when they caft their Species moft diftincftly upon it : And I found that this laft Place of the Paper was nearer to the Lens than its former Place by about two Inches and an half, or two and three quarters. So much fooner therefore did the Light in the violet end of the Image by a greater Refradion converge and meet, than the Light in the red end. But in trying this, the Chamber was as dark as I could make it. For, if thefe Colours be diluted and weak- ned by the Mixture of any adventitious Light, the diftance between the Places of the Paper will not be fo great. This diftance in the fe- cond Experiment, where the Colours of natural Bodies were made ufe of, was but an Inch and an half, by reafon of the Imperfection of thofe Colours. Flere in the Colours of the Prifm, which are manifeftly more full, intenfe, and lively than thofe of natural Bodies, the diftance is two Inches and three quarters. And were the Colours ftill more full, I queftion not but that the diftance would be confiderably greater. For the coloured Light of the Prifm, by the inter- fering of the Circles defcribed in the fecond
Figure
B O O K L 45
Figure of the fifth Experiment, and alfo by the Light of the very bright Cloiick next the Sun's Body intermixing with thefe Colours, and by the Light fcattered by the Inequalities in the Polifh of the Prifin, was fo very much com- pounded, that the Species which thofe faint and dark Colours, the indigo and violet, caft upon the Paper were not diilind enough to be well ob- ferved.
Exper. g. A Prifm, whofe two Angles at its Bafe were equal to one another, and half right ones, and the third a right one, I placed in a Beam of the Sun's Light let into a dark Cham- ber through a Hole in the Window-fhut, as in the third Experiment. And turning the Prifin flowly. about its Axis, until all the Light which went through one of its Angles, and was refradl- ed by it began to be refled:ed by its Bafe, at which till then it went out of the Glafs, I cb- ferved that thofe Rays which had fuifered the greateft Pvcfradiion were fooner reflected than the refi:. I. conceived therefore, that thofe Ravs of the refledled Light, which were mofi: re- frangible, did firfl of all by a total Reflexion become more copious in that Light than the refi:, and that afterwards the refi: alfo, by a total Reflexion, became as copious as thefe. To try this, I made the refledted Light pafs through another Prifm, and being refracted by it to fall afterwards upon a Sheet of white Paper placed at fome difiance behind it, and there by that Refradion to paint the ufual Colours of the Prifm. And then caufing the firfi: Prifm to be turned about its Axis as above, I obferved that
when
4<5 O P T I C K S.
when thofe Rays, which in this Prifm had fuf- fered the greateft Refraction, and appeared of a bkie and violet Colour began to be totally re- flected, the blue and violet Light on the Paper, which was moft refracted in the fecond Prifm, received a fenlible Increafe above that of the red and yellow, which was leafl refracted ; and afterwards, when the reft of the Light which was green, yellow, and red, began to be totally reflected in the firft Prifm, the Light of thofe Colours on the Paper received as great an In- creafe as the violet and blue had done before. Whence 'tis manifeft, that the Beam of Light reflected by the Bafe of the Prifm, being aug- mented firft by the more refrangible Rays, and afterwards by the lefs refrangible ones, is com- pounded of Rays diiferently refrangible. And that all fuch reflected Light is of the fame Na- ture with the Sun's Light before its Incidence on the Bafe of the Prifm, no Man ever doubt- ed y it being generally allowed, that Light by fuch Reflexions fuffers no Alteration in its Modi- fications and Properties. I do not here take No- tice of any RefraCtions made in the fides of the firft Prifm, becaufe the Light enters it perpendi- cularly at the firft fide, and goes out perpendicu- larly at the fecond fide, and therefore fuffers none. So then, the Sun's incident Light being of tlie fame Temper and Conftitution with his emer- gent Light, and the laft being compounded of Rays differently refrangible, the firft muft be in like manner compounded.
lUuJtratmi. In the twenty-firft Figure, ABC is the firft Prifm, B C its Bafe, B and C its
equal
B O O K I. 47
equal Angles at the Bafc, each of 4^ Degrees, A its reftangular Vertex, F M a beam of the €un's Light let into a dark Room through a hole F one third part of an Inch broad, M its Incidence on the Bafe of the Prifm, M G a lefs refrafted Ray, M H a more refradted Ray, M N the beam of Light refleded from the Bafe, V X Y the fecond Prifm by which this beam in paffing through it is refradled, N t the lefs re- fraded Light of this beam, and N/> the more refraded part thereof. When the firft Prifm A B C is turned about its Axis according to the order of the Letters ABC, the Rays MH e- merge^more and more obliquely out of that Prifm, and at length after their moft oblique Emergence are refleded towards N, and going on to p do increafe the Number of the Rays N^. Afterwards by continuing the Motion of the iirft Prifm, the Rays M G are alfo refleded to N and increafe the number of the Rays N f. And therefore the Light MN admits into its Compofition, firft the more refrangible Rays, and then the lefs refrangible Rays, and yet af- ter this Compofition is of the fame Nature with the Sun's immediate Light F M, the Reflexion of the fpecular Bafe B C caufing no Alteration therein.
Rxper. 10. Two Prifms, which were alike in Shape, I tied fo together, that their Axis and oppofite Sides being parallel, they compofed a Parallelopiped. x^nd, the Sun finning into my dark Chamber through a little hole in the Win- dow-fliut , I placed that Parallelopiped in his beam at fome diftancc from the hole, in fuch a
Pofi:urc\
O P T I C K S.
Pofture, that the Axes of the Prifms might be perpendicular to the incident Rays , and that thole • Rays being incident upon the firft Side of one Prifm, might go on through the two contiguous Sides of both Prifms, and emerge out of the laft Side of the fecond Prifm. This Side being parallel to the firft Side of the firfl Prifm, caufed the emerging Light to be paral- lel to the incident. Then, beyond thefe two Prifms I placed a third, which might refrad; that emergent Light , and by that Refradiion caft the ufual Colours of the Prifm upon the oppofite Wall, or upon a fheet of white Paper held at a convenient Diftance behind the Prifm for that refracCled Light to fall upon it. After this I turned the Parallelopiped about its Axis, and found that when the contiguous Sides of the two Prifms became fo oblique to the inci- dent Rays, that thofe Rays began all of them to be refled:ed, thofe Rays which in the third Prifm had fuffered the greateft Refraction, and painted the Paper with violet and blue, were firft of all by a total Reflexion taken out of the tranfmitted Light , the reft remaining and on the Paper painting their Colours of green, yel- low, orange and red, as before ; and afterwards by continuing the Motion of the two Prifms, the reft of the Rays alfo by a total Reflexion vanift^ed in order, according to their degrees of Refrangibility. The Light therefore which emerged out of the two Prifms is compound- ed of Rays differently refrangible, feeing the more refrangible Rays may be taken out of it, while the lefs refrangible remain. But this
Light
B O O K I. 4p
Light being trajeded only through the parallel Superficies of the two Prifms, if it fuffer'd any change by the Refradlion of one Superficies it lofl that Impreihon by the contrary Refraction of the other Superficies, and fo being refbor'd to its priftine Conftitution, became of the fame Na- ture and Condition as at firfl before its Incidence on thofe Prifms ; and therefore, before its Inci- dence, was as much compounded of Rays diffe- rently refrangible, as afterwaVds.
llliiftration. In the twenty fecond Figure ABC and BCD are the two Prifms tied together in the form of a Parallelopiped , their Sides B C and C B being contiguous, and their Sides A B and C D parallel. And H J K is the third Prifm, by which the Sun's Light propagated through the hole F into the dark Chamber, and there pafiing through thofe fides of the Prifms AB, BC, CBandCD, is refraded at O to the white Paper P T, falling there partly upon P by a greater Refra6ticn, partly upon T by a lefs Refraction, and partly upon R and other in- termediate places by intermediate Ref rations. By turning the Parallelopiped A C B D about its Axis, according to the order of tlie Letters A, C, D, B, at length when the contiguous Planes B C and C B become futhciently oblique to the Rays F M, which are incident upon them at M, there will vanifh totally out of the refraded Light OPT, firfl of ail the mofl refraded Rays OP, (the reft OR and O T remaining as be- fore ) then the Rays O R and other intermedi- ate ones, and laftly, the leaft refracted Rays OT- For when the Plane BC becomes fufficiently
E oblique
50 O P T I C K S.
oblique to the Rays incident upon it , tliofe Rays will begin to be totally refleded by it to- wards N J and firft the moft refrangible Rays will be totally refledted ( as was explained in the preceding Experiment ) and by Confequence muft firft difappear at P , and afterwards the reft as they are in order totally refledted to N, they niuft difappear in the fame order at R and T. So then the Rays which at O fuf- fer the greatefl Refraftion, may be taken out of the Light M O whilft the reft of the Rays remain in it , and therefore that Light M O is compounded of Rays differently refrangi- ble. And becaufe the Planes A B and C D are parallel, and therefore by equal and con- trary Refradlions deftroy one anothers Ef- fects, the incident Light F M muft be of the fame Kind and Nature with the emergent Light M O, and therefore doth alfo confifl of Rays differently refrangible. Thefe two Lights F M and M O, before the moft refrangible Rays are feparated out of the emergent Light M O, a- gree in Colour, and in all other Properties lo far as my Obfervation reaches , and therefore are defervedly reputed of the fame Nature and Conftitution, and by Confequence the one is compounded as well as the other. But after the moft refrangible Rays begin to be totally refledted, and thereby feparated out of the e- mergent Light M O, that Light changes its Co- lour from white to a dilute and faint yellow, a pretty good orange, a very full red fuccef- fively, and then totally vanifties. For after the moft refrangible Rays which paint the Paper at 2 P with
B O O K I. 51
P with a purple Colour^ are by a total P.efje^ xion taken out of the beam of Light M O, the reft of the Colours which appear on the Paper at R and T being mix'd in the Liglit M O compound there a faint yellow, and after the blue and part of the green which appear on the Paper between P and R are taken away, the reft which appear between R and T ( that is the yel- low, orange, red and a little green) being mix- ed in the beam MO compouiid there an orange; and when all the Rays are by Reflexion taken out of the beam M O, except: the leaft refran- gible, which at T appear of a full red, their Colour is the fame in that beam M O as after- wards at T, the Refrafticn of the Prifm H J K ferving only to feparate the differently refrangible Rays, without making any Alteration in their Colours, as ftiall be more fully proved hereafter. All which confirms as well the firft Propofition as the fecond.
Scholium. If this Experiment and the former be conjoined and made one by applying a fourth Prifm VX Y [in Fig. 22.] to refra(5t the refied:ed beam M N towards //>, the Conclufion will be clearer. For then the Light N/> v/hich in the fourth Prifm is more refracted,- will become ful- ler and ftronger when the Light O P, which in the third Prifm H J K is more refracted, va- nifties at P; and afterwards when the lefs re- fracted Light O T vanifhes at T, the lefs re- fraded Light N t will become increafed whilft the more refracted Light at p receives no far- ther increafe. And as the traje6ted beam M O in vanifbing is always of fuch a Colour as ought
52 o p T I c K s:
to refult from the mixture of the Colours which fall upon the Paper P T , fo is the refleded beam M N always of fuch a Colour as ought to refult from the mixture of the Colours which fall upon the Paper p t. For when the mofl refrangible Rays are by a total Reflexion taken out of- the beam M O, and leave that beam of an orange Colour, the Excefs of thofe Rays in the refled:ed Light, does not only make the vio- let, indigo and blue at p more full, but alfo makes the beam M N change from the yellowidi Colour of the Sun's Light, to a pale white in- clining to blue, and afterward recover its yel- lowifli Colour again, fo foon as all the reft of the tranfmitted Light M O T is reflected.
Now feeing that in all this variety of Expe- riments , whether the Trial be made in Light refledled, and that either from natural Bodies, as in the firft and fecond Experiment, or fpe- cular, as in the ninth; or in Light refrad:ed, and that either before the unequally refracted Rays are by diverging fepa rated from one an- other, and loling their whitenefs which they have altogether, appear feverally of feveral Co- lours, as in the fifth Experiment; or after they are feparated from one another, and appear co- lour'd as in the fixth, feventh, and eighth Ex- periments; or in Light trajedted through paral- lel Superficies, deftroying each others Eifedis, as in the tenth Experiment ; there are always found Rays, which at equal Incidences on the fame Medium fufFer unequal Refractions, and that without any fplitting or dilating of fmgle Rays, or contingence in the inequality of the 3. Refra-
B O O K I. 53
Refradtions, as is proved in the fifth and fixth Experiments. And feeing the Rays which dif- fer in Refranglbility may be parted and forted from one another, and that either by Refradion as in the third Experiment, or by Reflexion as in the tenth, and then the fcveral forts apart at equal Incidences fuffer unequal Refradions, and thofe' forts are more refracted than others after Separation, which were more refraded before it, as in the fixth and following Experiments, and if the Sun's Light be trajeded through three or more crofs Prifms fucceffively, thofe Rays •which in the firft Prilm are refraded more than others, are in all the following Prifms refraded more than others in the fame Rate and Propor- tion, as appears by the fifth Experiment j it's manifeft that the Sun's Light is an heterogeneous Mixture of Rays, fome of which are conftantly more refrangible than others, as was propofed.
PROP, m. Theor. III. 'The Suns Light conftjls of PMys differing in Reflexibility^ and thofe Puiys are more reflexible than others 'which are more refra?igible.
np H I 8 is manifeft by the ninth and tenth *■- Experiments : For in the ninth Experi- ment, by turning the Prifm about its Axis, un- til the Rays within it which in going out into the Air were refraded by its Bafe, became fo oblique to that Bafe, as to begin to be totally
E 3 refiede4
54 O P T I C K S.
refleded thereby; thofe Rays became iirft of all totally refledied, which before at equal Inciden- ces with the reft had fuffered the greateft Refra-. (Stion. And the fame thing "happens in the Refle- xion made by the commDn Bafe of the two Prifms in the tenth Experiment.
PROP. IV. Prob. L
7v fepa7^ate from one another the heteroge- neous Rays of compound Light,
^"T^ H E heterogeneous Rays are in fome mea- -*- fure feparated from one another by the Refradion of the Prifm in the third Experi^ ment, and in the fifth Experiment, by taking a-r way the Penumbra from the redilinear fides of the coloured Image, that Separation in thofe ve- ry rcdilinear lides or ftraight edges of the I- mage becomes perfed. But in all places be- tween thofe rectilinear edges, thofe innumera- ble Circles there defcribed, which are feveral- ly illuminated by homogeneal Rays, by interfe- ring with one another, and being every where commix'd , do render the Light fufficiently compound. But if thefe Circles, whilft their Centers keep their Diftances and Pofitions, could be made lefs in Diameter, their interfering one with another, and by Confequence the Mixture of the heterogeneous Rays would be propor- tionally diminiih'd. In the twenty third Figure let AG, BH, CJ, DK, EL, FM be the Cir- cles which fo many forts of Rays flowing frppi
the
B O O K I. 55
the fame dlfque of the Sun, do in the third Ex- periment illuminate j of all • which and innu- merable other intermediate ones lying in a con- tinual Series between the two rectilinear and pa- rallel edges of the Sun's oblong Image P T , that Image is compos'd, as was explained in the fifth Experiment. And let ^^, bh^ ci^ d ky e /, fm be fo many lefs Circles lying in a like continual Series between two parallel right Lines ^y and g m with the fame diftances between their Centers, and illuminated by the fame forts of Rays, that is the Circle a g with the fmie fort by which the correfponding Circle A G was il- luminated, and the Circle b h with the furie fort by which the correfponding Circle B H was illu- minated, and the reft of the Circles ci, d k, el, fm refped;ively, with the fame forts of Rays by which the feveral correfponding Circles C J, D K, EL, F M were illuminated. In the Fi- gure P T compofed of the greater Circles, three of thofe Circles A G, B H, C J, are fo ex- panded into one another, that the three forts of Rays by which thofe Circles are illuminated , together with other innumerable forts of inter- mediate Rays, are mixed at Q^^ in the middle of the Circle B H. And the like Mixture happens throughout almofl the whole length of the Fi- gure P T. But in the Figure p t compofed of the lefs Circles, the three lefs Circles a g^ b hy c /, which anfwer to thofe three greater, do not ex- tend into one another j nor are there any v/liere mingled fo much as any two of the three forts of Rays by which thofe Circles are illuminated, and
E 4 whicls
5^
O P T I C K S.
which in the Figure P T are all of them inter- mingled at B H.
Now he that fhall thus conlider It, will eafily underfland that the Mixture is diminifhed in the fame Proportion with the Diameters of the Circles. If the Diameters of the Circles whilil . their Centers remain the fame, be made three times lefs than before, the Mixture will be alfo three times lefs; if ten times lefs, the Mixture will be ten times lefs, and fo of other Propor- tions. That is, the Mixture of the Rays in the greater Figure P T will be to their Mixture in the lefs/>/, as the Latitude of the greater Fi- gure is to the Latitude of the lefs. For the La- titudes of thefe Figures are equal to the Dia- meters of their Circles. And iience it eafily fol- lows, that the Mixture of the Rays in the re- 'fra(fted Spedlrum pt is to the Mixture of the Rays in the dired: and immediate Light of the Sun, as the breadth of that Spedrum is to the difference between the length and breadth of the fame Specflrum.
So then, if we would diminifh the Mixture of the Rays, we are to diminifli the Diameters of the Circles. Now thefe would be diminifh- ed if the Sun's Diameter to which they anfwer could be made lefs than it is, or ( which comes to the fame Purpofe) if without Doors, at a great diflance from the Prifm towards the Sun, fom.e opake Body were placed, with a round iioje in the middle of it , to intercept ail the Sun's Light , excepting fo much as coming from the middle of his Body could pafs through
that
BOOK! 57
that Hole to the Prifm. For fo the Circles A G, B H, and the reft, would not any longer anfwer to the whole Difque of the Sun, but only to that Part of it which could be feen from the Prifm through that Hole, that it is to the apparent Mag- nitude of that Hole view'd from the Prifm. But that thefe Circles may anfwer more diftindtly to that Hole, a Lens is to be placed by the Prifm to cafl the Image of the Hole, (that is, every one of the Circles AG, BH, &c.) . diflindly upon the Paper at PT, after fuch a manner, as by a Lens placed at a Windovy% the Species of Ob- jects abroad are caft diftindtly upon a Paper within the Room, and the red:ilinear Sides of the oblong Solar Image in the fifth Experiment became diilind: without any Penum.bra. If this be done, it will not be neceflary to place that Hole very far off, no not beyond the Win- dow. And therefore inftead of that Hole, I ufed the Hole in the Window-lluit, as fol- lows.
Expcr. II. In the Sun's Light let into my darken'd Chamber through a fmall round Hole in my Window-fluit, at about ten or twelve Feet from the Window, I placed a I^ens, by which the Image of the Hole might be diilindly call upon a Sheet of white Paper, placed at the diftance of fix, eight, ten, or twelve Feet from the Lens. For, according to the diffe* rence of the Lenfes I ufed various diftances, which I think not worth the while to defcribe. Then immediately after the Lens I placed a Prifm, by which the trajeded Light might be refracted either upwards or fide-ways, and there-
' by
y8 O P T I C K S.
by the round Image, which the Lens alone did caft upon the Paper might be drawn out into a long one with Parallel Sides, as in the third Ex- periment. This oblong Image I let fall upon another Paper at about the fame diftance from the Prifm as before, moving the Paper either towards the Prifm or from it, until I found the juil diftance where the Redilinear Sides of the Image became moft diflind:. For in this Cafe, theCircular Images of the Hole, which compofe that Image after the fame manner, that the Cir- cles ag^ bh^ ci^ &c. do the Figure ^/ [in Fig.21^ were terminated moft diftindly without any Penumbra, and therefore' extended into one ano- ther the leaft that they could, and by confequence the Mixture of the heterogeneous Rays was now the leaft of all. By this means I ufed to form an oblong Image (fuch as is p t) [in Fig. 23, and 24.] of Circular Images of the Hole, (fuch as are agy bh, ciy &;c.) and by ufmg a greater or^lefs Hole in the Window-fhut, I made the Circular Images a g, b hy ciy Sec. of which it was formed, to become greater or lefs at pleafure, and thereby the Mixture of the Rays in the Image p t to be as much, or as little as I de- fired.
IlluJlratio7i. In the tu'enty-fourth Figure, F reprefents the Circular Hole in the Window- fhut, MN the Lens, whereby the Image or Spe- cies of that Hole is caft diftindly upon a Paper at J, ABC the Prifm, whereby the Rays are at their emerging out of the Lens refrafted from. J towards another Paper at p /, and the round Image at J is turned into an oblong Image pt
falling
B O O K I. s-p
falling on that other Paper. This Image // con- lifts of Circles placed one after another in a Recti- linear Order, as was fufficiently cxplaii^^ed in the fifth Experiment j and thefe Circles are equal to the Circle J, and confequently anfwer in magni- tude to the Hole F^ and therefore by diminifhing that Hole they may be at pleafure diminiihed, whilft their Centers remain in their Places. By this means I made the Breadth of the Image p t to be forty times, and fometimes fixty or feventy times lefs than its Length. As for inflance, if tlie Breadth of the Hole F be one tenth of an Inch, and MF the diflance of the Lens from the Hole be 12 Feet; and \i pV> or pM the diftance of the Image pi from the Prifm or Lens be 10 Feet, and the refracting Angle of the Prifm be 62 Degrees, the Breadth of the Image pt will be one twelfth of an Inch, and the Length about iix Inches, and therefore the Length to the Breadth as 72 to i, and by confequence the Light of this Image 71 times lefs compound than the Sun's dired: Light. And Light thus far iimple and homogeneal, is fufficient for trying all the Experiments in this Book about fimple Light. For the Compofition of heterogeneal Rays is in this Light fo little, that it is fcarce to be difcovered and perceiv'd by Senfe, except per- haps in the indigo and violet. For thefe being dark Colours, do eafily fuffer a fenfible Allay by that little fcattcring Light which ufes to be refraded irregularly by the Inequalities of the Prifm.
Yet inftead of the Circular Llole F, 'tis better to fubftitute an oblong Hole iliaped like a long
Paral-
6o O P T I C K S.
Parallelogram with its Length parallel to the Prifm ABC. For if this Hole be an Inch or two long, • and but a tenth or twentieth Part of an Inch broad, or narrower j the Light of the Image ft will be as fimple as before, or fimpler, and the Image will become much broader, and there- fore more fit to have Experiinents try'd in its Lisht than before.
Inftead of this Parallelogram Hole may be fub- ftituted a triangular one of equal Sides, whofe Bafe, for inftance, is about the tenth Part of an Inch, and its Height an Inch or more. For by this means, if the Axis of the Prifm be parallel to the Perpendicular of the Triangle, the Image />^ [in Fig. 25.] will now be form'd of equicrural Triangles ^o-j bh^ ci, dk^ el,f?ji, &c. and in- numerable other intermediate ones anfwering to the triangular Hole in Shape and Bignefs, and lying one after another in a continual Series between two Parallel Lines ^y^and gm. Thefe Triangles, are a little intermingled at their Bafes, but not at their Vertices ; and therefore the Light on the brighter Side af of the Image, where the Bafes of the Triangles are, is a little compounded, but on the darker Side gm \% altogether uncom- pounded, and in all Places between the Sides the Compofition is proportional to the diftances of the Places from that obfcurer Side gm. And ha-? ving a Spedrum pt oi fuch a Compofition, we m.ay try Experiments either in its fcronger and lefs fimple Light near the Side af^ or in its weaker and fimpler Light near the other Side gm, as. it fhall feem mofl convenient.
But
B O O K L 6 1
But ill making Experiments of this kind, the Chamber ought to be made as dark as can be, left any Foreign Light mingle it felf with the Light of the Spedrum p t^ and render it com- pound J efpecially if we would try Experiments in the more fmiple Light next the Side g m of the Spectrum J which being fainter, will have a lefs proportion to the Foreign Light ; and fo • by the mixture of that Light be more troubled, and made more compound. The Lens alfo ought to be good, fuch as may ferve for opti- cal Ufes, and the Prifm ought to have a large Angle, fuppofe of 65 or 70 Degrees, and to be well wrought, being made of Glafs free from Bubbles and Veins, with its Sides not a little convex or concave, as ufually happens, but truly plane, and its Polifli elaborate, as in working Optick-glalTes, and not fuch as is ufually wrought with Putty, whereby the edges of the Sand- holes being worn away, there are left all over the Glafs a numberlefs Company of very little convex polite Rifings like Waves. The edges alfo of the Prifm and Lens, fo far as they may make any irregular Refraftion, muft be covered with 2l black Paper glewed on. ilad all the Light of the Sun's-Beam let into the Chamber, which is ufelefs and unprofitable to the Experi- ment, ought to be intercepted v/ith black Pa- per, or other bkck Obftacles. For otherwife the ufelefs Light being refled:ed every way in the Chamber, will mix with the oblong Spe- ctrum, and help to difturb it. In trying thefe Things, fo much diligence is not altogether ne- celiary, but it will promote tlie Succefs of the
Expe-
6i O P T I C K S.
Experiments, and by a veiy fcrupulous Examiner of Things deferves to be apply'd. It's difficult to get Glafs Prifms lit for riiis Purpofe, and there- fore I ufed fometimes prifmatick VelTels made with pieces of broken Looking-glaffes, and filled with Rain Water. And to increafe the Refradion, I fometimes impregnated the Water ftrongly with Saccharum Saturni,
PROP. V. Theor. IV.
Homogeneal Light is refraSied regularly ^without any D Hat atio7if putting or Jhatter^ ing of the Rays ^ a7id the co?if ufed Vijion of ObjeBs feen through refraEiing Bodies by heteroge7ieal Light arifes from the diffe-^ rent Refrangibility of fever al forts of Rays,
TH E firft Part of this Propofition has been already fufficiently proved in the fifth Ex- periment, and will farther appear by the Experi- ments which follow.
Exper. 12. In the middle of a black Paper I made a round Hole about a fifth or fixth Part of an Inch in diameter. Upon this Paper I caufed the Spedrum of homogeneal Light defcribed in the former Propofition, fo to fall, that fome part of the Light m.ight pafs through the Hole of the Paper. This tranfmitted part of the Light I refrafted with a Prifm placed behind ^he Paper, and letting this refracted Light fall perpendicularly upon a white Paper two or three Feet diftant from the Prifm, 1 found that
the
B O O K I. 63
the Spe6trum formed on the Paper by this Light was not oblong, as when 'tis made ( in the third Experiment) by refra-fling the Sun's compound Light, but was (fo far as I could judge by my Eye ) perfedily circular, the Length being no greater than the Breadtl 1. Which fhev/s, that this Light is refracted regularly without any Dilatation of the Rays.
Exper. 13. In the homogeneal Light I placed a Paper Circle of a quarter of an Lich in diameter, and in the Sun's unrefra6ted heterogeneal white Light I placed another Paper Circle of the fame Bignefs. And going from the Papers to the di- ftance of fomeFeet, I viewed both Circles through a Prifm. The Circle illuminated by the Sun's he- terogeneal Light appeared very oblong, as in the fourth Experiment, the Length being many times greater than the Breadth j but the other Circle, illuminated with homogeneal Light, appeared cir- (iular and diftindtly defined, as when 'tis view'd with the naked Eye. Which proves the whole Pro- pofition.
Exper. 14. In the homogeneal Light I placed Flies, and fuch-like minute Objedls, and view- ing them through a Prifm, I faw their Parts as diftindlly defined, as if I had viewed them with the naked Eye. The fame Objed:s placed in the Sun's unrefradted hetero2;eneal Lig-ht, which was white, I viewed alio through a Prifm, and faw them rnoxl confufcdly defined, fo that I could not diftinguiili their fmaller Parts from one another. I placed alfo the Letters of a fmall print, one while in the homogeneal Light, and then in the heterogeneal, and viewing them
through
^4 O P T I C K S.
through a Prifm, they appeared in the latter Cafe fo confufed and indiftin^t, that I could not read them J but in the former they appeared fo diftindt, that I could read readily, and thought I faw them as diflind:, as when I view'd them with my naked Eye. In both Cafes I view'd the fame Objeds, through the fame Prifm at the fame diftance from me, and in the fame Situation. There was no difference, but in the Light by which the Objedts were illuminated, and which in one Cafe was iimple, and in the other compound ; and there- fore, the diftindl Vifion in the former Cafe, and confufed in the latter, could arife from nothing elfe than from that difference of the Lights. Which proves the whole Propofition.
And in thefe three Experiments it is farther very remarkable, that the Colour of homogeneal Light w^as never changed by the Refrad:ion.
PROP. VL Theor. V.
T'he Sine of Incidence of every Ray confi- dered apart ^ is to its Sine of RefraEiion i7i a given Ratio,
THAT every Ray confider'd apart. Is con- ftant to it felf in fome degree of Refran- gibility, is fufficiently manifeft out of what has been faid. Thofe Rays, which in the firfh Re- fra(5tion, are at equal Incidences moll refraded, are alfo in the following Refradions at equal
Inci-
BOOK!. S^
Incidences moft refracted ; and fo of the leaft refrangible, and the reft which have any mean Degree of Refrangibility, as is manifeft by the fifth, fixth, feventh, eighth, and ninth Expe- riments. And thofe which the firft Tiilie at like Incidences are equally refraded, are again at like Incidences equally and uniformly retract- ed, and that whether they be refraded before they be feparated from one another, as in the fifth Expernnent, or whether they be refradted apart, as in the twelfth, thirteenth and four- teenth Experiments. The Refraction therefore of every Ray apart is regular, and what Rule that Refradiion obferves we are now to (liew*.
The late Writers in Opticks teach, that the Sines of Incidence are in a given Proportion to the Sines of Refradion, as was explained in the fifth Axiom ; and fome by Inllruments fit- ted for meafuring of Refractions, or otherwife experimentally examining this Proportion, do acquaint us that they have found it accurate. But whilft they, not underftanding the difife- rent Refrangibility of feveral Rays, conceived them all to be refraCted according to one and the fame Proportion, 'tis to be prefumed that they adapted their Meafures only to the middle of the refracted Light ; fo that from their Mea- fures we may conclude only that the R^iys which have a mean Degree of Refrangibility, that is, thofe which when feparated from the reft appear green, are refraCted according to a given Proportion ,of their Sines. And there-
* This is •venfulh treated of in our Author'/ Left. Optic Part \, Seil.lL
F fore
6& O F T I C K S.
fore we are now to fhew, that the like given Proportions obtain in all the reft. That it fhould be fo is very reafonable, Nature being ever conformable to her felf -, but an experimen- tal Proof is defired. And fuch a Proof will be had, if we can fliew that the Sines of Refradion of Rays differently refrangible are one to another ia a given Proportion when their Sines of Incidence are equal. For, if the Sines of Refraction of all the Rays are in given Proportions to the Sine of Refractions of a Ray which has a mean Degree of Refrangibility, and this Sine is in a given Propor- , tion to the equal Sines of Incidence, thofe other Sines of Refradtion will alfo be in given Propor- tions to the equal Sines of Incidence. Now, when the Sines of Incidence are equal, it will appear by the following Experiment, that the Sines of Refradion are in a given Proportion tQ one another.
Exper. 15. The Sun fhining into a dark Cham- ber through a little round Hole in the Window- fhut, let S [in Fig. 26.] reprefent his round white Image painted on the oppofite Wall by his dired: Light, P T his oblong coloured Image made by refrading that Light with a Prifm placed at the Window -, and p t, or 2p 2.t^ or 3/> 3 Z', his oblong colour'd Image made by refrading again the fame Light fide- ways with a fecond Prilm placed immediately after the firft in a crofs Pontion to it, as was explained in the fifth Experiment j that is to fay, p t when the Refradion of the fecond Prifm is fmall, zp 2 t when its Refracftion is greater, and 3 /> 3 ^ when it is greateft. For
fuch
B O O K I. 6j
fuch will be the diverfity of the Pvefradions, if the refrading Angle of the fecond Prifm be of various Magnitudes 3 fuppofc of fifteen or twen- ty Degrees to make the Image pt^ of thirty or forty to make the Image 2p 2t^ and of fixty to make the Image 3/> 3/. But for want of folid Glafs Prifms with Angles of convenient Big- neffes, there may be Veffels made of poliflied Plates of Glafs cemented together in the form of Prifms and filled with Water. Thefe things be- ing thus ordered, I obferved that all the folar Images or coloured Spectrums P T , />/ , 2p 2.ty 3/> 3^ did very nearly converge to the place S on which the dired Light of the Sun fell and painted his white round Image when the Prifms were taken away. The Axis of the Spe- ctrum PT, that is the Line drawn through the middle of it parallel to its re(5tilinear Sides , did when produced pafs exadtly through the middle of that white round Image S. And when the RefracStion of the fecond Prifm \t^s equal to the Refradion of the firfi:, the refrading An* gles of them both being about 60 Degrees, the Axis of the Spectrum 3/^3^ made by that Re- fraction, did when produced pafs alfo throuo-h the middle of' the fame white round Imao-e S. But when the Refraction of the fecond Prifm was lefs than that of the firft, the produced Axes of the SpeClrums tp or 2t 2p made by that Refraction did cut the produced A^xis of the Spectrum TP in the points m and fi, a lit- tle beyond the Center of that white round I- mage S. Whence the proportion of the Line 3/ T to the Line 3/>P was a little greater than
F 2 the
6% O P T I C K S.
d^e Proportion of 2/T to 2/>P, and this Pro- portion a little greater than that of iT to p P. Now -^vhefi the Light of the Spedtrum P T falls perpendicularly upon the Wall , thofe Lines 3 4fT, 3/»P, and2^T, 2/P, and ^T, /P, are the Tangents of the Refra<5tions, and therefore hy this Experiment the Proportions of the Tan-- gents of the Refradions are obtained , from whence the Proportions of the Sines being de- rived, they come out equal, fo far as by view- ing the SpeftrumSj and ufing fome mathemati- cal R^albiiing i could eftimate. For I did not irtaJic an accurate Computation. So then the Propolition holds true in every Ray apart, fo hr as appears by Experiment. And that it is accurately true, may be demonftrated upon this Suppolition. 1'hat Bodies refi-a^ Light by a5fing zipoti its Rays in Li?i€s perpmdicular to their Sur^ faces. But in order to this Demonftration, I muil diftinguifh the Motion of every Ray into two Motions, the one perpendicular to the refradiing Surface, the other parallel to it, and concerning the perpendicular Motion lay down the follow- ing Propolition.
If any Motion or moving thing whatfoever he incident with any Velocity on any broad and thin fpace terminated on both fides by two paral- lel Planes , and in its Paffage through that fpace be urged perpendicularly towards the far- ther Plane by any force which at given diftances fi-om the Plane is of given Quantities ; the per- pendicular velocity of that Motion or Thing, at is emerging out of that fpace, fhall be always equal to the fquare Root of the funi of the 3 . fquare
B O O K I. 69
fquare of the perpendicular velocit}^ of xki'iX Motion or Thing at its Incidence on that fpace^ and of the fquare of the perpendicular velocity wliich that Motion or Tiling would have at its Emergence, if at its Incidence its perpendicular velocity '^vas infinitely little.
And' the fame Propofition holds true of any Motion or Thing perpendicul^ly retarded in its paffage through that Ipace, if inilead of the iura of the two Squares you take their ditference;. The Demonflration Mathematicians v*ill eafily find out, and therefore I iliall not trouble the Reader with it.
Suppofe now that a Ray coming mod oblique- ly in the LineMC [in Fig. i.] be refradted at C by the Plane RS into the Line CN, and.jf it be required to find the Line CE, into which any other Ray AC fliall be refradjed ; let MC, AD, be the Sines of Incidence of the two Rays, and NG, EF, their Sines -of Refradion, and let the equal Motions of the incident Rays be reprcfented by the equal Lines MC and AC, and the Motion M C being confidered as parai^ lei to the refracting Plane, let the other Motion AC be diflinguiflied into two Motions AD and DC, one of which AD is parallel, and tlie other DC perpendicular to the refracfting Sur- face. In like manner, let the Motions of the emerging Rays be diftinguifh'd into two, whereof
the perpendicular ones are -^ CG and ^ CF.
And if the force of the refracting Plane begins to a<ft upon the Rays either in that Plane or at a Certain diftance from it on the one fide, and ends ^t a certain diftance from it on the other
F 3 Side
^o OPTIC K s.
fide, and in all places between .thofe two limits ad:« upoa the Rays in Lines perpendicular to that refrading Plane, and the Actions upon the Rays at equal diftances from the refrading Plane be equal, and at unequal ones either equal or un- equal according to any rate whatever j that Mo- tion of the Ray which is parallel to the re- frading Plane, will fuffer no Alteration by that Fopce 5 and that Motion which is perpendicular to it will be altered according to the rule of the foregoing Proportion. If therefore for the per- pendicular velocity of the emerging Ray C N
you write -^^ CG as above, then the perpendi- cular velocity of any other emerging Ray CE which was -^-^CF, will be equal to the fquarc
Root of CD^ -h f§^ CGq. And by fquaring
thefe Equals, and adding to them the Equals AD^ and MC^ — CD^, and dividing the Sums by the Equals CF^-f-EF^ and CG^-f-
NG^', you will have ~-^ equal to jf^- Whence
to, the Sine of Incidence, is to E F the Sine of efradion, as MC to NG, that is, in a given ratio. And this Demonftration being general, without determining what Light is, or by what kind of Force i: is refraded, or alTuming any thing farther than that the refrading Body ada upon the Rays in Lines perpendicular to its Sur-. face J I take it to be a very convincing Argument of the full truth of this Propoiition,
So then, if the ratio of the Sines of Inci- dence and Refradion of any fort of Rays be
found
BOOK I. 7.1
' found in any one cafe, 'tis given in all cafes; and this may be readily found by the Method in the following Propofition.
PROP, VII. Theor. VI. ^he PerfeEiion of Telef copes is hnpeded by the different Refrangibilitj of the Rays of Light.
THE Imperfedtion of Telefcopes is vul- garly attributed to the fpherical Figures of the Glaffes, and therefore Mathematicians have propounded to figure them by the conical Sedi- ons. To fhew that they are miftaken, I have in- ferted this Propofition ; the truth of which will appear by the nieafure of the Refractions of the feveral forts of Rays ; and thefe meafures I thus determine.
In the third Experiment of this firft Part, .where the refracting Angle of the Prifm was 62^ Degrees, the half of that Angle 31 deg. 15 min. is the Angle of Incidence of the Rays at their go- ing out of the Glafs into the Air * ; and the Sine of this Angle is 5 188, the Radius being loooo. When the Axis of this Ptifm was parallel to the Horizon, and the Refraction of the Rays at their Incidence 6n this Prifm equal to that at their Emergence out of it, I obferved v/ith a Quadrant the Angle which the mean refrangible P ays, ( that is thofe which went to the middle of the Sun's coloured Image ) made with the Horizon, and by this Angle and the Sun's altitude obferved at the fame time, I found the
• Seesur AxiXhox's Left. Optic. Parti. Sed. II. §. 29.
F 4 Angle
7x O P T I C K S.
Angle which the emergent Rays contained with the incident to be 44 deg. and 40 min. and the half of this Angle added to the Angle of Incidence 3 1 deg. 15 min. makes the Angle of Refracflion, which is therefore 5 3 deg. 35 min. and its Sine 8047. Thefe are the Sines of Incidence and Refradtion of the m^an refrangible Rays, and their Proportion in round Numbers is 20 to 3 1. This Glafs was of a Colour inclining to green. The laft of the Prifms mentioned in the third Experiment was of clear white Glafs. Its refracting Angle 635 Degrees. The Angle which the emergent Rays contained, with the incident 45 deg. 50 min. The Sine of half the firft Angle 5262. The Sine of half the Sum of the Angles 8157. ^^^^ their Proportion in round Numbers 2a to 3 1, as before.
From the Length of the Image, which was about 95 or 10 Inches, fubdud its Breadth, which was 2s Inches, and the Rerhainder 71 Inches would be the Length of the Image were the Sun but a Point, and therefore fubtends the Angle which the moft and leafl refrangible Rays, when incident on the Prifm in the fame Lines, do
.'contain with one another after their Emergence. "Whence this x^^ngle is 2 deg. o'. f. For, the
^^if^ance between the Image and the Prifm where this Angle is made, was iSj- Feet, and at that diftance the Chord 7^ Inches fubtends an Angle of 2 deg. o'. y". Now half this Angle is the Angle which thefe emergent Rays con-
' taiH with the emergent mean refrangible Rays, and a quarter thereof, that is 30'. 2". may be accounted the Angle which they would contain with the fame emergent mean refrangible Rays,
were
B O OK I. 73
were they co-incident to them within the Clafs, and fuffered no other Refraction than that at.their Emergence. For, if two equal Refractions, the one at the Incidence of the Rays on the Prifm, the other at their Emergence, make half the Angle 2 deg. o'. 7''. then one of thofe RefraCtions will make about a quarter of that Angle, and this quarter added to, and fubduded from the Angle of Refraction of the mean refrangible Rays, which was 53 deg. 35', gives the Angles of Re- fraCtion of the moft and leaft refrangible Rays 54 deg. 5' 2", and 53 deg. 4' 58", whofe Sines are 8099 and 7995, the common Angle of In- cidence being 31 deg. 15', and its Sine 5188; and thefe Sines in the leafl round Numbers are in proportion to one another, as 78 and 'jj to 50.
Now, if you fubduCt the common Sine of In- cidence 50 from the Sines of RefraCtion 'jy and 78, the Remainders 27 and 28 fliew, that in fmall Refractions the RefraCtion of the leafl refrangi- ble Rays is to the Refraction of the moft refran- gible ones, as 27 to 28 very nearly, and that the difference of the RefraCtions of the leafl refran- gible and mofl refrangible Rays is about the 27kh Part of the whole RefraCtion of the mean refrangible Rays.
Whence they that are skilled in Opticks.will eafily underfland, *' that the Breadth of the leafl circular Space, into which ObjeCt-glaffes of Te- lefcopes can colleCt all forts of Parallel Rays, is about the 27^th Part of half the Aperture of the Glafs, or 55 th Part of the whole Aperture ; and
* This is demonfi rated in our AuihoiV Led. Optic. Part I. SeSI. IV. Fyp. 57.
that
74 O P T I C K a
that the Focus of the moft refrangible Rays is nearer to the Objeft-glafs than the Focus of the leaft refrangible ones, by about the 275th Part of the diflance between the Objed:-glafs and the Focus of the mean refrangible ones.
And if Rays of all forts, flowing from any one lucid Point in the Axis of any convex Lens, be made by the Refra(3:ion of the Lens to con- verge to Points not too remote from the Lens, the Focus of the mofl: refrangible Rays fliall be nearer to the Lens than the Focus of the leaft refrangible ones, by a diflance which is to the 275th Part of the diftpnce of the Focus of the mean refrangible Rays from the Lens, as the di- ftance between thrt Focus and the lucid Point, from whence the Rays flow, is to the diflance be- tween that lucid Point and the Lens very nearly.
Now to examine whether the Difference be- tween the Refra([lions, v^hich the mofl refrangi- ble and the leaft refrangible Rays flowing from the fame Point fuffer in the Objed-glafTes of Te- lefcopes and fuch-like Glafles, be fo great as is here defcribed, I contrived the following Experi- ment. •
Exper. 16. The Lens which I ufed in the fe- cond and eighth Experiments, being placed fix Feet and an Inch diflant from any Obje6t, col- leifled the Species of that Objed: by the mean refrangible Rays at the diflance of fix Feet and an Inch from the Lens on the other fide. And therefore by the foregoing P-ule, it ought to col- led the Species of that Objedl by the leafl re- frangible Rays at the diftance of fix Feet and 31 Inches from the Lens, and by the mofl re- • -' frangible
BOOK! 75
frangible ones at the diftance of five Feet and iQi Inches from it: So that between the two Places, where thefe lead and moft refrangible Rays colledl the Species, there may be the di- ftance of about 5^ Inches. For by that Rule, as fix Feet and an Inch (the diftance of the Lens from the lucid Obje6t) is to twelve Feet and two Inches ( the diflance of the lucid Objedt from the Focus of the mean refrangible Rays ) that is, as One is to Two; fo is the 27ith Part of fix Feet and an Inch '(the diftance between the Lens and the fame Focus) to the diftance between the Focus of the moft refrangible Rays and the Focus of the leaft refrangible ones, which is therefore 5g Inches, that is very nearly 5^ Inches. Now to know whether this Meafure was true, I repeated the fecond and eighth Ex- pariment with coloured Light, which was lefs compounded than that I there made life of: For I now feparated the heterogeneous Rays from one another by the Method I defcribed in the eleventh Experiment, fo as to make a coloured SpecStrum about twelve or fifte^sn Times longer than broad. This Spectrum I caft on a printed Book, and placing the above-mentioned Lens at the diftance of lix Feet and an Inch from this Spectrum to colleft the Species of the illuminated Letters at the fame diftance on the other lidey I found that the Species of the Letters illuminated with blue were nearer to the Lens than thole illuminated with deep red by about three Inches, or three and a quar- ter ; but the Species of the Letters illumi- nated with indigo and violet appeared fo con- I fufed
75 O P T I C K S.
fufed and indiftindt, that I could not read them : Whereupon viewing the Prifm, I found it was s^ full of Veins running from one end of the Glafs to the other j fo that the Refradion could not be regular. I took another Prifm therefore which was free from Veins, and inftead of the Letters I ufed two or three Parallel black Lines a little broader than the Strokes of the Let- ters, and calling the Colours upon thefe Lines in fuch manner, that the Lines ran along the Colours from one end of the Spedrum to the other, I found that the Focus where the indigo, or confine of this Colour and violet caft the Species of the black Lines mofl diilindly, to be about four Inches, or 4^ nearer to the Lens than the Focus, where the deepefl red caft the Species of th^ fame black Lines mofl diilind:- ly. The violet was fo faint and dark, that I could not difcern the Species of the Lines di- ilindly by that Colour j and therefore confi- dering that the Prifm was made of a dark co- loured Glafs inclining to green, I took another Prifm of clear white Glafs ; but the Spedrum of Colours which this Prifm made had long white Streams of faint Light (liooting out from both ends of the Colours, which made me con- clude that fomething w'as amifs j and viewing the Prifm, I found two or three little Bubbles ja the Glafs, which refraded the Light irregu- lar! v. Wherefore I covered that Part of the Glafs with black Paper, and letting the Light pafs throucrh another Part of it which was free from fuch Bubbles, the Spedrum of Colours became free from thofe irregular Streams of Light, and,
was
B o o k: I. >7
was now fuch as I defircd. But ftill^I found the violet fo dark and faint, that I could fcarce fee the Species of the Lines by the violet, and* not at all by the deepeft Part of it, which was next the end of the Spc,(5lrum. I fufpeded there- fore, that this faint and dark Colour might be allayed by that fcattering Light which was re- fraded, and refleded irregularly, partly by fome very fmall Bubbles in the GlafTes, and partly by the Inequalities of their Polifh ; which Light, tho' it was but little, yet it being of a white Colour, might fuffice to affed the Senfe fo ftrongly as to difturb the Phaenomena of that weak and dark Colour the violet, and there- fore I tried, as in the 12th, 13th, and 14th Ex- periments, whether the Light of this Colour did not confifl of a fenfible Mixture of heteroge- neous Rays, but found it did not. Nor did the Refradlions caufe any other fenfible Colour than violet to emerge ©ut of this Light, as they would have done out of white Light, and by confequence out of this violet Light had it been fenlibly compounded with white Light. And therefore I concluded, that the reafon why I could not fee the Species of the Lines diftindly by this Colour, was only the Darknefs of this Colour, and Thinnefs of its Light, and its di- ftance from the Axis of the Lens j I divided therefore thofe Parallel black Lines into equal Parts, by which I might readily know the di- ftances of the Colours in the Speftrum from one another, and noted the diftances of the Lens from the Foci of fuch Colours, as c<ift the . Species of the Lines dillindtly, and then confi-
dered
'7& O P T I C K S.
dered vvlaether the difference of thofe distances bear fuch proportion to 5| Inches, the greatefl Difference of the diftances, which the Foci of the deepefl red and violet ought to have from the Lens, as the diflance of the obferved Co- lours from one another in the Speftrum bear to the greatefl diflance of the deepeft red and violet meafured in the Redilinear Sides of the Spedrum, that is, to the Length of thofe Sides, or Excefs of the Length of the Spedrum above its Breadth. And my Obfervations were as fol- lows.
When I obferved and compared the deepefl fenfible red, and the Colour in the Confine of green and blue, which at the Redilinear Sides of the Spedirum was diftant from it half the Length of thofe Sides, the Focus where the Con- fine of green and blue cafl the Species of the Lines diflindly on the Paper, was nearer to the Lens than the Focus, where the red cafl thofe Lines diflind:ly on it by about 25 or 2~ Liches. For fometimes the Meafures were a Jittle greater, fometimes a little lefs, but feldom varied from one another above \ of an Inch. For it was very difficult to define the Places of the Foci, with- out fome little Errors. Now, if the Colours diflant half the Length of the Image, ( mea- fured at its Rectilinear Sides) give 25 or 2| Diffe- rence of the diflances of their Foci from the Lens, then the Colours dillant the whole Length ought to give 5 or 55 Inches difference of thofe diflances.
Bpt here it's to be noted, that I could not fee the red to the full end of the Sped:rum,
biit
B O O K I. 7p
but only to the Center of the Semicircle which bounded that end, or a little farther j and there- fore I compared this red not with that Colour which was exadlly in the middle of the Spedlrum, or Confine of green and blue, but with that which verged a little more to the blue than to the green : And, as I reckoned the whole Length of the Colours not to be the whole Length of the Spedjum, but the Length of its Redilinear Sides, fo compleating the femicircularEnds into Circles, when either of the obferved Colours fell within thofe Circles, I meafured the diftance of that Colour from the femicircular End of the Spe- drum, and fubdudting half this diftance from the meafured diftance of the two Colours, I took the Remainder for their corrected di- ftance; and in thefe Obfcrvations fet down this correfted diilance for the difference of the di- flances of their Foci from the Lens. For, as the Length of the Rectilinear Sides of the Spe- <3:rum would be the whole Length of all the Colours, were the Circles of which ( as we Ihewed) that Spedrum confifts contraded and reduced to Phyfical Points, fo in that Cafe this correded diftance would be the real diftance of the two obferved Colours.
When therefore I farther obferved tlie deepcft fenfible red, and that blue whofe correded di- . ftance from it was i_ Parts of the Length of the Redilinear Sides of the Spedrum, the diffe- rence of the diftances of their Foci from the Lens was about 3^ Inches, and as 7 to 12, fo is 3? ^o S'v
When
8o O P T I C K S.
When I obferved the deepeft fenfible red, and that indigo whofe corredied diftance was ~ or | of the Length of the Rediilinear Sides of the Spe- (ftrum, the difference of the diftances of theii^ Foei from the Lens, was about 3I Inches, and as 2 to 3, fois3|to 5I.
When I obferved the deepefl fenfible red, and that deep indigo whofe corredted diftance from one another was ^ or l of the Length of the Rectilinear Sides of the Spectrum, the diffe- rence of the diftances of their Foci from the Lens was about 4 Inches -, and as 3 to 4, fo is 4 to 5|.
When I obferved the deepeft feniible red, and that Part of the violet next the indigo, whofe corredled diftance from the red was {| or I of the Length of the Red:ilinear Sides of the Spedlrum, the difference of the diftances of their Foci from the Lens was about 4- Inches, and as 5 to 6, fo is 4i to 55. For fometimes, when the Lens was advantageoufly placed, fo that its Axis refpedted the blue, and all Things elfe were well ordered, and the Sun ftione clear, and 1 held my Eye very near to the Paper on which the Lens caft the Species of the Lines, I could fee pretty diftind:ly the Species of thofe Lines by that Part of the violet which was next .the indigo J and fometimes I could fee them by above half the violet. For in making thefe Experiments I had obferved, that the Species of thofe Colours only appear diftindt, which were in or near the Axis of the Lens : So that if the blue or indigo were in the Axis, I could fee their Species diftindlyj and then the red ap- peared
B O O K L 8i
peared much kfs diftin6t than before. Wherefore I contrived to make theSped:riim of Colours flior- ter than before, fo that both its Ends might be nearer to the Axis of the Lens. And now its Length was about 2t Inches, and Breadth a^ bout r 01* i of ^^^ Inch. Alfo inftead of the black Lines on which the Spectrum was caft, I made one black Line broader than thofe, that I might fee its Species more eafily j and this Line I divided by Ihort crofs Lines into equal Parts, for meafuring the diflances of the obferved Colours. And now I could fometimes fee the Species of this Line with its Divifions almofl: as far as the Center of the femicircular violet End of the -Spedrunij and made thefe farther Obferva-^ tions.
When I obferved the deepeft fenfible red, and that Part of the violet, whofe correfted diftance from it was about ' Parts of the Re<ftilinear Sides of the Spectrum, the Difference of the diftances of the Foci of thofe Colours from the Lens^ was one time 4], another time 47, another time 4t Inches J and as 8 to 9, fo are 47, 4t> 4t, to 5?> 5t'^^ 5^ refpedively.
When I obferved the deepeft fenfible red,, and deepeft fenfible violet, ( the correded di- ftance of which Colours, when all Things were ordered to the beft Advantage, and the Sun (hone very clear, was about H or iy Parts of the Length of the Rectilinear Sides of the colour- ed Spedrum ) I found the Difference of the di- ftances of their Feci from the Lens fometimes 4|- fometimes ^^y and for the moft part ^ In-
G . ehgsi
8i O P T I C K S.
ches or thereabouts ; and as ii to 12, or 15 to 16, fo is five Inches to 5* or 51. Inches.
And by this ProgreiTion of Experiments I fatif- fied my felf, that had the Light at the very Ends of the Spedrum been ftrong enough to make the Species of the black Lines appear plainly on the Paper, the Focus of the deepefh violet would have been found nearer to the Lens, than the Focus of the deepeft red, by about 5^ Inches at leaft. And this is a farther Evidence, that the Sines of Incidence and Refradion of the fe- veral forts of Rays, hold the fame Proportion to one another in the fmallefl Refractions w^hich they do in the greateft.
My Progrefs in making this^ice and trouble- fome Experiment I have fet down more at large, that they that iliall try it after me niay be aware of the Circumfpe(llion requifite to make it fuc- ceed well. And if they cannot make it fuc- ceed fo well as I did, they may notwithftand- ing coUedl by the Proportion of the diftance of the Colours of the Spedrum, to the Difference of the diftances of their Foci from the Lens, what would be the Succefs in the more diftant Colours by a better trial. And yet, if they ufe a broader Lens than I did, and fix it to a long ftrait Staif, by means of which it may be rea- dily and truly diredled to the Colour whofe Fo- cus is defired, I queftion not but the Experi- ment will fucceed better with them than it did with me. For I directed the Axis as nearly as I could to the middle of the Colours, and then the faint Ends of the Spedlrum being remote from the Axis, caft their Species lefs diflindtly
1 on
B O O K t 85
on the Paper than they would have done, had the Axis been fucceffively diredled to them.
Now by what has been faid, it's certain that the Rays which differ inRefrangibilitydo not converge to the fame Focus j but if they flow from a lucid Point, as far from the Lens on one fide as their Foci are on the other, the Focus of the moft re- frangible Rays fhall be nearer to the Lens than that of the leafl refrangible, by above the fourteenth Part of the whole diflance j and if they flow from a lucid Point, fo very remote from the Lens, that before their Incidence they may be accounted pa- rallel, the Focus of the moft refrangible Rays fliall be nearer to the Lens than the Focus of the kail refrangible, by about the 27th or 2 8 th Part of their whole diftance from it. And the Diameter of the Circle in the middle Space between thofe two Foci which they illuminate, when they fall there on any Plane, perpendicular to the Axis (which Circle is the leaft into which they can all be ga- thered ) is* about the 55th Part of the Diameter of the Aperture of the Glafs. So that 'tis a won- der, that Telefcopes reprefent Objeds fo diftindt as they do. But were all the Rays of Light equally refrangible, the Error ariflng only from the Sphericalnefs of the Figures of Glaffes would be many hundred times lefs. For, if the Obje6t- glafs of a Telefcope be Plano-convex, and the Plane fide be turned towards the Objedlj and the Diameter of the Sphere, whereof this Glafs is a Segment, be called D, and the Semidiame- ter of the Aperture of the Glafs be called S, and the Sine of Incidence out of Glafs into Air, be to the Sine of Refradtion as I to R j the Rays
G 2 which
84 O P T I C K S.
w hich come parallel to the Axis of the Glafs, fhall in the Place where the Image of theObjed: is moft diflindly made, be fcattered all over a little Circle,
whofe Diameter is — X very nearly, * as
Iq Dquad. ^ ^'
I gather by computing the Errors of the Rays by the Method of infinite Series, and rejecting the Terms, vi^hofe Quantities are inconfiderable. As for inflance, if the Sine of Incidence I, be to the Sine of Refradion R, as 20 to 3 1, and if D the Diameter of the Sphere, to which the Convex- fide of the Glafs is ground, be 100 Feet or 1200 Inches, and S the Semidiametcr of the Aperture be two Inches, the Diameter of the little Circle,
(that IS ^ -) will be , (or
Iq ycD quad. 20 X 20 X 1 200 X i zoo
961 X
72000000 ) Parts of an Inch. But the Diameter of
the little Circle, through which thefe Rays are fcattered by unequal Refrangibility, will be about the 55 th Part of the Aperture of the Objed-glafs, which here is four Inches. And therefore, the Error arifing from the Spherical Figure of the Glafs, is to the Error arifing from the different Re- frangibility of the Rays, as to - . that is
*^ ■ •' ■' 72000000 rj*
as I to 5449 ; and therefore, being in comparifon fo very little, deferves not to be confidered.
But you will fay, if the Errors caufed by the different Refrangibility be fo very great, how comes it to pafs, that Objeds appear through Telefcopes fo diflind: as they do ? I anfwer, 'tis
* Hovj to do this, is pezvn in our AuthorV Left. Optic. Part I. Se^. IV. Pnp.^x.
becaufe
B O O K I. 85
becaufe the erring Rays are not fcattered uni- formly over all that Circular Space, but colleded infinitely more denfely in tlie Center than in any other Part of the Circle, and in the Way from the Center to the Circumference, grow continually rarer and rarer, fo as at the Circum- ference to become infinitely rare 5 and by rea- fon of their Rarity are not flrong enough to be vifible, unlefs in the Center and very near it. Let ADE [in Fig. 27.] reprefent one of thofe Circles defcribed with the Center C, and Semi- diameter AC, and let BFG be a finaller Circle concentrick to the former, cutting with its Cir- cumference the Diameter AC in B, and bife<fl AC in N } and by my reckoning, the Denfity of the Light in any Place B, will be to its Denfity in N, as AB to BC; and the whole Light with- in the Icffer Circle BFG, will be to the whole Light within the greater A ED, as the Excefs of the Square of A C above the Square of A B, is to the Square of AC. As if B C be the fifth Part of AC, the Light will be four times dcn- fer in B than in N, and the whole Light within the lefs Circle, will be to the whole Light with- in the greater, as nine to twenty-five. Whence it's evident, that the Light within the lefs Cir- cle, mufl ftrike the Senfe much more ftrongly, than that faint and dilated Light round about between it and the Circumference of the grea- ter.
But it's farther to be noted, that the mcft lu- minous of the Prifmatick Colours are the yeU low and orange. Thefe aifed: the Senfes more ftrongly than all the reft together, and next to
G 3 thefc
S6 O P T I C K S.
thefe in flrength are the red and green. Th^ blue compared with thefe is a faint and dark Colour, and the indigo and violet are fnuch darker and fainter, fo that thefe compared with the ftronger Colours are little to be regarded^ The Images of Ohjecfls are therefore to be pla-? ced, not in the Focus of the mean refrangible Rays, which are in the Confine of green and blue, but in the Focus of thofe Rays which are in the middle of the orange and yellow j therQ where the Colour is moil: luminous and fulgent^ that is in the brighteft yellow, that yellow which inclines more to orange than to green. And by the Refraction of thefe Rays (whofe Sines of- incidence and Refraction in Glafs are as 17 apd 1 1 ) the Refradion of Glafs and Cryflal for Op- tical Ufes is to be meafured. Let us therefore place the Image of the Objed; in the Focus of thefe Rays, and all the yellow and orange will fall within a Circle, wnofe Diameter is about the 250th Part of the Diameter of the Aperture of the Glafs. And if you add the brighter half of the red, ( that half which is next the orange ) and the brighter half of the green, ( that half which is next the yellow ) about three fifth Parts of the Light of thefe two Coloi;irs will fall within the fame Circle, and two fifth Parts will fall without it round about y and that which falls without will be fpread through alinoil as much more fpace as that which falls within, and fo in the grofs be almoft three times rarer. Of the other half of the red and green, (that is of the deep dark red and willow green) about pne quarter will fall within this Circle, and
three
B O O K I. 87
three quarters without, and that which falls without will be fpread through about four o^ five times more fpace than that which falls with- in ; and fo in the grofs be rarer, and if com pared with the whole Light within it, will be about 25 times rarer than all that taken in the grofs J or rather more than 30 or 40 times ra- rer, becaufe the deep red in the end of the Spedtmm of Colours made by a Prifm is very- thin and rare, and the willow green is fome- thing rarer than the orange and yellow. The Light of thefe Colours therefore being fo very much rarer than that within the Circle, will fcarce affe<5t the Senfe, efpecially fince the deep red and willow green of this Light, are much darker Colours than the reft. And for the fame reafon the blue and violet being much darker Colours than thefe, and much more rarified, may be neglected. For the denfe and bright Light of' the Circle, will obfcure the rare and weak Light of thefe dark Colours round about it, and render them almoft infenfible. The fenfible Image of a lucid Point is therefore fcarce broader than a Circle, whofe Diameter is the 250th Part of the Diameter of the Aperture of the Objedt-glafs of a good Telefcope, or not much brorder, if you except a faint and dark mifty Light round about it, which a Spectator wifr. fcarce regard. And therefore in a Telefcope, whofe Aperture is four Liches, and Length an hundred Feet, it exceeds not 2" 45'", or 3". And in a Telefcope whofe Aperture is two Inches, and Length 20 or 30 Feet, it may be 5" or 6", and fcarce above. And this anfwers well to
G 4 Expe-
88 O P T I C K S.
Experience : For fpme Aftronomers have found the Diameters pf the fix'd Stars, in Telefcopes of between 20 and 60 Feet in length, to be a- bout 5" or 6", or at moft 8'' or 10" in diame- ter. But if the Eye-Glafs be tinfted faintly with the Smoak of a Lamp or Torch, to ob- fcure the Light of the Star, the fainter Light in the Circumference of the Star ceafes to be vilib .-, and the Star (if the Glafs be fufficiently foilta witli Smoak ) appears fomething more like a mathematical Point. And for the fame Reafon, the enormous Part of the Light in the Circumference of every lucid Point ought to be Icfs difcernible in fhorter Telefcopes than in lon- ger, becaufe the^fhorter tranfmit lefs Light to the Eye.
Now, that the fix'd Stars, by reafon of their immenfe Diliance, appear like Points, unlefs fo far as tl^eir Light is dilated by Refra6lion, may appear from hence j that when the Moon pafTes over them and eclipfes them, their Light vanifhes, not gradually like that of the Planets, but all at once J and in the end of the Eclipfe it returns into Sight all at once, or certainly in lefs time than the fecond of a Minute ; the Refradion of the Moon's Atmofphere a little protrading th^ time in which the Light of the Star firfl vaniilies, ^nd afterwards returns into Sight.
NoWj if we fuppofe the fenfible Image of a lu- cid Point, to be even 250 times narrower than the Aperture of the Glafs 5 yet this Image would be fciil much greater than if it were only from th^ fpherical Figure of the' Glafs. For were i^ not for the different Refrangibility of the
Raysj
B O O K I. 8p
Rays, its breadth in an loo Foot Tclefcope
whofe aperture is 4 Inches, would be but ^-^^^^—
parts of an Inch, as is manifeil by the foregoing Computation. And therefore in this cafe the greateft Errors arifing from the fpherical Figure of the Glafs, would be to the greateft fenfible Errors arihng from the different Refrangibihty
of the Rays as ^^^^ to ^ at moft, that is on- ly as I to 1200. And this fufficiently (hews that it is not the fpherical Figures of Glalfes, but the different Refrangibihty of the Rays which hin- ders the perfeftion of Telefcopes.
There is another Argument by w4iich it may appear that the different Refrangibihty of Rays, is the true caufe of the imperfed:ion of Tele- fcopes. For the Errors of the Rays arifmg from the fpherical Figures of Obje6t-glaffes, -Are as the Cubes of the Apertures of the Objed: Glaffes ; and thence to make Telefcopes of various Lengths magnify with equal diftindlnefs , the Apertures of the Objeft-glaffes, and the Charges or magnifying Powers ought to be as the Cubes of the fquare Roots of their lengths; which doth not anfwer to Experience. But the Errors of the Rays arifing from the different Refrangibihty, are as the Apertures of the Ob- jedt-glaffes ; and thence to make Telefcopes of various lengths, magnify with equal dillin6tnefs, their Apertures and Charges ought to be as the fquare Roots of their lengths ; and this anfwers to Experience, as is v/ell know^n. For Inffance, ^ Tclefcope of 64 Feet in length, with an Aper-
2 turQ
90 O P T I C K S.
ture of 2 1 Inches, magnifies about 120 times, with as much diftinftnefs as one of a Foot in length, with ^ of an Inch aperture, magnifies i^ times.
Now were it not for this different Refrangi- bility of Rays, Telefcopes might be brought to a greater perfeftion than we have yet defcrib'd, by compofmg the Objedi-glafs of two Glaffes with Water between them. Let A D F C [in Fig, 28.] reprefent the Objed:-glafs compofed of two Glaffes ABED and BEFC, alike convex on th® outfides AGD and CHF, and alike concave on the infides BME, BNE, with Water in the concavity BMEN. Let the Sine of Inci- dence out of Glafs into Air be as I to R, and out of Water into Air, as K to R, and by con- fequence out of Glafs into Water, as I to K: and let the Diameter of the Sphere to which the convex fides AGD and CHF are ground be D, and the Diameter of the Sphere to which the concave fides BME and BNE, are ground be to D, as the Cube Root of KK — KI to the Cube Root of R K-— R I : and the Refractions on the concave fides of the Glaffes, will very much corred the Errors of the Refradions on the convex fides, fo far as they arife from the fphericalnefs of the Figure. And by this means might Telefcopes be brought to fufiicient per- fection, were it hot for the different Refrangi- bility of feveral forts of Rays. But by reafon of this different Refrangibility, I do not yet fee any other means of improving Telefcopes by Refractions alone, than that of increafing their lengths, for which end the late Contrivance of
Hugenhis
B O O K I. pi
Jlugenius feems well accommodated. For very long Tubes are cumberfome, and fcarce to be readily managed, and by reafon of their length are very apt to bend, and fhake by bending, fo as to cauie a continual trembling in the Objects, whereby it becomes difficult to fee them difl;in(fl- ly: whereas by his Contrivance the Glaffes are readily manageable, and the Objed-glafs being fix'd upon a flrong upright Pole becomes more fteady.
Seeing therefore the Improvement of Tele- fcopes of given lengths by Refradions is defpe- ratej I contrived heretofore a Perfpedive by- Reflexion , ufmg inftead of an Objed-glafs a concave Metal. The diameter of the Sphere to which the Metal was ground concave was a- bout 25 Englijh Inches, and by confequence the length of the Inftrument about fix Inches and a quarter. The Eye-glafs v/as Plano-con- vex, and the diameter of the Sphere to which the convex iide was ground was about t of an Inch, or a little lefs, and by confequence it niagniiied between 30 and 40 times. By ano- ther way of meafuring I found that it magnified about 35 times. The concave Metal bore an Aperture of an Inch and a third part; but the Aperture was limited not by an opake Circle, covering the Limb of the Metal round about, but by an opake Circle placed between the Eye- glafs and the Eye, and perforated in the mid- dle with a little round hole for the Rays to pafs through to the Eye. For this Circle by being placed here, ftopp'd much of the errroneous Light, which otherwiie would have difturbed
the
p2 O P T I C K S.
the Vifion. By comparing it with a pretty good Perfped;ive of four Feet in length, made with a concave Eye-glafs, I could read at a greater diftance with my own Inftrument than with the Glafs. Yet Objedts appeared much darker in it than in the Glafs, and that partly becaufe more Light was loft by Reflexion in the Metal, than by Refraction in the Glafs, and partly be- caufe my Inftrument was overcharged. Had it. magnified but 30 or 25 times, it would have made the Obje(5t appear more brisk and pleafant, Tv/o of thefe I made about 16 Years ago, and have one of them flill by me, by which I can prove the truth of v/hat I write. Yet it is not fo 2:ood as at the firft. For the concave has been divers times tarnifhed and cleared again, by rub- bing it with very foft Leather. When I made thefe an Artifl in London undertook to imitate it; but ufing another way of polifhing them than I did, he fell much fhort of what I had attained to, as I afterwards underftood by difcourfmg. the Under- work man he had employed. The Polifh I ufed was in this manner. I had two round Copper Plates, each fix Inches in Diameter, the one convex, the other concave,' ground very true to one another, On the con- vex I ground the Objedt-Metal or Concave which was to be polifli'd, 'till it had taken the Figure of the Convex and was ready for a Poliih. Then I pitched over the convex very' thinly, by dropping melted Pitch upon it, and warming it to keep the Pitch foft, whilft I ground it with the. concave Copper wetted to make it fpread eavenly all over the convex. ^ Thus
BOOK I. 95
Thus by working it well I made it as thin as a Groat, and after the convex was cold I ground it again to give it as true a Figure as 1 could. Then I took Putty which I had made very fine by wafhing it from all its groiler Particles, and laying a little of this upon tlie Pitch, I ground it upon the Pitch with the concave Copper, till it had done making a Noife ; and then upon the Pitch I ground the Objed:-Metal with a brisk motion, for about two or three Minutes of time, leaning hard upon it. Then I put frefh. Putty upon the Pitch, and ground it again till it had done making a noife, and afterwards ground the Objed:-Metal upon it as before. And this Work I repeated till the Metal was poliflied, grinding it the laft time with all my llrength for a good while together , and frequently breathing upon the Pitch, to keep it moift with- out laying on any more frefli Putty. The Ob- jedl-Metal was two Inches broad, and about one third part of an Inch thick, to keep it from bending. I had two of thefe Metals, and when I had poliflied them both, I tried which was beft, and ground the other again, to fee if I could make it better than that which I kept. And thus by many Trials I learn'd the way of po- lifhing, till I made thofe two reflecting Perfpe- dlives I fpake of above. For this Art of po- lilhing will be better learn'd by repeated Pra- ctice than by my Defcription. Before I ground the Objedt-Metal on the Pitch, I always ground ' the Putty on it v/ith the concave Copper, till it had done making a noife, becaufe if the Parti- cles of the Putty were not by this means made
to
^4 O P T I C K S.
to flick faft in the Pitch, they would by rolling up and down grate and fret the Objed-Metal and fill it full of little holes.
But becaufc Metal is more difficult to polifll than Glafs, and is afterwards very apt to be fpoiled by tarnifhing, and reflects not fo much Light as Glafs quick-filver'd over does : I would propound to ufe inflead of the Metal, a Glafs ground concave on the forefide, and as much convex on the back-fide, and quick-filver'd o- ver on the convex fide. The Glafs mufl be e- very where of the fame thicknefs exactly. O- therwife it will make Objedls look colour'd and indiftind:. By fuch a Glafs I tried about five or fix Years ago to make a reflecfling Telefcope of four Feet in length to magnify about 150 times, and I fatislied my felf that there wants nothing but a good Artift to bring the Delign to perfe-- ftion. For the Glafs being wrought by one of our London Artifls after fuch a manner as they grind GlalTes for Telefcopes, though it feemed as well wrought as the Objed:-glaires ufe to be, yet when it was quick-filver'd, the Reflexion dif- covered innumerable Inequalities all over the Glafs. And by reafon of thefe Inequalities, Ob- jedls appeared indiftindl in this Inflrument. For the Errors of refledled Rays caufed by any Ine- quality of the Glafs, are about fix times greater than the Errors of refradled Rays caufed by the like Inequalities. Yet by this Experiment I fatisfied my felf that the Reflexion on the concave fide of the Glafs, which I feared would diflurb the Vifion, did no fenfible prejudice to it, and by confequence that nothing is wanting
to
B O O K I. p5
to perfed thefe Telefcopes, but good Workmen who can grind and polifh GlaiTes truly fpherical. An Objedt-glafs of a fourteen Foot Telefcope, made by an Artificer at Lo?ido)i, I once mended confiderably, by grinding it on Pitch with Put- ty, and leaning very eafily on it in the grinding, left the Putty {hould fcratch it. Whether this way may not do well enough for polifhing thefe reflecting Glaffes, I have not yet tried. But he that Ihall try either this or any other way of po- liftiing which he may think better, may do well to make his GlafTes ready for poliihing, by grind- ing them without that Violence, wherewith our Londofi Workmen prefs their Glafles in grinding. For by fuch violent preiTure, Glafles are apt to bend a little in the grinding, and fuch bendino^ will certainly fpoil their Figure. To recom- mend therefore the confideration of thefe refled- ing GlaiTes to fuch Artifts as are curious in fi- guring GlafTes, I fliall defcribe this optical Inftru- ment in the following Propofition.
PROP. VIII. Prob. II. To pjorten Telefcopes.
LET ABDC [mFig.2g.] reprefent a Glafs fpherically concave on the forefide AB, and as much convex on the backfide CD, fo that it be every where of an equal thicknefs. Let it not be thicker on one fide than on the other, left it make Objects appear colour'd and indi-
ftina,
^6 O P T I C K S.
flindl , and let it be very truly wrought and quick-filver'd over on the backfide; and fet in the Tube VXYZ which muft be very black within. Let EFG reprefent a Prifm of Glafs or Cryftal placed near the other end of the Tube, in the middle of it, by means of a han- dle of Brafs or Iron FGK, to the end of which made flat it is cemented. Let this Prifm be redangular at E, and let the other two Angles at F and G be accurately equal to each other, and by confequence equal to half right ones, and let the plane fides FE and GE be fquare, and by confequence the third fide F G a redlan- gular Parallelogram , whofe length is to its breadth in a fubduplicate proportion of two to one. Let it be fo placea in the Tube , that the Axis of the Speculum may pafs through the middle of the fquare fide EF perpendicularly and by confequence through the middle of the fide FG at an Angle of 45 Degrees, and let the fide E F be turned towards the Speculum, and the diftance of this Prifm from the Speculum be fuch that the Rays of the Light PQ, RS, ^c, which are incident upon the Speculum in Lines parallel to the Axis thereof, may enter the Prifm at the fide EF, and be reflected by the fide FG, and thence go out of it through the fide GE, to the point T, which muft be the com- mon Focus of the Speculum ABDC, and of a Plano-convex Eye-glafs H, through which thofe Rays muft pafs to the Eye. And let \ - Rays at their coming out of the. Glafs pafs . irough a fmall round hole, or aperture made in a lit* tie plate of Lead, Brafs, or Silver, wherewith
the
B O O K I. 97
the Glafs is to be covered, which hole mufl be no bigger than is neceflary for Light enovigh to pafs through. For fo it will render the Objedt diftindt, the Plate in which 'tis made intercept- ing all the erroneous part of the Light which comes from the verges of the Speculum AB. Such an Inftrument well made, if it be fix Foot long, (reckoning the length from the Speculum to the Prifm, and thence to the Focus T ) will bear an aperture of fix Inches at the Speculum, and magnify between two and three hundred times. But the hole H here limits the aperture with more advantage, than if the aperture was placed at the Speculum. If the Inftrument be made longer or fhorter, the aperture muft be in proportion as the Cube of the fquare-fquare Root of the length, and the magnifying as the aper- ture. But it's convenient that the Speculum be an Inch or two broader than the aperture at the leaft, and that the Glafs of the Speculum be thick, that it bend not in the working. The Prifm EFG muft be no bigger than is necelTary, and its back lide FG muft not be quick-lilver'd over. For without quickfilver it will refledl all the Light incident on it from the Speculum.
In this Inftrument the Objedl will be invertc^, but may be erected by making the fquare fides FF and EG of the Prifm EFG not plane but fpherically convex, that the Rays may crofs as well before they come at it as afterwards between it andj.rj-e Eye-glafs. If it be defired that the Inft^^ iie.it bear a larger aperture, that may be alfo Qone by compofmg the Speculum of two GlalTes with Water between them.
H If
pg O P T I C K S.
If the Theory of making Telefcopes could at length be fully brought into Pradtice, , yet there would ' be certain Bounds beyond which Tele- fcopes could not perform. For the Air through which we look upon the Stars, is in a perpetual Tremor J as may be ften by the tremulous Moti- on of Shadows call: from high Towers,- and by- the twinkling of the fix'd Stars. But thefe Stars do not twinkle when viewed through Telefcopes which have large apertures. For the Rays of Light which pafs through divers parts of the aperture, tremble each of them apart, and by means of their various and fometimes contrary Tremors, fall at one and the fame time upon dif- ferent points in the bottom of the Eye, and their trembling Motions are too quick and confufed to be perceived feverally. And all thefe illuminated Points conftitute one broad lucid Point, com- pofed of thofe many trembling Points confufed- ly and infenlibly mixed with one another by very ihort and fwift Tremors, and thereby caufe the Star to appear broader than it is, and without any trembling of the whole. Long Telefcopes may caufe Objeds to appear brighter and larger than fliort ones can do, but they cannot be fo formed as to take away that confuiion of the Rays which arifes from the Tremors of the At- mofphere. The only Remedy is a moft ferene and quiet Air, fuch as may perhaps be found on the tops of the higheft Mountains above the grof- . ier Clouds.
THE
THE
FIRST BOOK
O F
OPTICKS.
PART II.
PROP, I. Theor. I.
T%e Phczno7nena of Colours hi refraEled or refie&ed Light are not caufed by new Modifications of the Light varioufly im- frefsd^ according to the various Termi- nations of the Light and Shadow.
Exper. I.
The Proof by Experiments.
O R if the Sun fhine into a I very dark Chamber through an obiong hole F, [in Fig. i.] whofe breadth is tlie fixth or eighth part of an Inch, or fomething lefs j and his beam F H do afterwards pafs firft through a
H 2 very
i6o O P T i C K S.
very large Prifm ABC, diftant about 20 Feet from the hole, and parallel to it, and then ( with it3 white part) through an oblong hole H, whofe breadth is about the fortieth or lixtieth part of an Inch, and which is made in a black opake Body GI, and placed at thediftanceof two or three Feet from the Prifm, 'in a parallel Situa- tion both to the Prifm and to the former hole, and if this white Light thus tranfmitted through the hole H, fall afterwards upon a white Paper //, placed after that hole H, at thediftanceof three or four Feet from it, and there paint thC; ufual ' Colours of the Prifm, fuppofe red at /, yellow at s, green at r, blue at ^, and violet at p ', you may with an Iron Wire, or any fuch like (lender opake Body, whofe breadth is a- bout the tenth part of an Inch, by intercepting the Rays at k, /, w, ;z or 0, take away any one of the Colours at t, s, r, q or />, whilft the other Colours remain upon the Paper as before j or with an Obftacle fomething bigger you may tak away any two, or three, or four Colours together, the reft remaining: So that any one of the Colours as well as violet may become outmoft in the Confine of the Shadow towards ^, and any one of them as well as red may be- come outmoft in the Confine of the Shadow to- wards /, and any" one of them may alfo bor- der upon the Shadow made within the Colours by the Obftacle R intercepting fome interme- diate part of the Light; and, laftly, any one of them by being left alone, may border upon the Shadow on either hand. All the Colours have themfelves indifferently to any Confines of Sha-
I dow.
BOOK I. lor
dow, and therefore the differences, of thefe Co- lours from one another, do not arife from the different Confines of Shadow, whereby Light is varioufly modified, as has hitherto been the Opinion of Philofophcrs. In trying thefe things *tis to be obferved, that by how much the holes F and H are narrower, and the Intervals be- tween them and the Prifm greater, and the Chamber darker, by fo much the better doth the Experiment fucceed ; provided the Light be not fo far diminifhed, but that the Colours at pt he fufficiently vifible. To procure a Prifm of folid Glafs large enough for this Experiment will be difficult, and therefore a prifmatick Vef- fel muft be made of poliili'd Glafs Plates ce- mented together, and filled with fait Water or clear Oil.
Exper. 2. The Sun's Light let into a dark Chamber through the round hole F, [in Fig. 2.] half an Inch wide, paffed firft through the Prifm ABC placed at the hole, and then through a Lens PT fomething more than four Inches broad^ and about eight Feet diflant from the Prifm, and thence converged to O the Focus of the Lens diftant from it about three Feet, and there fell upon a white Paper D E. If that Paper was perpendicular to that Light incident upon it, as 'tis reprefented in the pollure DE, all the Colours upon it at O appeared white. But if the Paper being turned about an Axis parallel to the Prifm, became very much incli- ned to the Light, as 'tis reprefented in the Po- fitions de-Andi ^i-, the fame Light in the one cafe appeared yellow and red, in the other blue.
H 3 Here
102 O P T I C K S.
Here one and the fame part of the Light in one and the fame place, according to the various In- clinations of the Paper, appeared in one cafe white, in another yellow or red, in a third blue, whilft the Confine of Light and Shadow, and the Refradions of the Prifm in all thefe cafes remained the fame.
Expcr. 3. Such another Experiment may be more eaiily tried as follows. Let a broad beam of the Sun's Light coming into a dark Cham- ber through a hole in the Window-fhut be re- fracted by a large Prifm ABC, [in Fig. 3.] whofe refradting Angle C is more than 60 De- grees, and fo foon as it comes out of the Prifm, let it fall upon the white Paper DE glewed up- on a ilifF Plane; and this Light, when the Pa- per is perpendicular to it, as 'tis reprefented in DE, will appear perfed:ly white upon the Pa- per; but when the Paper is very much inclin'd to it in fuch a manner as to keep always paral- lel to the Axis of the Prifm, the whitenefs of the whole Light upon the Paper will according to the inclination of the Paper this way or that way, change either into yellow and red, as in the pofture J^, or into blue and violet, as in the pofture ^ e. And if the Light before it fall upon the Paper be twice refracted the fame way by two parallel Prifms, thefe Colours will become the more confpicuous. Here all the middle parts of the broad beam of white Light which fell upon the Paper, did without any Confine of Shadow to modify it, become co- lour'd all over with one uniform Colour, the Colour being always the fame in the middle of
the
B O O K I. 103
the Paper as at the edges, and this Colour chan- ged according to the various Obliquity of the reflefting Paper, without any change in the Re- fradlions or Shadow, or in the Light which fell upon the Paper. And therefore thefe Colours are to be derived from fome other Caufe than the new Modifications of Light by Refradions and Shadows.
If it be aiked, what then is their Caufe ? I anfwer, That the Paper in the poilure Jt', being more oblique to the more refrangible Rays than to the lefs refrangible ones, is more ilrongly illu- minated by the latter than by the former, and therefore the lefs refrangible Rays are predomi- nant in the refledted Light. And where-ever they are predominant in any Light, they tinge it with red or yellow, as may in fome meafure ap- pear by the firft Propofition of the firfl Part of this Book, and will more fully appear hereafter. And the contrary happens in the poflure cf the Paper ^e, the more refrangible Rays being then predominant which always tinge Light with blues and violets.
Exper 4. The Colours of Bubbles with which Children play are various, and change their Si- tuation varioufly , without any refped to any Confine or Shadow. If fuch a Bubble be co- ver'd with a concave Glafs, to keep it from be- ing agitated by any Wind or Motion of the Air, the Colours will flowly and regularly change their Situation , even whilll the Eye and the Bubble, and all Bodies which emit any Light, or caft any Shadow , remain unmoved. And therefore their Colours arife from fome regular
H 4 Caufe
104 O P T I C K S.
Caufe which depends not on any Confine of Sha- dow. What this Caufe is will be fliewed in the next Book.
To thefe Experiments may be added the tenth Experiment of the firft Part of this firft Book, where the Sun's Light in a dark Room be- ing trajeded through the parallel Superficies of two Prifms tied together in the form of a Paralle- lopipede, became totally of one uniform yellow or red Colour, at its emerging out of the Prifms. Here, in the production of thefe Colours, the Confine of Shadow can have nothing to do. For the Light changes from white to yellow, orange and red fuccefiively, without any alte- ration of the Confine of Shadow : And at both edges of the emerging Light where the con- trary Confines of Shadow ought to produce different Effeds , the Colour is one and the fame, whether it be white, yellow, orange or red : And in the middle of the emerging Light, where there is no Confine of Shadow at all, the Colour is the very fame as at the edges, the whole Light at its very firft Emergence being of one uniform Colour, whether white, yellow, orange or red, and going on thence perpetual- ly without any change of Colour, fuch as the Confine of Shadow is vulgarly fuppofed to wotk in refradted Light after its Emergence. Nei- ther can thefe Colours arife from any new Mo- difications of the Light by Refradions, becaufe they change fuecefiively frorri white to yellow, orange and red, v^hile the Refradtions remain the fame, and alfo becaufe the Refradions are made contrary ways by parallel Superficies which
deftro'y
B O O K I. 105
deftroy one another's Effeds. They arife not therefore from any Modifications of Light made byRefradions and Shadows, but have foire or her Caufe. What that Caufe is we (hewed abov-e in this tenth Experiment, and need not here re- peat it.
There is yet another material Circumftance of this Experiment. For this emerging Light being by a third Prifm HIK" [in Fig. 22. Part L] re- fradled towards the Paper FT, and there painting theufual Colours of the Frifm, red, yellow, green, blue, violet : If thefe Colours arole from the Re- fradions of that Frifm modifying the Light, they would not be in the Light before its Incidence on that Frifm. And yet in that Experiment we found, that when by turning the two firft Prifms about their common Axis all the Colours were made to vanifh but the red; the Light which makes that red being left alone, appeared of the very fame red Colour before its Incidence on the third Frifm. And in general we find by other Experiments, that when the Rays which differ in Refrangibility are feparated from one another, and any one Sort of them is con- fidered apart, the Colour of the Light which they compofe cannot be changed by any Re- fraction or Reflexion whatever, as it ought to be were Colours nothing elfe than Modifica- tions of Light caufed by Refractions, and Re- flexions, and Shadows. This Unchangeablenefs of Colour I am now to defcribe in the following Propofition.
PROP,
io6 O P T I C K S.
PROP. IT. Theor. II.
u47/ homogeneal Light has its proper Colour anfweriftg to its Degree of Refrangibi- lity^ and that Colour cannot be changed by Reflexions and RefraSiions,
IN the Experiments of the fourth Propofition of the firfh Part of this firft Book, when I had leparated the heterogeneous Rays from one ano- ther, the Spedrum pt formed by the feparated Rays, did in the Progrefs from its End^, on which the moft refrangible Rays fell, unto its other End /, on which the leaft refrangible Rays fell, appear tinged with this Series of Colours, violet, indigo, blue, green, yellow, orange, red, together with all their intermediate Degrees in a continual Succeffion perpetually varying. So that there ap- peared as many Degrees oi Colours, as there were forts of Rays differing in Refrangibility.
Exper.^. Now, that thefe Colours could not be changed by Refradtion, I knew by refradiing with aPrifm fometimes one very little Part of tbisLight, fometimes another very little Part, as is defcribed in the twelfth Experiment of the firft Part of this Book. For by this Refradtion the Colour of the Light was never changed in the leaft. If any Part of the red Light was refracted, it remained totally of the fame red Colour as before. No orange, no yellow, no green or blue, no other new Colour was produced by that Refradtion. Neither did the Colour any ways change by repeated Refradtions, but continued always the
fame
B O O K I. 107
fame red entirely as at firft. The like Con- ftancy and Immutability I found alfo in the blue, green, and other Colours. So alfo, if I looked through a Prifm upon any Body illuminated with any Part of this homogeneal Light, as in the four- teenth Experiment of the firfl Part of this Book is defcribed ; I could not perceive any new Co- lour generated this way. All Bodies illumina- ted with compound Light appear through Prifms confufed, (as was faid above) and tinged with various new Colours, but thofe illuminated with homogeneal Light appeared through Prifms neither lefs diflincfl, nor otherwife colour'd, than when viewed with the naked Eyes. Their Colours were not in the leaft changed by the Refrad:ion of the interpofed Prifm. I fpeak here of a fenfible Change of Colour : For the Light which I here call homogeneal, being not abfolutely homogeneal, there ought to arife fome little Change of Colour from its Hetero- geneity. But, if that Heterogeneity was fo lit- tle as it might be made by the faid Experiments of the fourth Propofition, that Change was not fenfible, and therefore in Experiments, where Senfe is Judge, ought to be accounted none at all.
Exper. 6. And as thefe Colours were not changeable by Refradions, fo neither were they by Reflexions. For all white, grey, red, yel- low, green, blue, violet Bodies, as Paper, Afhes, red Lead, Orpiment, Lidico, Bife, Gold, Sil- ver, Copper, Grafs, blue Flowers, Violets, Bubbles of Water tinged with various Colours, Peacock's Feathers, the Tindure of Lignum
NepbrU
io8 G P T I C K S.
Nephriticiwi^ and fuch-like, in red homogeneal Light appeared totally red, in blue Light totally blue, in green Light totally green, and fo of other Colours. In the homogeneal Light of any Cc- lour they all appeared totally of that fame Co- lour, with this only Difference, that fome of them reflected that Light more ftrongly, others more faintly. I never yet found any Body, which by reflecting homogeneal Light could fenfibly change its Colour.
From all which it is manifeft, that if the Sun's Light confifted of but one fort of Rays, there wduld be but one Colour in the whole World, nor would it be poflible to produce any new Co- lour by Reflexions and Refradlions, and by confe- quence that the Variety of Colours depends upon the Compofition of Light.
DEFINITION.
TH E homogeneal Light and Rays which appear red, or rather make Obje<fls apr pear fo, I call Rubrifick or Red-making ; thofe which make Objects appear yellow, green, blue, and violet, I call Yellow-making, Green-making, Blue-making, Violet-making, and fo of the reft. And if at any time I fpeak of Light and Rays as coloured or endued with Colours, I would be underftood to fpeak not philofophically and properly, but grolly, and accordingly to fuch Conceptions as vulgar People in feeing all thefe Experiments would be apt to frame. For the Rays to fpeak properly are not coloured. In them there is nothing elfe than a certain Power
and
B O O K I. lop
dndDifpofition to ftir up aSenfatlon of this or that Colour. For as Sound in a Bell or mufical String, or other founding Body, is nothing but a trem- bling Motion, and in the Air nothing but that Motion propagated from the Objed, and in the Senforium 'tis a Senfe of that Motion under the Form of Sound ; fo Colours in the Objedt are no- thing but a Difpofition to refledl this or that fort of Rays more copioufly than the reftj in the Rays they are nothing but their Difpolitions to propagate this or that Motion into the Senforium, and in the Senforium they are Senfations of thofe Motions under the Forms of Colours.
PROP, III. Prob. I.
To defifte the Refra77gibility of the fever al forts of homogeneal Light anfwering to the feveral Colours,
FOR determining this Problem I made the following Experiment. * Exper, 7. When I had caufed the Redtilinear Sides AF, GM, [in /%4.] of the Spedrum of Colours made by the Prifm to be dirtiniflly de- fined,^ as in the fifth Experiment of the firft Part of this Book is defcribed, rhere were found in it all the homogeneal Colours in the fame Order and Situation one among another as in the Spe^rum of fimple Light, defcribed in the fourth Proportion of that Part. For the Cir- cles of which the Spedrum of compound Light * 5^^ «Ar AuthorV Lea. Optic. Partll. Se^.U. /. 239.
PT
jio O P T I C K S.
P T is compofed, and which in the middle Parts of the Spectrum interfere, and are intermix'd with one another, are not intermix'd in their outmoft Parts where they touch thofe Redilinear Sides AF and GM. And therefore, in thofe Redi- linear Sides when diftindly defined, there is no n^w Colour generated by Refradlion. I obferved alfo, that if any where between the two outmoft Circles TMF and PGA a Right Line, as y^, w^as crofs to the Spectrum, fo as both Ends to fall perpendicularly upon its Rectilinear Sides, there appeared one and the fame Colour, and de- gree of Colour from one End of this Line to the other. I delineated therefore in a Paper the Perimeter of the Speft'rum FAP GMT, and in trying the third Experiment of the firft Part of this Book, I held the Paper fo that the Spe([lrum might fall upon this delineated Figure, and agree with it exactly, whilft an Affiiiant, whofe Eyes for diftinguilhing Colours were more critical than mine, did by Right Lines cc{Bj ^^, g^, &c. drawn crofs the Spe- ctrum, note the Confines of the Colours, that is of the red M a /3 F, of the orange a ^ ^ /3, of the yellow ye^^, of the green g ^9 ^, of the blue »iix9, of the indico iXfjua, and of the vio- let AGA^. And this Operation being divers times repeated both in the fame, and in feveral Papers, I found that the Obfervations agreed well enough with one another, and that the Redilinear Sides MG and FA were by the faid crofs Lines divided after the manner of a Mufi- cal Chord. Let GM be produced to X, that MX may be equal to GM, and conceive 2 GX,
BOOK L III
GX, aX, iX, «X, gX, yX, aX, MX, to be
in proportion to one another, as the Numbers, I, I, f, 1, f, f, i'tt, 4, and fo to reprefent the Chords of the Key, and of a Tone, a third Minor, a fourth, a fifth, a fixth Major, a feventh and an eighth above that Key : And the Intervals M a, ay, ye, in, »', 'A, and aG, will be tlie Spaces which the feveral Colours ( red, orange, yel- low, green, blue, indigo, violet ) take up.
.Now thefe Intervals or Spaces fubtending the Differences of the Refradlions of the Rays go- ing to the Limits of thofe Colours, that is, to the Points M, a, y, g, y\, j, A, G, may without any fenfible Error be accounted proportional to the Difierences of the Sines of Refradion of thofe Rays having one common Sine of Inci- dence, and therefore fince the common Sine of Incidence of the mofl and leaft refrangible Rays out of Glafs into Air was ( by a Method defcri- bed above) found in proportion to their Sines of Refraction, as 50 to yy and 78, divide the Difference between the Sines of Refradiion 77 and 78, as the Line GM is divided by thofe Intervals, and you will have 77, 77?, yy^, 77-f, 77t> 77h 77iy 78, the Sines of Refradion of thofe Rays out of Glafs into Air, their common Sine of Incidence being 50. So then the Sines of the Incidences of all the red-making Rays out of Glafs into Air, were to the Sines of their Re- fradions, not greater than 50 to yy, nor lefs than 50 to yyiy but they varied from one ano- ther according to all intermediate Proportions. And the Sines of the Incidences of the green- making
Ill O P T t C K S.
making Rays were to the Sines of their Refradli-. ons in all Proportions from that of 50 to 'j'jl^ unto that of 50 to 'j'j^. And by the like Limits above-mentioned were the Refrddlions of the Rays belonging to the reft of the Colours .de- fined, the Sines of the red-making Rays extend- ing from 77 to 'j'j^^ thofe of the orange-making from 771- to.77-f, thofe of the yellow-making from j'j}^ to 77 j, thofe of the green-making from 'j'jy^ to "jji^^ thofe of the blue-making from 77 i to 'J'j^i thofe of the indigo-making from 'i']^ to ji^L^ and thofe of the violet from 77I to
Thefe are the Laws of the Refradlons made out of Glafs into Air, and thence by the third Axiom of the iirfl Part of this Book, the Laws of the Refractions made out of Air into Glafs are ea- fily derived.
Exper. 8. I found moreover, that when Light goes out of Air through feveral contiguous re- fracting Mediums as through Water and Glafs, and thence goes out again into Air, whether the refracting Superficies be parallel or inclin'd to one another, that Light as often as by con- trary Refractions 'tis fo corrected, that it emer- geth in Lines parallel to thofe in which it was incident, continues ever after to be white. But if the emergent Rays be inclined to the inci- dent, the Wnitenefs of the emerging Light will by degrees in paffing on from the Place of Emer- gence, become tinged in its Edges with Co- lours. This I try'd by refraCting Light with Prifms of Glafs placed within a Prifmatick Vef- iel of Water. Now thofe Colours argue a di- verging
B O O K I. 113
▼erging and feparation of the heterogeneous Rays from one another by means of their unequal Re- fractions, as in what follows will more fully ap- pear. And, on the contrary, the permanent whitenefs argues, that in like Incidences of the Rays there is no fuch feparation of the emerging Rays, and by confequence no inequality of their whole Refrad:ions. Whence I feem to gather the two following Theorems.
1. The Exceffes of t-he Sines of Refracflion of feveral forts of Rays above their common SiAe of Incidence when the Refractions are made out of divers denfer Mediums immediately into one and the fame rarer Medium, fuppofe of Air, are to one another in a given Proportion.
2. The Proportion of the Sine of Incidence to the Sine of Refradtion of one and the fame fort of Rays out of one Medium into another, is compofed of the Proportion of the Sine of Incidence to the Sine of Refradtion out of the firft Medium into any third Medium, and of the Proportion of the Sine of Incidence to the Sine of Refradtion out of that third Medium into the fecond Medium.
By the firft Theorem the Refradtlons of the Rays of every fort made out of any Medium in- to Air are known by having the Refradtion of the Rays of any one fort. As for inftance, if the Refradtions of the Rays of every fort out of Rain-water into Air be defired, let the com- mon Sine of Incidence out of Glafs into Air be fubdudted from the Sines of Refradtion, and
I the
114 O P T I C K S.
the ExcelTes will be 27, 27^, 27 1, 27J, ^jl, 2j\, 275, 28. Suppofe now that the Sine of Incidence of the leaft refrangible Rays be to their Sine of Refraction out of Rain-water into Air as 3 to 4, and fay as i the difference of thofe Sines is to 3 the Sine of Incidence, fo is 27 the leaft of the ExcefTes above-mentioned to a fourth Number 8 1 j and 8 1 will be the common Sine of Incidence out of Rain-water into Air, to which Sine if you add all the abovementioned ExcefTes, you will have the defired Sines of the Refrad:ions 108, io8f, 108-I, iq8', 108 ", 1085, io8|, 109.
By the latter Theorem the Refradlion out of one Medium into another is gathered as often £s you have the Refractions out of them both in- to any third Medium. As if the Sine of Inci- dence of any Ray out of Glafs into Air be to its Sine of Refradion, as 20 to 3 i, and the Sine of Incidence of the fame Ray out of Air into Wa- ter, be to its Sine of Refraction as 4 to 3; the Sine of Incidence of that Ray out of Glafs into Water will be to its Sine of RefraCtion as 20 to 3 1 and 4 to 3 jointly, that is, as the FaCtum of '20 and 4 to the FaCtum of 3 1 and 3, or as 80 to 93.
And thefe Theorems being admitted into Op- ticks, there would be fcope enough of hand- ling that Science voluminoufly after a new man- ner *j not only by teaching thofe things which tend to the perfection of Vifion, but alfo-by determining mathematically all kinds of Phae- nomena of Colours which could be produced
* Js is done in our Author'i Left. Optic. Part I. SeSl. III. and IV. and Par til. Se^. II.
by
BOOK I. rx5*
by Refradlions. For to do this^ there is nothing elle requifite than to find out the Separations of heterogeneous Rays, and their various Mixtures and Proportions in every Mixture. By this way of arguing I invented almoft all the Phsenomena defcribed in thefe Books, befide fome others lefs neceffary to the Argument; and by the fuccelles I met with in the Trials, I dare promife, that to him who fhall argue truly, and then try all things with good 'Glaffes and fufficient Circumfpeclion, the cxpeded Event will not be wanting. But he is firft to know what Colours will arife from any others mix'd in any affigned Proportion.
PROP. IV. Theor. hi. Colours may be produced by Compofttion ix^hich Jljall belike to the Colours of homO" ■ geneal Light as to the Appear a7ice of Co- lour^ hut not as to the hrmiut ability of Colour and Co7iflitution of Light. Aftd thofe Colours by how much they are more co7npounded by fo much are they lefs full and inte?ife^ a?id by too much Compofition they may be diluted and weflke?id till they ceafey and the Mixture beco77ies white or grey, 'There may be alfo Colours produced by Compoftio?tj which are not fully like any of the Colours of homoge?2eal Light.
FOR a Mixture of homogeneal red and yel- low compounds an Orauge, like in appea- I 2 ranee
ii6 O P T I C K S.
ranee of Colour to that orange which in the feries of unmixed prifmatick Colours lies between them; but the Light of one orange is homogeneal as to Refrangibility, and that of the other is he- terogeneal, and the Colour of the one, if viewed through a Prifm, remains unchanged, that of the other is changed and refolved into its compo- nent Colours red and yellow. And after the fame manner other neighbouring homogeneal Colours may compound new Colours , like the in- termediate homogeneal ones, as yellow and green, the Colour between them both, and afterwards, if blue be added, there will be made a green the middle Colour of the three which enter the Compofition. For the yellow and blue on either hand, if they are equal in quantity they draw the intermediate green equally towards themfelves in Compofition, and fo keep it as it were in i^qui- librio, that it verge not more to the yellow on the one hand, and to the blue on the other, but by their mix'd Actions remain ftill a middle Colour. To this mix'd green there may be farther added fome red and violet, and yet the green will not prefently ceafe, but only grow lefs full and vivid, and by increalingthe red and violet, it will grow more and more dilute, until by the prevalence of the added Colours it be overcome and turned into whitenefs, or fome other Colour. So if to the Colour of any homogeneal Light, the Sun's white Light compofed of all forts of Rays be added, tliat Colour will not vanifh or change its Species, but be diluted, and by adding more and more white it will be dikited more and more perpetu- ally. Laflly, If r^d and violet be mingled, there 1 will
B O O K I. 117
will be generated according to their various Pro- portions various Purples, fuch as are not like in appearance to the Colour of any homogeneal Light, and of thefe Purples mix'd v^dth yellow and blue may be made other nev^ Colours.
PROP. V. Theor. IV. Whiumjs and all grey Colours hetwee?i white and blacky may be compounded of Colours^ and the whitenefs of the Suns Light is compounded of all the primary ^Colours mix'd in a due Proportion,
The Proof by Experiments. Exper. 9.np H E Sun fliining into a dark Cham-
-*- ber through a little round hole in the Window-fliut , and his Light being there refraded by a Prifm to cafl his coloured Image PT [in Fig. 5.] upon the oppofite Wall : I held a white Paper V to that Image in fuch manner that it might be illuminated by the colon r'd Light refle(5ted from thence, and yet not inter- cept any part of that Light in its paflage from the Prifm to the Spectrum. And I found that when the Paper was held nearer to any Colour than to the reft, it appeared of that Coiour to which it approached neareft^ but when it was equally or almoft equally diftant from all the Colours, fo that it might be equally illumina- ted by them all it appeared white. And in this laft fituation of the Paper, if fome Colours were
I 3 inter-
ii8 O P T I C K S.
, intercepted, the Paper loft its white Colour, and appeared of the Colour of the reft of the Light which was not intercepted. So then the Pa- per was illuminated with Lights of various Co- lours, namely, red, yellow, green, blue and violet, and every part of the Light retained its 'proper Colour, until it was incident on the Pa- per, and became refleded thence to the Eycj fo that If it had been- either alone ( the reft of the Light being intercepted ) or if it had a- bounded moft , and been predominant in the Light refled:ed from the Paper, it would have tinged the Paper with its own Colour j and yet being mixed with the reft of the Colours in a due pi:oporti6n, it made the Paper look white, and therefore by a Compoiition with the reft produced that Colour. The feveral parts of the coloured Light refleded from the Spectrum, whilft they are propagated from thence through the Air, do perpetually retain their proper Co- lours, becaufe wherever they fall upon the Eyes of any Spedator, they m.ake the feveral parts of the Spectrum to appear under their proper Co- lours. They retain therefore their proper Co- lours when they fall. upon the Paper V, and fo \)y the confuficn and perfed: mixture of thofe' Colours compound the whitenefs of the Light refleded from thence.
Expcr. lo. Let that Spe6trum or folar Image ]^T [in Fig. 6,'\ f^ll now upon the Lens MN above four Liches broad, and about fix Feet di- ftarit fi'om the Prifm ABC and fo figured that it may caufe the coloured Light which diverg-^ ^ph from the Prifm to converge and meet again-
"i a*.
"B O O K I. iig
at its Focus G, about fix or eight Feet diflant from the Lens, and there to fall perpendicularly upon a white Paper DE. And if you move this Paper to and fro, you will perceive that near the Lens, as at de^ the whole folar Image (fuppofe 2X pt) will appear upon it intenfely coloured after the manner above-explained, and that by receding from the Lens thofe Colours will perpetually come towards one another, and by mixing more and more dilute one another continually, until at length the Paper come to the Focus G, where by a perfed: mixture they will wholly vanifh and be converted into white- nefs, the whole Light appearing now upon the Paper like a little white Circle. And after- wards by receding farther from the Lens, the Rays which before converged will now crofs one another in the Focus G, and diverge from thence, and thereby make the Colours to appear again, but yet in a contrary order; fuppofe at ^i, where the red t is now above which before was below, and the violet p is below which be- fore was above.
Let us now flop the Paper at the Focus G, where the Light appears totally white and cir- cular, and let us confider its whitenefs. I fay, that this is compofed of the converging Colours. For if any of thofe Colours be intercepted at the Lens, the whitenefs will ceafe and degene- rate into that Colour which arifeth from the compofition of the other Colours which are not intercepted. And then if the intercepted Co- lours be let pafs and fall upon that compound Colour, they mix with it, and by their mixture
I 4. reilore
I20 O P T I C K S.
ilore the whitenefs. So if the violet, blue and green be intercepted, the remaining yellow, orange and red will compound upon the Paper an orange, and then if the intercepted Colours be let pafs, they will fall upon this compounded orange, and together with it decompound a white. So alfo if the red and violet be inter- cepted, the remaining yellow, green and blue, will compound a green upon the Paper, and then the red and violet being let pafs will fall up- on this green, and together with it decompound a white. And that in this Compoiition of white the feveral Rays do not fuffer any Change in their colorific Qualities by ading upon one another, but are only mixed, and by a mixture of their Colours produce white, may farther appear by thefe Arguments.
If the Paper be placed beyond the Focus G, fuppofe at h^i, and then the red Colour at the Lens be alternately intercepted, and let pafs a- gain, the violet Colour on the Paper will not fuf^ fer any Change thereby, as it ought to do if the feverai forts of Rays adted upon one another in the Focus G, where they crofs. Neither will the red upon the Paper be changed by any alter- nate flopping, and letting pafs the violet which crolieih it.
And if the Paper be placed at the Focus G, and the white round Image at G be viewed through the Pnfm HIK, and by the Refradiion of that Prifm be tranllated to the place ri', and there sppear tinged with various Colours, name- ly, the violet at v and red at r, and others be- tween, and then the red Colours at the Lens
be
B O O K I. 121
be often ftopp'd and let pafs by turns, the red at r will accordingly difappear, and return as of- ten, but the violet at v will not thereby fuffer any Change. And fo by flopping and letting pafs alternately the blue at the Lens, the blue at v will accordingly difappear and return, without any Change made in the red at r. The red there- fore depends on one fort ot Rays, and the blue on another fort, which in the Focus G v/here they are commix'd, do not acTt on one another. And there is the fame Reafon of the other Co- lours.*
I confidered farther, that when the moft re- frangible Rays P/>, and the leaft refrangible ones T t, are by converging inclined to one ano- ther, the Paper, if held very oblique to thofe Rays in the Focus G, might refled: one fort of them more copioully than the other fort, and by that Means the remedied Light would be tinged in that Focus with the Colour of the pre- dominant Rays, provided thofe Rays feverally retained their Colours, or coloriiic Qualities in the Compofition of White made by them, in tliat Focus. But if they did not retain them in that White, but became all of them feverally endued there with a Difpof^tion to flrike the Senfe with the Perception of White, then they could never lofe their Whitenefs by fuch Reflexions. I in- clined therefore the Paper to the Rays very oblique- ly, as in the fecond Experiment of this fecondPart of the firft Book, that the moft refrangible Rays might be more copioufiy refieded than the refl, and the Whitenefs at Length changed fucceffively into blue, indigo, and violet. Then I inclined it
the
122 O P T I C K S.
the contrary Way, that the leaft refrangible Rays might be more copious in the reflected Light than the reft, and the Whitenefs turned fucceffively to yellow, orange, and red.
Laftly, I made an Inftrument X Y in fafhion of a Comb, whofe Teeth being in number fix- teen, were about an Inch and an half broad, and the Intervals of the Teeth about two Inches wide. Then by interpofmg fucceffively the Teeth of this Inftrument near the Lens, I inter- cepted Part of the Colours by the interpofed Tooth, whilft the reft of them went on through the Interval of the Teeth to the Paper DE, and there painted a round Solar Image. But the Pa- per I had iirft placed fo, that the Image might appear white as often as the Comb was taken away j and then the Comb being as was faid in- terpofed, that Whitenefs by reafon of the inter- cepted Part of the Colours at the Lens did al- ways change into the Colour compounded of thofe Colours which were not intercepted, and that Colour was by the Motion of the Comb perpetually varied fo, that in the paffing of every Tooth over the Lens all thefe Colours, red, yel- low, green, blue, and purple, did alw^ays fuc- ceed one another. I caufed therefore all the Teeth to pafs fucceffively over the Lens, and when the Motion w^as flow, there appeared a perpetual Succeffion of the Colours upon the Paper : But if I fo much accelerated the Mo- tion, that the Colours by reafon of their quick Succeffion could not be diftinguiffied from one another, the Appearance of the fmgle Colours ceafed. There was no redj no yellow, nq
green.
B O O K I. 123
green, no blue, nor purple to be feen any lon- ger, but from a Confulion of rhem all there a- rofe one uniform white Colour. Of the Light which now by the Mixture of all the Colours ap- peared white, there was no Part really white. One Part was red, another yellow, a third green, a fourth blue, a fifth purple, and every Part re-» tains its proper Colour till it ftrike the Senfo- rium. If the Impreffions follow one another flowly, fo that they may be feverally perceived, there is made a diftind: Senfation of all the Co- lours one after another in a continual SucceA fion. But if the Impreffions follow one ano- ther fo quickly, that they cannot be feverally perceived, there arifeth out of them all one common Senfation, which is neither of this Colour alone nor of that alone, but hath it felf indifferently to 'em all, and this is a Senfation of Whitenefs. By the Quicknefs of the Succei^ lions, the Impreffions of the feveral Colours are confounded in the Senforium, and out of that Confufion arifeth a mix'd Senfation. If a burn- ing Coal be nimbly moved round in a Circle with Gyrations continually repeated, the whole Circle will appear like Fire ; the reafon of which is, that the Senfation of the Coal in the feve- ral Places of that Circle remains imprefs'd on the Senforium, until the Coal return again to the fame Place. And fo in a quick Confecu- tion of the Colours the Impreffion of every Co- lour remains in the Senforium, until a Revolu- tion of all the Colours be compleated, and that firit Colour return again. The Impreffions there- fore of all the fucceffive Colours are at once in
the
124 O P T I C K S.
the Senforium, and jointly ftir up a Senfation of , them all ; and fo it is manifeft by this Experi- inent, that the commix'd Impreffions of all the Colours do ilir up and beget a Senfation of white, that is, that Whitenefs is compounded of all the Colours.
And if the Comb be now taken away, that all the Colours may at once pafs from the Lens to the Paper, and be there intermixed, and toge- ther refleded thence to the Spectator's Eyes; their Impreffions on the Senforium being now more fubtilly and perfe(5lly commixed there, ought much more to ftir up a Senfation of White- nefs.
You may inftead of the Lens ufe two Prifms HIK and LMN, which by refracting the co- loured Light the contrary Way to that of the ^rft Refraction, may make the diverging Rays converge and meet again in G, as you fee repre-, fented in the feventh Figure. For where they meet and mix, they will Qompofe a white Light, as when a Lens is ufed.
Exper. 1 1. Let the Sun's coloured Image P T [in Fig. 8.] fall upon the Wall of a dark Cham- ber, as in the third Experiment of the firft Book, and let the fame be viewed through a Prifm aifCy held parallel to the Prifm ABC, by whofe Refraction that Image was made, and let it now appear lower than before, fuppofe in the Place S over-againft the red Colour T. And if you go near to the Liiage P T, the SpeCtrum S will appear oblong and coloured like the Image P T $ but if you recede from it, the Colours of the SpeCtrum S will be contracted more and more,
and
B O O K T. 125
and at length vanifli, that Sped:rum S becoming perfedly round and white j and if you recede yet farther, the Colours will emerge again, but in a contrary Order. Now that Spedlrum S appears white in that Cafe, when the Rays of feveral forts which converge from the feveral' Parts of the Image P T, to the Prifm abc, are fo re- fradted unequally by it, that in their PalTage from the Prifm to the Eye they may diverge from one and the fame Point of the Spedirum S, and fo fall afterwards upon one and the fame Point in the bottom of the Eye, and there be mingled.
And farther, if the Comb be here made ufe of, by whofe Teeth the Colours at the Image PT may be fucceffively intercepted ; the Spe(ftrum S, when the Comb is moved llowly, will be perpe- tually tinged with fucceiTive Colours: But when by accelerating the Motion of the Comb, the Succeffion of the Colours . is fo quick that they cannot be feverally feen, that Spedrum S, by a confufed and mix'd Senfation of them all, will appear white.
Exper. 12. The Su.i ihining* through a large Prifm ABC [in Fig, 9.] upon a Comb X Y, placed immediately behind the Prifm, his Light which pafTed through the Interftices of the Teeth fell upon a white Paper D E. The Breadths of the Teeth were equal to their In- terftices, and feven Teeth together w^th their Interftices took up an Inch in Breadth. Now, when the Paper was about two or three Inches diftant from the Comb, the Light which paf- fed through its. feveral Interftices painted fo
many
126 O P T I C K S.
many Ranges of Colours, kl^ mn, op^ qr^ &c. which were parallel to one another^ and conti- guous, and without any Mixture of white. And thefe Ranges of Colours, if the Comb was moved continually up and down with a reciprocal Mo- tion, afcended and defcended in the Paper, and when the Motion of the Comb was fo quick, that the Colours could not be diftinguiflied from one another, the whole Paper by their Con- fufion and Mixture in the Senforium appeared white.
Let the Comb now reft, and let the Paper be removed farther from the Prifm, and the fe- veral Ranges of Colours will be dilated and expanded into one another more and more, and by mixing their Colours will dilute one ano- ther, and at length, when the diftance of the Paper from the Comb is about a Foot, or a little more (fuppofe in the Place 2D 2E) they will fo far dilute one another, as to become white.
With any Obftacle, let all the Light be now ftopp'd which paffes through any one Literval of the Teeth, fo that the Range of Colours which comes from thence may be taken away, and you will fee the Light of the reft of the Ranges to be expanded into the Place of the Range taken away, and there to be coloured. Let the in- tercepted Range pafs on as before, and its Co- lours falling upon the Colours of the other Ranges, and mixing with them, will reftore the Whitenefs.
Let the Paper 2 D 2 E be now very much in- clined to the RaySj fo that the moft refrangible
Rays
BOOK I. 127
Rays may be more copioufly refleded than the reft, and the white Colour of the Paper through the Excefs of thofe Rays will be changed into blue and violet. Let the Paper be as much in- clined the contrary way, that the leaft refran- gible Rays may be now more copioufly refledl- ed than the reft, and by their Excefs the White- nefs will be changed into yellow and. red. The feveral Rays therefore in that white Light do retain their colorific Qualities, by which thofe of any fort, whenever they become more co- pious than the reft, do by their Excefs and Pre- dominance caufe their proper Colour to ap-
And by the fame way of arguing, applied to the third Experiment of this fecond Part of the firft Book, it may be concluded, that the white Colour of all refracted Light at its very firft Emergence, where it appears as white as before its Incidence, is compounded of various Colours.
Exper, 13. In the foregoing Experiment the feveral Intervals of the Teeth of the Comb do the Office of fo many Prifms, every Interval pro- ducitig the Phcenomenon of one Prifm. Whence inftead of thofe Intervals ufing feveral Prifms, I try'd to compound Whitenefs by mixing their Colours, and did it by ufing only three Prifms, as alfo by ufing only two as follows. Let two Prifms ABC and a be, [in Fig. 10.] whofe re- frading Angles B and b are equal, be fo placed parallel to one another, that the refrading An- gle B of the one may touch the Angle c at the Bafe of the other, and their Planes C B and cbj at which the Rays emerge, may lie in Di-
redum.
128 O P T I C K S.
re(5luin. Then let the Light trajedied through them fall upon the Paper M N, diiftant about 8 or 12 Inches from the Prifms. And the Co- lours generated by the interior Limits B and c of the two Prifms, will be mingled at P T, and there compound white. For if either Prifm be taken away, the Colours made by the other will appear in that Place P T, and when the Prifmi is reftored to its Place again, fo that its Co- lours may there fall upon the Colours of the other, the Mixture of them both will reftore the White nefs.
This Experiment fucceeds alfo, as I have tried, when the Angle b of the lower Prifm, is a lit- tle greater than the Angle B of the upper, and between the interior Angles B and f, there in- tercedes fome Space B c, as is reprefented in the Figure, and the refrading Planes B C and b c, are neither in Directum, nor parallel to one another. For there is nothing more requilite to the Succefs of this Experiment, than that the Rays of all forts may be uniformly mixed upon the Paper in the Place P T. If the moft refrangible Rays coming from the fuperior Prifm take up all the Space from M to P, the Rays of the fame fort which come from the in- ferior Prifm ought to begin at P, and take up all the reft of the Space from thence towards N. If the leaft refrangible Rays coming from the fuperior Prifm take up the Space M T, the Rays of the fame kind which come from the other Prifm ought to begin at T, and take up the remaining Space TIN. If oric fort of the Rays which have intermediate Degrees of Re-
frangibility,
B O O K I. 129
frangibillty, and come from the fuperlor Prifm be extended through the Space M Q^ and ano- ther fort of thofe Rays through the Space M JR., and a third fort of them through the Space M S, the fame forts of Rays coming from the lower Prifm, ought to illuminate the remaining Spaces QN, R N, S N, refpedively. And the fame is to be underftood of all the other forts of Rays. For thus the Rays of every fort will be fcattered uniformly and evenly through the whole Space MN, and fo being every where mix'd in the fame Proportion, they muft every where produce the fame Colour. And therefore, fince by this Mix- ture they produce white in the Exterior Spaces MP and TN, they muft alfo produce white in the Interior Space PT. This is the reafon of the Compolition by which Whitenefs was pro- duced in this Experiment, and by what other way foever I made the like Compofition, the Re- fult was Whitenefs.
Laftly, If with the Teeth of a Comb of a due Size, the coloured Lights of the two Prifms which fall upon the Space PT be alternately in- tercepted, that Space P T, when the Motion of the Comb is flow, will always appear coloured, but by accelerating the Motion of the Comb fo much that the fucceffive Colours cannot be diftinguifhed from one another, it will appear white.
Exper, 14. Hitherto I have produced White- nefs by mixing the Colours of Prifms. If now the Colours of natural Bodies are to be min- gled, let Water a little thicken'd with Soap be agitated to raife a Froth, and after that Froth
K has
130 O P T I C K S.
has ftood a little, there will appear to one that {hall view it intently various Colours every where in the Surfaces of the feveral Bubbles j but to one that fliall go fo far off, that he cannot diftin- guifh the Colours from one another, the whole Froth will grow white with a perfedl White- nefs.
Exper. 15. Laftly, In attempting to compound a white, by mixing the coloured Powders which Painters ufe, I conlider'd that all coloured Pow- ders do fupprefs and flop in them a very confi- derable Part of the Light by which they are illu- minated. For they become coloured by refledl- ing the Light of their own Colours more co- pioufly, and that of all other Colours more fpa- ringly, and yet they do not refied: the Light of their own Colours fo copioufly as white Bodies do. If red Lead, for inflance, and a white Pa- per, be placed in the red Light of the colour'd Spedtrum made in a dark Chamber by the Re- fraction of a Prifm, as is defcribed in the third Experiment of the firfl Part of this Book ; the Pa- per will appear more lucid than the red Lead, and therefore refledis the red-making Rays more copioufly than red Lead doth. And if they be held in the Light of any other Colour, the Light reiledled by the Paper will exceed the Light reflefted by the red Lead in a much greater Proportion. And the like happens in Powders of other Colours. And therefore by mixing fuch Powders, we are not to exped; a flrong and full White, fuch as is that of Pa- per, but fome dusky obfcure one, fuch as might arife from a Mixture of Light and Darknefs,
I or
BOOK I. 131
or from white and black, that is, a grey, pr dun, or ruflet brown, fuch as are the Colours' of a Man's Nail, of a Moufe, of Afhcs, of or- dinary Stohes, of Mortar, of Dull: and Dirt in High-ways, and the like. And fuch a dark white I have often produced by mixing colour 'd Pow- ders. For thus one Part of red Lead, and five Parts of Viridc lEris, compofed a dun Colour like that of a Moufe. For thefe two Colours were feverally fo compounded of others, that in both together were a Mixture of all Co- lours; and there was lefs red Lead ufed than Viride Mr is, becaufe of the Fulnefs of its Co- lour. Again, one Part of red Lead, and four Parts of blue Bife, compofed a dun Colour verging a little to purple, and by adding to this a certain Mixture of Orpiment and Viride Mris in a due Proportion, the Mixture loft its purple TinQure, and became perfed:ly dun. But the Experiment fucceedcd belt without Mi- nium thus. To Orpiment I added by little and little a certain full bright purple, which Painters ufe, until the Orpiment ceafed to be yellow, and became of a pale red. Then I di- luted that red by adding a little Vitide JEris, and a little more blue Bife than Viride Mris, un- til it became of fuch 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 Whitenefs to that of Afhes, or of Wood newly cut, or of a Man's Skin. The Orpiment re- fledled more Light, than did any other of the Powders, and therefore conduced more to the Whitenefs of the com.pounded Colour than thev. . K 2 fo
132 O P T I C K S.
To affign the Proportions accurately may be diffi- cult, by reafon of the different Goodnefs of Pow- ders of the fame kind. Accordingly, as the Co- lour of any Powder is more or lefs full and lumi- nous, it ought to be ufed in a lefs or greater Pro- portion.
Now, confidering that thefe grey and dun Co- lours may be alfo produced by mixing Whites and Blacks, and by confequence differ from perfedt Whites, not in Species of Colours, but only in degree of Luminoufnefs, it is manifefl that there is nothing more requifite to make them perfectly white than to increafe their Light fuffici- ently ; and, on the contrary, if by increafmg their Light they can be brought to perfedl White- nefs, it will thence alfo follow, that they are of the fame Species of Colour with the beft 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, Biie. and Viride Mrh ) and rubbed it thickly upon the Floor of my Chamber, where the Sun {hone upon it through the opened Cafement ; and by it, in the fhadow, I laid a Piece of white Paper of the fame Bignefs. Then going from them to the diflance of 12 or 18 Feet, fo that I could not difcern the Unevennefs of the Sur- face of the Powder, nor the little Shadows let fall from the gritty Particles thereof j the Pow- der appeared intenfely white, fo as to tranfcend even the Paper it felf in Whitenefs, efpecially if the Paper were a little fliaded from the Light of the Clouds, and then the Paper compared 5 with
,A
B O O K I. 133
with the Powder appeared of fuch a grey Colour as the Powder had done before. But by laying the Paper where the Sun fliines through the Glafs of the Window, or by fhutting the Win- dow that the Sun might fhine through the Glafs upon the Powder, and by fuch other fit Means of iiicreafing or decreafnig the Lights wherewith the Powder and Paper were illuminated, the Light wherewith the Powder is illuminated may be* made ilronger in fuch a due Proportion than the Light wherewith the Paper is illuminated, that they fhall both appear exadly alike in Whitenefs. For when I was trying this, a Friend coming to vifit me, I ftopp'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 beft, and wherein they dif- fered ? And after he had at that diflance viewed them well, he anfwer'd, that they were both good Whites, and that he could not fay which was beft, nor wherein their Colours differed. Now, if you confider, that this White of the Powder in the Sun-fliine was compounded of the Co- lours which the component Powders ( Orpi- ment. Purple, Bife, and Viride JEris ) have in the fame Sun-fhine, you muft acknowledge by this Experiment, as well as by the former, that perfedt Whitenefs may be compounded of Co- lours.
From what has been faid it is alfo evident, that the Whitenefs of the Sun's Lisrht is com- pounded of all the Colours wherewirh the feve- ral forts of Rays whereof that Light confifts, when by their feveral Refrangibilities they are
K 3 fepa-
134 O P T I C K S.
feparated from one another, do tinge Paper or any other white Body whereon they fall. For thofe Colours {hy Prop.ll. Part 2.) are unchangeable, and whenever all thofe Rays w^ith thofe their Co- lours are mix'd again, they reproduce the fame white Light as before.
PROP. VI. Prob. II.
Lt a mixture of Primary Colour s-^ the ^luantity and S^uality of each bei7tg given^ to know theColour of the Compound,
WITH the Center O [m Fig. 11.] and Radius OD defcribe a Circle ADF, and diltinguiih its Circumference into feven Parts DE, EF, FG, GA, AB, B C, CD, propor- tional to the feven Mufical Tones or Intervals of the eight Sounds, «So/, /^, fa^ fol^ la^ mi, fa, fol, contained in an eight, that is, proportional to the Number ~, 75, ts, |, 15, is, \. Let the firfl Part I>E reprefent a red Colour, the fecond E F orange, the third F G yellow, the fourth C A green, the fifth AB blue, the fixth BC indigo, and the feventh C D violet. And conceive that thefe are all the Colours of uncompounded Light gradually pafiing into one another, as they do when made by Prifms j the Circumference DEFGABCD, reprefenting the whole Series of Colours from one end of the Sun's colour'd Image to the other, fo that from D to E be all degrees of red, at E the m.ean Colour be- tween red and orange, from E to F all de- crees
B O O K I. 135
grees of orange, at F the mean between orange and yellow, from F to G all degrees of yellow, and fo on. Let p be the Center of Gravity of the Arch D E, and q^ r, j, t, u^ Xy the Cen- ters of Gravity of the Arches E F, F G, G A, - A B, B C, and C D refpedively, and about thofe Centers of Gravity let Circles proportio- nal to the Number of Rays of each Colour in the given Mixture be defcrib'd ; that is, the Circle p proportional to the Number of the red-making Rays in the Mixture, the Circle q proportional to the Number of the orange-ma- king Rays in the Mixture, and fo of the reft. Find the common Center of Gravity of all thofe Circles p, q^ r, s, t, z/, x. Let that Center be Z; and from the Center of the Circle ADF, through Z to the Circumference, drawing the Right Line O Y, the Place of the Point Y in the Circumference Ihall ihew the Colour arifmg from the Compofition of all the Colours in the given Mixture, and the Line OZ fhall be propor- tional to the Fulnefs or Intenfenefs of the Cok)ur, that is, to its diftanCe from Vv^iitenefs. As if Y fall in the middle between F and G, the compounded Colour fliall be the beft yel- low J if Y verge from the middle towards F or G, the compound Colour fliall accordingly be a yellow, verging towards orange or green. If Z fall upon the Circumference, the Colour fhall be intenfe and florid in the higheft Degree ; if it fall in the mid- way between the Circum- ference and Center, it fhall be but half fo intenfe, that is, it fhall be fuch a Colour as would be made by diluting the intenfeil yellow
K 4 with
136 O P T I C K S.
with an equal quantity of whitenefs ; and if it fall upon the center O, the Colour fhall have loft all its intenfenefs, 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 fhall not be any of the prifmatick Colours, but a purple, inclining to red or violet, according- ly as the point Z lieth on the fide of the line DO towards E or towards C, and in general the compounded violet is more bright and more fiery than the uncompounded. Alfo if only two of the primary Colours which in the circle are pppofite to one another be rnixed in an equal proportion, the point Z {hall fall upon the cen- ter O, and yet the Colour compounded of thofe two fhall not be perfectly white , but fome faint anonymous Colour, For I could never yet by mixing only two primary Colours pro- duce a perfeft white. Whether it may be com- pounded of a mixture of three taken at equal diftances in the circumference I do not know, but of four or five I do not much queftion but it may. But thefe are Curiofities of little or no moment to the underflanding the Phaenomena of Nature. For in all whites produced by Na- ture, there ufes to be a mixture of all forts of Rays, and by confequence a compofition of all Colours.
To give an inftance of this Rule; fuppofe a Colour is compounded of rhefe homogeneal Colours, of violet one part, of indigo one part, of blue two parts, of gi^een three parts, of yel- )pw five parts, of orange fix parts, and of red
ten
B O O K I. 137
ten parts. Proportional to thefe parts defcribe the Circles x, v, /, s, r, q, p, refpedively, that is, fo that if the Circle x be one, the Circle 1; may- be one, the Circle f two, the Circle s three, and the Circles r, q and/>, five, fix and ten. Then I find Z the common center of gravity of thefe Circles, and through Z drawing the Line OY, the Point Y falls upon the circumference between E and F, fomething nearer to E than to F, and thence I conclude, that the Colour compounded of thefe Ingredients will be an orange, verging a little more to red than to yellow. Alfo I find that OZ is a little lefs than one half of O Y, and thence I conclude, that this orange hath a little lefs than half the fulnefs or intenfenefs of an un- compounded orange j that is to fay, that it is fuch an orange as may be made by mixing an ho- mogeneal orange with a good white in the pro- portion 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 pra- dtice, though not mathematically accurate ; and the truth of it may be fufliciently proved to Senfe, by flopping any of the Colours at the Lens in the tenth Experiment of this Book. For the refi: of the Colours which are not fi:opp'd, but pafs on to the Focus of the Lens, will there compound either accurately or very nearly fuch a Colour, as by thi^ Rule ought to refult from their Mixture.
FRO P.
138 O P T I C K S.
PROP. VIL The OR. V.
/ill the Colours in the Univerfe which are made by Lights and depend not on the Power of Imagination^ are either the Colours of homogeneal Lights^ or com- founded of thefe-^ and that either accu- rately or very nearly^ according to the, Rule of the foregoing Problem,
FOR it has been proved (in Frop. i. Fart 2.) that the changes of Colours made by Refra- d:ions do not arife from any new Modifications of the Rays imprefs'd by thofe Refradions, and by the various Terminations of Light and Shadow, as has been the conftant and general Opinion of Philofophers. It has alfo been proved that the feveral Colours of the homogeneal Rays do con- ftantly anfwer to their degrees of Refrangibility, [Prop. I. Part i. andPrc/^. 2. Part 2.) and that their degrees of Refrangibility cannot be changed by Refractions and Reflexions [Prop. 2. Part i.) and by confequence that thofe their Colours are likewife immutable. It has alfo been pro- ved diredlly by refrafting and reflecting homo- geneal Lights apart, that their Colours cannot be changed, [Prop. 2. Part 2.) It has been proved alfoj that when the feveral forts of Rays are mix- ed, and in croflmg pafs through the fame'fpace, they do not ad- on one another fo as to change each others colorific qualities. [Exper. 10. Part 2.) but by mixing their Adions in the Senforium be- get
BOOK I. 139
get a Senfation differing from what either would do apart, that is a Senfation of a mean Colour between their proper Colours j and particularly when by the concourfe and mixtures of all forts of Rays, a white Colour is produced, the white is a mixture of all the Colours which the Rays would have apart, [Frop. 5. Part 2.) The Rays in that mixture do not lofe or alter their feveral colorific qualities, but by all their various kinds of Adions mix'd in the Senforium, beget a Sen- fation of a middling Colour between all their Co- lours, which is whitenefs. For whitenefs is a mean between all Colours, having it felf indiffe- rently to them aU, fo 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 prefcnrly lofe its Colour, but a white Powder mix'd with any Colour is prefently tinged with that Colour, • and is equally capable of being tinged with any Colour whatever. It has been fhewed alfo, that as the Sun's Light is mix'd of all forts of Rays, fo its whitenefs is a mixture of the Colours of all forts of Rays -, thofe Rays ha- ving from the beginning their feveral colorific qualities as well as their feveral Refrangibilities, and retaining them perpetually unchanged not- withftanding any Refradtions or Reflexions they may at any time fuffer, and that whenever any fort of the Sun's Rays is by any means (as by Reflexion in Exper. g. and 10. Part i. or by Refradion as happens in all Refractions) fepara- ted from the reft, they then manifell; their proper Colours. Thefe things have been prov'd, and the fujn of all this amounts to the Propofitioa
here
I40 O P T I C K S.
here to be proved. For if the Sun's Light is mix'd of feveral forts of Rays, each of which have originally their feveral Refrangibilities and colorific Qualities, andnotwithftanding their Re- .fraftions and Reflexions, and their various Sepa- rations or Mixtures, keep thofe their original Properties perpetually the fame without alterati- on ; then all the Colours in the World muft be fuch as conftantly ought to arife from the origi- nal colorific qualities of the Rays whereof the Li2;hts confift by which thofe Colours are feen. And therefore if the reafon of any Colour what- ever be required, we have nothing elfe to do than to confider how the Rays in the Sun's Light have by Reflexions or Refraftions, or other caufes, been parted from one another, or mixed together j or otherwfe to find out what forts of Rays are in the Light by which that Colour is made, and in what Proportion ; and then by the laft Problem to learn the Colour which ought to arife by mixing thofe Rays (or their Colours) in that proportion. I fpeak here of Colours fo far as they arife from Light. For they appear fometimes by other Cau- fes, as when by the power of Phantafy wc fee Co- lours in a Dream, or a Mad-man fees things be- fore him which are not there; or when we fee Fire by flriking the Eye, or fee Colours like the Eye of a Peacock's Feather, by prefTing our Eyes in either corner whilft we look the other way. Wliere thefe and fuch like Caufes interpofe nor, the Colour always anfwers to the fort or forts of the Rays whereof the Light confifts, as I have conftantly found in whatever Phasnomena of Colours I have hitherto been able to examine.
I aiall
B O O K I. 141
I {hall in the following Proportions give inftan- ces of this in the Phaenomena of chiefeft note.
PROP, VIII. Prob. III.
By the difcove7'ed Properties of Light to explain the Colours made by Prijms.
LET ABC [in Fig. 12.] reprefent a Prifnl refracting the Light of the Sun, which comes into a dark Chamber through a hole F <j> almofl as broad as the Prifm, and let M N re- prefent a white Paper on which the refracted Light is caft, and fuppofe the moil refrangible or deepeft violet-making Rays fall upon the Space Pttj the leaft refrangible or deepeft red- making Rays upon the Space T7, the rniddle, fort between the Indigo-making and blue-mu- king Rays upon the Space Qv, the middle fort of the green-making Rays upon the Space Rp, the middle fort between the yellow-making and orange-making Rays upon the Space S a-, and o- ther intermediate forts upon intermediate Spa- ces. For fo the Spaces upon which the feveral forts adequately fall will by reafon of the diffe- rent Refrangibility of thofe forts be one lower than another. Now if the Paper MN be fo near the Prifm that the Spaces PT and ^-j do not interfere with one another, the diftance be- tween them T it will be illuminated by all the forts of Rays in that proportion to one another which they have at their very firft coming out
of
142 O P T I C K S.
of the Prifm, and confequently be white. But the Spaces P T and ttT on either hand, will not be illuminated by them all, and therefore will appear coloured. And particularly at P, where the outmofl violet-making Rays fall alone, the Colotir mufi: be the deepeft violet. At Q^here the violet-making and indigo-making Rays are mixed, it mufl: 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 muft (by the conftrudtion of the fecond Pro- blem ) compound a middle Colour between in- digo arid blue. At S where all the Rays are mixed, except the red-making and orange-ma- king, their Colours ought by the fame Rule to compound a faint blue, verging more to green than indigo. And in the progrefs 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 whitenefs. ^
So again, on the other fide of the white at r, where the leaft refrangible or utmoft red-ma- king Rays are alone, the Colour mull: be the deepeft red. At a the mixture of red and o- range will compound a red inclining to orange. At ^ the mixture of red, orange, yellow, and one half of the green muft compound a middle Colour between orange and yellow. At ^ 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 progrefs
from
B O O K I. 143
from V to TT, where by a mixture of all forts of Rays it will become white.
Thefe Colours ought to appear were the Sun*s Light perfedly white: But becaufe it inclines to yellow, the Excefs 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 fo the Colours In order from P to r ought to be violet, indigo, blue, very faint green, white, faint yellow, o- range, red. Thus it is by the computation : And they that pleafe to view the Colours made by a Prifm will find it fo in Nature.
Thefe are the Colours on both fides the white when the Paper is held between tlie Prifm and the Point X where the Colours meet, and the interjacent white vaniflies. For if the Paper be held flill farther off from the Prifm, the mofl refrangible and leaft refrangible Rays will be wanting in the middle of the Light, and the refl . of the Rays which are found there, will by mix- ture produce a fuller green than before. Alfo the.yellowand blue will now become lefs com- pounded, alid by confequence more intenfe than before. And this alfo agrees with experience.
And if one look through a Prifm upon a white Objed: cncompafTed with blacknefs or darknefs, the reafon of the Colours arifing on the edges is much the fame, as will appear to ons that fhall a little confider it. If a black Ob- jed: be encompafTed with a white one, the Co- lours which appear through the Prifm are to be derived from the Light of the white one, fpread- ing into the Regions of the black, and therefore
they
144 O P T I C K S.
they appear in a contrary order to that, when a white Objeft is furrounded with black. And the fame is to be underftood when an Obje6l is view- ed, whofe parts are fome of them lefs luminous than others. For in the borders of the more and lefs luminous Parts, Colours ought always by the fame Principles to arife from the Excefs of the Light of the more luminous, and to be of the fame kind as if the darker parts were black, but yet to be more faint and dilute.
What is faid of Colours made by Prifms may be eafily applied to Colours made by the GlalTes of Telefcopes or Microfcopes, or by the Hu- mours of the Eye. For if the Objedl-glafs of a Telefcope be thicker on one fide than on the other, or if one half of the Glafs, or one half of the Pupil of the Eye be cover'd with any opake fubftance j the Objedi-glafs, or that part of it or of the Eye which is not cover'd, may be confider'd as a Wedge with crooked Sides, and * every Wedge of Glafa or other pellucid Subftance has the effect of a Prifm in refradiing the Light which paffes through it *.
How the Colours in the ninth and tenth Ex- periments of the lirfl Part arife from the diffe- rent Reflexibility of Light, is evident by whar was there faid. But it is obfervable in the ninth Experiment, that whilft the Sun's dired: Light is yellow, the Excefs of the blue-making Rays in the refleded beam of Light MN, fuffices only to bring that yellow to a pale white incli- ning to blue, and not to tinge it with a mani-
* See eur AuthorV Left. Optic. Part II. Se^. II. fa^. i6g, &(.
feftly
B Q O K I. 145
feftly blue Colour. To obtain therefore a better blue, I ufed inftead of the yellow Light of the Sun the white Light of the Clouds^ by varying a little the Experiment, as follows.
Exper, 16. Let HFG [in Fig. 13.] repre- fent a Prifm in the open Air, and S the Eye of the Spedator, viewing the Clouds by their Light coming into the Prifm at the Plane Side FIGK, and refleded in it by its Bafe HEIG, and thence going out through its Plane Side H E F K to the Eye. And when the Prifm and Eye are conveniently placed, fo that the Angles of Incidence and Reflexion at the Bafe may be about 40 Degrees, the Spe£latpr will fee a Bow MN of a blue Colour, running from one End of the Bafe to the other, with the Concave Side towards him, and the Part of the Bafe IMNG beyond this Bow will be brighter than the other Part E M N H on the other Side of it. This blue Colour M N being made by nothing elfe than by Reflexion of a fpecular Superficies, feems fo odd a Phaenomenon, and fo difficult to be explain- ed by the vulgar Hypothefis of Philofophers, that I could not but think it deferved to be taken Notice of. Now for underftanding the Rea- fgn of it, fuppofe the Plane. ABC to cut the Plane Sides and Bafe of the Prifm perpendicu-r larly. From the Eye to the Line B C, wherein that Plane cuts the Bafe, draw the Lines S^ and S/', in the Angles S^^: 50 degr. i, and Stc 49 degr. Vt, and the Point p will he the Limit beyond which none of the moft refrangible Rays can pafs through the Bafe of the Prifm, and be refraded, whofe Incidence is fuch thai;
L t'hey
14,6 OPTIC K S.
they may be refieded to the Eye ; and the Point t will be the like Limit for the leaft refrangi- ble. Rays, that is, beyond which none of them can pafs through the Bafe, whoie Incidence is fuch that by Reflexion they may come to the Eye. . And the Point r taken in- the middle Way betv/een p and ^, will be the like Limit for the meanly . refrangible Rays. And there- fore all the leaft refrangible Rays which fall upon the Bafe beyond /, that is, between t and B, and can come from thence to the Eye, will be refledted thither : But on this fide t^ that is, between t and f, many of thefe Rays will be tranfmitted through the Bafe. And all the moft refrangible Pvays which fall upon the Bafe be- yond ^, that is, between p and B, and can by Reflexion come from thence to the Eye, will be refleded thither, but every where between p and r, many of thefe Rays will get through the Bafe, and be refraded j and the fame is to be underftood of the meanly refrangible Rays on either fide of the Point r. Whence it follows, that the Bafe of the Prifm rriufl every where between t and B, by a total Reflexion of all forts of Rays to the Eye, look white and bright. And every where between p and C, by reafon of the Tranfmiflion of many Rays of every fort, look more pale, obfcure, and dafk. But at r, and in other Places between p and /, where all the more refrangible Rays are refledied to the Eye, and many of the lefs refrangible are. tranf- .mitted, the Excefs of the moft refrangible in the refleded Light will tinge that Light with their Colour, which is violet and blue. Arid-
this
B O O K I. 147
this happens by taking the Line C/r/B any .where between the Ends of the Prilm H G and EI.
PROP, IX. prob. r\^.
By the difcGvered Pf'operties of Lighi to explain the Colours of the Rain-bow,
THIS Bow never appears, but where it n|ins in the Sun-fhine, and may be made artiticially by fpouting up Water which may break aloft, and fcatter into Drops, and fall down like Rain. For the Sun fliining upon thefe Drops certainly caufes the Bow to appe^f* to a Spectator ftanding in a due Polition 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 un- derllood by fome of the Antients, and of late more fully difcover'd and explain'd by the fa- mous Antoniiis de Dominis Archbilhop of ^pa- lato, in his Book De Radiis Visits & Liicis, pub- lifhed by his Friend Bartolus at Venice^ in the Year 161 1,. and written above 20 Yeai's before. For he teacher' there how the interior Bow is made in round Drops of Raiii by two Refracti- ons of the Sun's Light, and one Reflexion be- tween them, and the exterior by two Refradti- ons, and two forts of Reflexions between them in each Drop of Vv^ater, and proves his Expli- cations by Experiments made witba Phial full lof Water, and with Globes of Glafs filled
L 2 with
148 O P T I C K S.
with Water, and placed in the Sun to make the Colours of the two Bows appear in them. The fame Explication Des-Cartes hath purfued in his- Meteors, and mended that of the exterior Bow. But whilft they underftood not the true Ori- gin of Colours, it's neceffary to purfue it here a little farther. For underftanding therefore how the Bow is made, let a Drop of Rain, or any other fpherical tranfparent Body be reprefented by the Sphere BNFG, [in Fig. 14.] defcribed with the Center C, and Semi-diameter C N. And let AN be one of the Sun's R^s inci- dent upon it at N, and thence refradled to F, where let it either go out of the Sphere by Re- fraction towards V, or be refle<5ted to G ; and at G " let it either go out by Refradion to R, or be refledled to H; and at H let it go out by Refrad:ion 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 Per- pendiculars CD and CE, and produce CD till it fall upon the Circumference at L. Parallel to the incident Ray AN draw the Diameter B Q^ and let the Sine .of Incidence out of Air into Water be to the Sine of Refradion as I to R. Now, if you fuppofe the Point of Incidence N to move from the Point B, continually till it come to L, the Arch Q F will firil increafe and then decrcafe, and fo will the Angle A X R which the Rays A N and G R contain ; and the Arch QJ' and Angle AXR will be biggeft when ND is to CN as -/H^RR to v/ 3 RR, in which cafe NE will be to ND as 2 R to I. Alfo the Angle AYS, which the Rays AN and HS
contain
B O O K I. 149
contain will firft decreafe, and then increafe and grow leaft when ND is to CN as y'llZlRK to ^8RR, in which cafe NE will be to ND, as 3 Rtol. And fo the Angle which the next emer- gent Ray ( that is, the emergent Ray after three Reflexions) contains with tlie incident Ray AN will come to its Limit when ND is to CN as y/li— KR to / 15 RR, in which cafe NE will be to N D as 4 R 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 N D is to CN as /ii — KK to v/ 24 RR, in which cafe NE will be to ND as 5 R to I i and fo on infinitely, the Numbers 3,8, 15, 24, &c. being gather'd by continual Addition of the Terms of the arithme- tical Progreflion 3, 5, 7, 9, ^c. The Truth of all this Mathematicians will ealily examine.* > .
Now it is to be obferved, that as when the Sun comes to his Tropicks, Days increafe and decrcafe but a very little for a great while together j fo when by increaling the diflance CD, thefe Angles come to their Limits, they vary their quantity but very little for fome time together, and therefore a fir greater Number of the Rays which fill upon all the Points N in the Quadrant BL, {hall emcrg. in theLimits of thefe Angles, than in any other Incli- nations. And farther it is to be obferved, that the Rays which differ in Refrangibility will have dif- ferent Limits of their Angles of Emergence, and by confequence according to their different De^ grees of Refrangibility emerge moft copioufly
_, * This is demonjirated in our Author'j Ledl. Optic Part I. Se^l. IV. Prop. 35 and 36.
L 3 in
150 O P T I C K S.
in different Angles, and being feparated from one another appear each in their proper Colours, And v/hat thole Angles are may be eaiily ga- ther'd from the foregoing Theorem by Com- putation.
For in the leaft refrangible Rays the Sines I and R (as was found above) are io8 and 8i, and thence by Computation the greateft Angle AXR will be found 42 Degrees and 2 Minutes, and the kail Angle AYS, 50 Degrees and c^j Minutes. And in the moll refrangible Rays the Sines I and R are 109 and 81, and thence by Computation the greateft Angle AXR wilh be found 40 Degrees and 17 Minutes, and the leaft Angle AYS 54 Degrees and 7 Minutes.
Suppofe now \^\'^x. O [ in Fig. 15. ] is the Spe- 6lator's Eve, 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 Mm. 50 Degr. c^-j Min. and 54 Degr. 7 Min. refpe6tively, and thefe Angles turned about their common Side O P, fhall with their other Sides OE, OF; OG, OH, defcribe the Verges of two Rain-bows AF BE and CHDG. Foi* if E, F, G, H, be drops placed any where in the conical Superficies defcribed by OE, OF, OG, OH, and be illuminated by the Sun's Rays SE, SF, SG, SH; the Angle SEO being e- qual to the Angle POE, or 40 Degr. 17 Min. ihall be the greateft Angle in which the moft refrangible Rays can after one Pvetiexion be re- fradled to the Eye, and therefore all the Drops in the Line O E Inall fend the moft refrangible Rays moft copioufly to the Eye, and thereby
ftrike
BOO KllC fi5a
i\nkt the ^fes with the deepeft violet Colour in that Region. And in like manner the^^ngle SFO being equal to the Angle POF, or 42 Degr. 2 Min. fhall be the greateft in which the Icall: re- frangible Rays after one Reflexion can emerge out of the Drops, and therefore thofe Rays .fliall come moft copioufly to the Eye from the Drops in the Line O F, and flrike the Senfes with the deepeft red Colour in that Region. And by ■the fame Argument, the Rays which have inter- mediate Degrees of Refrangibility fliall comeiinofl copioufly from Drops between E and F, and'llirike the Senies with the intermediate Colours, in the Order which their Degrees of Refrangibility rc- €|uiie, that is in the Progfefs 'from E toF, or from the infide of the Bow to the outfide in this order, violet, indigo, blue, green, ycllow,"^^ orange, red. But the violet, by the mixtiue of the white Light of the Clouds, will appear laint and in- cline to purple.
- Again, the Angle SGO being equal to the Angfe POG, or 5oGr. 51 Min. fhall be the Iciift Angle in which the leaft refrangible Rays can after two Reflexions emerge out of the Drops, and therefore the leafl refrangible Rays lliall come moffc copioufly to the Eye from the Drops i-n the Line OG, and firike the StnfQ with the deepeft red in that Region. And the Angle SHO being equal to the Angle POH, or 54 Gr.- 7 Min. fliall be the leafl Angle, in which the moft refrangible Rays after two Pvcfiexions can emerge out of the Drops J and therefore thofe Rays fhall come mofl copioufly to the Eye froni^ the Drops in the Line OFI, and ilrike the Senfes
L 4 with
152 O P T I C K S.
with the deepeft violet in that Region. And by the fame Argument, the Drops in the Regions be- tween G and H fliall ftrike the Senfe with the in- termediate Colours in the Order which their Degrees of Refrangibility require, that is, in the Progrefs from G to H, or from the infide of the Bow to the outiide in this order, red, orange, yel- low, green, blue, indigo, violet. And fmce thefe four Lines OE, OF, OG, OH, may be ■fituated any where in the above-mention'd co- iiical Superficies ; what is faid of the Drops and Colours in thefe Lines is to be underftood of the Drops and Colours every where in thofe Superficies.
Thus iliall there be made tv^o Bows of Co- lours, an interior and ftronger, by one Reflexion jn the Drops, and an exterior and fainter by two J for the Light becomes fainter by every Reflexion. And their Colours fhall lie in a con- trary Order to one another, the red of both Bows bordering upon the Space GF, which is be- tween the Bows. The Breadth of the inte- rior Bow EOF meafured crofs the Colours fhall be I Degr. 45 Min. and the Breadth of the ex- terior GOH fhall be 3 Degr. 10 Min. and the diflance between them GOF fhall be 8 Gr. 15 Min. the greateft Semi-diameter of the inner- mofl, that is, the Angle POF being 42 Gr. 2 Min. and the leafl Semi-diameter of the outer- mofl POG, being 50 Gr. 57 Min. Thefe are the Meafures 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 in^ creafed, and ^heir Diflance decreafed by half a
Degree,'
B O O K I. 153
Degreq, and (o the breadth of the interior Iris will be 2 Degr. J5 Min. that of the exterior 3 Degr. 40 Min. their diftance 8 Degr. 25 Min. the greateft Semi-diameter of the interior Bow 42 Degr. 17 Min. and the leail of the exterior 50 Degr. 42 Min. And fuch are the Dimenfions of the Bows in the Heavens found to be very nearly, when their Colours appear ftrong and perfed:. For once, by fuch means as I then liad, I .meafured the greateft 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, befides the outmoft faint red ob- fcured by the brightnefs of the Clouds, for which we may allow 3 or 4 Minutes more. , The breadth of the blue was about 40 Minutes more belides the violet, .which was fo much obfcu- red by the brightnefs of the Clouds, that I could not meafure its breadth. But fuppofing 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 t De- grees, as above. The leail diftance between this Iris and the exterior Iris was about 8 De2;rees and 30 Minutes. The exterior Iris was broader than the interior, but fo faint, efpecially on the blue fide, that I could not meafure its breadth di- ftindlly. At another time when both Bows ap- peared more diftind:, I meafured 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 fame Colours in the interior as 3 to 2.
this
154 O P T I C K S.
This Explication of the Rain-bow is yet far- ther confirmed by the known Experiment (made by Antonius de Domini s and Des-Cartes ) of hanging up any where in the Sun-iliine a Glafs Globe filled with Water, and viewing it ih fuch a poflure, 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 ( fuppofe at O ) {hall fee a full i:ed Colour in that fide of the Globe oppofed to the Sun as 'tis reprefented at F, and if that An- ^gle become lefs (fuppofe by depreflnig the Globe to E) there will appear other Colours, yellow, green and blue fucceflive in the fame fide of the Globe. But if the- Angle be made about 50 Degrees (fuppofe by lifting up the Globe to G) there will appear a red Colour in that Me of the Globe towards the Sjun, and if the An- gle be made greater (fuppofe by lifting up tlie Globe to H) the red will turn fucceffively to the other Colours, yellow, green and blue. The fame thing I have tried, by letting a Globe reft, and raifing or depreifing the Eye , or other- wife moving it to make the Angle of ajufl mag* nitude. ;u y-.
I have heard it reprefented, that if the Light of a Candle be refraded by a Prifm to the Eye ; when the blue Colour falls upon the Eye, the Spe<5tator {hall fee red in the Prifm, and when the red falls upon the Eye he fhall fee blue ; and if this were certain , the Colours of . the Globe and Rain-bow ought to appear in a. con- nary order to what we find. But the Colours ^ of
BOOK I. 155
of the Candle being very faint, the miftake feems to arife from the difficulty of difcerning what Colours fall on the Eye. For, on the contrary, I have fometimes had occafion to obferve in the Sun's Light refraded by a Prifm, that the Spe- ctator always fees that Colour in the Prifm which falls upon his Eye. And the fame I have found true alfo in Candle-light. For when the Prifm is moved (lowly from the Line which is drawn diredly from the Candle to the Eye, the red ap- pears firft in the Prifm and then the blue, and therefore each of them is feen when it falls upon the Eye. For the red pafTes over the Eye firft, and then the blue.
The Light which comes through drops of Rain by two Refra6tions without any Reflexion, ought to appear ftrongeft at the diftance of a- bout. 26- Degrees from the Sun, and to decay gradually both ways as the diftance from him in- creafes and decreafes. And the fame is to be un- derftood of Light tranfmitted through fphe- "rical Hail-ftones. And if the Hail be a little flatted , as it often is , the Light tranfmitted may grow fo ftrong at a little lefs diftance than that of 26 Degrees, as to form a Halo about the Sun or Moon ; which Halo, as often as the Hail-ftones are duly figured may be colour'd, and then it muft be red within by the leaft re- frangible Rays, and blue without by the moft refrangible ones, efpecially if the Hail-ftones have" opake Globules of Snow in their center to intercept the Light within the Halo {asHu^ genius has obferv'd) and make the infide there- of more diftind')y defined than it would other- wife
156 O P T I C K S.
wife be. For fuch Hail-ftones, though fpheri- cal, by terminating the Light by the Snow, may make a Halo red within and colourlefs without, and darker in the red than without, as Halos ufed to be. For of thole Rays which pafs clofe by the Snow the Rubriform will be ieaft refracted, and fo come to the Eye in the di- refteft Lines.
The Light which pafTes through a drop of Rain after two Refra6:ions, and three or more Reflexions, is fcarce ftrong enough to caufe a fenfible Bow; but in thofe Cylinders of Ice by which Hiigenius explains the Parhelia^ it may perhaps be fenfible.
PROP. X. Prob. V. By the difccvered Properties of Light to explain the permanent Colours of Natu- ral Bodies,
THESE Colours arife from hence , that fome natural Bodies refled: fome forts of Rays, others other forts more copioufly than the reft. Minium refledts the Ieaft refrangible or red-rfiaking Rays moft copioufly, and thence ap- pears red. Violets refled: the moft refrangible moft copioufly, and thence have their Colour, and fo of other Bodies. Every Body refledls the Rays of its own Colour more copioufly than the reft, and from their excefs and predominance in the refleded Light has its Colour.
Exper^
B O O K I. 157
Exper. ij. For if in the homogeneal Lights obtained by the folution of the Problem pro- pofed in the fourth Propolition of the firft Part of this Book, you place Bodies of feveral Co- lours, you will find, as I have done, that every Body looks mofl fpiendid and luminous in the Light of its own Colour. Cinnaber in the ho- mogeneal red Light is mofl refplendent, in the .green Light it is manifeftly lefs refplendent, and in jhe blue Light ftill lefs. Lidigo in the vi- olet blue Light is moll refplendent, and its fplen- dor is gradually diminiih'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 com- pound green, are more flrongly refle6ted than the other Colours red and violet, and fo of the reft. But to make thefe Experiments the more mani- feft, fuch Bodies ought to be chofen as have the fulleft and moft vivid Colours, and two of thofe Bodies are to be compared together. Thus, for inftance, if Cinnaber and ultra-nMxv'mt blue, or fome other full blue be held together in the red homogeneal Light, they will both appear red, but the Cinnaber will appear of a ftrongly lumi- nous and refplendent red , and the ultra-mz- rine blue of a faint obfcure and dark red ; and if they be held together in the blue homogeneal ' Light, they will both appear blue, but the ultra- marine will appear of a ftrongly luminous and refplendent blue, and the Cinnaber of a faint and dark blue. Which puts it out of difpute, that the Cinnaber reflecfts the red Light much more copioufly than the ////n;-marine doth, and 2 the
158 O P T I C K S.
the ulfra-m^i'lne refleds the blue Light much more copioully than theCinnaber doth. The fame Experiment may be tried fuccefsfully with red Lead and Indigo, or with any other two colour'd Bodies, if due allowance be made for the diffe- rent ftrength or wealoiefs of their Colour and Light.
And as the reafon of the Colours of natural Bodies is evident by thefe Experiments, fo it is. farther confirmed and put pafl difpute by ,the two firft Experiments of the firft Part, where- by 'twas proved in fuch Bodies that the reflefed Lights which differ in Colours do differ alfo in degrees of Refrangibility.^ For thence it's cer- tain, that fome Bodies reflect the more refran- gible, others the lefs refrangible Rays more co- piouily.
And that this is not only a true reafon of thefe Colours, but even the only reafon, may appear farther from this Confideration, that the Colour of homogeneal Light cannot be changed by the Reflexion of natural Bodies.
For if Bodies by Reflexion cannot in the leafl change the Colour of any one fort of Rays, they cannot appear colour'd by any other means than by refle(^ting thofe which either are of their own Colour, or which by mixture muft pro- duce it.
But in trying Experiments of this kind care muft be had that the Light be fufficiently ho- mogeneal. For if Bodies be illuminated by the ordinary prifmatick Colours, they will appear neither of their own Day-light Colours, nor of the Colour of the Light caft on them, but of
fome
BOOK!. 159
feme middle Colour between both, as I have found by Experience. Thus red Lead (for in- ftance ) illuminated with the ordinary prifma- "tick 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 lefs compounded. For becaufe red Lead appears red when illumi- nated with white Light , wherein all forts of Rays are equally mix'd, and in the green Light all forts of Rays are not equally mix'd, the Lx- cefs of the yellow-making , green-making and blue-making Rays in the incident green Light,' will caufe thofe Rays to abound fo niuch in the refle<^ted Light, as to draw the Colour from red towards their Colour. And becaufe the red Lead refle(fts the red-making Rays moft copioufly in proportion to their number, *and next after them the orange-making and yellow-making Rays ; thefe Rays in the refledted Light will be more in proportion to the Light than they were in the in- cident green Light, and thereby will draw the refleded Light from green towards their Co- lour. And therefore the red Lead will appear neither red nor green, but of a Colour between both.
In tranfparently colour'd Liquors 'tis obfer- vable, that their Colour ufes to vary with their thicknefs. Thus, for inftance, a red Liquor in a conical Glafs 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 ftili thicker becomes red, and where 'tis thickeft
V the
i6o O P T I C K S.
the red is.deepefl anddarkeft. For it is to be conceiv'd that fuch a Liquor flops the indigo- making and violet-making Rays moft eafily, the blue-making Rays more difficultly, the green-' making Rays ftill more difficultly, and the red- making moft difficultly : And that if the thick- nefs of the Liquor be only fo much as fuffices to Hop a competent number of the violet-ma- king and indigo-making Rays, without dimi- nifliing much the number of the reft, the reft muft (by Prop. 6. Part 2.) compound a pale yellow. But if the Liquor be fo much thicker as to ftop alfo a great number of the blue-ma- king* Rays, and fo^ie of the ^reen-making, the reft muft compound an orange j and where it is fo thick as to ftop alfo a great number of the green-making and a confiderable number of the yellow-making, the I'eft muft begin to compound a red, and this red muft grow deeper and darker as the yellow-making and orange-making Rays are more and more ftopp'd by increafmg the thicknefs of the Liquor, fo that few Rays befides 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 Veftel, found in a clear Sun- fhine Day, that when he was funk many Fa- thoms deep into the Water, the upper part of his Hand on which the Sun ftione dired:ly through the Water and through a fmall Glafs Window in the Vefiel appeared of a red Co- lour, like that of a Damask Rofe, and the Wa- ter below and the under part of his Hand illuminated by Light refleded from the Water
below
BOOK I. i6i
below look'd green. For thence it may be ga- ther'd, that the Sea- Water refleds back the violet and bhie-making Rays moft eafily, ,and lets the • red-making Rays pafs moft freely and copioufly to ffreat Depths. For thereby the Sun's direct Light at all great Depths, by reafcn of the predomi- nating red-making Rays, muft appear red j and the greater the Depth is, the fuller and in- tenfer muft that red be. And at fuch Depths as the violet-making Rays fcarce penetrate unto, the blue-making, green-making, and yellow- making Rays being refleded from below more copioully than the red-making ones, muft com- pound a green.
Now, if there be two Liquons of full Colours, fiif)pofe a red and a blue, and both of them fo thick as fuffices to tnake their Colours fufficiently full; though either Liquor be fufficiently tranfpa- tenz apart, yet will you not bfe able to fee through Doth together. For, if only the red-making Rays pafs through one Liquor, arid only the blue* making through the other, no 'Rays can pafs through both. This Mr. H^ok' tried cafuilly ^ith Glafs Wedges filled with red and blue Li- quors, and was furprized at the unexpeded Event, the reafon of it being then unknown ; which makes me truft the more to his Experiment, though I have not tried it my felf. But he that would repeat it, muft take care the Li- quors be of very good and full Colours.
Now, whilft Bodies become coloured by refled:- ing or tranfmitting this or that fort of Rays more eopiouily than the reft, it is to be conceived that they ftop and ftrfle in themfelves the Rays
M > which
i62 O P T I C K S.
which they do not refledt or tranfmit. For, if Gold be foliated and held between your Eye and . the Light, the Light looks of a greenifh blue, and therefore mafTy Gold lets into its Body the blue-making Rays to be reflected to and fro within it till they be ftopp'd and ftifled, whilft it refle(5ls the yellow-making outwards, and thereby looks yellow. And much after the fame manner that Leaf Gold is yellow by refle<ited, and blue by tranfmitted Light, and maify Gold .is yellow in all Pofitions of the Eye -, there are foqie Liqi:jors, as the Tincfture of Lignum Nephriticumy and fome forts of Glafs which tranfmit one fort of Light moft copioufly, and refled another fort, and thereby look of feve- 4^al Colours, according to the Pofition of the Eye to the Light. But, if thefe Liquors or .Glafles were fo thick and mafTy that no Light could get through them, I queftion not but they fwould like all other opake Bodies appear or ohe and the fame Colour in all Pofitions of the Eye, though this I cannot yet affirm by Expe^ rience. For all colour'd Bodies, fo far as my Obfervation reaches, may be feen through if made fufficiently thin, and therefore are in fome meafure tranfparent, and differ only in degrees of Tranfparency from tinged tranfparent Li- <juors; thefe Liquors, as well as thofe Bodies, by a fufficient Thicknefs becoming opake. A tranfparent Body which looks of any Colour by tranfmitted Light, may alfo look of the fame 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
BOOK L .161
then the refleded Colour will be diminlfhed, and perhaps ceafe, by making the Body very thick, and pitching it on the backfide to diminifh the Reflexion of its farther Surface, fo that the Light refle(3;ed from the tinging Particles may predomi- nate. In fuch Cafes, the Colour of the reflecfted Light will be apt to vary from that of the Light tranfmitted. But whence it is that tinged Bo- dies and Liquors refledt fome fort of Rays, and intromit or tranfmit other forts, fhall be faid in the next Book. In this Propofition I content my felf to have put it paft difpute, that Bodies have fuch Properties, and thence appear colour'd.
PROP. XI. Prob. VI.
By mixing colour d Lights to compound a beam of Light of the fa^ne Colour and Nature with a beam of the Su?is direEi Light y and therein to experience the Truth of the foregoing Propoftions,
LET ABC abc [in Fif[. 16.] reprefent a Prifm, by which the Sun's Light let into a dark Chamber through the Hole F, may be refradted towards the Lens MN, and paint upon it at py q, r, j, and /, the ufual Colours vio- let, blue, green, yellow, and red, and let the diverging Rays by the Refrad:ion of this Leng converge again towards X, and there, by the mixture of all thofe their Colours, compound a white according to what was fhewo above.
M 2 Then
i64 OPTIC K S.
Then let another Prifm DEG deg, parallel to the former, be placed at X, to refrad: that white Light upward* towards Y. Let the refracting, Angles of the Prifms, and their diflances from the Lens be equal, fo that the Rays which con- verged from the Lens towards X, and without Refradion, would there have crofled and di- verged again, may by the Refradtion of the fe- cond Prifm be reduced into Parallelifm and diverge no more. For then thofe Rays will re- compofe a beam of white Light XY. If the refradting Angle of either Prifm be the bigger, that Prifm muft be fo much the nearer to the Lens. You will know when the Prifms and the Lens are well fet together, by obferving if the beam of Light X Y, which comes out of the fe- cond Prifm be perfectly white to the very edges of the Light, and at all diftances from the Prifm continue perfectly and totally white like a beam of the Sun's Light. For till this happens, the Polition of the Prifms and Lens to one another muft be correded ; and then if by the help ©f a long beam of Wood, as is reprefehted in the Figure, or by a Tube, or fbme other fuch In- ftrument made for that Purpofe, they- be made faft in that Situation, you may try all the fame Experiments in this compounded beam of Light X Y, which have been made in the Sun's dired: Light. For this compounded beam of Light has the fame appearance, and is endow'd with all. the fame Properties with a diredt beam of the Sun's Light, fo far as my Obfervation reaches. And in trying Experiments in this beam you may by flopping any of the Colours /, q^ r, />
and
B O O K I. 165
and /, at the Lens, fee how the Colours produce^ in the Experiments are no other than thofe which the Rays had at the Lens before they entered the Compofition of this Beam : And by confcqijence> that they arife not from any new Modifications of the Light by Refradtions and Reflexions, but from the various Separations and Mixtures of the Rays originally endow'd with theircolour-making Qua- lities.
So, for inftance, having with a Lens 4, Liches broad, and two Prifms on either hand 6i Feet diftant from the Lens, made fuch a beam of compounded Light ; to examine the reafon of the Colours made by Prifms, I rcfraded this com- pounded beam of Light XY with another Prifm. HIK kh, and thereby call the ufual Prifma- tick Colours PQRST upon the Paper LV placed behind. And then by flopping any of the Colours />, ^, r, j, /, at the Lens, I found that the fame Colour would vanifh at the Pa- per. So if the Purple p was ftopp'd at the Lens, the Purple P upon the Paper would vanifh, and the reft of the Colours would remain un- alter'd, imlefs perhaps the blue, fo far as fome purple latent in it at the Lens might be fepa- rated from it by the following RefraSions. And fo by intercepting the green upon the Lens, the green R upon the Paper would vanifli, and fo of the refl j which plainly fhews, that as the white beam of Light XY was compounded of feveral Lights varioufly colour'd at the Lens, fo the Colours which afterwards emerge out of it by new Refradlions are no other than thofe of which its Whitenefs was compounded. The
M 3 Refradion
i66 O P T I C K S.
Refradion of the Prifm HIK /^^ generates the Colours PQ^ST upon the Paper, not by chan- ging the colorific Qualities of the Rays, but by feparating the Rays which had the very fame colo- rific Qualities before they enter'd the Compofition of the refradied beam of white Light X Y. For otherwife the Rays which were of one Colour at the Lens might be of another upon the Paper, contrary to what we find.
So again, to examine the reafon of the Co- lours of natural Bodies, I placed fuch Bodies in the Beam of Light XY, and found that they all appeared there of thofe their own Colours which they have in Day-light, and that thofe Colours depend upon the Rays which had the fame Colours at the Lens before they enter'd the Compofition of that beam. Thus, for inflance, Cinnaber illuminated by this beam appears of the fame red Colour as in Day-light ; and if at the Lens you intercept the green-making and blue-making Rays, its rednefs will become more full and lively : But if you there intercept the red-making Rays, it will not any longer ap- pear red, but become yellow or green, or of lome other Colour, according to the forts of Rays which you do not intercept. So Gold in this Light XY appears of the fame yellow Colour as in Day-light, but by intercepting at the Lens a due Quantity of the yellow-making Rays it will appear white like Silver ( as I have tried ) which Ihews that its yellownefs arifes from the Excefs of the intercepted Rays tinging that Whitenefs with their Colour when they are let pafs. So the Infuiion of Ugmm Nephriticum
(as
B O O K I. 167
(as I have alfo tried) when held in this beam of Light XY, looks blue by the reflected Part of the Light, and red by the tranfrrjitted Part of it, as when 'tis view'd in Day-light j but if you intercepc the blue at the Lens the Infufion will lofe its re- fled:ed blue Colour, whilft its tranfmitted red re- mains perfect, and by the lofs of fome blue- making Rays, wherewith it was allay'd, becomes more intenfe and full. And, on the contrary, if the red and orange-making Rays be intercepted at the Lens, the Infufion will lofe its tranfmitted red, whilft its blue will remain and become more full and perfedl. Which fhews, that the Infufion does not tinge the Rays with blue and red, but only tranfmit thofe mofl copioufiy which were red-making before, and refledts thofe moft copi- oufly which were blue-making before. And after the fame manner may theReafons of other Phaeno- mena be examined, by trying thorn in this artificial beam of Light XY.
M 4 THE
THE
SECOND BOOK
OF
OPTICKS.
P A R T I.
Obfervations concerning the Reflexions y Re- fraBionSy and Colours of thi^t tranfpa- rent Bodies,
T has been obferved by others, that tranfparent Subftances, as Glafs, Water, Air, &V. when made very thin by being blown into Bubbles, or otherwife formed into Plates, do exhibit various Co- lours according to thcjr various thinnefs, altho' at
a greater
BOOK II. 169
a greater tlucknefs they appear very clear and colour! efs. In the former Book I forbore to treat of, thefe Colours, becaufe they feemed of a more difficult Confideration, and were not necef- fary for eftabliihing the Properties of Light there difcourfed of. But becaufe they may conduce to farther Difcpveries for compleating the Theory of Light, efpecially as to the conftitution of the parts of natural Bodies, on which their Colours or Tranfparency depend j I have here fet down an account of thern. To render this Difcourfe fhort and didindt, I have fiifl defcribed the prin- cipal of my Obfervations , and then confider'd and made ufe of them. The Obfervations are thefe.
Ohf. I., Comprefiing two Prifms hard toge- ther that their fides (which by chance were a very little convex) might fomewhere touch one another : I found the place in which they touch- ed to become abfolutely tranfparent, as if they had there been one continued piece of Glafs, For when the Light fell fo obliquely on the Air, which in other places was between them, as to be all refledcds ic feemed in that place of contact to be wholly tranfmitted, infomuch that when look'd upon, it appeared like a black or dark fpot, by reafon that little or no fenfible Light was refledled from thence, as from other places ; and when looked through it feemed ( a^ it were) a hole in that- Air which was formed into a thin Plate, by being comprefs'd between the Glafles. And through this hole Objeds that were beyond might be feen diftindly , which could not at all be feen through other parts of
the
lyo O P T I C K S.
the GlafTes where -the Air was interjacent. Al- though the GlafTes were a little convex, yet this transparent fpot was of a confiderable breadth, which breadth feemed principally to proceed from the yielding inwards of the parts of the GlafTes, by reafon of their mutual prefTure. For by prefTing them very hard together it would be- come much broader than otherwife.
Obf. 2. When the Plate of Air, by turning the Prifms about their common Axis, became (o little inclined to the incident Rays, that fome of them began to be tranfmitted, there arofe in it many flender Arcs of Colours which at firfl were fhaped almofl like the Conchoid , as you fee them delineated in the firfl Figure. And by con- tinuing the Motion of the Prifms, thefe Arcs increafed and bended more and more about the faid tranfparent fpot, till they were compleated into Circles or Rings incompafling it, and af- terwards continually grew more and more con- tradted.
Thefe Arcs at their firfl appearance were of a violet and blue Colour, and between them were white Arcs of Circles , which prefently by continuing the Motion of the Prifms became a little tinged m their inward Limbs with red and yellow, and to their outward Limbs the blue was adjacent. So that the order of thefe Colours from the central dark fpot, was at that time white, blue, violet j black, red, orange, yellow, white, blue, violet, &c. But the yel- low and red were much fainter than the blue and violet. *
2 ' The
BOOK 11. 171
The Motion of the Prifms aBout their Axis being continued, thefe Colours contracl^ed more and more, Shrinking towards the whitenefs on either fide of it, until they totally vaniihed into it. And then the Circles in thofe parts appear'd black and white, without any other Colours in~ termix'd. But by farther moving the Prifms about, the Colours again emerged out of the whitenefs, the violet and blue at its inward Limb, and at its outward Limb the red and yel- low. So that now their order from the central Spot was white, yellow, red; black; violet, .blue, white, yellow, red, ^c, contrary to what it was before.
Obf. 3. When the Rings or fome parts of them appeared only black and white, they were very diftindl and well defined, and the blacknefs feemed as intenfe as that of the central Spot. Alfo in the Borders of the "Rings, where the Colours began to emerge out of the white- nefs, they were pretty diftind: , which made them vifible to a very great multitude. I have fometimes number'd above thirty Succeffions (reckoning every black and white Ring for one Succeflion) and feen more of them, which by reafon of their fmalnefs I could not number. But in other Pofitions of the Prifms, at which the Rings appeared of many Colours, I could not diftinguiih above eight or nine of them, and the Exterior of thofe were very confufed and dilute.
In thefe two Obfervations to fee the Rings di- ilin<5t, and without any other Colour than bl^ck and white, I found it neceflary to hold my Eye
at
172 O P T I C K S.
at a good diftance from them. For by ap- proachijfjg nearer, although in the fame inclina- tion of my Eye to the Plane of the Rings, there emerged a bluifH Colour out of the white, which by dilating it felf more and more into the black, render'd the Circles lefs diflindt, and left the white a little tinged with red and yel- low. I found alfo by looking through a flit or oblong hole, which was narrower than the pupil of my Eye, and held clofe to it pjirallel to the Piifms, I could fee the Circles much diftindter and vifible to a far greater number than other- wife.
Ohf.\> To obferve more nicely the order of the Colours which arofe out of the white Cir- cles as the Rays became lefs and lefs inclined to the Plate of Airj I took two Objed-glafTes, the one a Plano-convex for a fourteen Foot Telefcope, and the other a large double Con- vex for one of about fifty Footj and upon this, laying the other with its plane fide downwards, I prelfed them (lowly together,, to make the Colours fucceffively emerge in the middle of the Circles, and then fiowly lifted the upper Glafs from the lower to make them fuccefTively vaniih again in the fame place. The Colour, which by preffing the GlalTes together, emerged laft in the middle of the other Colours, would upon its firft appearance look like a Circle of a Colour almoft uniform from the circumference to the center, and by compreffing the GlaiTes ftill more, grow continually broader until a new Colour emerged in its center, afid thereby it becanie a Ring encompaihng ^hat new Colour. And by
2 com-
BOOK IL t73
domprefiing the Gkfles ftill more, the diameter of this Ring would increafe, and the breadth of its Orbit or Perimeter decreafe until another new Colour emerged in the center of the laft: And fo on until a third, a fourth, a fifth, and other following new Colours fuccefiively emerged there, and became Rings encompalfmg the inner- moft Colour, the laft of which was the black Spot. And, on the contrary, by lifting up the upper Glafs from the lower, the diameter of the Rings would decreafe, and the breadth of their Orbit increafe, until their Colours reached fuc- cefiively to the center ; and then they being of a confiderable breadth, I could more eafily difcern and diftinguifti their Species than before. And by this means I obferv'd their Succeflion and Quantity to be as foUoweth.
Next to the pellucid central Spot made by the contadl of the Glaffes fucceeded blue, white, yellow, and red. The blue was ib little in quan- tity, that I could not difcern it in the Circles made by the Prifms, nor could I well diftinguifti any violet in it, but the yellow and red were pretty copious, and feemed about as much in extent as the white, and four or five times more than the blue. The next Circuit in order of Colours immediately encompaffmg thefe were violet, blue, green, yellow, and red: and thefe were all of them copious and vivid, excepting the green, which was very little in quantity, and feemed much more faint and dilute than the other Colours. Of the other four, the vio- let was the leaft in extent, and the blue lefs than the yellow or red. The third Circuit or
^ Order
174. O P T I C K S.
Order was purple, blue, green, yellow, and red ; in which the purple feemed more reddifh than the violet in the former Circuit, and the green was much more confpicuous , being as brisk and copious as any of the other Colours, except the yellow, but the red began to be a lit- tle faded, inclining very much to purple. Af- ter this fucceeded the fourth Circuit of green and red. The green was very copious and live- ly, inclining on the one lide to blue, and on the othtr fide to yellow. But in this fourth Circuit there was neither violet, blue, nor yel- low, and the red was very imperfe6l and dir- ty. Alfo the fucceeding Colours became more and more imperfed: and dilute, till after three or four revolutions they ended in perfedt whitenefs. Their form, when the Glafles were moft comprefs'd fo as to make the black Spot appear in the center, is delineated in the fe- Gond Figure ; where a, b, f, ^, e : /, ^, h, /, k : /, w, w, 0, p: q, r : s, t : v, x : )\ z, de- note the Colours reckon'd in order from the center, black, blue, white, yellOw, red: vio- let, blue, green, yellow, red: purple, blue, green, yellow, red: green, red: greenifh blue, red: greenifli blue, pale red: greenifli blue, reddifh white.
Obf. 5. To determine the interval of the Glalfes, or thicknefs of the interjacent Air, by which each Colour was produced, I meafured the Diameters of the firfl fix Rings at the moft lucid part of their Orbits, and fquaring them, I found their Squares to be in the arithmetical Pro- greffion of the odd Numbers, i, 3, 5, 7, 9, 1 1.
And
BOOK II. 175
And fince one of thefe Glafles was plane, and the other fpherical, their Intervals at thofe Rings jnuft be in the fame Progreffion. I meafured alio the Diameters of the dark or faint Rings between the more lucid Colours, and found their Squares to be in the arithmetical Progrelfion of the. even Numbers, 2, 4, 6, 8, 10, 12. And it being very nice and difficult to take thefe meafures exadly; I repeated them divers times at divers parts of ihe GlafTes, that by their Agreement I might be confirmed in them. And the lame method I ufed in determining fome others of the following Ob- fervations.
Obf. 6. The Diameter of the fixth Ring at
the moil lucid part of its Orbit was -^ parts of
an Inch, and the Diameter of the ' Sphere on which the double convex Objedt-glals was ground was about 102 Feet, and hence I ga- thered the thicknefs of the Air or Aereal Inter- val of the Glaffes at that Ring. But fome time after, fufpedting that in making this Obfervatioii I had not determined the Diameter of the Sphere with fufficient accuratenefs, and being uncertain whether the Plano-convex Glafs was truly plane, and not fomething concave or con- vex on that fide which I accounted plane ; and whether I had not preiTed the GlafiTes together, as I often did, to make them touch j ( For by preffing fuch GlalTes together their parts eafily yield inwards, and the Rings thereby become fenfibly broader than they would be, did the GlalTes keep their Figures.) I repeated the Experiment , and found the Diameter of the
fixth
176 O P T I C K S.
fixth Iticid Ring about -^ parts of an Inch. 1
repeated the Experiment alfo with fuch an Ob- jed-glafs of another Tclefcope as I had at hand. This was a double Convex ground on both fides to one and the fame Sphere, and its Fo- cus was diftant from it 83 f Inches. And thence, if the Sines of Incidence and Refraction of the bright yellow Light be affumed in proportion as II to 17, the Diameter of the Sphere to which the Glafs was figured will by computa- tion be fougd 182 Inches. This Glafs I laid upon a flat one, fo that the black Spot appear- ed in the middle of the Rings of Colours with- out any other PrelTure than that of the weight of the Glafs. And now meafuring the Diame- ter of the fifth dark Circle as accurately as I could, I found it the fifth part of an Inch pre- cifely. This Meafure was taken with the point$ of a pair of CompaiTes on the upper Surface on the upper Glafs, and my Eye was about eight or nine Inches diftance from the Qlafs, almofl perpendicularly over it, 'and the Glafs was r of an Inch thick, and thence it is eafy to colled: that the true Diameter of the Ring be- tween the Glaffes was greater than its meafur'd Diameter above the Glaffes in the Proportiort of 80 to y9, or thereabouts, and by confequence equal to ^| parts of an Inch, and its true Semi- diameter equal to tV parts. Now as the Dia- meter of the Sphere (.182 Inches) is to the Se- mi-diameter of this fifth dark Ring .(t* parts of an Inch) fo is this Semi-diameter to the thick- : nefs of the Air at this fifth dark Ring j which is
there-
BOOK II. ?t77
therefore -7^^— or — ^^ Parts of an Inch ; and ^ 567931 1774784 ^
the fifth Part thereof, viz. tke -r^ Part of an
•0739
Inch, is the Thicknefs of the Air at thefirft of thefe dark Rings.
The fame Experiment I repeated with another double convex Objed'-glafs ground on both fides to one and the fame Sphere. Its Focus was di- flarit from it i68j Inches, and therefore the Dia- meter of that Sphere was iS'4 Inches. This Glafs being laid upon the fijme plain, Glafs, the Diameter of the fifth of the dark Rings, when the black Spot in their Center appear'd plainly without preffing the Glailes, was by the meafure of the Compafles upon fhe upper Glafs
!ii Parts of an Inch, and by. confequence be- tween theGlaffes it was ~^:.. For the upper Glafs
was ^ of an Inch thick, arid rhy Eye was diitant from it 8 Inches. And a third proportional to "half this from the Diameter ,,©jf the/Sphere is
,,-r- Parts of an Inch. Thi^ is therefore the Thicknefs of the Air at this. Ring, and a fifth Part thereof, viz. the ~— th Part of. an Incli is
the Thicknefs thereof at the firfl of the Rings, as above.
I tried the fame Thing, by laying thefe Obje(5t- glafies upon flat Pieces of a broken Looking- glafs, and found the fame Meafures of the Rings: Which makes me rely upon them till
N they
178 O P T I C K S.
.they can be determin'd more accurately byGlailes ground to larger Spheres, though in fuch GlafTes greater care muft be taken of a true Plane.
Thefe Dimenfions were taken, when my Eye was placed almoft perpendicularly over the Glaf- fes, being about an Inch, or an Inch and a quar- ter, diilant from the incident Rays, and eight Inches diftant from the Glafs j fo that the Rays were inclined to the Glafs in an Angle of about four Degrees. Whence by the following Obfer- vation you will underftand, that had the Rays been perpendicular to the GlafTes, the Thicknefs of the Air at thefe Rings would have been lefs ia the Proportion of the Radius to the Secant of four Degrees, that is, of loooo to 10024. Let the ThicknefTes found be therefore dimini{h'd in this
Proportion, and they will become —^ and --^ — ^.
or ( to ufe the nearefl round Number ) the
g~^th Part of an Inch. This is the Thicknefs of
the Air at the darkeft Part of the iirft dark Ring made by perpendicular Rays; and half this Thick- nefs multiplied by the ProgreiTion,' i, 3, 5, 7, g^ iiy^^c. gives the Thicknefles of the Air at the moft luminous Parts of all the brighteft Rings, viz,
{^y T^o) T^oy r78^> ^^' ^heir arithme- tical Means ^^, - g^~, ^j^^, &c. being its ThicknefTes at the darkefl Parts of all the dark ones.
Oi/.j.
BOOK IL
179
Obf. 7. The Rings were leaft, when my Eye was placed perpendicularly over theGlafTes in the Axis of the Rings : And when I view'd them obliquely they became bigger, continually fwel- ling as I removed my Eye farther from the Axis. And partly by meafuring the Diameter of the fame Circle at feveral Obliquities of my Eye, partly by other Means, as alfo by making ufe of the two Prifms for very great Obliquities, I found its Diameter, and confequently the Thicknefs of the Air at its Perimeter in all thofe Obliquities to be very nearly in the Proportions exprefs'd in this Table.
Angle of In- |
Angle of Re- |
Diameter |
"Ihickricf |
cidence on |
f ration in- |
of the |
of the |
the Air. |
to the Air. |
Ring. |
Air. . |
Deg. Min. |
|||
00 00 |
00 00 |
10 |
\^ |
06 26 |
10 00 |
IOtV |
IOtV |
12 45 |
20 00 |
lOf |
IQi |
18 49 |
30 00 |
lOA |
Ilf |
24 30 |
40 00 |
IIv |
13 |
29 37 |
50 00 |
12k |
i5i |
33 58 |
60 00 |
14 |
20 |
35 47 |
65 00 |
i5i |
23t |
37 19 |
70 00 |
i6t |
28^ |
3S 33 |
7S 00 |
'^I |
37 |
39 27 |
'80 00 |
22f |
52i |
40 00 .. 40 II |
85 GO |
29 |
Hu |
90 00 |
3< |
\ 122', |
N 2
In
i8o O P T I C K S.
* In the two firll Columns are exprefs'd the Obli- quities of the incident and emergent Rays to the Plate of the Air, that is, their Angles of Inci- dence and Refraction. In the third Column the Diameter of any colour'd Ring at thofe Obliqui- ties is exprelTed in Parts, of which ten conffcitute that Diameter when the Rays are perpendicular. And in the fourth Column the Thicknefs of the Air at the Circumference of that Ring is exprelTed in Parts, of which alfo ten eonfti- tute its Thicknefs when the Rays are perpen- dicular.
And from thefe Meafures I feem to gather this Rule: That the Thicknefs of the Air is pro- portional to the Secant of an Angle, whofe Sine* is a certain mean Proportional between the Sines.' of Incidence and Refradlion. Arid that mean . Proportional, fb far as by thefe Meaftires I caw determine it, is the firft of an hundred and fix arithmetical mean Proportionals between thofe» Sines counted from the bigger Sine, that; is, * from the Sine of Refradion when the Re- fraction is made out of the Glafs into the^ Plate of Air, or from the Sine of Incidence when* the Refraftion is made out oi the ■ Plate of Air into the Glafs. ,
O^.' 8. The dark Spot in the middle of the Rings increafed alfo by the Obliquation of the Eye, although almofl infenfibly. But, if inftead of the ObjeS-glafTes the Prifms were made ufe of, its Increafe was more manifefl when viewed fo, obliquely that no Colours appeared about it. ' It was leafl when the Rays were incident moll obliquely on the interjacent Air, and as
the
BOOK II. i8i
the obliquity decreafed it increafed more and more until the colour'd Rings appear'd, and then decreafed again, but not fo much as it in- creafed before. And hence it is evident, that the Tranfparency was not only at the abfolute Contad of the GlalTes, but alfo^here they had fome little Interval. I have fometimes obferved the Diameter of that Spot to be between half and two fifth parts of the Diameter of the ex- terior Circumference of the red in the firft Cir- cuit or Revolution of Colours when view'd al- moft perpendicularly ; whereas when view'd ob- liquely it hath wholly vanifli'd and become opake and -white like the other parts of the Glafs 3 whence it may be coUeded that the Glaffes did then fcarcely, or not at all, touch one another, and that their Interval at the pe- rimeter of that Spot when view'd perpendicu- larly was about a fifth or fixth part of their In- terval at the circumference of the faid red.
O/y^rT'. 9.. By looking through the two conti- guous Objed-glafies, I found that the interja- cent Air exhibited Rings of Colours, as well by tranfmitting Light as by refleding it. The central Spot was now white, and from it the order of the Colours were yellowifli red; black, violet, blue, white, yellow, red; violet, blue, green, yellow, red, &c. But thefe Colours were very faint and dilute, unlefs when the Light was trajecled very obliquely through the Glaffes : For by that means they became pretty vivid. Only the firft yellowifh red , like the blue in the fourth Obfervation, was fo little and faint as fcarcely to be difcern'd. Comparing
N 3 the
i82 O P T I C K S.
the colour'd Rings made by Reflexion, with thefe made by tranfmilTion of the Light j I found that white was oppofite to black, red to blue, yellow to violet, and green to a Compound of red and violet. That is, thafe parts of the Glafs were black when looked through, which when looked upon appeared white, and on the contrary. And fo thofe which in one cafe exhi- bited blue, did in the other cafe exhibit red. And the like of the other Colours. The man- ner you have reprefented in the third Figure, where A B, CD, are the Surfaces of theGlaifes contiguous at E, and the black Lines between them are their Diftances in arithmetical Progref-. iion, and the Colours written above are feen by refiedied Light, and thofe below by Light tranf- mitted.
Oof. 10. Wetting the Objed-glafTes a little
■ at their edges, the Water crept in flowly be- tween them, and the Circles thereby became lefs and the Colours more faint : Infomuch that as the Water crept along, one half of them at which it firft arrived would appear broken off from the other half, and contracted into a lefs Room. By meafuring them I found the Pro- portions of their Diameters to the Diameters of the like Circles made by Air to be about itvtu. to eight, and confequently the Intervals of the Glaffes at like Circles, caufed by thofe two Me- diums Water and Air, are as about three to four.
• Perhaps it may be a general Rule, That if any other Medium more or lefs denfe than Water be comprefs'd between the Glaffes, their Inter- vals at the Rings cavifed thereby will be to their
Intervals
BOOK II. 183
Intervals caufed by interjacent Air, as the Sines are which meafure the Refrad;ion made out of that Medium into Air.
Obf. II. When the Water was between the Glafles, if I prefTed the upper Glafs varioully at its edges to make the Rings move nimbly from one place to another, a little white Spot would immediately follow the center of them, which upon creeping in of the ambient Water into that place would prefently vanilh. Its appearance was fuch as interjacent Air would have caufed, and it exhibited the fame Colours. But it was not Air, for where any Bubbles of Air were in the Water they would not vanilli. The Refle- xion- muft have rather been caufed by a fubtiler Medium, which could recede through the Glaf-^ fes at the creeping in of the Water.
Obf. 12. Thefe Obfervations were made in the open Air. But farther to examine the Effects of colour'd Light falling on the Glaffes, I dar- 3cen'd the Room, and view'd them by Reflexion of the Colours of a Prifm caft on a Sheet of white Paper, my Eye being fo placed that I could fee the colour'd Paper by Reflexion in the Glalfes , as in a Looking-glals. And by this means the Rings became diftind:er and vifible to a far greater number than in the open Air. I have fometimes feen more than twenty of them, whereas in the open Air I could not difcern above eight or nine.
Obf. 13. Appointing an A ffiftant to move the Prifm to and fro about its Axis, that ail the Colours might fucceffively fall on that part of the Paper which I faw by Reflexion from that
N 4 part
j84 OPTIC K S.
part of "the GlafTes, where the Circles appear'd, £o thax all. the Colours might be fucceffively re, fiefted from the Circles to my Eye whilft I held it immovable, I found, the Circles which the red Light made to be manifeftly bigger than thofe which were made by the blue and violet. And it was very pleafant to fee them gradually fwell or contrad: accordingly as the Colour of the Light was changed. The Interval of the Glaf- fes at any of the Rings when they were made by |:he utmoft red Light, was to their Interval at the fame Ring when made by the utmoft violet, greater than as 3 to 2, and lefs than as 13 to 8. By the moft of my Obfer vat ions it was as 14 to 9. And this Proportion feem'd very nearly the fame in all Obliquities of my Eye ; unlefs whea two Prifms were made ufe of inftead of the Ob^ jedi-glafTes. For then at a certain great obliquity of my Eye, the Rings made by the feveral Co- lours {eem'd equal, and at a greater obliquity thofe made by the violet would be greater than the fame Rings made by the red: the Refrad:ion of the Prifm in this cafe caafing the moft refran^ gible Rays to fall more obliquely on that plate of the Air than the leaft refrangible ones. Thus the Experiment fucceeded in the colour'd Light, which was fufhciently ftrong and copious to jnake the Rings fenfible. And thence it may be gather'd, that if the moft refrangible and leaft refrangible Rays had been copious enough to make the Rings fenfible without the mixture of other Rays, the Proportion which here was 14 to 9 would have been a little greater, fuppofe 14? or 14T to 9.
BOOK IT. 185
Obf. 14. Whilft the Prifm was turn'd about its Axis with an uniform Motion, to make all the feveral Colours fall fucceffively upon the Objedi-glafles, and thereby to marke the Rings contrad: and dilate : The Contradion or Dilata- tion of each Ring thus made by the variation of its Colour was fwifteft in the red, and floweft in the violet, and in the intermediate Colours it had intermediate degrees of Celerity. Com- paring the quantity of Contrad:ion and Dilata- tion made by all the degrees of each Colour, I found that it was greatefl in the red j lefs in the yellow, ftill lefs in the blue, and leaft in the violet. And to make as juft an Eftimation as I could of the Proportions of their Contrad:ions or Dilatations, I obferv'd that the whole Con- traction or Dilatation of the Diameter of any Ring made by all the degrees of red, was to that of the Diameter of the fame Ring made by all the degrees of violet, as about four to three, or five to four, and that when the Light was of the middle Colour between yellow and green, the Diameter of the Ring was very nearly an arithmetical Mean between the greatefl Diame- ter of the fame Ring made by the outmoft red, and the leaft Diameter thereof made by the outmoft violet : Contrary to what happens in the Colours of the oblong Spedlrum made by the Refraction of a Prifm, where the red is moft contracted , the violet moft expanded , and in the midft of all the Colours is the Con- fine of green and blue. And hence I feem to collect that the thicknefies of the Air between the GlaiTcs there, where the Ring is fucceffive- ly
i86 O P T I C K S.
ly made by the limits of the five principal Co- lours ( red, yellow, green, blue, violet ) in or- der ( that is, by the extreme red, by the limit of red and yellow in the middle of the orange, by the limit of yellow and green, by the limit of green and blue, by the limit of blue and violet in the middle of the indigo, and by the extreme violet ) are to one another very nearly as the fixth lengths of -aXhord which found the Notes in a fixth Major, Jhl^ la, mi\ fa, Jol, la. But it agrees fomething better with the Obferva- tion to fay, that the thickneffes of the Air be- tween the GlafTes there, where the Rings are fuccefTively made by the limits of the feven Co- lours, red, orange, yellow, green, blue, indi- go, violet in order, are to one another as the Cube Roots of the Squares of the eight lengths ^f a Chord, which found the Notes in an eighth, Jhl, la, fa, Jbl, la, mi, fa, fol ; that is, as the Cube Roots of -the Squares of the Nurinbers, i,
8 f J i i ^ I
§> 5> 4J 1; Si '^J 2*
Obf 15. Thefe Rings were not of various Colours like thofe made in the open Air, but appeared all over of that prifmatick Colour on- ly witli which they were illuminated. And by projediing the prifmatick Colours immediately upon the GlalTes, I found that the Light which fell on the dark Spaces which were between the colour'd Rings was tranfmitted through the GlalTes without any variation of Colour. For on a white Paper placed behind, it would paint Rings of the fame Colour with thofe which were refleded, and of the bignefs of their im- mediate Spaces. And from thence the origin
I of
BOOK II. 187
of thefe Rings Is manifefl; namely, that the Air .between the Glaffes, according to its various thicknefs, is difpofed in fome places to refledt, and in others to tranfmit the Light of any one Colour (as you may fee reprefented in the fourth Figure ) and in the fame place to refled: that of one Colour where it tranfmits that of another. ,
Obf. 16. The Squares of the Diameters of thefe Rings made by any prifmatick Colour were in arithmetical Progrefilon, as in the fifth Ob- fervation. And the Diameter of the fixth Cir- cle, when made by the citrine yellow, and
viewed almofl perpendicularly, was about ^
parts of an Inch, or a little lefs, agreeable to the fixth Obfervation.
The precedent Obfervations were made with a rarer thin Mediuni; terminated by a denfer, fuch as was Air or Water comprefs'd between two GlalTes. In thofe that follow are fet down the Appearances of a denfer Medium thin'd within a rarer, fuch as are Plates of Mufcovy Glafs, Bubbles of Water, and fome other thin Subftances terminated on all fides with Air.
Obf. 17. If a Bubble be blown with Water firft made tenacious by dilTolving a little Soap in it, 'tis a common Obfervation, that after a while it will appear tinged with a great variety of Colours. To defend thefe Bubbles from being agitated by the external Air (whereby their Co- lours are irregularly moved one among ano- ther, fo that no accurate Obfervation can be made of themj as foon as I had blown any of
thorn
i88 OPTIC K S.
them I cover'd it with a clear Glafs, and by that means its Colours emerged in a very regular order, like fo many concentrick Rings encom- paffing the top of the Bubble. And as the Bub- ble grew thinner by the continual fubfiding of the Water, thefe Rings dilated flowly and over- fpread the whole Bubble, defcending in order to the bottom of it, where they vanifn'd fuc- celTively. In the mean while, after all the Co- lours were emerged at the top, there grew in the center of the Rings a fmall round black Spot, like that in the firft Obfervation, which con- tinually dilated it felf till it became fometimes more than i or ^ of an Inch in breadth before the Bubble broke. At firft I thought there had been no Light refleded from the Water in that place, but obferving it more curioufly, I faw within it feveral fmaller round Spots, which appeared much blacker €nd darker than the reft, whereby I knew that there was fome Re- flexion at the other places which were not fo dark as thofe Spots. And by farther Tryal I found that I could fee the Images of fome things (as of a Candle or the Sun) very faintly refled:ed, not only from the great black Spot, but alfo from the little darker Spots which were within it.
Belides the aforefaid colour'd Rings there would often appear fmall Spots of Colours, af- cending and defcending up and down the fides of the Bubble, by reafon of fome Inequalities in the fubfiding of the Water. And fometimes fmall black Spots generated at the fides would 2 afcend
BOOK II. 189
afcend up to the larger black Spot at the top of the Bubble, and unite with it.
ObJ. 18. Becaufe the Colours of thefe Bubbles were more extended and lively than thofe of the Air thinn'^d between two GlafTes, and fo more eafy to be diiliinguilli'd, I Ihall here give you a farther defcription of their order, as they were obferv'd in viewing them by Reflexion of the Skies when of a white Colour, whilft a black fubftance was placed behind the Bubble. And they were thele, red, blue; red, blue; red, blue; red, green; red, yellow, green, blue, purple; red, yellow, green, blue, violet; red, yellow, white, blue, black.
The three fir ft Succeffions of red and blue were very dilute and dirty, efpecially the firft, where the red feem'd in a manner to be white. Among thefe there was fcarce any other Colour fenfible befides red an^ blue, only the blues ( and principally the fecond blue ) inclined a little to
green.
The fourth red was alfo dilute and dirtv, bur not fo much as the former three ; after that fuc- ceeded little or no yellow , but a copious green, which at firft inclined a little to yellow, and then became a pretty brisk and good wil- low green, and afterwards changed to a bluiib Colour; but there fucceeded neither blue noF violet. •
The fifth red at firft inclined very much to purple, and afterwards became more bright and brisk, but yet not very pure. This was fucceeded with a very bright and intenfe yel- low» which was but little in quantity, and foon
chang'd
xgo O P T I C K S.
chang'4 to green: But that green was copious and fomething more pure, deep and lively, than the former green. After that follow'd an ex- cellent blue of a bright Sky-colour, and then a purple, which was lefs in quantity than the blue, and much inclined to red.
The fixth red was at firft of a very fair and lively fcarlet, and foon after of a brighter Co- lour, being very pure and brisk, and the beft of all the reds. Then after a lively orange fol- low'd an intenfe bright and copious yellow, which was alfo the beft of all the. yellows, and this changed firft to a greenifti yellow, and then to a greenifli bluej but the green between the yellow and the blue, was very little and dilute, feeming rather a greenifli white than a green. The blue which fucceeded became very good, and of a very fair bright Sky-colour, but yet fomething inferior to the former blue 3 and the violet was intenfe and deep with little or no rednefs in it. And lefs in quantity than the blue.
In the laft red appeared a tin6lure of fcarlet next to violet, which foon changed to a bright- er Colour, inclining to an orange j and the yel- low which follow'd was at firft pretty good and lively, but afterwards it grew more dilute, until by degrees it ended in perfed: whitenefs. And this whitenefs, if the Water was very te- nacious and well-temper'd, would fiowly fpread and dilate it felf over the greater part of the Bubble; continually growing puler. at the top, where at length it would crack in many places, and thofe cracks, as they dilated, would appear
of
BOOK II. . rgt
of a pretty good, but yet obfcure and dark Sky-colour; the white between the blue Spots diminifliing, until it refembled the Threds of an irregular Net-work, and foon after vanifh'd, and left all the upper part of the Bubble of the faid dark blue Colour. And this Colour, after the aforefaid manner, dilated it felf downwards, until fometimes it hath overfpread the whole Bubble. In the mean while at the top, which was of a darker blue than the bottom, and ap- pear'd alfo full of many round blue Spots, fome- thing darker than the reft, there woiild emerge one or more very black Spots, and within thofe, other Spots of an intenfer blacknefs, which I mention'd in the former Obfervation ; and thefe continually dilated themfelves until the Bubble broke.
If the Water was not very tenacious, the black Spots would break forth in the white, without any fenfible intervention of the blue. And fome- times they would break forth within the prece- dent yellow, or red, or perhaps within the blue of the fecond order, before the intermediate Co- lours had time to difplay themfelves.
By this defcription you may perceive how great an affinity thefe Colours have with thofe of Air defcribed in the fourth Obfervation, although fet down in a contrary order, by reafon that they begin to appear when the Bubble is thick- eft, and are moft conveniently reckon'd from the loweft and thickeft part of the Bubble up- wards.
Obf. 19. Viewing in feveral oblique Poiitions of my Eye the Rings of Colours emerging on
the
192 O P T I C K S.
the top of the Bubble, I found that they were fenfibly dilated by increafing the obliquity, but yet not fo much by far as thofe made by thinn'd Air in the feventh Obfervation. For there they v/ere dilated fo much as, when view'd moft ob- liquely, to arrive at a part of the Plate more than twelve times thicker than that where they ap- pear'd when viewed perpendicularly j whereas ii;i this cafe the thicknefs of the Water, at which they arrived when viewed moil obliquely, was to that thicknefs which exhibited them by per- pendicular Rays, fomething lefs than as 8 to 5'. By the beft of my Obfervations it was between 15 and 15; to 10; an increafe about 24 times lefs than in the other cafe.
Sometimes the Bubble would become of an uniform thicknefs all over, except at the top of it near the black Spot, as I knew, becaufe it would exhibit the fame appearance of Colours in all Portions of the Eye. And then the Co- lours which were feen at its apparent circumfe- rence by the obliquefl Rays, would be different from thofe that were feen in other places, by Rays lefs oblique to it. And divers Spedtators might fee the fame part of it of differing Co- lours, by viewing it at very differing Obliqui- ties. Now obferving how much the Colours at the fame places of the Bubble, or at divers pla* ces of equal thicknefs, were varied by the fe- veral Obliquities of the Rays; by the affiflance of the 4th, 14th, 1 6th and i8th Obfervations, as they are hereafter explain'd, I colled: the thicknefs of the Water requifite to exhibit any one and the fame Colour, at feveral Obliquities,
to
BOOK II.
193
to be very nearly in the Proportion expTeffed in
this Table.
Incidence on the Water. |
Rejra5lion into the Water. |
Thicknefs of the Water. |
Deg. Min. |
Deg. Min. |
|
00 00 |
00 00 |
10 |
15 00 |
II II |
loi |
30 00 |
22 I |
10^ |
45 00 60 00 7S 00 90 00 |
32 2 40 30 • 46 25 48 35 |
I If 13 |
In the two firft Columns are exprefs'd the Obliquities of the Rays to the Superficies of the Water, that is, their Angles of Incidence and Refradion. Where I fuppofe^ that the Sines which meafure them are in round Numbers, as 3 to 4, though probably the DifTolution of Soap in the Water, may a little alter its refradive Virtue. In the third Colpmn, the Thicknefs of the Bubble, at which any one Colour is exhibit- ed in thofe feveral Obliquities, is exprefs'd in Parts, of which ten conftitute its Thicknefs when the Rays are perpendicular. And the Rule found by the feventh Obfervation agrees well with thefe Meafures, if duly apply'd -, namely, that the Thicknefs of a Plate of Water requifite to exhibit one and the fame Colour at feveral Obliquities of the Eye, is proportional to the Secant of an Angle, whofe Sine is the firft of an hundred and fix arithmetical mean. Proportion
O. nals
194 OP TIC KS.
nals between the Sines of Incidence and Refradion ^ counted from the lelTer Sine, that is, from the Sine of Refrad:ion when the Refradion is made out of Air into Water, otherwife from the Sine of Incidence.
I ,have fometimes obferv'd, that the Colours whi<;h arife on polifh'd Steel by heating it, or on Bell-metal, and fome other metalline Sub- ftances, when melted and pour'd on the Ground, where they may cool in the open Air, have, like the Colours of Water-bubbles, been a little changed by viewing them at divers Obliquities, and particularly that a deep' blue, or violet, when view'd very obliquely, hath been changed to a deep red. But the Changes of thefe Co- lours are not fo great and fenfible as of thofe made by Water. For the Scoria, or vitrified Part of the Metal, which mofl Metals when heated or melted do continually protrude, and fend out to their Surface, and which by covering the Metals in form of a thin glafly Skin, caufes thefe Colours, is much denfer than Water ; and I find that the Change made by the Obliquation x)f the Eye is leaft in Colours of the denfeft thin Subilances.
Obf. 20. As in the ninth Obfervation, fo here, the Bubble, by tranfmitted Light, appear'd of a contrary Colour to that which it exhibited by Reflexion. Thus when the Bubble being look'd on by the Light of the Clouds reflected from it, feemed red at its apparent Circumference, if the Clouds at the fame time, or immediately after, were view'd through it, the Colour at its Circumference would be blue-. And, on the
contrary.
BOOK IL 19$
.contrary, when by refleded Light it appeared blue, it would appear red by tranfmitted Light.
Obf. 2 1. By wetting very thin Plates of Muf- CGvy Glals, whole thmnels made the like Co- lours appear, the Colours became more taint and languid , efpecially by wetting the Plates on that fide oppofite to the Eye: But I could not perceive any variation of their Species. So then the thicknefs of a Plate requiiite to produce any Colour, depends only on the denlity of the Plate, and not on that of the ambient Medium. And hence, by the loth and i6th Obfervations, may be known the thicknefs which Bubbles of Water, or Plates of Mufco'-cy Glafs, or other Subftances, have at any Colour produced by them.
Obf, 22. A thin tranfparent Body, which is denfer than its ambient Medium, exhibits more brisk and vivid Colours than that which is fo much rarer; as I have particularly obferved iii the Air and Clafs. For blowing Glafs very thin at a Lamp Furnace, thofe Plates encompalTed with_ Air did exhibit Colours much more vivid than thofe of Air made thin between two Glaf- fes.
Obf. 23. Comparing the quantity of Light refledted from the feveral Rings, I found that it was mpft copious from the iiril or inniofi;, and in the exterior Rings became gradually lef^ and lefs. Alfo the whitenefs of the iirft Ring was flronger than that refleded from thofe parts of the thin Medium or Plate which wxre without the Rings j as I co aid manifeftly per- ceive by viewing at a diftance the Rings made
C a by
196 O P T I C K S.
by the two Objed-glafTes ; or by comparing tw6 Bubbles of Water blown at diflant Times, in the firft of which the Whitenefsappear'd, which fuc- ceeded all the Colours, and in the other, the Whitenefs which preceded them all.
Obf. 24. When the two Objeil-glafTes were lay'd upon one an cither, fo as to make the Rings- of the Colours appear, though with my naked Eye I could not difcern aljove eiffht or nine of thofe
o
Rings, yet by viewing them through a Prifm I have feen a far greater Multitude, infomuch that I could number more than forty, befides many others, that were fo very fmall and clofe together, that I could not keep my Eye fteady on them fe- verally fo as to number them, but by their Extent I have fometimes eftimated them to be more than an hundred. And I believe the Expe- riment may be improved to the Difcovery of far greater Numbers. For they feem to be really un- limited, though vifible only fo far as they can be feparated by the Refradion of the Prifm, as I (hall hereafter explain.
But it was but one fide of thefe Rings, namely, that towards which the Refraction was made, which by that Refradion was render'd diftind:, and the other fide became more confufed than when view'd by the naked Eye, infomuch that there I could not difcern above one or two, and fometimes none of thofe Rings, of which I could difcern eight or nine with my naked Eye. And their Segments or Arcs, which on the other fide appear'd fo numerous, for the moft part exceeded not the third Part of a Cir- cle. If the Refraction was very great, or the
Prifm
B O O K II. 197
Prilm very diftant from the Ohjed-glalTes, the middle Part of thofe Arcs became alfo confu- fed, fo as to difappear and conftitute an even Whitenefs, whiUl on either fide their Ends, as alfo the whole Arcs farthefl from the Center, became diftinder than before, appearing in the Form as you fee them defign'd in the hfth Fi- gure.
The Arcs, where they feem'd diflindteft, were only white and black fuccellively, without any other Colours intermix'd. But in other Places there appeared Colpurs, whofe Order was inverted by the Kefradtion in fuch manner, that if I firft held the Prifm very near the Objedt-glafles, and then gradually removed it farther off towards my Eye, the Colours of the 2d, 3d, 4th, and fol- lowing Rings flirunk towards the white that emerged between them, until they wholly va- nifli'd into it at the middle of the Arcs, and afterwards emerged again in a contrary Order. But at the Ends of the Arcs they retain'd their Order unchanged.
I have fometimes fo lay'd one Objed-glafs upon the other, that to the naked Eye they have all over feem'd uniformly white, without the leaft Appearance of any of the colour'd Rings ; and yet by viewing them through a Prifm, great Multitudes of thofe Rings have difcover'd themfelves. And in like manner Plates of Miifcovy Glafs, and Bubbles of Glafs blown at a Lamp-Furnace, which were not fo tlijn as to exhibit any Colours to the naked Eye, have through the Prifm exhibited a great Va^ riety of them ranged irregularly up and down in
O 3 the
198 O P T I C K S.
the Form of Waves. And fo Bubbles of Water, before they began to exhibit their Colours to the naked Eye of aBy-ftander, have appeared through fl Prlfrn, girded about with many parallel and horizontal Rings ^ to produce v^hich Effed:, it was neceffary to hpld the Prifm parallel, or very nearly parallel to the Horizon, and to difpofe it {q th^t the Rays might be refraded upwards.
T H»E
THE
SECOND BOOJ^
O F
OPTICKS
PART II.
Remarks tipo-n the foregoing Obfervatio?ts,
A V I N G given my Obfervations of thefe Colours, before I make life of them to unfold the Caufes of the Colours of natural Bodies, it is convenient that by the fim- pleft of them,fuch asare the ad, 3d, 4th, 9th, I2thj 1 8th, 20th, and 24th, I firft ex-
O 4 plaiu
20O ; O P T I C K S.
plain the more compounded. And firft to fhew now the Colours in the fourth and eighteenth Obiervations are produced, let there be taken in any Right Line from the Point Y, [in Ffg.6.] the Lengths YA, YB, YC, YD, YE, YF, YG, YH, in proportion to one another, as the Cube-RoOts of the Squares of the Numbers, 5, f^g, t, |, ^, |, |, i, whereby the Lengths of aMulical Chord to found all the Notes in an eighth are reprefented; that is, in the Proportion of the Numbers 6300, 68 14, 71 14, 7631, 8255, 8855, 9243> loooo. And at the Points A, B, C, D, E, F, G, H, let Perpen- diculars A a, B /3, &c, be erefted, by whofe In- tervals the Extent of the feveral Colours fet under- neath againft them, is to be reprefented. Then divide the Line A a in fuch Proportion as the lumbers i, 2, 3, 5, 6, 7, 9, xo, 1 1, &c. fet at the Points of Divifion denote. And through thofe Divifions from Y draw Lines 1 1, 2 K, 3 L, 5 M, 6 N, 7 O, &c.
Now, if A 2 be fuppofed to reprefent the Thicknefs of any thin tranfparent Body, at which the outmoft Violet is moft copioully reflected in the firft Ring, or Series of Colours, then by the 13th Obfervation, HK will reprefent its Thicknefs, at which the utmoft Red is moft co- pioufly refleded in the fame Series. Alfo by the 5th and i6th Obfervations, A 6 and HN will denote the ThicknelTes at which thofe ex- treme Colours are moft copioufly refledied in the fecond Series, and A 10 and HQ^he Thick- neffes at which they are moft copioufly refledl- ed in the third Series, ■ and fo on. And the Thicknefs at which any of the intermediate Co- i lours
BOOK II. 20I
iours are reflefted moft copioufly, will, accor- ding to the 14th Obfervation, be defined by the diftance of the Line AH from the intermediate parts of the Lines 2 K, 6N, 10 Q, &c. againft 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 leajft thicknels, and A 3 the greateft thi,ck- nefs , at which the extreme violet in the firft Series is reiledted, and let HI, 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 il, and 3L, a- gainfi; which the Names of thofe Colours are written, and fo on: But yet with this caution, that the Reflexions be fuppofed flrongefl at the intermediate Spaces, 2K, 6N, ioQ> ci?r. and from thence to decreafe gradually towards thefe limits, 1 1, 3L, 5M, 7O, &c. on either fide; where you muft not conceive them to be pre- cifely limited, but to decay indefinitely. And whereas I have afiign'd the fame Latitude to e- very Series, I did it, becaufe although the Co- lours in the firfl Series feem to be a little broad- er than die* reft, by reafon of a ftronger Re- flexion tliere, yet that inequality is fo infenfi- ble 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, 5M O7, 9P R 1 1, ^c. and tranfmitted at the Spaces AHIi, 3LM5, 7 OP 9, &c, it is eafy to know
wliat
202 O P T I C K S.
what Colour muft in the open Air be exhi- bited at any thickneis of a tranlparent thin Bo- dy. For if a Ruler be -applied parallel to AH, at that diftance from it by which the thicknefs of the Body is reprefented, the alternate Spaces il L3, 5M O7, &c. which it croiTeth will de- note the reflected original Colours, of which the Colour exhibited in the open Air is com- pounded. Thus if the conftitutiop of the green in the third Series of Colours be defired, apply the Ruler as you fee at tt p cr 9, and by its paffing through fome of the blue at tt and yellow at cr, as' well as through the green at ^, you may con- clude that the green exhibited at that thicknefs of the Body is principally conflituted of original green, but not without a mixture of fome blue and yellow.
By this means you may know how the Co- lours from the Center of the Rings outward ought to fucceed in order as they were defcri- bed in the 4th and i8th Obfervations. For if you move the Ruler gradually from AH through all diflances, having pafs'd over the firfl Space which denotes little or no Reflexion to be made by thinneft Subftances, it will firft 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 yellow 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 fucceffive dehci- cnce of its component Colours, turns firfl to co-mpound yellow, and then to red, and lafl of 9 all
BOOK IT. 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 lively than before , becaufe more expanded and fevered. -And for the fame reafon, inftead of the former v^hite there intercedes between the blue and yellow a mixture of orange, yellow, green, blue and indigo, all which together ought to exhibit a dilute and imperfect 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 inclined to a reddifli purple; then the blue and green, which are lefs mix'd with other Colours, and confequently more lively than be- fore, efpecially the green: Then follows the yellow, forne of which towards the green is di- Itintt 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 fliould 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 lively 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 v/eaker Colour is fcarce able to iTiew it felf.
After
204 O P T I C K S.
After this the feveral Series interfere more and more, and their Colours become more apd more intermix'd, 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 15th Obfervation the Rays endued with one Colour are tranfmitted, where thofe of another Colour are reflected, the reafon of the Colours made by the tranfmitted Light in the 9th and 20th 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 affiftance of the 6th or i6th Obfer- vations. For according to thofe Obfervations the thicknefs of the thinned Air, which be- tween two GlalTes exhibited the moil luminous
fjarts of the firfl fix Rings were ^7^^ -^^
-4 — —1— — 1— —V- parts of an Inch,
178000 178000^ 178000^ 178000 -I
Suppofe the Light refle(5ted moll copioufly at thefe thicknefles be the bright citrine yellow, or confine of yellow and orange, and thefe thick- nefles will be Fa, Fyu, Fr, F|, Fo, F7. And this being known, it is eafy to determine what thicknefs of Air is reprefented by G(p, or by any other difl:ance of the Ruler from A H.
But farther, fince by the loth Obfervation the thicknefs of Air was to the thicknefs of Water,
which
BOOK 11. 205
which between the fame GlaiTes 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 j the thick- nefs of a Bubble of Water, exhibiting any Co- lour, will be J of the thicknefs of Air produ- cing the fame Colour. And fo according to the fame loth and 21ft Obfervat ions, the thiok- nefs of a Plate of Glafs, whofe Refradion of the mean refrangible Ray, is meafured by the proportion of the Sines 31 to 20, may be \° of the thicknefs of Air producing the fame Co- lours; and the lijce of other Mediums. I do not affirm , that this proportion of 20 to 3 r, 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 Table, wherein the thicknefs of Air, Water, and Glafs, at which each Colour is mofl intenfe and fpeci- fick, is exprelfed in parts of an Inch divided in- to ten hundred thoufand equal parts.
• me
2o6
O P T I C K a
I'he thicknefs of colour d Plates and Particles of
-^
Their Colours of the 4kft Order, *\
^Very black
Black
Beginning of Black
Blue
White I Yellow
Orange vRed
r Violet
V Indigo
A Blue
Of thcfecond Order, J Green Alellow y Orange / Bright red L Scarlet
of the third Order,<
Purple
Indigo
Blue
Green
Yellow
Red
Bluifh red
Bluifli green Green
Yellowiih green Red
Ofihe fifth Order, {Gre^eniih blue
-rvr 1 r 1- « J TGreenifli blue Of the fixth Order, \^q^
of the fevemh Or-rGreeniih blue der, (.Ruddy white
of the fourth Order,*
^ Jir. |
Water. |
Ghfs. |
1 |
J |
J-' |
1 |
T |
^ [ |
I |
} |
2 a |
+ |
Tr |
|
2 |
Ij- |
It |
^1 |
I'r |
lir |
5t |
3^ . |
3f |
7^ |
5f |
41 |
8 |
6 |
5t |
9 |
H |
5t- |
II*- |
81- |
7t |
li^ |
^f |
8tt |
14 |
loi- |
9 |
i5t |
11^ |
^t |
16} |
I2| |
lof |
17^ |
1? |
ii> |
i8f |
'3^ |
u^ |
i9f |
i+i |
12f |
21 |
i5i |
i3t^ |
22t'- |
i6± |
147 |
23?- |
T-lVo |
I5t',- |
^51 |
18-,^, |
16^ |
27^ |
20.1 |
i7t |
^9. |
^4 |
1%^ |
1L_ |
24 |
20} |
34 |
ijf |
22 |
5 54 |
2cr; |
2Z^ |
3^ |
27 |
237- |
Jf7_ |
2<5 |
|
4<? |
34t |
/-9i |
52f |
391- |
34 |
5H |
44 |
38 |
^5 |
48} 1 |
42 |
71 |
557 57|- |
45t |
77 |
49f |
Now
BOOK IL 20 j
• Now if this Table be compared with the 6th Scheme, you will there fee the conftitntion of each Colour, as to its Ingredients, or the ori- ginal Colours of which it is compounded, and dience be enabled to judge of its Intenfenefs or Imperfection ; which may fuffice in explication of the 4th and i8th Obfervations, unlefs it be farther delired to delineate the manner how the Colours appear, when the two Objed;-glaf- fes are laid upon one another. To do which, let there be defcribed a large Arc of a Circle, and a ftreight Line which may -touch that Arc, and parallel to that Tangent feveral occult Lines, at fuch diftances 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 Glalles termi- nating the interjacent Air; and the places where the occult Lines cut the Arc will (how at what diftances from the center, or Point of contadl, each Colour is refiedled.
There are.alfo other Ufesof this Table: For by its afiirtance the thicknefs of the Bubble in the 19th Obfervation was determin'd by the Co- lours which it exhibited. And fo the-bignefs of the parts of natural Bodies may be conje- diured by their Colours, as ihall be hereafter fhewn. 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- flance, Mr. Hook obferved, as is mentioned in his Micrograpkia^ that a faint yellow Plate of Miijccoy Glafs laid upon a bli^e one, conftituted
a very
2o8 O P T I C K S.
a very deep purple. Tke yellow of the firfl Or- der is a faint one, and the thicknefs of the Plate exhibiting it, according to the Table is 42, to which add 9, the thicknefs exhibiting blue of the fecond Order, and the Sum will be 13I, which is the thicknefs exhibiting the purple of the thir4 Order.
To explain, in the next place, the circum- ftances of the 2d and 3d Obfervations 5 that is, how the Rings of the Colours may ( by turning the Prifms about their common Axis the con- trary way to that expreffed 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 GlalTes, and that according to the Table in the 7th Ob- fervation, their Dilatation or Increafe of their Diameter is mofl manifeft and fpeedy when they are obliquefl:. Now, the Rays of yellow being more refra(5led by tne firft Superficies of the faid Air than thofe of red, are thereby made more oblique to the fecond Superficies, at which they are refieded 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 laft 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
ftill.
BOOK II. 209
iibill 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 mull be coincident, and by their mixture exhibit a white Ring. And thefe white Rings muft have black and dark Rings between them, becaufe they do not fpread and interfvire with one another, as before. And for that rea- fon alfo they mufl become diftindler, 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 Co- lours, 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 Rines, the Colours muft 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 and yellow at the in- terior. And the violet, by reafon of the great- eft obliquity of its Rays, being in proportion moft of all expanded, will fooneft appear at the exterior Limb of each white Ring, and be- come more confpicuous than the reft. 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 diftindt, and not vifible to fo great numbers.
P If
2IO O P T I C K S.
If inflead of the Prifms the Objed-glafleS be made ufe of, the Rings which they exhibit be- come not white and diilindl by the obhquity of the Eye, by reafon that the Rays in their paflage through that Air which intercedes tne Glafles are very nearly parallel to thofe Lines in which they were lirft incident on the GlafTes, 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 circumftance of thefe Experiments to be confider'd, and that is why the black and white Rings which when view'd at a diftance appear diftincft, fliould not only be- come confufed 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 mofl oblique, if confi- der'd apart, would reprefent the Rings bigger than thofe which are the leaft oblique. Whence the breadth of the Perimeter of every white Ring is expanded outwards by the obliquefl Rays, and inwards by the leafi oblique. And this Expanfion is fo much the greater by how much the greater is the difference of the Obli- quity ; that is, by how much the Pupil is wider^ or the Eye nearer to the Glafles. And the breadth of the violet muft be mofb expanded, becaufe the Rays apt to excite a Senfation of that Colour arc mofl oblique to a fecond or farther Superficies of the. thinn'd Air at which they are rcfiedted, and have alfo the grearefl
varia-
BOOK II. 211
variation of Obliquity, which makes that Co- lour fooneft emerge out of the edges of the white. And as the breadth of every Ring is thus augnaented, the dark Intervals niufl be di- minifli'd, until the neighbouring Rings become continuous, and are blended, the exteiior iiril, and then thofe nearer the center j fo that they can no longer be diftinguifh'd apart, but feem to conflitute an even and uniform whitenefs.
Among all the Obfervations there is none ac- companied with fo odd circumftances as the twenty-fourth. Of thofe the principal are, that in thin Plates, v/hich 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 colour'd only there where they are ter- minated with Shadows, or have parts unequal- ly luminous ; and that it fliould make thofe Kings exceedingly diftindl and white, although it ufually renders Objeds 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 tiie Plate, when vie w'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 conflitute an uniform whitenefs. But when the Rays oafs through the Prifm to the Eye, the Orbits of the feveral Colours in every Ring are refraded, fome more than others, ac- cording to their degrees of Pvcfrangibility : By which means the Colours on one fide of the
P 2 Ring
212 O P T I C K S.
Ring (that is in the circumference on one fide of its center, ) become more unfolded and dilated, and thofe on the othef fide more complicated and contraded. And where by a due Refra(3:ion they are fo much contradied, that the feveral Rings' become narrower than to interfere with one ano- ther, they muft appear diftind:, and alfo white, if the conftituent Colours be fo much contrad:ed as to be wholly coincident. But on the other fide, where the Orbit of every Ring is made broader by the farther unfolding of its Colours, it muft interfere more with other Rings than be- fore, and fo become lefs diftind;.
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, conllitute 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 tranllated 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 inftance -, if the red be tranflated to a v, the violet may be tranflated to I? x, fo as to ap- proach nearer to it at x than before y and if the red be farther tranllated to av, the violet may be fo much farther tranflated to b x as to con- vene with it at X ; and if the red be yet farther tranflated to a T, the violet may be ftill fo much farther tranflated to /? | as to pafs beyond it at §, and convene with it at e and f. And this being underllood not only of the red and vio- let, but of all the other intermediate Colours,
and
BOOK II. 213
and alfo of every revolution of thofe Colours, you will ealily perceive how thofe of the fame revolution or order, by their nearnefs at x v and T J, and their coincidence at x v, e and J\ ought to conftitute pretty diftindt Arcs of Cir- cles, efpecially at x v, or at e and f; and that they will appear feverally at x Vy and at x v ex- hibit whitenefs by their coincidence, and again appear feveral at T |, but yet in a contrary or- der to that which they had before, and ftill re- tain beyond e and f. But on the other fide, at a I?, a b, or a l3, thefe Colours mufl: become much more confufed 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 diftant from the Objcdt-glaf- fes : In which cafe no parts of the Rings will be feen, fave only two little Arcs at e and J\ whofe diftance from one another will be aug- mented by removing the Prifm flill farther from the Objed-glafTes : And thefe little Arcs mult be diftindtefl and w^hiteft at their middle, and at their ends, where they begin to grow con- fufed, they mull be colour'd. 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 g, 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 J, will on the contrary be blue and violet on that fide to-
P 2 ^ya^ds
214 O P T I C K S.
wards the center, and on the other fide red and yellow.
Now as all thefe things follow from the pro- perties of Light by 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 affiftant caufes to. move to and fro upon a Wall or Paper from whence they are reflected, whilft the Spe6:ator's Eye, ihe Prifm, and the Objed:- glaffes, (as in the 13th Obfervation,) are placed Iteadyj the Polition of the Circles made fuc- ceifively by the feveral Colours, will be found fuch, in refped: of one another, as I have de- scribed in the Figures a b x ^0^ or a b x v, or a /S I 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- derftood. But in fmall fragments of thofe Plates there is this farther obfervable, that where they lie flat upon a Table, and are turned about their centers whilfl they are view'd through a Prifm, they will in fome poflures exhibit Waves of va- rious Colours ; and fome of them exhibit thefe Waves in one or two Pofitions only, but the mofc of them do in all Pofitions exhibit them, and make them for the mofl part appear al- mioft all over the Plates. The reafon is, that the Superficies of fuch Plates are not even, but have many Cavities and Swellings, which, how fhallow foever, do a little vary the thicknefs of
th^
BOOK II. 215
tlie Plate. For at the feveral fides of thofe Ca- vities, for the Reafons newly defcribed, there ought to be produced Waves in feveral po- llures of the Prifm. Now though it be but fome very fmall and narrower parts of the Glafs, by which thefe Waves for the niofl 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- fleded, which by Refraction of the Prifm are unfolded, feparated, and, according to their degrees of Refraction, difperfed to feveral pla- ces, fo as to conftitute fo many feveral Waves, as there were divers orders of Colours promifcu- oufly reflected 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 agree with them, even to their very leaft circumftancesj and not only fo, but do very much tend to their proof. Thus, by the 24th Obfervation it appears, that the Rays of feveral Colours, made as well by thin Plates or Bubbles, as by Refradions of a Prifm, haye feveral degrees of Refrangibility j 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 Refraction, and aflbciated together fo as to become vifible by themfelves like Arcs of Cir- cles. For if the Rays were all alike refrangi- ble, 'tis impofiible that the whitenefs, which
P 4 to
2i6 O P T I C K S.
to the naked Senfe appears uniform, fhould by Refraction have its parts tranfpofed and ranged into thofe black and white Arcs.
It appears alfo that the unequal Refradlions of difforin Rays proceed not from any contin- gent irregularities ; fuch as are Veins, an uneven Polifh, or fortuitous Polition of the Pores of Glafs ; unequal and cafual Motions in the Air or /Ether, the fpreading, breaking, or dividing the fame Ray into many diverging parts ; or the like. For, admitting any fuch irregularities, it v^ould be impoiTible for Refractions to render ihofe Rings fo very diflincft, and well defined, as they do in the 24th Obfervation. It is ne^ cefTary therefore that every Ray have its proper and conftant degree of Refrangibility connate with it, according to which its refraction is ever juflly ^nd regularly perform'd^ and that feveral flays have feveral of thofe degrees.
And what is faid of their Refrangibility may be alfo underflood of their Reflexibility, that is, of their Difpofitions to be refle<^ed, fome at a greater, and others at a lefs thicknefs of thin Plates or Bubbles j namely, that thofe Difpofi- tions are alfo connate with the Rays, and im- mutable ; a^ may appear by the 13 th, 14th, and J 5 th Obfervations, compared with the fourth and eighteenth.
By the precedent Obfervations it appears al- fo, that whitenefs is a diihmilar mixture of all polours, and that Light is a mixture of Rays endued with all thofe Colours. .For, confider- ing the multitude of the Rings of Colours in jhe ^d^ I2th5 and 24th Obfervations, itismani- "■■^ ■ ; feft,
BOOK 11. 217
feft, that although in the 4th and i8th Obfer- vations there appear no more than eight or jiine 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 conllitute an even and fenfibly uniform whitenefs. And confequently that whitenefs muft be 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 J by the 24th Obfervation it ap- pears, that there is a conftant relation between Colours and Refrangibility ; the moft refrangi- ble Rays being violet, the leaft refrangible red, and thofe of intermediate Colours having pro- portionably intermediate degrees of Refrangibi- lity. And by the 13th, 14th, and J5th Obfer- vations, compared with the 4th or i8th, there appears to be tlie fame conftant relation be- tween Colour and Reflexibility ; the violet be- ing in like circumftances refleded at leaft thick- nelfes of any thin Plate or Bubble, the red at greateft thicknelTes, and the intermediate Co- lours at intermediate thicknefles. 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 Irom the various Mixtures or Separations of |lays, by virtue of their different Refrangibility
or
-^
218
O P T I C K S.
or Reflexibility. And in this refped the Scicncd 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 v of Imagination, or by ilriking or preffing the Eye.
THE
THE
SECOND BOOK
O F
OPTICKS.
PART III.
Of the permanejit Colours of natural Bo- dies^ and the Analogy between them and the Colours of thiii tranfparent Plates*
AM now come to another part of this Defign, which is to confider how the PhiEnomena of thin tranfparent Plates fland 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 O P T I C K S.
lours, accordingly as they are difpofed to refled: moft copiouily the Rays originally endued with thofe Colours. But their Conflitutions, where- by they refied: fome Rays more copiouily than others, remain to be difcover'd ; and thefe I lliall endeavour to manifeft in the following Propo- iitions.
P R O p. I.
*ith'ofe Superficies of t ran/ parent Bodies refieEi the greatejl quantity of Lights which have the great- eft refraBing Power ^ that is, which i7itercede Mediums that differ mofi in their refraBiije Den- Jities. And in the Confines of equally refraBing Mediums there is no Kefiexion.
TH E Analogy between Reflexion and Re- fradion will appear by confidering, that when Light paffeth obliquely out of one Medi- um into another which refracts from the per- pendicular, the greater is the difference of their refradive Denfuy, the lefs Obliquity of Inci- • dence is requifite to caufe a total Reflexion, For as the Sines are which meafure the Refra- (Ttion, 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 leaft where there is the greateft difl^e- rence of the Sines; Thus in the paffing of Light out of Water into Air, where the Refra- ction 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
BOOK II. ill
Iti pafling out of Glafs into Air, where the Re- fradiion is meafured by the Ratio of the Sines 20 to 31, the total Reflexion begins when the Angle of Incidence is 40 Degrees 10 Minutes; and fo in paffing out of Cryftal, or more flrong- ly refrading Mediums into Air, there is ftill a lefs obliquity requifite to caufe a total reflexion. Superficies therefore v/hich refrad; mofl: do fooneft refled: all the Light which is incident on them, and fo muft be allowed moft flrongly 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, Cryftal, me- talline Glafies, Ifland Glafl^es, white tranfparent Arfenick, Diamonds, ^c.) the Reflexion is ftronger or weaker accordingly, as the Super- ficies hath a greater or lefs refrading Power. For in the Confine of Air and Sal-gem 'tis ftronger than in the Confine of Air and Water, and ftill ftronger in the Confine of Air and .com- mon Glafs or Cryftal, and ftronger in the Con- fine of Air and a Diamond. If any of thefe, and fuch like tranfparent Solids, be immerged in Water, its Reflexion becomes much weak- er than before j and ftill weaker if they be im- merged in the more ftrongly refrading Liquors of well rectified Oil of Vitriol or Spirit of Tur- pentine. If Water be diftinguifli'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 little ; in that of Water and Oil 'tis fomething greater;
la
222 O P T I C K S.
in that of Water and Sal-gem ftill greater ; and in that of Water and Glafs, or Cryftal, or other denfer Subftances ftill greater, accordingly as thofe Mediums differ more or lefs in their re- frading Powers. Hence in the Confine of com- mon Glafs and Cryftal, there ought to be a weak Reflexion, and a ftronger Reflexion in the Confine of common and metalline Glafs; though I have not yet tried this. But in the Confine of two Glafies of equal denfity, there is not any fenfible Reflexion ; as was fliewn in the firft Obfervation. And tlie fame may be underftood of the Superficies interceding two Cryftals, or two Liquors, or any other Sub- ftances in which no Refradion is caufed. So then the reafon why uniform pellucid Mediums (fuch as Water, Glafs, or Cryftal,) have no fen- fible Reflexion but in their external Superficies, where they are adjacent to other Mediums of a diflferent denfity, is becaufe all their conti- guous parts have one and the fame degree of denfity.
Prop. II.
^he leajl parts of almojl all jtatiiral Bodies are in fome meajure tranfparent : And the Opa- city of thofe Bodies arifeth from the multi- tude of "Reflexions caufed in their intertial Parts,
'Tp HAT this is fo has been obferved by o-
-*• thers, and will eafily be granted by them
that have been converfant with Microfcopes.
And it may be alfo tried by applying any fub-
flancc
BOOK JL 223
ftance to a hole through which fome Light is immitted into a dark Room. For how opake foever that Subftance may feem in the opea Air, it will by that means appear very manifeft- ly tranfparent, if it be of a fufficient thiniiefs. Only white metalline Bodies miift be excepted, which by reafon of their exceffive denfity feem to refled: almoft all the Light incident on their firft Superficies j unlefs by folution in Menftru- ums they be reduced into very fmall Particles, and then they become tranfparent.
Prop. IIL
Between the parts of opake mid colour d Bodies are many Spaces^ either empt)\ or repleniJUd with Mediians of other DenfitieSy as Water between the tingijig Corpufcles wherewith a- ny Liquor is impregnated ^ Air between the aqueous Globules that confiitute Clouds or Mijh\ and for the mofl part Spaces loid of both Air and Water ^ but yet perhaps not wholly ^coid of all Subjlance^ between the parts of hard Bo- dies,
' I ^ H 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 firll Propoiition, would not happen if the parts of thole Bodies were continued without any fuch Interftices between them ; becaufe Re- flexions are caufed only in Superficies, which intercede Mediums of a differing denfity, by 'Frop, I.
• ^ Buc
224 O P T I C K S.
But farther, that this difcontinuity of parts is the principal Caufe of the opacity of Bodies, will appear by confidering, that opake Subftan- ces become tranfparent by filling their Pores with any Subftance of equal or almoft equal den- fity with their parts. Thus Paper dipped in Water or Oil, the O cuius Mundi Stone fteep'd in Water, Linnen Cloth oiled or varniih'd, and many other Subilances foaked in fuch Liquors as will intimately pervade their little Pores, be- come by that means more tranfparent than other- wife ; fo, on the contrary, the mofh tranfparent Subftances may, by evacuating their Pores, or feparating their parts, be render'd fufficiently o* pake ; as Salts or wet Paper, or the Oculus Mun- di Stone by being dried, Horn by being fcraped, Glafs by being reduced to Powder, or otherwife flawed; Turpentine by being ftirred about with Water till they irdx imperfectly, and Water by being form'd into many fmall Bubbles, either a- lone in the form of Froth, or by fliaking it to- gether with Oil of Turpentine, or Oil Olive, or with fome other convenient Liquor, with which it will not perfectly incorporate. And to the in- creafe of the opacity of thefe Bodies, it condu- ces fomething, tliat by the 23d Obfervation the Reflexions of very thin tranfparent Subftances are conliderably ftronger than thofe made by the faipe Subftances of a greater thicknefs,
Prop*
BOOK IL 225
Prop. IV.
The Farts of Bodies and their Interftices mi/fl not be lefs than of feme definite bignefs^ to render^ them opake and colour d.
■p.OR the opakeft Bodies, if their parts be ■*- fubtilly divided, (as Metals, by being diflbl- ved in acid Menftruums, ^c^ become perfect- ly tranfparent. And you may alfo remember, that in the eighth Obfervation there 'was no fenfible reflexion at the Superficies of the Ob- ied-glaffes, where they were very near one an- other, though they did not ablblutely touch. And in the 1 7th Obfervation the • Reflexion of the Water- bubble where it became thinriell was almofl infenfible, fo as to caufe very black Spots to appear on the top of the BubblCj by the want of reflected Light.
On thefe grounds I perceive it is that Water, Salt, Glafs, Stones, and fuch like Subftances, are tranfparent. For, upon divers Confidera- tions, they feem to be as full of Pores or Inter- ftices between their parts as other Bodies are, but yet their Parts and Interftices to be too fmall to caufe Reflexions in their common Sur- faces.
Q^ Prop.
226 O P T I C K S.
P R O p. V.
^he tranfparcnt farts of Bodies, according to their Je-veral Jizes^ reJieEl Rays of one Colour^ and traifmit thofe of another y on the fame grounds that thin Plates or Bubbles do refeB or tranfmit thofe Rays, Atid this, I take to be the ground of all'their Colours.
*P O R if a thinn'd or plated Body, which -■- being of an even thicknefs, appears all o- ver of one uniform Colour, fliould be flit into Threads, or broken into Fragments, of the fame thicknefs with the Plate j I fee no reafon why every Thread or Fragment fhould not keep its Colour, and by confequence why a heap of thofe Theads or Fragmmts fliould not conflitute a Mafs or Powder of the fame Colour, which the Plate exhibited before it was broken. And the parts of all natural Bodies being like fo many Fragments of a Plate, muft on the fame grounds exhibit the fame Colours.
Now, that they do fo will appear by the affi- nity of their Properties. * The finely colour'd Feathers of fome Birds, and particularly thofe of Peacocks Tails, do, in the very fame part of the Feather, appear of feveral Colours in feveral Pofitions of the Eye, after the very fame man- ner that thin Plates were found to do in the 7th and 1 9th Obfervations, and therefore their Colours arife from the thinnefs of the tranfpa- rent parts of the Feathers; that is, from the flendernefs of the very fine Hairs, or Capilla- menta^ which grow put of the fides of the
groifer
BOOK II. 227
grofler lateral Branches or Fibres of thofe Fea- thers. And to the fame purpofe it is, that the "Webs of fome Spiders, by being fpun very fine, have appeared colour'd, as fome have oblerv'd, and that the colour'd Fibres of fome Silks, by varying the Pofition of the Eye, do vary their Colour. Alfo the Colours of Silks, Cloths, and other Subftances, which Water or Oil can intimately penetrate, become more faint and obfcure by being immerged in thofe Liquors, and recover their Vigor again by being dried ; much after the manner declared of thin Bodies in the loth and 21ft Obfervations. Leaf-Gold, fome forts of painted Glafs, the Infufion of Lignutn Nephritiaun, and fome other Subilan-' ces, refledl one Colour, an(i tranfmit another;, like thin Bodies in the 9th and 20th Obferva- tions. And fome of thofe colour'd Powder5 which Painters ufe, may have their Colours a little changed, by being very elaborately and finely ground. Where I fee not what can be juftly pretended for thofe changes, befides the breaking of their parts into lefs parts by that contrition, after the fame manner that the Co- lour of a thin Plate is changed by varying its thicknefs. For which reafon alfo it is that the colour'd Flowers of Plants and Vegetables, by being bruifed, ufually become more tranfparenz than before, or at leafl in fome degree or o- ther change their Colours. Nor is it much lefs to my purpofe, that, by mixing divers Liq^uors, very odd and remarkable Produd:ions and Changes of Colours may be effected, of which no caufe can be more obvious and rational than
Q^ that.
228 O P T I C K S.
tha:t the faiine Corpufcles of one Liquor da vari- oufly ad upon or unite with the tinging Corpufcles of another, fo as to make them fwell, or fhrink, ( whereby not only their bulk but their denfity alfo may be changed,) or to divide them into fmaller Corpufcles, (whereby a colour'd Liquor may become tranfparent,) or to make many of them affociate into one clufter, whereby two tranfparent Liquors may compofe a colour'd one. For we fee how apt thofe faiine Menftruums are to penetrate and diffolve Subftances to which they are applied, and fome of them to precipi- tate what others diilblve. In like manner, if we confider the various Phaenomena of the Atmo- fphere, we may obferve, that when Vapours are iirft raifed, they hinder not the tranfparcncy of the Air, being divided into parts too fmall to caufe any Reflexion in their Superficies. But when in order to compofe drops of Rain they begin to coalefce and conflitute Globules of all intermediate lizes, thofe Globules, when they become of a convenient fize to refle6t fome Co- lours and tranfmic others, may conftitute Clouds of various Colours according to their fizes. And I fee not what can be rationally conceived in fo tranfparent a Subftance as Water for the produ- ction of thefe Colours, befides the various fizes of its fluid and globular Parcels.
Prop,
BOOK 11. 229
Prop. VI.
^he parts of Bodies 011 ivhich their Colours depend ^ are denjer than the Medium which pervadet their Interjiices,
np HIS will appear by confidering, that the -■" Colour of a Body depends not only on the Rays which are incident perpendicularly on its parts, but on thofe alfo which arc inci- dent at all other Angles. And that according to the 7th Oblervation, a very little variation of obliquity will change the refled:ed Colour, where the thin Body or fmall Particle is rarer than the ambient Medium, infomuch that fuch a fmall Particle will at diverfly oblique Inci- dences refledl all forts of Colours, in fo great a variety that the Colour refuking from them all, confufedly refled:ed from a heap of fuch Parti- cles, muft rather be a white or grey than any other Colour, or at beft it muft be but a very imperfecft and dirty Colour. Whereas if the thin Body or fmall Particle be much denfer than the ambient Medium, the Colours, according to the 19th Obfervation, are fo little changed by the variation of obliquity, that the Rays which are refled;ed leafl obliquely may predominate over the feft, fo much as to caufe a heap of fuch Particles to appear very intenfely of their Co- lour.
It conduces alfo fomething to the confirma- tion of this Propolition, that, according to the 22d Obfervation, the Colours exhibited by the denfer thin Body within the rarer,' are more
0^3 ^ brisk
130 O P t I C K S.
brisk than thofe exhibited by the rarer within the denfer.
I Prop. VII.
*the bignefs of the component parts of natural Bo- dies may be conjellured by their Colours.
FO R fince the parts of thefe Bodies, by Frop, 5. do mofl probably exhibit the fame Colours with a Plate of equal thicknefs, provided they have the fame refradiive denlity ; and fince their parts feem for the mcft part to have much the fame dehfity with Water or Glafs, as by many circumftances is obvious to colledt J to determine the fizes of thofe parts, you need only have recourfe to the precedent Tables, in which the thicknefs of Water or Glafs exhibiting any Colour is exprefled. Thus if it be defired to know the diameter of a Cor- p.ufcle, which being of equal denlity with Glafs ihall refled: green of the third Orders the Num- ber 165 (hews it to be ^-^ parts of 'an Inch. ^ I 0000 A
The greatefl: difficulty is here to know of what Order the Colour of any Body is. And for this end we muft have recourfe to the 4th and 1 8th Obfervations ; from whence may be coUedted thefe particulars.
■Scarlets y and other reds^ oranges y and yel~ JowSy if they be pure and intenfe, are mofl pro- bably of the fecond order. Thofe of fhe firfl and third order alfo may be pretty goodj only the yellow of the firfl order is faint, and the
_ orange
BOOK II. 231
orange and red of the third Order have a great Mixture of violet and bkie.
There may be good Greens of the fourth Order, but the pureft are of the third. And of this Order the green of all Vegetables feenis to be, partly by reafon of the Intenfenefs of their Co- lours, and partly becaufe when they wither fome of them turn to a greenifh yellow, and others to a more perfed: yellow or orange, or perhaps to red, paiTing firft through all the aforefaid in- termediate Colours. Which Changes feem to be effected by the exhaling of the Moifture which may leave the tinging Corpufcles more denfe, and fomething augmented by the Accre- tion of the oily and earthy Part of that Moifture. Now the green, without doubt, is of the fame Order with thofe Colours into which it changeth, becaufe the Changes are gradual, and thofe Co- lours, though ufually not very full, yet ar& often too full and lively to be of the fourth Order.
Blues and Purples may be either of the fe- cond or third Order, but the beft are of the third. Thus the Colour of Violets feems to be of that Order, becaufe their Syrup by acid Li- quors turns red, and by urinous and alcaiizate turns green. For fince it is of the Nature of Acids to diffolve or attenuate, and of Alcalies to precipitate or incrailate, if the Purple Co^ lour of the Syrup was of the fecond Order, an acid Liquor by attenuating its tinging Cor- pufcles would change it to a red of the in ft Or- der, and an Alcali by incralTating them would change it to a green of the fecond Order ;
Qjj. which
232 O P T I C K S.
which red and green j efpecially the green, feem too imperfed: to be the Colours produced by thefe Changes. But if the faid Purple be fup- pofed of the third Order, its Change to red of the fecond, and green of the third, may without any Inconvenience be allow'd.
If there be found any Body of a deeper and lefs reddifh Purple than that of the Violets, its Colour moft probably is of the fecond Order. But yet there being no Body commonly known whofe Co- lour is conftantly more deep than theirs, I have made ufe of their Name to denote the deepeft and leaft reddilh Purples, fuch as manifeftly tranfccnd their Colour in purity.
The blue of the firft Order, though very faint and little, may poffibly be the Colour of fome Subftances j and particularly the azure Colour of the Skies feems to be of this Order. For all Vapours when they begin to condenfe and coa- lefce into fmall Parcels, become firft of that Big- nefs, whereby fuch an Azure muft be reflected be- fore they can conftitute Clouds of other Colours. And fo this being the firft Colour which Vapours begin to refled, it ought to be the Colour of the fineft and moft tranfparent Skies, in which Va- pours are not arrived to that Grofliiefs requifite to refled: other Colours, as we find it is by Expe- rience.
JVhitenefs, if moft intenfe and luminous, is that of the firft Order, if lefs ftrong and lumi- nous, a Mixture of the Colours of feveral Or- ders. Of this laft kind is the Whitenefs of Froth, Paper, Linnen, and moft white Sub- ftances j of the former I reckon that of white
Metals
BOOK II. 233
Metals to be. For whilft the denfell of Metals, Gold, if foliated, is tranfparent, and all Metals become tranfparent if dilfolved in Menftriiums or vitrified, the Opacity of white Metals ari- feth not from their Denfity alone. They be- ing lefs denfe than Gold would be more tranf- parent than it, did not fome other Caufe con- cur with their Denfity to make them opake. And this Caufe I take to be fuch' a Bignefs of their Particles as fits them to refledl the white of the firft order. For, if they be of other Thick- nefi!es they may refled: other Colours, as is ma- nifeft by the Colours which appear upon hot Steel in tempering it, and fometimes upon the Surface of melted Metals in the Skin or Scoria which arifes upon them in their cooling. And as the white of the firfl order is the Itrongefl which can be made by Plates of tranfparent Subftances, fo it ought to be ftronger in the denfer Subftances of Metals tlian in the rarer of Air, Water, and Glafs. Nor do I fee but that metallick Subftances of fuch a Thicknefs as may fit them to reflect the white of the firft or- der, may, byreafon of their great Denfity (ac- cording to the Tenor of the firft of thefe Pro- pofitions) refled: all the Light incident upon them, andfo be as opake and fplendent as it's poflible for any Body to be. Gold, or Copper mix'd with lefs than half their Weight of Silver, or Tin, or Regulus of Antimony, in fufion, or amalgamed with a very little Mercury, become white J which fhews both that the Particles of white Metals have much more Superficies, and fo are fmaller, than thofe of Gold and Copper,
and
234- O P T I C K S.
and alfo that they are fo opake as not to fuflef the Particles of Gold or Copper to fhine through them. Now it is fcarce to be doubted, but that the Colours of Gold and Copper are of the fecond or third order, and therefore the Particles of white Metals cannot be much big- ger than is requifite to make them reflect the white of the firft order. The Volatility of Mer- cury argues that they are not much bigger, nor may they be much lefs, left they lofe their Opacity, and become either tranfparent as they do when attenuated by Vitrification, or by Solu- tion in Menftruums, or black as they do when ground fmaller, by rubbing Silver, or Tin, or Lead, upon other Subftances to draw black Lines. The firft and only Colour which white Metals take by grinding their Particles fmaller, is black, and therefore their white ought to be that which borders upon the black Spot in the Center of the Rings of Colours, that is, the white of the firft order. But, if you would hence gather the Bignefs of metallick Particles, you muft allow for their Denfity. For were Mercury tranfparent, its Denfity is fuch that the Sine of Incidence upon it ( by my Compu- tation) would be to the Sine of its Refraction, as 7 1 to 20, or 7 to 2. And therefore'the Thick- nefs of its Particles, that they may exhibit the fame Colours with thofe of Bubbles of Water, ought to be lefs than the Thicknefs of the Skin of thofe Bubbles in the Proportion of 2 to 7. Whence it's pofiible, that the Particles of Mercury m.ay be as little as* the Particles of
fome
BOOK II. 235
(ome tranfparent and volatile Fluids, and yet refled the white of the firft order.
Laftly, for the produdtion of blacky the Cor- pufcles mufl be lefs than any of thofe which ex- hibit Colours. For at all greater fizes there is too much Light reflected to conftitute this Co- lour. But if they be fuppofed a little lefs than is requifite to refled^ the white and very faint blue of the firfl order, they will, according to the 4th, 8th, i7thand iSthObfervations, refled: fo very little Light as to appear intenily black, and yet may perhaps varioully refrad it to and fro within themfelves fo long, until it happen to be ftifled and loft, by which means they will appear black in all pofitions of the Eye without any tranfparency. And from hence may be under- flood why Fire, and the more fubtile diffolver Pu- trefaction, by dividing the Particles of Subftan- ces, turn them to black, why fmall quantities of black Subftances impart their Colour very freely and intenfly to other Subftances to which they are applied ; the minute Particles of thefe, by reafon of their very great number, eaftly o- verfpreading the grofs Particles of others ; why Glals ground very elaborately with Sand on a Copper Plate, 'till it be well poliftVd, mukes the Sand, together with what is worn off" from the Glafs and Copper, become very black : wiiy black Subftances do fooneft of all others become hot in the Sun's Light and burn, (which Effed: may proceed partly from the multitude of Refradions in a little room, and partly from the eafy Cominotion of fo very fmall Cor- pufcies; ) and why blacks are ufually a little in- clined
236 O P T I C K S.
clined to a bluifli Colour. For that they are Co may be feen by illuminating white Paper by Light refie.ded from black Subftances. For the Paper will ufually appear of a bluifh white j and the reafon is, that black borders on the obfcure blue of the order defcribed in the i8th Obferva- tion, and therefore refled:s more Rays of that Co- lour than of any other.
In thcfe Defcriptions I have been the more particular, becaufe it is not impoffible but that Mifcrofcopes may at length be improved to the difcovery of the Particles of Bodies on which their Colours depend, if they are not already in fome meafure arrived to that degree of per- fedion. For if thofe Inftruments are or can be fo far improved as with fufficient diflindtnefs to reprefent Objedls five or fix hundred times bigger than at a Foot diftance they appear to our naked Eyes, I fliould hope that we might be able to difcover fome of the greatefi; of thofe Corpufcles. And by one that would magnify three or four thoufand times perhaps they might all be difcover'd, but thofe which produce blacknefs. In the mean while I fee nothing ma- terial in this Difcourfe that may rationally be doubted of, excepting this Pofition : That tran- fparent Corpufcles of the fame thicknefs and denfity with a Plate, do exhibit the fame Co- lour. And this I would have underftood not without fome Latitude,, as well becaufe thofe Corpufcles may be of irregular Figures, and many Rays muft be obliquely incident on them, and fo have a fliorter way through them than the length of their DiameterSj as becaufe the
flraitnels
B O O K II. 237
ftraknefs of the Medium put in on all fides within fuch Corpufcles may a little alter its Mo- tions or other qualities on which the Reflexion depends. But yet I cannot much fufped: the laft , becaule I have obferved of fome fmall Plates of Mufcovy Glafs which were of an even thicknefs, that through a Microfcope they have appeared of the fame Colour at their edges and corners where the included Medium was ter- minated, which they appeared of in other pla- ces. However it will add much to our Satif^ fadion, if thofe Corpufcles can be difcover'd with Microfcopes ; which if we fhall at length attain to, I fear it will be the utmofl improve- ment of this Senfe. For it feems impoflible to fee the more fecret and noble Works of Nature within the Corpufcles by reafon of their tranfpa- rency.
Prop. VIII.
^he Cmife of Refcxion is not the impinging of Light on thefolid or impervious parts of Bodies^ as is commonly believed.
np HIS will appear by the following Confi- -°- derations. Firft, That in the paflage of Light out of Glafs into Air there is a Reflexion as ftrong as in its palTage out of Air into Glafs, or rather a little ftronger, and by many degrees ilronger than in its pallage out of Glafs into Wa- ter. And it feems not probable that Air {hould have more flrongly refleding parts than Waf^r or Glafs. But if that ihould poflibly be fuppo- fed, yet it will avail nothing j for the Reflexion
238 O P T I C K S. '
is as flrong or ftronger when the Air is drawn away from the Glafs, ( fuppofe by the Air-Pump invented by Otto Gueriet^ and improved and made ufeful by Mr. Boyle) as when it is adjacent to it. Secondly, If Light in its pafTage out of Glafs into Air be inqident more obUquely than at an Angle of 40 or 4 1 Degrees it is wholly refleded, if lefs obliquely it is in great meafure tranfmit- ted. Now it is not to be imagined that Light at one degree of obliquity fhould meet with Pores enough in the Air to tranfmit the greater part of it, and at another degree of obliquity fliould meet with nothing but parts to refled: it wholly, efpecially coniidering that in its palTage out of Air into Glafs, how oblique foever be its Inci- dence, it finds Pores enough in the Glafs to tranf- mit a great part of it. If any Man fuppofe that it is not refledled by the Air, but by the outmofl fuperficial parts of the Glafs, tliere is itill the fame dithculty: Befides, that fuch a Suppofition is unintelligible, and will alfo appear to be falfe by applying Water behind fome part of the Glafs inllead of Air. For fo in a convenient obliquity of the Rays, fuppofe of 45 or 46 Degrees, at which they are all refleded where the Air is adja- cent to the Glafs, they Ihall be in great meafure tranfmitted where the Water is adjacent to it; which argues, that their Reflexion or Tranfmiffi- on depends on the conilitution of the Air and W^ater behind the Glafs, and not on the ftriking of the Rays upon the parts of the Glafs. Third- ly, If the Colours made by a Prifm placed at the entrance of a Beam of Light into a darken'd Room te lucceffively call: on a fecond Prifm
placed
BOOK II. 239
placed at a greater diftance from the former, in luch manner that they are all alike incident upon it, the fecond Prifm may be lo inclined to the incident Rays, that thole which are of a blue Colour fliall be all refleded by it, and yet thofe of a red Colour pretty copioufly tranlmit- ted. Now if the Reflexion be caufed by the parts of Air or Glafs, I would ask, why at the fame Obliquity of Incidence tiie blue fliould wholly impinge on thofe parts, fo as to be all reflected, and yet the red find Pores enough to be in a great meafure tranfmitted. Fourth- ly, Where two Glaffes touch one another, there is no fejifible Reflexion, as was declared in the iirft Obfervation; and yet I fee no feafon why the Rays fhould not impinge on the parts of Glafs, as much when contiguous to other Glafs as when contiguous to Air. Fifthly, When the top of a Water-Bubble (in the 17th Obfer- vation, ) by the continual fubflding and exha- ling of the Water grew very thin, there Vv^as fuch a little and almofl infenfible quantity of Light reflected from it, that it appeared in- tenfly black; whereas round about that black Spot, where the Water was thicker, -the Refle- xion was fo ftrong as to make the Water feem very white. Nor is it only at the leaft thick- nefs of thin Plates or Bubbles, that there is no manifeft Reflexion, but at many other thick- neffes continually greater and greater. For in the 15th Obfervation the Rays of the fame Co- lour were by turns tranfmitted at one thicknefs, and refledied at another thicknefs, for an in- determinate number of Succeflions. And yet I in
2/,o , O P T I C K S.
in the Superficies of the thinned Body, where it is of any one thicknefs, there are as many parts for the Rays to impinge on, as where it is of any other thicknefs. Sixthly, If Reflexion were caufed by the parts of reflecting Bodies, it would be impoilible for thin Plates or Bub- . bles, at one and the fame place, to refled; the Rays of one Colour, and tranfmit thofe of ano- ther, as they do according to the 13 th and 15 th Obfervations. For it is not to be imagined that at one place the Rays which, for infliance, exhibit a blue Colour, fliould have the fortune to dalh upon the parts, and thofe which exhi- bit a red to hit upon the Pores of the Body 5 and tfien at another place, where the Body is either -a little thicker, or a little thinner, that on the contrary the blue fhould hit upon its pores, and the red upon its parts. Laftly, Were the Rays of Light refleded by impinging on the folid parts of Bodies, their Reflexions from polifh'd Bodies could not be fo regular as they are. For in polifliing Glafs with Sand, Putty, or Tripoly, it is not to be imagined that thofe Subftances can, by grating and fretting the Glafs, bring all its leafl: Particles to- an accurate Polifh; fo that all their Surfaces fliall be truly plain or truly fpherical, and look all the fame way, fo as together to compofe one even Surface. The fmaller the Particles of thofe Subftances are, the fmalier will be the Scratches by which they continually fret and wear away the Glafs until it be polifli'd j but be they never fo fmall they can wear away the Glafs no otherwife than by grating and fcratching it, and breaking the 3 Protu-.
BOOK 11. 241
Protuberances; and therefore polifli it no o- therwife than by bringing its roughnefs to a ve- ry fine Grain, lb that the Scratches and Fret- tings of the Surface become too fmall to be vifible. And therefore if Light were refled:ed by impinging upon the folid parts of the Giafs, it would be fcatter'd as much by the moll po- lilh'd Glafs as by the rougheft. So then it re- anains a Problem, how Glafs poliili'd by fretting Subftances can refled; Light lb regularly as it does. And this Problem is fcarce otherwife to be folved, than by faying, that the Reflexion of a Ray is etfe(5ted, not by a lingle point of the reflecting Body, but by Ibme power of the Bo- dy which is evenly diffufed all over its Surface, and by which it a6ls upon the Ray without im- mediate Contad:. For that the parts of Bodies do a(fl upon Light at a diftance Ihall be Ihewn hereafter.
Now if Light be refled:ed, not by impinging on the folid parts of Bodies, but by fome other principle j it's probable that as many of its Rays as impinge on the folid parts of Bodies are not refleded but ftifled and loll in the Bodies. For otherwife we mull allow two forts of Refle- xions. Should all the Rays be refledled which, , impinge on the internal parts of clear Water or Cryllal, thofe Subftances would rather have a cloudy Colour than a clear Tranfparency. To make Bodies look black, it's necefiary that ma- ny Rays be llopp'd, retained, and loft in them ; and it feems not probable that any Rays can be llopp'd and ftifled in them which do not im- pinge on their parts.
R And
a+2 O P T I C K S.
And heilce we may underftand that Bodies are much more rare and porous^, than is com- monly believed. Water is nineteen times light- er, and by confequence nineteen times rarer than Gold ; and Gold is fo rare as very readily and vv^ithout the leafl oppofition to tranfmit the magnetick Effluvia, and eafily to admit Quick- filver into its Pores, and to let Water pafs through it. For a concave Sphere of Gold fil- led with Water, and folder'd up, has, upon pref- fmg the Sphere with great force, let the Water fqueeze through it, and ftand all over its out- fide in multitudes of fmall Drops, like Dew, without burfting or cracking the Body of the Gold, as I have been inform'd by an Eye-wit- nefs. From all which we may conclude, that Gold has more Pores than folid parts, and by confequence that Water has above forty times more Pores than Parts. And he that fhall find out an Hypothefls, by which Water may be fo rare, and yet not be capable of compreffion by force, may doubtlefs by the fapie Hypothefis make Gold, and Water, and all other Bodies, as much rarer as he pleafesj fo that Light may find a ready pafTage through tranfparent Sub- ftances.
The Magnet ads upon Iron through all denfe Bodies not magnetick nor red hot,' without a- ny diminution of its Virtue ; as for inftance, through Gold, Silver, Lead, Glafs, Water. The gravitating Power of the Sun is tranfmit- ted through the vafl Bodies of the Planets with- out any diminution, fo as to ad; upon all their parts to their very centers with the fame Force
and
B O O K II. 243
and according to the fame Laws, as if the part upon which it ads were not furrounded with the Body of the Planet. .The Rays of Light, whether they be very fmall Bodies . projeded, or only Motion or Force propagated, are mo- ved in right Lines ; and whenever a Ray of Light is by any Obftacle turned out of its rcdi- linear way, it will never return into the fame redilinear way, unlefs perhaps by very great ac- cident. And yet Light is tranfniittcd through pellucid folid Bodies in right Lines to very .great diftances. How Bodies can have a futikient quantity of Pores for producing thefe EtfcAs is very difficult to conceive, but perhaps not al- together impolTible. For the Colours of Bodies arife from the Magnitudes of the Particles winch refled them, as was explained above. Now if we conceive thefe Particles of Bodks to be fo difpofcd amongll themfelves, that the Intervals or empty Spaceb between them may be equal in magnitude to them all j and that tne£e i^arii- cles may be compufed of other Particles nmch fmaller, which have as much empty Space be- tween them as equals all the Magnitudes of thefe fmaller Particles: And that in like man- ner theie fmaller Particles are again compufed of others much fmaller, all which together are equal to all the Pores or empty Spaces between them; and fo on perpetually till \ou come to fond Particles, fuch 2.\ have no Pores or empty Spaces within them : And if in any grofs Lody there be, for inftance, three fuch degrees of Particles, the leaft of which are folid ; this Bo- dy will have feven times more Pores than folid
R 2 Parts.
244 O P T I C K S.
Parts. But if there be four fuch degrees of Particles, the leaft of which are folid, the Bo- dy will have fifteen times more Pores than folid Parts. If there be five degrees, the Body will have one and thirty times more Pores than folid Parts. If fix degrees, the Body will have fixty and three times more Pores than folid Farts. And fo on perpetually. And there are other ways of conceiving how Bodies may be exceeding porous. But what is really their inward Frame is not yet known to us.
Prop. IX.
Bodies refeB and refradf Light by o?ie and the fame power, ^varioiijly exercijed in 'various- Cir- cumjiances.
THIS appears by feveral Confiderations. Firft, Becaufe when Light goes out of Glafs into Air, as obliquely as it can pofiibly do. If its Incidence be made ftill more oblique, it becomes totally refledted. For the power of the Glafs after it has refracfled the Light as ob- liquely as is poflible, if the Incidence be ftill made more oblique, becomes too firong to let any of its Rays go through, and by confequence caufes total Reflexions. Secondly , Becaufe Light is alternately reflected and tranfmitted by thin Plates of Glafs for many Succeflions, accordingly as the thicknefs of the Plate increa- fes in an arithmetical Progreflion. For here the thicknefs of the Glafs determines whether that Power by which Glafs ad:s upon Light ihall caufe it to be rcfle(5ted, or fufier it to be
tranf-
BOOK 11.
245
tranfmitted. And, Thirdly, becaufe thofe Sur- faces of tranfparent Bodies which have the great- eft refradling power, refled the greateft quan- tity of Light, as was fliewn in the fir'll Propofi- tion.
Prop. X.
If Light be fwifter in Bodies 'than in Vacuo, in the proportion of the Sines which 7ncafure the RefraElion of the Bodies, the Forres of the Bodies to refcB and refrafl Light, are very nearly proportional to the denfities of the fame Bodies ; excepting that unBuous a?id fulphureous Bodies refraSt more than others of this fame den-
LE T AB reprefent the refrading plane Sur- face of any Body, and IC a Ray incident very obliquely upon the Body in C, fo that the
Angle ACI may be Infinitely little, and let CR be the refracfled Ray. From a given Point B perpendicular to the refradling Surface ered: B R meeting with the refrading Ray C R in R, and if C R reprefent the Motion of the refraded Ray, and this Motion be diftinguifh'd into two Motions CB and BR, whereof C B is paral-
R 3 lei
246 O P T I C K S.
lei to the refracting Plane, and BR perpendi- cular, to it: CB fhall reprefent the Motion ^o.f the incident Ray, and B R the Motion genera- ted by the Reiradtion, as Opticians have of late explain'd.
Now if any Body or Thing, in moving through any Space of a given breadth terminated on both fides by two parallel Planes, be urged for- ward in all parts of that Space by Forces tend- ing direftly forwards towards the laft Plane, and before its Incidence on the firil Plane, had no Motion towards it, -or but an infinitely little one J and if tlie Forces in all parts of that Space, between the Planes, be at equal diftances from the Planes equal to one another, but at feveral diftances be bigger or lefs in any given Propor- tion, the Motion generated by the Forces in the whole pafiage of the Body or thing through that Space fliall be in a fubduplicate Proportion of the Forces, as Mathematicians will eafily underftand. And therefore, if the Space of adti- vity of the refrafting Superficies of the Body be confider'd as fuch a Space, the Motion of the Ray generated by the refracting Force of the Body, during its pafiage through that Space, that is, the Motion B R, muft be in fubdupli- cate Proportion of that refracting Force. I fay therefore, that the Square of the Line B R, and by confequence the refracting 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 the Refracftions of feveral Bodies, the Square of B R, fuppofing C B an unite, the Den-
fities
BOOK II. 247
fities of the Bodies eftimated by their Specifick Gravities, and their Refradtive Power in refpea of their Denfities are fet down in feveral Co- lumns.
The P report |
ion 1 The Square |
Theden- |
The re- |
||
of the %i |
ncs of B R, |
ffy and |
fiaSliz'e |
||
of Incidt |
nee |
to which |
fpccifick |
Pcicer |
|
The refrafting Bo- |
and Refra- |
the refra- |
gravi- |
of the |
|
dies. |
ftion of yel- |
Slingforce |
ty of |
Bod^ i n |
|
lovj Light |
of the Bo- |
thi Bo- |
refpeH |
||
dy is pro- |
dy. |
of its |
|||
portionate |
denfity . |
||||
APieudo-Top.-.zius, |
|||||
being a natural, |
|||||
pellucid, brittle, |
23 to |
H |
I '699 |
4*27 |
3979 |
hairy Stone, of a |
|||||
yellow Colour. |
|||||
Air. |
3201 to 3 |
200 |
o''ooo62 5 |
0'00I2 |
5208 |
Glafs of Antimony. |
17 to. |
9 |
2*568 |
5'28 |
4864 |
A Selenitis. |
61 to |
41 |
I '2 1 3 |
2*252 |
5386 |
Glafs vulgar. |
31 to |
20 |
I '4025 |
2'58 |
543^ |
Cryibl 0*" the Rock. |
25 to |
16 |
1^445 |
2*65 |
5450 |
Jfl.lnd Cryftal. |
5 to |
3 |
i'778 |
2*72 |
6536 |
Sal GemmDC. |
17 to |
II |
i'388 |
2*143 |
6477 |
Alume. |
35 to |
24 |
1*1267 |
1*714 |
6570 |
Borax. |
22 to |
»5 |
I'lSii |
1*714 |
67.6 |
Niter. |
32 to |
21 |
i'345 |
i'9 |
7079 |
Dantzick Vitriol. |
303 to |
200 |
1*295 |
1*715 |
755 » |
Oil of Vitriol. |
10 to |
7 |
1*041 |
>'7 |
6124 |
Rain Water. |
529 to |
396 |
0*7845 |
i' |
7845 |
Gum Arabick. |
31 to |
21 |
1*179 |
i'37S |
8574 |
Spirit of Wine well reftified. |
100 to |
73 |
0*8765 |
0*866 |
10121 |
Camphire. |
3 to |
2 |
1*25 |
0*996 |
12551 |
Oil Olive. |
22 to |
15 |
1*1511 |
0*913 |
12607 |
Linfeed Oil. |
40 to |
27 |
1*1948 |
0*932 |
12819 |
SpiritofTurpcntipe. |
25 to |
17 |
1*1626 |
0*874 |
13222 |
Amber. |
14 to |
9 |
1*42 |
1*04 |
13654 |
A Diamond. |
1 00 -to |
41 l4'949 |
3*4 |
i4556__ |
The Refradibn of the Air in this Table is de- termin'd by that of the Atmofphere obferved
R 4 by
248 O P T I C K S.
by Aftronomers. For, if Light pafs through many refradling Subftances or Mediums gradually denfer and denfer, and terminated with parallel Surfaces, the Sum of all the Refradions will be equal to the iingle Refraction which it would have fuirer'd in paffing immediately out of the firft Medium into the lafl. And this holds true, though the Number of the refradling Subftances be increafed to Infinity, and the Diftances from one another as much decreafed, fo that the Light may be refraded in every Point of its Paflage, and by continual Refradions bent into a Curve-Line. And therefore the whole Refradlion of Light in paffing through the Atmofphere from the higheft and rareft Part thereof down to the loweft and denfeil Part, mufl be equal to the Re- fradion which it would fuffer in paffing at like Obliquity out of a Vacuum immediately into Air oi equal Denfity with that in the loweft 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 ftony alcalizate Concretes, and Air which probably arifes from ftich Subftances by Fermentation, be Subftances very differing from one another in Denfity, yet by this Table, they have their refradive Powers almoft in the fame Proportion to one another as their Denfities are, excepting that the Re- fradion of that ftrange Subftance, Ifland Cryftal is a little bigger than the reft. And parti- cularly Air, which is 3500 Times rarer than the Pfeudo-Topaz, and 4.400 Times rarer than a Glafs
BOOK IL 249
Glafs of Antimony; and 2000 Times rarer than the Seleniti8, Glafs vulgar, or Cryflal of the Rock, has notwithftanding its rarity the fame re- fradive Power in refped: of its Denfity which thofe very denfe Subftances have in refped of theirs, excepting fo far as thofe differ from one another.
Again, the Refraction of Camphire, Oil Olive, Linfeed Oil, Spirit of Turpentine and Amber, which are fat fulphureous unduous Bodies, and a Diamond, which probably is an unduous Sub- ftance coagulated, have their refradive Powers in Proportion to one another as their Denlities with- out any confiderable Variation. But the re- fradive Powers of thefe undluous Subftances are two or three Times greater in refpedt of their Denfities than the refradive Powers of the former 5ubftances in refped of theirs.
Water has a refradive Power in a middle de- gree between thofe two forts of Subflances, and probably is of a middle nature. For out of it grow all vegetable and animal Subftances, which confift 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 Subflances and Water, and accordingly are compofed of thofe two forts of Subflances. For by dill illation 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 fix'd Earth capable of Vitrification.
Spirit
250 O P T I C K S.
Spirit of Wine has a refradiv^e Power in a middle degree between thofe of Water and oily Subftances, and accordingly feems to be compo- fed of both, united by Fern^.entation; the Water, by means of fome faline Spirits with which 'tis impregnated, dillolving the Oil, and volatizing it by the Ad;ion. For Spirit of Wine is inflama- blc by means of its oily Parts, and being diftilled often from Salt of Tartar,, grow by every diftil- lation more and more aqueous and phlegma- tick. And Chymiils obferve, that Vegetables (as Lavender, Rue, Marjoram, (^f. ) diftilled ^^r fe^ before fermentation yield Oils without any burning Spirits, but after fermentation yield ar- dent Spirits without Oils : W^hich fliews, that their Oil is by fermentation converted into Spi- rit. They find alfo, that if Oils be poured in a fmall quantity upon fermentating Vegetables, they diftil over after fermentation in the form of Spirits*
So then, by the foregoing Table, all Bodies feem to have their retradive Powers propor- tional to their Denfities, (or vei'y nearly;) ex- cepting fo far as they partake more or lefs of iulphureous oily Particles, and thereby have their refradiive Power made greater or lefs. Whence it feems rational to attribute the refrad-ive Power of all Bodies chiefly, if not wholly, to the ful- phureous Parts with which they abound. For it's probable that all Bodies aJDOund more or lefs with Sulphurs. And as Light congregated by a Burning-glafs ads moft upon fulphureous Bo- dies, to turn them into Fire and Flame ; fo, fince all Adion is mutual. Sulphurs ought to a6t
moft
BOOK II. 251
moil upon Light. For that the action between Light and Bodies is mutual, may appear from this Confideration ; That the denfeil Bodies which rtfrad: and reflect Light moft Wrongly, grow hotteft in the Summer Sun, by the adtion of the refradcd or refied:ed Light.
I have hitherto explain'd the power of Bo- dies to reflect and refradt, and (liew'd, that thin tranfparent Plates, Fibres, and Particles, do, ac- cording to their feveral thickneifes and dcnli- ties, refled: feveral forts of Ravs, and thereby appear of feveral Colours; and by confecjuence that nothing more is requifitc for producing all the Colours of natural Bodies, than the feveral fizes and denfities of their tranfparent Particles. But whence it is that thefe Plates, Fibres, and Particles, do, according to their feveral thick- nelTes and denfities, refledt feveral forts of kays, 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 fhall conclude this part with a few more Proportions. Thofe which preceded refpeft the nature of Bodies, thefe the nature of Light : For both mufl be underftood, before the reafon of their Adlions upon one another can be known. And becaufe the laft Propofition depended upon the velocity of Light, I will begin with a Propofition of that kind.
Prop.
252 O P T I C K S.
Prop. XL
Light is propagated from luminous Bodies in time, and Jpends about feven or eight Mi- nutes of an Hour in paffing from the Sun to the Earth,
'l ^ HIS was (obferved firfl by Roemer, and -*- then by others, by means of the Eclipfes of the Satellites of Jupiter. For thefe Eclipfes, when the Earth is between the Sun and Jupiter, happen about itvtn. or eight Minutes fooner than they ought to do by the Tables, and when the Earth is beyond the Sun they happen about feven or eight Minutes later than they ought to do; the reafon bemg, that the Light of the Satellites has farther to go in the latter cafe than* in the former by the Diameter of the Earth's OrbiL 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 Poiition and Diftance of the Earth from the Sun. The mean motions of Jupiter s Satellites is alfo fwifter in his defcent from his Aphelium to his Perihelium, than in his afcent in the other half of his Orb. But this inequality ha^ no refpcd: to the pofition of the Earth, and in the three interior Satellites 5s infenfible, as I find by computation from the Theory of their Gravity.
Prop.
BOOK IL
Prop. XII.
253
Every Ray of Light in its pajfagc through any refraBing Surface is put into a certain trajijicnt Conjlitution or State ^ which in the progrefs of the Ray returns, at equal Intervals^ and difpofes the Ray at every return to be eafily tranfmitted through ' the next refraSfitjg Sur- face, and betiveen the returns to be eafdy refieSied by it.
TH I S is manifeil by the 5th, 9th, 12th, and 15th jObfervations. For by thofe Ob- fervations it appears , that one and the fame fort of Rays at equal Angles of Incidence on a- ny thin tranfparent Plate, is alternately refledled and tranfmitted for many Succeffions according- ly 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 Reflexion ( that which makes the firfl: or inner- moft of the Rings of Colours there defcribed ) be made at the thicknefs i, the Rays fliall be tranfmitted at the thicknelTes o, 2, 4, 6, 8, lo,
12, ^c. and thereby make the central Spot and Rings of Light, which appear by tranfmillion, and be refledied at the thicknefs i, 3, ^, 7, o,
I I, ^c. and thereby make the Rings which appear by Reflexion. And- this alternate Re*- flexion and TranfmilTion, as I gather by the 24th 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
254 O P T I C K S.
the other, though the thicknefs of the Plate be a quarter of an Inch or above : So that this al- ternation feems to be propagated from every refrading Surface to all diflances w^ithout end or limitation.
This alternate Reflexion and Refradtion de- pends on both the Surfaces of every thin Plate, becaufe it depends on their diflance. By tlie 21 ft Obfervation, if either Surface of a thin Pjate of Miifcovy Glafs be wetted, the Colours caufed by the alternate Reflexion and Refraction grow faint, and therefore it depends on them both.
It is therefore performed at the fecond Surface; for if it were perform'd at the firft, before the Rays arrive at the fecond, it would not depend on the fecond.
It is alfo influenced by fome action or difpo- fition, propagated from the firft to the fecond, becaufe other wife at the fecond it v^ould not depend on the firft. And this adion or difpo- fition, in its propagation, intermits and returns by equal Intervals, becaufe in all its progrefs it inclines the Ray at one diftance from the- firft Surface to be reflefted by the fecond, at ano- ther to be tranfmitted by it, and that by equal Intervals for innumerable viciflitudes. And be- caufe the Ray is difpofed to Reflexion at the diliances i, 3, 5, 7, 9, ^c. and to Tranfmiflion at the diftances o, 2, 4, 6, 8, 10, Gfr. (for its tranfmillion through the firft Surface, is at the diftance o, and it is tranfmitted tiirough both together, if their diftance be infinitely little or much lefs than i ) the difpofition to be tranf- I mit.e4
BOOK 11. 255
mitted at the diftances 2, 4, 6, 8, 10, &c. is to be accounted a return of the lame difpofition which the Ray firft had at the diftance o, that is at its tranfmiffion through the firft refradling Surface. All which is the thing I would prove.
What kind of adion 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 Hy- pothecs, may for the prefent fuppofe, that as Stones by falling upon Water put the Watef in- to an undulating Motion, and all Bodies by percufTion excite vibrations in the Air; fo the Rays of Light, by impinging on any refracting or reflecfting Surface , excite vibrations in the refrafting or refiecfting Medium or Subftance, and by exciting them agitate the folid parts of the refrad:ing or reflecting Body, and by agita- ting them caufe the Body to grow warm or hot; that the vibrations thus excited are pro- pagated in the refradting or reflecfting Medium or Subftance, much after tlie manner that vibra- tions are propagated in the Air for caufing Sound, and move fafter than the Rays fo as to overtake thenij 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 reflected ; and, by confequence, that e- very Ray is fucceftively difpofed to be eafily re- flected, or eafliy tranfmitted, by every vibration
which
256 O P T I C K S.
which overtakes it. But whether this Hypothe- lis be true or falfe I do not here conlider. I con- tent my felf with the bare Difcovery, that the Rays of Light are by fome caufe or other alter- nately difpofed to be refled:ed or refraded for many viciffitudes.
DEFINITION.
I'he returns of the difpofition of any Ray to be refeBed I will call its Fits of eafy Reflexion, and thofe of its difpoftion to be tranfmitted its Fits of eafy Tranfmiffion, and the [pace it pa[fes between every return and the next re- tunty the Interval of its Fits.
Prop. XIII,
'The reafon why the Surfaces of all thick tranf- farent Bodies refledi part of the Light inci^ dent on thein^ and refraSi the reji ^ isy that fome Rays at their Incidence are in Fits of eafy Reflexion^ a7id others in Fits of eafy Tranf- mifjion.
np HIS may be gather'd from the 24th Ob- -*- fervation, where the Light reflected by thin Plates of Kv: and Glafs, which to the naked Eye appear'd evenly white all over the Plate, did through a Prifm appear waved with many Suc- ceffions of Light and Darknefs made by alter- nate Fits of eafy Reflexion and eafy Tranfmiffi- on, the Prifm fevering and difl:inguifliing the Waves of which the white refledled Light was compofed, as was explain' d above.
And
BOOK II; 2^7
And hence Light is in Fits of cafy Reflexion and eafy Tranfmiflion, before its Incidence on tranfparent Bodies. And probably it is put in- to fuch Fits at its firfl emilTion from luminous Bodies, and continues in them during all its pro- grefs. For thefe Fits are of a lafting naturcj as will appear by the next part of this Book.
In this Proportion I fuppofe the tranfparent Bodies to be thick j becaufc if the thicknefs of the Body be much lefs than the Interval of the Fits of eafy Reflexion and Tranfmitiion of the Rays, the Body lofeth its refleclling power. For if the Rays, which at their entering into the' Body are put into Fits of eafy Tranfmiflion, ar- tive at the farthefl Surface of the Body before they be out of thofe Fits, they muil: be tranfmit- ted. And this is the reafon why Bubbles' of Water lofe their refledling power when they grow very thin ; and why all opake Bodies, when reduced into very fmall parts, become tranfpa^ rent.
Prop. XIV.
'Thofe Surfaces cf tranfparent Bodies^ which if the Ray be in a Fit of 'Refratlicn do rfra6i it vicf: fli-ongly^ if the Ray be in a Fit of Rcfiexion do refeB it 7nofi eafdy.
FO R we fhewed above, in Frop. 8. that thai 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 ad; on Light at a diilance. We fhewed alio in Frop, 9. that Bodies refled: and refrad:
S Lighc
258 O P T I C K S.
Light by one and the fame power, varloufly ex- ercifed in various circumftances; and in Prop. i. that the moft ftrongly refracting Surfaces refledt the moft Light: All which compared together evince and ratify both this and the laft Propo- rtion.
Prop. XV.
In any one and the fame fort of Rays, emerging in any Angle out of any refraSling Surface into one and the fame Medium, the hitervalaf the fol- lowing Fits of eafy Refexion and 'T^ranfmifjion are either accurately or very nearly, as the ReB- angle of the Secaiit of the Angle of RefraSlion, and of the Secant of another Angle, whofe Sine is the firfi of 106 arithmetical mean Rroporti- onals, between the Sines of Incidence and Refra- Bion, counted from the Si?2e of RefraBion.
T^ H I S is manifefl by the 7th and 19th Obfcr- ••■" vations.
Prop.
B O O K n. 259
Prop. XVI.
Lt fever al forts of Rays e-merging in equal Anglci. out of any refradiing Surface into the fame Me^ dium^ the Litervals of the foiio'wing hits of eafy 'Reflexion and eafy T'ranfniJJion are either accu- rately, or very nearly, as the Cube-Roots of the Squares of the lengths of a Chord, which fownd the Notes in an Eight, fol, la, fa, fol, la, mi, fa, fol, ivith all their imter mediate degrees an- fuoering to the Colours of thofe Rays, accordtfg to the Analogy defcrihed in the feventh Experiment of the fecond Part of theflrft Book.
np H I S is manifeft by the 13th and 14th Ob- ■*■ fervations.
Prop. XVII.
Jf Rays of any fort pafs perpendicularly ifito feve^ ral Mediums, the hitcrvcls of the Fits cf eafy Reflexion and l^ranfmiflion in any one Medium, are to thofe Intervals in any other, as the Sine of Incidence to the Sine of RefraBion, wlmi the Rays pafs out of the flrfl of thofe ti^o Mediums into the fecond.
T^ H I S is manifeft by the loth Obferva- -^ tion.
S 2 Prop,
26o O P T I C K S.
Prop. XVIII.
If the Rays nvhich paint the Colour in the Confine of yellow and orange pafs perpejidicularly out of any Medium into Air, the Intervals of their Fits
of eafy Reflexion are the th part of an Inch,
And of the fa?ne length are the Intervals of their Fits of ' eafy I^ranfmifjion,
^ I ^ H I S 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 Tranfmiffion of any fort of Rays refra- ined in any Angle into any Medium j and thence to know, whether the Rays fhall be reflected, or tranfmitted at their fubfequent Incidence upon any other pellucid Medium. Which thing, be- ing ufeful for underflanding the next part of this Book, was here to be fet down. And for the fame reafon I add the two following Propofi- tions.
Prop,
BOOK II. 261
Prop. XIX.
If any fort of Rays faUi7ig on the polite Surface of any pellucid Medium be refeBed back^ the Fits of eafy Refexion^ which they have at the point of Refexion, fall fill continue to return j a?jd the Returns fiall be at diftances from the point of Refexicn in the arithmetical prcgrejfon of the 'Numbers 7.^ 4, 6, 8, 10, 12, &c. and between thefe Fits the Rays pall be in Fits of eafy 7'rafif mijjion.
"P O R fiRce the Fits of eafy Reflexion and •*- Qafy TranfmilTion are of a returning na- ture, there is no reafoa why thefe Fits, which continued till the Ray arrived at the reflecting Medium, and there inclined the Ray to Refle- xion, ihould there ceafe. And if the Ray at the point of Reflexion was in a Fit of eafy Reflexion, the progreflion of the diftances of thefe Fits from that point mufl: begin from o, and fo be of the Numbers o, 2, 4, 6, 8, &c. And therefore the progreffion of the dillances of the interme- diate Fits of eafy Tranfmiflion, reckon'd from the fame point, mufl be in the progreflion of the odd Numbers i, 3, 5, 7, 9, ^c. contrary to what happens when the Fits are propagated from points of Refradion.
S3 Prop,
262 O P T I C K S.
Prop. XX.
^he Intervals of the Fits of eafy Reflexion and, eafy T'ranfmifjion^ propagated from points of KeHexion into afiy Medium^ are equal to the Intervals of the like Fits^ which the fame Rays would ba-vey if refraBed into the fame Medium in Angles of Rejraciion equal to their Angles of Reflexion,
'P O R when Light is refleded by the fecond ■"- Surface of thin Plates, it goes out after- wards fieely at the firft Surface to make the Rin^s of Colours which appear by Reflexion j and, by the freedom of its egrefs, makes the Colours of thefe Rings more vivid and ftrong than thofe which appear on the other fide of the Plates by the tranfmitted Light. The re- fieded Rays are therefore in Fits of eafy Tranf- miffion at their egrefs; v/hich would not always happen, if the Intervals of the Fits within the Plate after Reflexion were not equal, both in kngth and number, to their Intervals before it. And this confirms alfo the proportions fet down in the former Propofition. For if the Rays both in going in and out at the firfh Surface be in Fits of eafy Tranfmiffion, and the Intervals and Numbers of thofe Fits between the firft and fecond Surface, before and after Reflexion, be equal, the diftances of the Fits of eafy Tranfmiflion from either Surface, muft be in the fame prpgreffion after Reflexion as before ; that is, from the firft Surface which tranfmit- ted them, in the progreffion of the even Num-.
bers
B O O K IL 263
bers o, 2, 4, 6, 8, (^c. and from the fecond which refledled them, in that of the odd Num- bers I, 3, 5, 7, &c. But thefe two Propofi- tions will become much more evident by the Obfervations in the following part of this Book.
S4
THE
THE
SECOND BOOK
O F
OPTICKS
PART IV.
Qbfervations concerning the Reflexions and Colour^ of thick tranfparent polij^d Platzs.
HERE Is no Glafs or Speculum how well foever polifliedjbut, befides the Light which it refradts or refledls re-, gularlyj fcatters every way irregularly a faint Light, by means of which the polifh'd Surface, v/hen illuminated in a dark room
by
BOOK II. 265
by a 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 firft obferved them, feem'd very flrange and furprizing to me. My Obfervations were as fol- lows.
Obf. I. The Sun fhining into ray darkened Chamber through a hole one third of an Inch wide, riet the intromitted beam of Light fall perpendicularly upon a Glafs Speculum ground concave on one fide 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 diftance of about live Feet and eleven Inches from the Speculum, in fuch manner, that the beam ©f Light might pafs through a little hole made in the middle of the Chart to the Specu- lum, and thence be reflected back to the fime hole: I obferved upon the Chart four or five concentric Irifes or Rings of Colours, like Rain- bows, encorapaffing 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 Objedl-glaiTes, 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 llione very clear, there appear'd faint Lineaments of a fixth and fe- vgnth. If the diftance of the Chart from the
S,pecu-»
266 O P T I C K S.
Speculum was much greater or much lefs than that of fix Feet, the Rings became dilute and vaniQi'd. And if the diftance of the Speculum from the Window was much greater than that of fix Feet, the refledied 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 innermoft Rings. And therefore I ufually placed the Speculum at a- bout fix Feet from the Window j fo that its Focus might there fall in with the center of its concavity at the Rings upon the Chart. And this Pofiiure is always to be underfi:ood in the following Obfervations where no other is ex- prefs'd.
Obf. 2. The Colours of thefe Rain-bows fuc- ceeded one another from the center outwards, 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 refledled, but tranfmitted through the two Objedi-glafiTes. For, firfi:, there was in their common center a white round Spot of faint Light, fomething broader than the refleded beam of Light, which beam fometimes fell upon the middle of the Spot, and fometimes by a little inclination of the Specu- lum receded from the middle, and left the Spot white to the center.
This white Spot was immediately encompaf- fed with a dark grey or rufleti and that dark grey with the Colours of the firfi: 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
BOOK 11. 267
little greenifh yellow, and after that a brighter yellow, and then on the outward edge of the Iris a red which on the outfide inclined to pur- ple.
This Iris was immediately encompaffed with a fecond, whofe Colours were in order from the in- fide outwards, purple, blue, green, "yellow, light red, a red mix'd with purple.
Then immediately foUow'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 bluifli green within, and red without, but fo faintly that it was difficult to difcern the Colours.
Obf. 3. Meafuring the Diameters of thefe Rings 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 tranf- mitted through the two Objed-glafies. For the Diameters of the four iirfl of the brjf^ht Rings meafured between the brightefl parts of their Orbits, at the diftance of fix Feet from the Speculum were 144, 2I, 2— 3^ Inches, whofe Squares are in arithmetical progreffion of the numbers i, 2, 3, 4. If the white circular Spot in the middle be reckon'd amongfl the Rings, and its central Light, where it fsems to be n:oil luminous, be put equipollent to an infinitely little Ring ; the Squares of the Diameters of the Rings will be in the progrefiion 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 progreflion of the num- bers
268 O P T I C K S.^
bers T, It, 2^, 3^, '&c. the Diameters of the firft four at the diftance of fix Feetsfrom the Speculum, being i.?^, 2tV, 2t, 3tt Iiiches. If the diftance of the Chart from the Speculum was increafed or diminilhed, the Diameters of the Circles were increafed or diminifhed pro- portionally.
Obf. ^. By the analogy between thefe Rings and thofe defcribed in the Obfervations of the firft Part of this Book, I fufpedted 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 therefore through a Prifm, as I did thofe in the 24th Ob- fervation of the firft Part of this Book. And when the Prifm was fo placed as by refradling the Light of their mix'd Colours to feparate them, and diftinguilh the Rings from one ano- ther, as it did thofe in that Obfervation, I could then fee them diftind:er 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 queftion not but that I might have feen many more.
Ohf. 5. Placing a Prifm at the Window to re- fradl the intromitted beam of Light, and caft the oblong Speftrum 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 Spe- culum, whilft the reft were intercepted by the Paper. And now I found Rings of that Co- lour only which fell upon the Speculum. If
the
BOOK II. 269
the Speculum was illuminated with red, the Rings were totally red with dark Intervals, if with blue they were totally blue, and fo of the other Colours. And when they v/ere illumi- nated wi'th any one Colour, the Squares of their Diameters meafured between their moil lumi- nous Parts, were in the arithmetical Progreilion of the Numbers, o, i, 2, 3, 4, and the Squares of the Diameters of their dark Intervals in the Progreffion of the intermediate Numbers j, It, 2f, 33. But if the Colour was varied, they va- ried their Magnitude. In the red they were lar- geft, in the indigo and violet leaft, and in the intermediate Colours yellow, green, and blue, they were of feveral intermediate Bigneffes an- fwering to the Colour, that is, greater in yel- low than ia green, and greater in green than in blue. And iicnce I knew, that when the Spe- culum was illuminated with white Light, the red and yellow on the outlide of the Rings were produced by the hoA refrangible Rays, and the blue and violet by the moir 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 firft and fe- cond Part of this Book, and by mixing diluted one another fo tliat they could not be diflin- guifli'd, unlefs near the Center where they were leaft mix'd. For in this Obfervation I could fee the Rings more diftindly, and to a greater Number than before, being able in the yellow Light to number eight or nine of them, be- iides a faint ihadow of a tenth. To fatisfy my felf how much th^ Colours of the feveral Rings
fpread
270 O P T I C K S.
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 fuccefiively by the red, yellow, and green, differ'd more from one another than thofe made fuccefTively 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 outmoft 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 outmoft violet, are in pro- portion as the Differences of the Lengths of a Monochord which found the Tones in an Eight j jbl, la^ fa, Jol, la, mi, fa, fol, , that is, as the Numbers ir, tV, tV, t'-, tV, tV> ■^' ^"d 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 outmoft red, and by the Con- fine of red and orange, as tV -1- tt A- rV -^ tV ^o \, that is as tV to \, or 8 to 3, and to the diffe- rence of the Circles m.ade by the outmoft vio- let, and by the Confine of blue and indigo, as
TT 4- TT -1- tV 4- vT to rr 4- iV, that is, as -iy to tV>
or
BOOK IL 271
or as 16 to 5. And therefore thefe differences will be g A and /g A. Add the firft to 9 A and fubdud the lafi: from 8 A, and you will have the Diameters of the Circles made by the leafl and
moft refrangible Rays ''i. A and -^ A. Thefe di- ameters are therefore to one another as 75 to 61^ or 50 to 41, and their Squares as 2500 to 168 1, that is, as 3 to 2 very nearly. Which proportion differs not much from the proportion of the Diameters of the Circles made by the outmoft red and outm-oft violet, in the 13 th Ob- fervation of the firft part of this Book.
Ol?f. 6. Placing my Eye where thefe Rings appear'd plaineft, I faw the Speculum tinged all over with Waves of Colours, (red, yellov/, green, blue J ) like thofe which in the Obfervations of the firft part of this Book appeared between the Obje(3:-glaffes, and upon Bubbles of Water, but much largei". And after the manner of thofe, they were of various magnitudes in various Po- litions of the Eye, fwellin-^ and ihrinking as I moved my Eye this way and that way. They were formed like Arcs of ccnccntrick Circles, as thofe were 5 and v/hen my Eye was over againft the center of the concavity of tho Speculum, (that is, 5 Feet and 10 Inches diftant from the Specu- lum,) their common center was in a right Line with that center of concavity, and with the hole in the Window. But m other poftures of my Eye their center had other pofitions. They appear'd by the Light of tlie Clouds propagated to the Speculum through the hole in the Win- dow J and when the Sun {hone through that
2 hole
272 O P T I C K S.
hole upon the Speculum, his Light upon it was of the Colour of the Ring whereon it fell, but by its fplendor obfcured the Rings made by the Light of the Clouds, unlefs when the Speculum was removed to' a great diftance from the Window, fo that his Light upon it might be broad and faint. By varying the polition of my Eye, and moving it nearer to or farther from the direct beam of the Sun's Light, the Colour of the Sun's refleded Light conflantly varied upon the Speculum, as it did upon my Eye, the fame Colour always ap- pearing to a By-ftander upon my Eye which to me appear'd upon the Speculum. And thence I knew that the Rings of Colours upon the Chart were made by thefe refledled Colours, propagated thither from the Speculum in feveral Angles, and that their produdion depended not upon the ter- mination of Light and Shadow.
Obf. J. By the Analogy of all thefe Pheno- mena with thofe of the like Rings of Colours defcribed in the f rft part of this Book, it feem- ed to me that thefe Colours were produced by this thick Plate of Glafs, much after the manner that thofe were produced by very thin Plates. For, upon trial, I found that if the Quick-fil- ver were rubb'd off from the backfide of the Speculum, the Glafs alone would caufe the fame Rings of Colours, but much more faint than before j and therefore the Phaenomenon depends not upon the Quick-lilver, unlefs fo far as the Quick-hlver by increaiing the Reflexion of the backfide of the Glafs increafes the Light of the Rings of Colours. I found alfo that a Speculum of Metal without Glafs made fome
Years
BOOK II. 273
Years fince for optical ufes, and very well wrought, produced none of thofe Rings j and thence I underfbood that thefe Rings arifc not from one fpecular Surface alone, but d'epend upon the two Surfaces of the Plate of Glafs whereof the Speculum was made, and upon the thicknefs of the Glafs between them. For as in the 7th and 19th Obfervations of the firft part of this Book a "thin Plate of Air, Water, or Glafs of an even thicknefs appeared of one Colour when the Rays were perpendicular to it, of another v/hen they were a little oblique, of another v/hen more oblique, of another when ftill more oblique, and fo on y fo here, in the lixth Obfervation, the Light which emerged out of the Glafs in feveral Obliquities,- made tlie Glafs appear of feveral Colours, and being pro- pagated in thofe Obliquities to the Chart, tiierc painted Rings of thofe Colours. And as the reafon why a thin Plate appeared of feveral Co- lours in feveral Obliquities of the Rays, v/as, that the Rays of one and the fame fort are re- fleded by the thin Plate at one obliquity and tranfmitted at another, and thofe of other forts tranfmitted where thefe are refleded, and re- flected where thefe are tranfmitted : So the reafon why .the thick Plate of Glafs whereof the Speculum was made did appear of various Colours in various Obliquities, and in thofe Obliquities propagated thofe , Colours to the Chart, was, that the Rays of one and the fame fort did at one Obliquity emerge out of the Glafs, at another did not emerge, but were refleded back towards the Quick-filver
T . by
t74 O P T I C K S.
by the hither Surface of the Glafs, and according- ly as the Obliquity became greater and greater, emerged and were refiedted alternately for ma- ny Succeffignsj and that in one and the fame Obliquity the Rays of one fort were refled:ed, and thofe of another tranfmitted. This is ma- nifeft by the fifth Obfervation of this part of this Book. For in that Obfervation, when the Spe- culum was illuminated by any one of the prif- matick Colours, that Light made many Rings of the fame Colour upon the Chart with dark Intervals, and therefore at its emergence out of the Speculum was alternately tranfmitted and not tranfmitted from the Speculum to the Chart for many SuccefTions, according to the various Obliquities of its Emergence. And when the Colour caft on the Speculum by the Prifm was varied, the Rings became of the Colour cafl on it, and varied their bignefs with their Colour, and therefore the Light was now alternately tranfmitted and not tranfmitted from the Spe- culum to the Chart at other Obliquitiss than before. It feemed to me therefore that thefe Rings were of one and the fame original with thofe of thin Plates, but yet with this difference, that thofe of thin Plates are made by the alter- nate Reflexions and Tranfmiffions of the Rays at the fecond Surface of the Plate, after one paf- fage through itj but here the Rays go twice through the Plate before they are alternately re- ileded and tranfmitted. Firft, they go through it from the firfi: Surface to the Quick-filver, and then return through it from the Quick-filver to the firil Surface, and there are either tranf- mitted
BOOK II. 275
micted to the Chart or refledled back to the Quick-filver, accordingly as they are in their Fits of eafy Reflexion or Tranfmiffion when they arrive at that Surface. For the Intervals of the Fits of the Rays which fall perpendicu- larly on the Speculum,, and are reiledled back in the fame perpendicular Lines, by rcafon" of the equality of tbefe Angles and Lines, are of the fame length and number within the Glafs after Reflexion as before, by the 19th Propofl- tion of the third part of this Book. And there- fore fince all the Rays that enter through the iirll: Surface are in their Fits of eafy Tranfmif- fion at their entrance, and as many of thefe as are refledted by the fecond are in their Fits of eafy Reflexion there, all thefe mufl: be again in their Fits of eafy Tranfmiffion at their return to the firil, and by confequence there go Out of the Glafs to the Chart, and form upon it the white Spot of Light in the center of the Rings. For the reafon holds good in all forts of Rays, and therefore all forts mufl go out promifcu- oufly to that Spot, and by their mixture " caufe it to be white. But the Intervals of the Fits of thofe Rays which are reflected more obliquely than they enter, mull: be greater after Reflexion than before, by the 15th and 20th Propcfitlons. And thence it may happen that the Rays at their return to the firli Surface, may in certain Ob- liquities be in Fits of eafy Reflexion, and return back to the Qu]ck-f:!ver, and in other interme- diate Obliquities be again in Fits of eafy Tranf- miffion, and fo go out to the Chart, and paint on it the Rings of Colours about the white Spot.
T 2 And
276 O P T I C K S.
And becaufe the Intervals of the Fits at equal obliquities are greater and fewer in the lefs re- franf^ible Rays, and lefs and more numerous in rhe more refrangible, therefore the lefs refrangi- ble at equal obliquities fhall make fewer Rings than the more refrangible, and the Rings made by thofe iliall be larger than the like number of Rings made by thefej that is, the red Rings fhali be larger than the yellow, the yellow than the green, the green than the blue, and the blue than the violet, as they were really found to be in the fifth Obfervation. And therefore the firll Ring of all Colours encompaffing the white Spot of Light lliall be red without any violet within, and yellow, and green, and blue in the middle, as it was found in the fecond Obferva- tion ; and thefe Colours in the fecond Ring, and thofe that follow, fliall be more expanded, till they fpread into one another, and blend one an- other by interfering.
Thefe feem to be the reafons of thefe Rings in general j and this put me upoi;i obferving the thicknefs of the Glals, and confidering whether the dimenfions and proportions of the Rings may be truly derived from it by computation.
Obf. 8. I meafured therefore the thicknefs of this concavo-convex Plate of Glafs, and found it every where \ of an Inch precifely. Now, by the fixth Obfervation of the firft Part of this Book, a thin Plate of Air tranfmits the brighteft Light of the firft Ring, that is, the bright yel- low, when its thicknefs is the g-^ th part of an
Inchi and by the tenth Obfervation of the fame
Part,
BOOK IT. 277
Parr, a thin Plate of Glafs trLinfmits the fame Light of" the farrie Ring, when its diicknefs k lefs in proportion of tb.e Sine of Refrad:ion to the Sine of Incidence, that is, when its thick-
nefs is the ,-- 1 '";;;;;; th or - ' — th part of an Inch, 1^13000 137545 ^
fappofing the Sines are as 1 1 to 17. And it this thickncfs be doubled, it tranfmits the fame bright Light of thefecond Ring; if trippled, it tranf- mits that "of tlie third, and fo on; the bright yellow Light in all thefe cafes being in its Fits of Tranfmiiiion. And therefore if its thickncfs be multiplied 34386 times, fo as to become J of an Inch, it tranfmits the fame bright Liglit of the 34386th Ring. Suppofe this be the bright yellow Light tranfmitted perpendicularly from the refled-ing convex lide of the Glafs through the concave fide to the white Spot in the cen- ter of the Rings of Colours on the Chart: And by a Rule in the 7th and igvh Obfervations in the firft Part of this Book, and by the J5ch and 20th Propofitions of the third Part of this Book, if the Rays be made oblique to the Glafs, the thickncfs of the Glafs requilite to tranfmit the fame bright Light of the fame Ring in any ob- liquity, is to this fliickncfs of; of an Inch, as the- Secant of a certain Angle to the Radius, the Sine of which. Angle is the firfl of an hundred and fiX arithmetical Means between the Sines of Incidence and Rcfrartion, counted from the Sine of Incidence when the Refrac^liion is made out of any plated Body into any Medium en- compafTmg it ; that isj in this cafe, out of Glafs into Air. Now if the thicknefs of the Glafs be
T 3 increafed
278 O P T I C K S.
increafed by degrees, fo as to bear to its firft thicknefs, (viz. that of a quarter of an Inch,)' the Proportions which 34386 .(the number of Fits of the perpendicular Rays in ^oing through the Glafs tov/ards the white Spot in the center of the Rings,) hath to 34385, 34384, 34383, and 34382, (the' numbers of the Fits of the oblique Rays in going through the Glafs towards the firft, fecond, third, and fourth Rings of Co- lours, ) and if the firfl thicknefs be divided in- to 1 00000000 equal parts, the increafed thick- nefies will be 1 00002908, 1 00005 8 1 6, 1 00008725, and 100011633, and the Angles of which thefe thicknelTes are Secants will be 26' 13", 37' 5", 45' 6", and 52' 26", the Radius being looooooooj and die Sines of thefe Angjjes are 762, 1079, 1321, and 1525, and the proportional Sines of Refradion 1 172, 1659, 203 1, and 2345, the Ra- dius being 1 00000. For fmce the Sines of In- cidence out of Glafs into Air are to the Sines of Refraiftion as 11 to 17, and to the above- mentioned Secants as 1 1 to the iirft of 106 arith- metical Means betVv^een 11 and 17, that is, as;
1 1 to II —>, thofe Secants will be to the Sines 106'
of Refradion as 11 -j^ to 17, and by this Ana- logy will give thefe Sines. So then, if the ob- liquities of the Rays to the concave Surface of the Glafs be fuch that the Sines of their Refra- dion in paiTing out of the Glafs through that Surface into the Air be 1172, 1659, 2031, 2345, the bright Light of the 34386th Ring fhall e- jnerge at the thickneffes of the Glafs, which are
2 to
BOOK II. 279
to 5 of aninch as 34386 to 34385,.34384, 34383, 34382, refpedively. And therefore, if the thick- nefs in all thefe Cafes T3e 5 of an Inch (as it is in the Glafs of which the Speculum was made) the bright Light of the 34385th Ring fhall e- merge where the Sine of Refracftion is 1 172, and that of the 34384th, 34383th, and 34382th Ring where the Sine is 1659, 2031, and 2345 refpedtively. And in thefc Angles of Refra- ction the Light of thefe Rings fliall be propaga- ted from the Speculum to the Chart, and there paint Rings about the white central round Spot of Light which we faid was the Light of thp 34386th Ring. And the Semidiameters of thefe Rings fhall fubtend the Angles of Refraction made at the Concave-Surface of the Speculum, and by confequence their Diameters flrjll be to the diftance of the Chart from the Speculum as thofe Sines of Refraction doubled are to the Radius, that is, as 1172, 1659, 2031, and 2345, doubled are to 1 00000. And therefore, if the diftance of the Chart from the Concave-Surface of the Speculum be fix Feet ( as it was in the third of thefe Obfervations ) the Diameters of the Rings of this bright yellov/ Light upon the Chart fhall be i'688, 2*389, 2*925, 3*375 Inches: For thefe Diameters are to fix Feet, as the above- mention'd Sines doubled are to the Radius. Now, thefe Diameters of the bright yellow Rings, thus found by Computation are the very fame with thofe found in the third of thefe Obfervations by meafuring them, viz. with I IS, 2g, 2ii, and 3g Inches,, and therefore the 1 heory of deriving thefe Rings from the thick-
T 4 nsfs
28o O P T I C K S.
nefs of the Plate of Glafs"* of which the Specu- .lurii was made, and from the Obliquity of the emerging P.ays agrees with the Obfervation. In this Computation 1 have equalled the Diameters of the bright Rings made by Light of all Co- lours, to the Diameters of the Rings made by the bright yellow. For this yellow makes the brighteft Part of the Rings of all Colours. If you defire theDiameters of the Rings made by the Light of any other unmix'd Colour, you may find them readily by putting them to the Diame- ters of the bright yellow ones in a fubduplicate Proportion of the Intervals of the Fits of the Rays of thofe Colours when equally inclined to the refrading or reflecting Surflice which caufed thofe Fits, that is, by putting the Diameters of the Rings made by the Rays in the Extremities and Limits of the feven Colours, red, orange, yellow, green, blue, indigo, violet, proportio- nal to the Cube-roots of the Numbers, i, |, ^, J, |, 55 -^5 ly which exprefs the Lengths of a Mono- chord founding the Notes in an Lighth: For by this m.eans the Diameters of the Rings of thefe Colours will be found pretty nearly in the fame Proportion to one another, which they ought to have by the fifth of thefe Obferva- tions.
And thus I fatisfy'd my felf, that thefe Rings were of the fame Kind and Original with thofe of thin Plates, and by confequenxe that the Fits or alternate Difpofitions of the Rays to be refleded and tranfmirted are propagated to great diftances from every refleding and re- frading Surface. But yet to put the mat- ter
BOO K II, 281
ter out of doubt, I added the following Obfer- vation.
Obf. 9. If ^thefe Rings thus depend on the thicknels of the Plate of Glafs, ' their Diameters at equal diilances from feveral Speculums made of iuch CDncavo-convex Plates of Glafs as are ground on the fame Sphere, ought to be recipro- cally in a fubduplicate Proportion of the thick- neffes of the Plates of Glafs. And if this Pro- portion be found true by experience it will amount to a demonftratlon that thefe Rings (like thofe formed in thin Plates) do depend on the thick- nefs of the Glafs. I procured therefore ano- ther concavo-convex Plate of Glafs ground on both lides to the fame Sphere with the former Plate. Its thicknefs was l^ Parts of an Inch ; and the Diameters of the three hYi\. bright Rings meafured between the brightell Parts of their Orbits at the diftance of fix Feet from the Glafs were 3. 4^-. 5J. Inches. Now, the thick- nefs of the other Glafs being \ of an Inch v/as to the thicknefs of this Glafs as ? to 4 that is as 31 to 10, or 310000000 to icooooooo, and the Roots of thefe Numbers are 1 7607 and loooo, and in the Proportion of the iirlt of thefe Roots to the fecond are the Diameters of the brip-ht Rings made in this Obfervation by the tliinner Glafs, 3. 4fi. 57, to the Diam.eters of the fime Rings made in the tliird of thefe Obfervations" by the thicker Glafs i-.^. 2!. 2^k, that is, the Dia- meters of the Rings are reciprocally in a fubdu- plicate Proportion of the thickneffcs of the Plates of Glafs.
282 O P T I C K S.
So then in Plates of Glafs which are alike concave on one fide, and alike convex on the other fide, and alike quick-filver'd on the con- vex fides, and differ in nothing but ' their thick- nefs, the Diameters of the Rings are reciprocally in a fubduplicate Proportion of the thickneffes of the Plates. And this fhew^s fufticiently that the Rings depend on both the Surfaces of the Glafs, They depend on the convex Surface, becaufe they lare more luminous when that Surface is quick- filver'd over than when it is without Quick-filver. They depend alfo upon the concave Surface, be- caufe without that Surface a Speculum makes them not. They depend on both Surfaces, and on the difiiances between them, becaufe their bignefs is varied by varying only that diftance. And this dependance is of the fame kind with that which the Colours of thin Plates have on the difi:ance of the Surfaces of thofe Plates, becaufe the big- nefs of the Rings, and their Proportion to one another, and the variation of their bignefs arifing from the variation of the thicknefs of the Glafs, and the Orders of their Colours, is fuch as ought to refult from th© Propofitions in the end of the third Part of this Book, derived from the Phaeno- mena of the Colours of thin Plates fet down in the firfi: Part.
There are yet other Phenomena of thefe Rings of Colours, but fuch as follow from the fame Propofitions, and therefore confirm both the Truth of thofe Propofitions, and the Analogy be^ tween thefe Rings and the Rings of Colours made by very thin Plates. I fhali fubjoin fome of them.
ObJ\
BOOK II. 283
Obf. 10. When the beam of the Sun's Light was refleded back from the Speculum not di- redly to the hole in the Window, but to a pLce a little diftant from it, the common center of that Spot, and of all the Rings of Colours fell in the middle way between the beam of the in- cident Light, and the beam of the refleded Light, and by confequence in the center of the fpherical concavity of the Speculum, whenever the Chart on which the Rings of Colours fell was placed at that center. And as the beam of refledfed Light by inclining the Speculum re- ceded more and more from the beam of inci- dent Light and from the common center of the colour'd Rings between them, thofe Rings grew bigger and bigger , and fo alfo did the white round Spot, and new Rings of Colours emer- ged fucceffively out of their common center, and the white Spot became a white Ring en- compaffing them 3 and the incident and reflected beams of Light always fell upon the oppofite parts of this white Ring, illuminating its Peri- meter like two mock Suns in the oppofite parts of an Iris. So then the Diameter of this Ring, meafured from the middle of its Light on one lide to the middle of its Light on the other fide, was always equal to the diftance between the middle of the incident beam of Light,'' and the middle of the refleded beam meafured at the Chart on which the Rings appeared: And the Rays which form'd this Ring were reflected by the Speculum in Angles equal to their Angles of Incidence, and by confequence to their Angles pf Refradion at their entrance into the Glafs,
but
284 O P T I C K S.
but yet their Angles of Reflexion were not in the fame Planes with their Angles of Inci- dence.
' Obf. 1 1. The Colours of the new Rings Were in a contrary order to thofe of the former, and arofe after this manner. • The white round Spot of Light in the middle of the Rings continued white to the center till the diftance of the inci- dent and refleded beams at the Chart was about 8 parts of an Inch, and then it began to grow dark in the middle. And when that diftance was a- bout ItV of an Inch, the white Spot was become a Ring encompaffing a dark round Spot which in the middle inclined to violet and indigo. And the luminous Rings encompafling it were grown equal to thofe dark ones which in the four firft Obfervations encompafled them, that is to fay, the white Spot was grown a white Ring equal to the firft of thofe dark Rings, and the firft of thofe luminous Rings was now grown equal to the fecond of thofe dark ones, and the fe- cond of thofe luminous ones to the third of thofe dark ones, and fo on. For the Diameters of the luminous Rings were now itV, 2'V, 2j, 3 iV, S^c. Inches.
When the diftance between the incident and reflected beams of Light became a little big- ger, there emerged out of the middle of the dark Spot after the indigo a blue, and then out of that biue a pale green, and foon after a yel- low and red. And when the Colour at the center was brighteft, being between yellow and red, the bright Rings were grown equal to thofe Rings -which in the four firft Obfervations next
encom-
BOOK II. 285
encompaiTed them; that is to fay, the white Spot in the middle of thofe Rings was now be- come a white Ring equal to the iirft of thofe bright Rings, and the firft of thofe bright ones was now become equal to the fecond of thofe, and fo on. For the Diameters of the white Ring, and of the other luminous Rings encom- paffing it, were now 1 44, 2|, 2|i, 3|., J^c. or thereabouts.
When the diftance of the two beams of Light at the Chart was a little more increafed, there emerged out of the middle in order after the red, a purple, a blue, a green, a yellow, and a red inclining much to purple, and when the Colour was brighteft being between yellow and red, the former indigo, blue, green, yel- low and, red, were become an Iris or Ring of Colours equal to the firlt of thofe luminous Rings which appeared in the four firfh Obfer- vations, and the white Ring which was now become the fecond of the luminous Rings was grown equal to the fecond of thofe, and the lirft of thofe which was now become the third Ring was become equal to the third of thofe, and fo on. For their Diameters were Itx, 2g, 2-rT, 3 1- Inches, the diftance of the two beams of Light, and the Diameter of the v/hite Ring being 2t Inches.
When thefe two beams became more diflant there emerged out of the middle of the pur- plifh red, firft a darker round Spot, and then out of the middle of that Spot a brighter. And now the former Colours ( purple, blue, green, yellow, and purplilh red) were become a Ring
equal
286 O P T. I C K S.
equal to the firft of the bright Rings mentioned in the four firfl Obfervations, and the Rings about this Ring were grown equal to the Rings about that refpedtively j the diftance between the two beams of Light and the Diameter of the white Ring ( which was now become the third Ring ) being about 3 Inches.
The Colours of the Rings in the middle be- gan now to grow very dilute, and if the di- ftance between the two Beams was increafed half an Inch, or an Inch more, they vanifh'd whilfl the white Ring, with one or two of the Rings next it on either fide, continued ftill vi- able. But if the diftance of the two beams of Light was ftill more increafed, thefe alfo va- . nifhed: For the Light which coming from fe- veral parts of the hole in the Window fell up- on the Speculum in feveral Angles of Incidence, made Rings of feveral bigneffes, which diluted and blotted out one another, as I knew by inter- cepting fome part of that Light. For if I in- tercepted that part which was neareft to the Axis of the Speculum the Ring's would be lefs, if the other part which was remoteft from it they would be bigger.
Obf. 12. When the Colours of the Prifm were caft fucceffively on the Speculum, that Ring which in the two laft Obfervations was white, was of the fame bignefs in all the Co- lours, but the Rings without it were greater in the green than in the blue, and ftill greater in the yellow, and greateft in the red. And, on the contrary, the Rings within that white Circle were lefs in the green than in the blue, and ftill
lefs
BOOK II. 287
lefs in the yellow, and leaft in the red. For the Angles of Reflexion of thofe Rays which made this Ring, being equal to their Angles of Inci- dence, the Fits of every reflected Ray within the Glafs after Reflexion are equal in length and number to the Fits of the fame Ray with- in the Glafs before its Incidence on the refled:- ing Surface. And therefore flnce all the Rays of all forts at their entrance into the Glafs were in a Fit of Tranfmiffion, they were alfo in a Fit of Tranfmiflion at their returning to the fame Surface after Reflexion j and by confequence were tranfmitted, and went out to the white Ring on the Chart. This is the reafon why that Ring was of the fame bignefs in all the Co- lours, and why in a mixture of all it appears white. But in Rays which are reflefted in o- ther Angles, the Intervals of the Fits of the leaft refrangible being greateft, make the Rings of their Colour in their progrefs from this white Ring, either outwards or inwards, increafe or decreafe by the greateft fteps ; fo that the Rings of this Colour without are greateft, and within leaft. And this is the reafon why in the laft Obfervation, when the Speculum was illumina- ted with white Light, the exterior Rings made by all Colours appeared red without and blue within, and the interior blue without ^nd red within.
Thefe. are the Pha?nomena of thick convexo- concave Plates of Glafs, which are every where of the fame thicknefs. There are yet other Phaenomena when thefe Plates are a little thick- er on one fide than on the other, and others
when
288 O P T I C K S.
when the Plates are more or lefs concave than convex, or plano-convex, or double-convex. For in all thefe cafes the Plates make Rings of Co- lours, but after various manners; all which, fo far as I have yet obferved, follow from the Pro- pofitions in the end of the third part of this Book, and fo confpire to confirm the truth of thofe Propofitions. But the Phaenomeiia are too various, and the Calculations whereby they follow from thofe Proportions too intricate to be here profecuted. I content my felf with ha- ving profecuted this kind of Phaenomena fo far -as to difcover their Caufe, and by difcovering it to ratify the Propofitions in the third Part of this Book.
Obf. 13. As Light reflecSled by a Lens quick- iilver'd on the backfide makes the Rings of Co- lours above defcribed, fo it ought to make the like Rings of Colours in pafling through a drop of Water. At the firft Reflexion of the Rays within the drop, fome Colours ought to be tranfmitted, as in the cafe of aj^ens, and others to be refie(^l:ed back to the Eye. For inftance, if the Diameter of a fmall drop or globule of "Water be about the 500th part of an Inch, fo that a red-making Ray in paffing through the middle of this globule has 250 Fits of eafy Tranlhiifiion within the globule, and that all the red-making Rays which are at a certain di- ftance from this middle Ray round about it have 249 Fits within the globule, and all the like Rays at a certain farther diftance found a- bout it have 248 Fits, and all thofe at a cer- tain farther diftance 247 Fits, and fo on; thefe
concern-
BOOK II. 2S9
concentrick Cirdes of Rays after their tranf- miiTion, falling on a white Paper, will make concentrick Rings of red upon the Paper, fup- pofing the Light .which pafles through one An- gle globule, llrong enough to be fenlible. And, in like manner, the Rays of other Colours will make Rings of other Colours. Suppole now that in a fair Day the Sun ihines through a thin Cloud of fuch globules of Water or Hail, and that the globules are all of the fame bignefs; and the Sun feen through this Cloud fhall ap- pear encompaffed with the like concentrick Rings of Colours, and the Diameter of the firfl: Ring of red fliall be 7 1. Degrees, that of the fe- cond 10 i Degrees, that of the third 12 Degrees 33 Minutes. And accordingly as the Globules of Water are bigger or lefs, the Rings lliall be lefs or bigger. This is the Theory, and Expe- rience anfwers it. For in 'jiuh; 1692, I faw by reflexion in a Veflel of ftagnating Water three Halos, Crowns, or Rings of Colours about the Sun, like three little Rain-bows, concentrick to his Body. The Colours of the firft or In- nermoft Crown were blue next the Sun, red without, and white in the middle between the blue and red. Thofe of the fecond Crown were purple and blue within, and pale red with- out, and green in the middle. And thofe of the third were pale blue within, and pale red without; thefs Crowns enclofed one another immediately , fo that their Colours proceeded in this continual order from the Sun outward: blue, white, red 3 purple, blue, green, pale
U yello;v
290 O P T I C K S.
yellow and red j pale blue, paid red. The Di- ameter of the fecond Crown meafured from the middle of the yellow and red on one fide of the Sun, to the middle of the fame Colour on the other fide was gr Degrees, or therea- bouts. The Diameters of the firfl and third 1 had not time to meafure, but that of the firfl feemed to be about five or fix Degrees, and that of the third about twelve. The like Crov/ns appear fometimes about the Moon; for in the beginning of the Year 1664, Fel?r, 19th at Night, I faw two fuch Crowns about her. The Diameter of the firfi: or innermoft was about three Degrees, and that of the fe- cond about five Degrees and an half Next a- bout the Moon was a Circle of white, and next about that the inner Crown, which was of a bluifli green within next the white, and of a yellow and red without, and next about thefe Colours were blue and green on the infide of the outward Crown, and red on the outfide of it. At the fame time there appear'd a Halo a- bout 22 Degrees 35' diftant from the center of the Moon. It was elliptical, and its long Dia- meter was perpendicular to the Horizon, verg- ing belovv farthefk from the Moon. I am told that the Moon has fometimes three or more concentrick Crowns of Colours encompafiing one another next about her Body. The more equal the globules of Water or Ice are to one another, the more Crowns of Colours will ap- pear, and the Colours will be the more lively. The Halo at the diilance of 22t Degrees from
the
BOOK
IL 291
By its beino; oval
the Moon is of another fort, and remoter from the Moon beiow than above, I conclude, that it v^cis made by Refradlion in fome fort of Hail or Snow floating in the Air in an horizontal pofture, the refra<5ting Angle being about 58 or 60 Degrees.
U 2
THE
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THE
THIRD BOOK
O F
OPTICKS
PART 1.
Ohfervations concerning the Inflexions of the Rays of Lights and the Colours made thereby.
RIMALDO has inform'd us, that if a beam of the Sun's Light be let in- to a dark Room through a very fmall hole, the Shadows of things in this Light will be larger than they ought to be if the Rays went on by the Bodies in ilrait Lines,
and
BOOK III. 293
and 'that thefe Shadows have three parallel Fringes, Bands or Ranks of colour'd Light ad- jacent to them. Rut if the Hole be enlarged the Fringes grow broad and run into one ano- ther, fo that they cannot be diftinguifh'd. Thefe broad Shadows 'and Fringes have been reckon'd by fome to proceed from the ordinary refra6tion of the Air, but without due examination of the Matter. For the circumftances of the Phano- nienon, fo far as I have obferved them, are as follows.
Obf. I. I made in a piece of Lead a fmall Hole with a Pin, whofe breadth was the 42d part of an Inch. For 2 1 of thofe Pins laid to- gether took up the breadth of half an Inch. Through this Hole I let into my darken'd Chamber a beam of the Sun's Light, and found that the Shadows of Hairs, Thred, Pins, Straws, and fuch like flender Subftances placed in this beam of Light, were confiderably broader than they ought to be, if the Rays of Light pa fled on by thefe Bodies in right Lines. And parti- cularly a Hair of a Man's Head, whofe breadth was but the 280th part of an Inch, being held in this Light, at the diftance of about twelve Feet from the Hole, did caft a Shadow which at the diftance of four Inches from the Hair was the fixtieth part of an Inch broad, that is, above " four times broader than the Hair, ' and at the di- ftance of two Feet from the Hair Vs^as about the eight and twentieth part of an Inch broad, that is, ten times broader than the Hair, and at the diftance of ten Feet was the eighth part of an Inch bsoad, that is 35 times broader,
U 3 Nor
294 O P T I C K S.
Nor is it material whether the Hair be en- compaffed with Air, or with any other pellucid Subllance. For I wetted a polifli'd Plate of Glafs, and laid the Hair in the Water upon the Glafs, and. then laying another polifli'd Plate of Glafs upon it, fo that the Water* might fill up the fpace between the GlafTes, I held them in the aforefaid beam of Light, fo that the Light might pafs through them perpendicularly, and the Shadow of the Hair was at the fame di- flances as big as before. The Shadows of Scratches made in polifh'd Plates of Glafs were alfo much broader than they ought to be, and the Veins In polifh'd Plates of Glafs did alfo caft* the like broad Shadows. And therefore the great breadth of thefe Shadows proceeds from feme other caufe than the" Refraction of the Air.
Let the Circle X [in Fig. i.] reprefent the middle of the Hair; ADG, BEH, CFI, three Rays pafTmg by one fide of the Hair at feveral diflances ; KNQ^LOR, MPS, three other Rays paffmg by the other fide of the Hair at the like diflancesj D, E, F, and N, O, P, the places where the Rays are bent in their paf- fage by the Hair j G, H, I, and Q^, S, the places where the Rays fall on a Paper GQ^ I S the breadth of the Shadow of the Hair cafl on the Paper, and TI, VS, two Rays paffing to the Points 1 and S without bending when the Hair is taken away. And it's manifefl that all the Light between thefe two Rays TI and VS is bent in paffmg by the Hair, and turned alide from the Shadow I S, becaufe if any part
cf
BOOK III. 295
of this Light were not bent it would fall on the Paper within the Shadow, and there illuminaie the Paper, contrary to experience. And becaufe when the Paper is at a great diftance from the Hair, the Shadow is broad, and ■ therefore the Rays TI and VS are *at a great diftance from one another, it follows that the Hair ads unon the Rays of Light at a good diltance in their paf- fing by it. But the Action is frrongeft on the Rays which pafs by at leaft^ diflances, and grows weaker and weaker accordingly as the Rays pafs by at diftances greater and greater, as is reprefented in the Scheme : For thence it comes to pafs, that the Shadow of the Hair is much broader in proportion to the diflance of the Paper from the Hair, when the Paper is nearer the Hair, than when it is at a great diftance from it.
0I?j:2. The Shadov/s of all Bodies (Metals, Stones, Glafs, Wood, Horn, Ice, &c. ) in this Light were border'd with three Parallel Fringes or Bands of coloured Light, whereof that which was contiguous to the Shadow was broadeft and moft luminous, and that which was remo- teft from it was narroweft, and fo faint, ^ as not eafily to be vifible. It v/as difficult to diftinguiili the Colours, unlefs when the Light fell very ob- liquely/upon a fmooth Pap:-r, or fome other fmooth white Body, fo as to make them appear much broader than they would otherwife do. And then the Colours were plainly vifible in this Order: The tirft or innermoft Fringe wViS violet and deep blue next the Shadow, and then light blue, green, and yellow in the middle, ai :d
U 4 .r^^d
2o6 O P T I C K S.
red without. The fecond Fringe was almoft contiguous to the firft, and the third to the fe- cond, and both were blue within, and yellow and red without, but their Colc^rs were very faint, cfpecially thofe of the third. The Colours there- fore proceeded in this order from the Shadow ; violet, indigo, pale blue, green, yellow, red ; blue, yellow, red; pale blue, pale yellow and red. The Shadows made by Scratches and Bubbles in polifh'd Plates of Glafs were bor- der'd with the like Fringes of colour'd Light. And if Plates of Looking-glafs floop'd off near the edges with a Diamond-cut, be held in the fame beam of Light, the Light which paffes through the parallel Planes of the Glafs will be border'd with the like Fringes of Colours where thofe Planes meet with the Diamond-cut, and by this means there will fometimes appear four or five Fringes of Colours. Let AB, CD [in Vig. 2.] reprefent the parallel Planes of a Look- ing-glafs, and B D the Plane of the Diamond- cut, making at B a very obtufe Angle with the Plane AB. And let all the Light between the Rays ENI and FBM pafs diredly through the parallel Planes of the Glafs, and fall upon the Paper between I and M, and all the Light be- tween the Rays GO and HD be refraded by the oblique Plane of the Diamond-cut BD, and fall upon the Paper between K and L; and the Light which paffes diredly through the parallel Planes of the Glafs, and falls upon the Paper between I and M, will be border'd with three or more Fringes at M.
So
BOOK III. 297
So by looking on the Syn through a Feather or black Rifcband held clofe to the Eye, feveral Rain-bows will appear j the Shadows which the Fibres or Threds caft on the T'unica Retina^ being border'd wi^h' the like Fringes of Co- lours.
^kf'Z' When the Hair was twelve Feet diftant from this Hole, and its Shadow fell obliquely upon a flat white Scale of Inches and Parts of an Inch placed half a Foot beyond it, and alfo when the Shadow fell perpendicularly upon the fame Scale placed nine Feet beyond it j I meafured the breadth of the Shadow and Fringes as accu- rately as I could, and found them in Parts of an Inch as follows.
The
298
O P T I C K S.
At tloe I)iftance of |
hcAf a Foot |
Nine Feet I 9 |
The breadth of tliC Shadow |
1 |
|
The breadth between the Middles of the brightefl Light of the in- nermofl Fringes oh either fide the Shadow . '^ |
h or ,\ I ^3i |
1 d T I ~l~ r ?T I TT |
The breadth between the Middles of the brightefl Light of the middlemoft Fringes on either fide the Shadow |
||
The breadth between the Middles of the brighteft Light of the outmofl Fringes on either fide the Shadow |
I I |
|
The diflance between the Middles of the brightefl Light of the firfl: and fecond Fringes |
||
The diflance between the Middles of the" brightefl Light of the fe- cond and third Fringes |
I To |
|
The breadth of the luminous Part (green, white, yellow, and red) of tiie firfl Fringe |
1 70 |
|
The bread tlx oi tne darker bpact between the firfl and fecond Fringes |
I 140 |
|
The breadcli of the luminous Pan of the fecond Fringe |
27^ |
|
The breadth ot the darker Space between the fecond and third Fringes |
T4~ |
Tiiefe
BOOK III. 299
Thefe Meafures I took by letting the Shadow of the Hair, at half a Foot diflance, fall fo ob- liquely on the Scale, as to appear twelve times broader than when it fell perpendicularly on it atthe fame diftance, and fetting down in this Table the twelfth part of the Meafures I then took.
ObC. 4. When the Shadow and Fringes were caft obliquely upon a fmooth white Body, and that Body was removed farther and farther from the Hair, the firft Fringe began to appear and look brighter than the reft of the Light at the diftance of lefs than a quarter of an Inch from the Hair, and the dark Line or Shadow between that and the fecond Fringe began to appear at a lefs diftance from the Hair than that of the third part of an Inch. The fecond Fringe began to appear at a diftance from the Hair of lefs than half an Inch, oand the Shadow between that and the third Fringe at a diftance lefs than ail Inch, and the third Fringe at a diftance lefs than three Inches. At greater diftances they became much more fenlible, but kept very nearly the fame proportion of their breadths and intervals which they had at their firft ap- pearing. For the diftance between ♦ the middle of the firft, and middle of the fecond Fringe, was to the diftance between the middle of the fecond and middle of the third Fringe, as three to two, or ten to feven. And the laft of thefe two diftances was equal to the breadth of the bright Light or luniinous part of the firft Fringe. And this breadth was to the breadth of the bright Light of the fecond Fringe as feven to
four,
30O O P T I C K S.
four, and to the dark Interval of the firft and fecond Fringe as three to two, and to the like dark Interval between the fecond and third as two to one. For the breadths of the Fringes feem'd to be in the progreffion of the Numbers I) v^i v^l, and their Intervals to be in the fame progreffion with them j that is, the Frin- ges and their kitervals together to be in the continual progreffion of the Numbers i, /?, /f, </!, v'i-, or thereabouts. And thefe Proportions held the fame very nearly at all diftances from the Hair ; the dark Intervals of the Fringes be- ing as broad in proportion to the breadth of the Fringes at their firil appearance as afterwards at great dillances from the Hair, though not fo dark and diftind:. •
Obf. 5. The Sun fhining into my darken'd Chamber through a hole a quarter of an Inch broad, I placed at the diilance of two or three Feet from the Hole a Sheet of Pafteboard, which was black'd all over on both fides, and in the middle of it had a hole about^ three quarters of an Inch fquare for the Light to pafs through. And behind the hole I faften'd to the Palte- board with Pitch the blade of a ffiarp Knife, to intercept fome part of the Light which paffied through the hole. The Planes of the Pafte- board and blade of the Knife were parallel to one another, and perpendicular to the Rays. And when they w^re fo placed that none of the Sun's Light fell on the Pafteboard, but all of it pafied through the h.ole'to t*he Knife, and there part of it fell upon the blade of the Knife, and part of it paifed by its edge j I let this part of
the
BOOK III. 301 '
the Light which paiTed by, fall on a white Pa- per two or three Feet beyond the Knife, and there faw two ftreams of faint Light fhoot out both ways from the beam of Light into the flia- dow, like the Tails of Comets. But becaufe the Sun's dired: Light by its brightnefs upon the Paper obfcured thefe faint ftreams, fo that I could fcarce fee them, I made a little hole in the midft of the Paper for that Light to pafs through and fall on a black Cloth behind it ; and then I faw the two ftreams plainly. They were like one another, and pretty nearly equal in length, and breadth, and quantity of Light. Their Light at that end next the Sun's direct Light was pretty ftrong for the fpace of about a quarter of an Inch, or half an Lich, and in all * its progrefs from that direct Light decreafed gradually till it became infenfible. The whole length of either of thefe ftreams meafured up- on the Paper at the diftance of three Feet from the Knife was about fix or eight Inches ; fo that it fubtended an Angle at the edge of the Knife of about 10 or 12, or at moft 14 Degrees. Yet fometimes I thought I faw it ftioot three or four Degrees farther, but with a Light fo very faint that I could fcarce perceive it, and fufpe(5ted it might ( in fome meafure at leaft ) arife from fome other caufe than the two ftreams did. For placing my Eye in that Light beyond the end of that ftream which was behind the Knife, and looking towards the Knife, I could fee a line of ^ • Light upon its edge, and that not only when my Eye was in the line cf the Streams, but al- fo when it was without that line either towards
the
302 O P T I C K S.
the point of the Knife, or towards the handle. This line of Light appear'd contiguous to the edge of the Knife, and was narrower than the Light of the innermofl Fringe, and narroweft when my Eye was fartheft from the dired: Light, and therefore feem'd to pafs between the Light of that Fringe and the edge of the Knife, and that which palTed nearefl the edge to be mofl . bent, though not all of it.
Ohf. 6. I placed another Knife by this, fo that their edges might be parallel, and look to- wards one another, and that the beam of Light might fall upon both the Knives, and fome part of it pafs between their edges. And when the diflance of their edges was about the 400th part of an Inch, the ftream pjlrted in the mid- ^ die, and left a Shadow between the two parts. This Shadow was fo black and dark that all the Light which pafTed between the Knives feem'd to be bent, and turn'd afide to the one. hand or to the other. And as the Knives ftill approach'd one another the Shadow grew broader, and the ftreams ihorter at their inward ends which were next the Shadow, until upon the contad; of the Knives the whole Light vahilh'd, leaving its place to the Shadow.
And hence I gather that the Light which is leaft bent, and goes to the inward ends of the ftreams, palTes by the edges of the Knives at the greatefh diftance, and this diflance when the Shadow begins to appear between the ftreams, is about the Sooth part of an Inch. And the Light which paffes by the edges of the Knives at diftances ftill lefs and lefs, is more and
more
BOOK III. 303
more bent, and goes ta thofe parts of the ftreams which are farther and farther from the diredt Light; becaufe when the Knives approach one another till they touch, thofe parts of the ftreams vanifti laft v/hich are fartheil from the dired Light.
Obf. 7. In the fifth Obfervation the Fringes did not appear, but by reafon of the breadth of the hole in the Window became fo broad as to run into one another, and by joining, to rriake one continued Light in the beginning of the ftreams. But in the fixth, as the Knives approached one another, a little before the Shadow appeared between- the two ftreams, the Fringes began to appear on the inner ends of the Streams on either fide of the dired: Light ; three on one fide made by the edge of one Knife, and three on the other fide made by the edge of the o- ther Knife. They Were diftindeft when the Knives were placed at the greateft diftance from the hole in the Window, and ftill became more diftind: by making the hole lefs, infomuch that I could fometimes fee a faint lineament of a fourth Fringe beyond the three above men- tion'd. ' And as the Knives continually ap- proach'd one another, the Fringes grew di- ftinder and larger, until they vanifh'd. The outmoft Fringe vanifli'd firft, and the middle- moft next, and the innermoft laft. And after they were all vanifh'd', and the line of Light which was in the middle between them was grown very broad, enlarging it felf on both fides into the ftreams of Light defcribed in the fifth" Obfervation, the above-rnention'd Shadow be-
.1 ■ gan
304- O P T I C K S.
gan to appear in the middle of this line, and divide it along the middle into two lines of Li^ht, and increafed until the whole Light va- nilh'd. This enlargement of the Fringes was fo great that the Rays which go to the inner- moft Fringe feem'd ' to be bent above twenty • times more v/hen this Fringe was ready to va- nifh, than when one of the Knives was taken away.
And from this and the former Obfervation compared, I gather, that the Light of the firffc Fringe pafTed by the edge of the Knife at a di- flance greater than the Sooth part of an Inch, and the Light of the fecond Fringe paiTed by the edge of the Knife at a greater diftance than the Light of the firft Fringe did, and that of the third at a greater diftance than that of the fecond, and that of the ftreams of Light defcri- bed in the fifth and fixth Obfervations pafTed by the edsies of the Knives at lefs diftances than that of any of the Fringes.
Obf. 8. I caufed the edges of two Knives to be ground truly ftrait, and pricking their points into a Board fo that their edges might look towards one another, and meeting near their, points contain a redtilinear Angle, I faften'd their Handles together with Pitch to make this Angle invariable. The diftance of the edges of the Knives from one another at the diltance of four Inches from the angular Point, where the edges of the Knives met, was the eight;: part of an Inch j and therefore the Angle contain'd ' by the edges was about one Degree 54'. The Knives thus fix'd together I placed in a beam
of
BOOK III. 305
of the Sun's Light, let into my darken'd Cham- ber through a Hole the 420! Part of an Inch wide, at the diftance of 10 or 15 Feet from the Hole, and let the Light which pafled between their edges fall very obliquely upon a fmooth white Ruler at the diftance of half an Inch, or an Inch from the Knives, and there faw the Fringes by the two edges of the Knives run along the edges of the Shadows of the Knives in Lines parallel to thofe edges without growing fenfibly broader, till they met in Angles equal to the Angle contained by the edges of the Knives, ai d where they met and joined they ended without croffing one another. But if the Ruler was held at a much greater diftance from the Knives, the Fringes w^here they were firther from the Place of their Meeting, were a little narrower, and became fomething broader and broader as they approach'd nearer and nearer to one another, and after they met tiiey crofs'd one another, and then became much broader than before.
Whence I gather that the diftances at which the Fringes pafs by the Knives are not increafed nor alter'd by the approach of the Knives, but the Angles in whicli the Rays are there bent are much increafed by that approach ; and that the Knife which is neareli any Ray determines which way the Ray ftiall be bent, and the other Knife increafes the bent.
Obf, 9. When the Rays fell very obliquely upon the Ruler at the diftance of the third Part, of an Inch from the Knives, the dark Line be- tween the firft and fecond Fringe of the Sha-
X dow
3o6 O P T I C K S.
dow of one Knife, and the dark Line between the firft and fecond Fringe of the Shadow of the other Knife met with one another, at the diftance of the fifth Part of an Inch from th« end of the Light which pafTed between the Knives at the concourfe of their edges. And therefore the diftance of the edges of the Knives at the meeting of thefe dark Lines was the i6oth Part of an Inch. For as four Inches to the eighth Part of an Inch, fo is any Length of the edges of the Knives meafured from the point of their concourfe to the diftance of the edges of the Knives at the end of that Length, and fo is the fifth Part of an Inch to the i6oth Fart. So then the dark Lines above-mention'd meet in the middle of the Light which pafTes be- tween the Knives where they are diftant the i6oth Part of an Inch, and the one half of that Light pafles by the edge of one Knife at a di- ftance not greater than the 320th Part of an Inch, and falling upon the Paper makes the Fringes of the Shadow of that Knife, and the other half pafies by the edge of the other Knife, at a diftance not greater than the 320th Part of an Inch, and falling upon the Paper makes the Fringes of the Shadow of the other Knife. But if the Paper be held at a diftance from the Knives greater than the third Part of an Inch, the dark Lines above-mention'd meet at a greater diftance than the fifth Part of an Inch from the end of the Light which pafTed between the Knives at the concourfe of their edges ; and therefore the Light which falls upon the Paper where thofe dark Lines meet pafles between the .
Knives
BOOK III.
307
Knives where the edges are diftant above the 160th part of an Inch.
For at another time, when the two Knives were diltant eigiit Feet and five Inches from the little hole in the Window, made with a fmall Pin as above, the Light which fell upon the Pa- per where the aforefaid dark lines met, paffed between the Knives, where the dillance between their edges was as in the following Table, w^hen the diftance of the Paper from the Knives was alfo as follows.
Dijiaiices of the Paper from the Knhes i}i Inches. |
Dijtances betixeen . the edges of the Kfiizrs in millefmal parts of an Inch. |
. 3i- 32. 96. 131- |
o'oi2 0'020 •^ o'o34 ■ o'o^7 o'oSi o'oS/ |
And hence I gather, that the Light which makes the Fringes upon the Paper is not the fame Light at all diftances of the Paper from the Knives, but when the Paper is held near the Knives, the Fringes are made by Light which pafTes by the edges of the Knives at a lefs diftance, and is more bent than when the Paper is held at a greater diftance from the Knives.
X 2
Obf
3o8 OPTIC K S.
Obf. 10. When the Fringes of the Shadows of the Knives fell perpendicularly upon a Paper at a great diftance from the Knives, they'w^ere in the form of Hyperbola's, and their Dimen- fions were as follows. Let CA, CB [in Fig. 3.] reprefent Lines drawn upon the Paper parallel to the edges of the Knives, and between which all the Light would fall, if it pafled between the edges of the Knives without inflexion ; DE a Right Line drawn through C making the An- gles A CD, BCE, equal to one another, and terminating all 'the Light which falls upon the Paper from the point where the edges of the Knives meet; eisy fkt^ and glv^ three hyper- bolical Lines reprefenting the Terminus of the Shadow of one of the Knives, the dark Line between the firft and fecond Fringes of that Shadow, and the dark Line between the fecond and third Fringes of the fame Shadow ; xip, ykq, and z/r, three other hyperbolical Lines repre- fenting the Terminus of the Shadow of the other Knife, the dark Line between the firfl and fecond Fringes of that Shadow, and the dark line be- tween the fecond and third Fringes of the fame Shadow. And conceive that thefe three Hyper- bola's are like and equal to the former three, and crofs them in the points /', i, and /, and that the Shadows of the Knives are terminated and diflin- guifh'd from the lirft luminous Fringes by the lines e i s and x ip, until the meeting and crof- fmg of the Fringes, and then thofe lines crofs the Fringes in the form of dark lines, termina- ting the firft luminous Fringes within fide, and diftinguifhing them from another Light which
begins
BOOK III. 309
begins to appear at /, and illuminates all the triangular fpace /j^DEj. comprehended by thefe dark lines, and the right line DE. Of thefe Hyperbola's one Afymptote is the line DE, and their other Afymptotes are parallel to the lines C A and C B. Let r 'v reprefent a line drawn any where upon the Paper parallel to the Afym- ptote DE, and let this line crofs the right lines AC in w, and B C in «, and the fix dark hy- perbolical lines in />, ^, ^ 3 J, ^, i' ; and by mea- suring the diftances /) J, gt, r'-j, and thence collecting the lengths of the Ordinates n p, n q^ nr or m s^ m /, m v^ and doing this at feveral diftances of the line r v from the Afymptote DD, you may find as many points of thefe Hyperbo- la's as you pleafe, and thereby know that thefe curve lines are Hyperbola's differing little from the conical Hyperbola. And by meafuring the lines C /, C k, C /, you may find other points of thefe Curves.
For inftance; when the Knives were diftant from the hole in the Window ten Feet, and the Paper from the Knives nine Feet, and the An- gle contained by the edges of the Knives to which the Angle ACBis equal, was fubtend- ed by a Chord which was to the Radius as i to 32, and the diftance of the line rv from the Afymptote DE was half an Inch: I meafured the lines pSy qt, rv, and found them 0*35, o'65, o'98 Inches refped;ively ; and by adding to their halfs the line r m n^ ( w^hich here was the 128th part of an Inch, or 0*0078 Inches,) the Sums «^, nq^nVy were o' 1828, ©'3328, 0*4978 Inches. I meafured alfo the diftances of the
X 3 brighteft
3IO O P T I C K S.
brightefl parts of the Fringes which run between fq and st, qr and t 'U, and next beyond r and 'u> and found them o'5, o'B, and iij Inches.
Obf. II. The Sun fhining into my darkened Room through a fmall round hole made in a Plate of Lead with a flender Pin, as above ; I placed at the hole a Prifm to refrad the Light, and form on the oppofite Wall the Spedtrum of Colours, defcribed in the third Experiment of the firft Book. And then I found that the Shadows of all Bodies held in the colour'd Light between the Prifm and the Wall, were border'd with Fringes of the Colour of that Light in which they were held. In the full red Light they were totally red without any fenfi- ble blue or violet, and in tiie deep blue Light they were totally blue without any fenfible red or yellow ; and fo in the green Light they were totally green, excepting a little yellow and blue, which were mixed .in the green Light of the Prifm. And comparing the Fringes made in the feveral colour'd Lights, I found that thofe made in the red Light were largeft, thofe made in the violet were leail, and thofe made -in the green Vv^ere of a middle bignefs. For the Fringes with which the Siradow of a Man's Hair were bordered, being meafured crofs the Shadow at the diftance of fix Liches from the Hair, the diflance between the middle and moil; luminous part of the iirfl or innermoft Fringe on one. fide of the Shadow, and that of the like Fringe on the other iide of the Shadow, was in
the full red Lieht -~ of an Inch, and in the full
violet
BOOK III. 311
violet ?V. And the like diftance between the middle and mofl luminous parts of the fecond Fringes on either iide the Shadow was in the full red Light »'=-, and in the violet tV of an Inch. And thefe diftances of the Fringes held the fame proportion at all diftances from the Hair without any fenfible 'variation.
So then the Rays which made thefe Fringes in the red Light paffed by the Hair at a greater diftance than thofe did which made the like Fringes in the violet j and therefore the Hair in caufing thefe Fringes adied alike upon the red Light or leaft refrangible Rays at a greater diftance, and upon the violet or moft refrangi- ble Rays at a lefs diftance, and by thofe adions difpofed the red Li^ht into larger Fringes, and the violet into fmaller, and the Lights of inter- mediate Colours into Fringes of intermediate big- neftes without changing the Colour of any fort of Light.
When therefore the Hair in the firft and fe- cond of thefe Obfervations was held in the white beam of the Sun's Light, and caft a Sha- dow which was border'd with three Fringes of coloured Light, thofe Colours arofe not from any new modifications imprefs'd upon the Rays of Light by the Hair, but only from the vari- ous inflexions whereby the feveral Sorts of Rays were feparated from one another, which before feparation, by the mixture of all their Colours, compofed the white beam of the Sun's Light, but whenever feparated compofe Lights of the feveral Colours which they are originally difpo- fed to exhibit. In this i ithObfervation, where
X 4 the
312 O P T I C K S.
!Dhe Colours are feparated before the Light paf- fes by the Hair, the leaft refrangible Rays, which when feparated from the reft make red, were infleded at a greater diftance from the Hair, fo as to make three red Fringes at a greater di- ftance from the middle of the Shadow of the Hair j and the moft refrangible Rays which when feparated make violet, were inflected at a lefs diftance from the Hair, fo as to make three violet Fringes at a lefs diftance from the middle of the Shadow of the Hair. And other Rays of intermediate degrees of Refrangibility were inflefted at intermediate diftances from the Hair, fo as to make Fringes of intermediate Colours at intermediate diftances from the mid- dle of the Shadow of the Hair. And in the fecond Obfervation, where all the Colours are mix'd in the white Light which pafles by the Hair, thefe Colours are feparated by the vari- ous inflexions of the Rays, and the Fringes which they make appear all together, and the innermoft Fringes being contiguous make on^^ broad Fringe compofed of all the Colours in . due order, the violet lying on the infide of the Frmge next the Shadow, the red on the out- fide fartheft from the Shadow, and the blue, green, and yellow, in the middle. And, in like manner, the middlemoft Fringes of all the Co- lours lying in order, and being contiguous, make another broad Fringe compofed of all the Colours -J and the outm.oft Fringes of all the Colours lying in order, and being contiguous, make a third broad Fringe compofed of all the Colours. Thefe are the three Fringes of co-
lour'd
BOOK III. 313
lour'd Light with which the Shadows of all Bo- dies are border'd in the fecond Cbfervation.
When I made the foregoing Obfervations, I defign'd to repeat moft of thcm.with more care and exadnefs, and to mJike fome new ones for determining the manner how the Rays of Light are bent in their palTage by Bodies, for making the Fringes of Colours with the dark lines be- tween them. But I was then interrupted, and cannot now think of taking thefe things into far- ther Confideration. And fince 1 have not finifh'd this part of my Defign, I fhall conclude with propofing only fome Queries, in order to a far- ther fearch to be made by odiers.
^ery i. Do not Bodies a<5t upon Light at a diltance, and by their action bend irs Raysj and is not this action ( cceteris paribus ) flrongeft at the leaft diftance ?
^. 2. Do not the Rays which differ in Re- frangibility differ alfo in Flexibity j and are they not by their different Inflexions feparatcd from one another, fo as after feparation to niake the Colours in the three Fringes above defer ibed ? And after what manner are they infle(5ted to make thofe Fringes ?
^. 3 Are not the Rays of Light in pafling by the edges and fides of Bodies, bent feveral times backwards and forwards, with a motion like that of an Eel ? And do not the three Frin- ges of colour'd Light above-mention'd arife from three fuch bendings ?
^. 4. Do not the Rays of Light which fall upon Bodies, and are refleded or refraded, be- gin
314 O P T I C K S.
gin to bend before they arrive at the Bodies ; and are they not reflecfled, refrafted, and infledied, by one and the fame Principle, ading varioufly in various Circumftances ?
^. 5. Do not Bodies and Light ad mutually upon one another ; that is to fay. Bodies upon Light in emitting, receding, refrading and in- fleding it, and Light upon Bodies for heating them, and putting their parts into a vibrating motion vs^herein heat confifts ?
^. 6. Do not black Bodies conceive heat more eafily from Light than thofe of other Co- lours do, by reafon that the Light falling on them is not refleded outw^ards, but enters the Bodies, and is often refleded and refraded within them, until it be ftifled and loft ?
^. 7. Is not the ftrength and vigor of the a^ion between Light and fulphureous Bodies ob- ferved above, one reafon why fulphureous Bodies take fire more,readily, and burn more vehement- ly than other Bodies do ?
^. 8. Do not all fix'd Bodies, when heated beyoiifl a certain degree, emit Light and fhine ; and is not this Emiffion perform'd by the vi- brating motions of their parts ? And do not all Bodies which abound with terreflrial parts, and efpecially with fulphureous ones, emit Light as often as thofe parts are fufficiently agitated j whether that agitation be made by Heat, or by Fridicn, or Percuffion, or Putrefadion, or by any vital Motion, or any other Caufe? As for infliance ; Sea- Water in a raging Storm ; Quick- filver agitated in ^jacuo ; the Back of a Cat, or Neck of a Horfe, obliquely ftruck or rubbed in
a dark
BOOK III. 315
a dark place ; Wood, Flefh and Fifli while they putrefy ; Vapours ariling from putrefy 'd Wa- ters, ufually call'd Ignes Fatui ; Stacks of moifl Hay or Corn growing hot by fermentation ; Glcfw-worms and the Eyes of fome Animals by vital Motions J the vulgar Phofphoriis agitated by the attrition of any Body, or by the acid Particles of the Air; Amber and fome Dia- monds by ftriking, preffing or rubbing them; Scrapings of Steel ftruck off with a Flint ; Iron hammer'd very nimbly till it become fo hot as to kindle Sulphur thrown upon it ; the Axle- trees of Chariots taking fire by the rapid rota- tion of the Wheels ; and fome Liquors mix'd with one another whofe Particles come toge- ther with an Impetus, as Oil of Vitriol diftilled from its weight of Nitre, and then mix'd with twice its weight of Oil of Annifeeds. So alfo a Globe of Glafs about 8 or 10 Inches in diameter, being put into a Frame where it may be fwiftly turn'd round its Axis , will in turning fhine where it rubs againft the palm of ones Hand apply 'd to it: And if at the fame time a <^iece of white Paper or white Cloth, or the end of ones Finger be held at the diftance of about a quarter of an Inch or half an Inch from that part of the Glafs where it is mojft in motion, the eled:rick Vapour which is excited by the fri6lion of the Glafs againft the Hand, will by dafhing againft the white Paper, .Cloth or Fin- ger, be put into fuch an agitation as to emit Light, and make the white Paper, Cloth or Fin- ger, appear lucid like a Glow-worm ; and in rufhing out of the Glafs will fometimes pufti
againft
3i6 * O P T I C K S.
againft the Finger fo as to be felt. And the fame things have been found by rubbing a long and large Cylinder of Glafs or Amber with a Paper held in ones hand, and continuing the fridiion till the Glafs grew warm.
^. 9. Is not Fire a Body heated fo hot as to emit Light copioufly? For what elfe is a red hot Iron than Fire? And what elfe is a burning Coal than red hot Wood ?
§u. 10. Is not Flame a Vapour, Fume or Ex- halation heated red hot, that is, fo hot as to fhine ? For Bodies do not flame without emit- ting a copious Fume, and this Fume burns in the Flame. The Igms Fatuus is a Vapour fhi- ning without heat, and is there not the fame difference between this Vapour and Flame, as between rotten Wood fhining without heat and. burning Coals of Fire ? In diftilling hot Spirits, if the Head of the Still be taken off, the Va- pour which afcends out of the Still will take fire at the Flame of a Candle, and turn into Flame, and the Flame will run along the Vapour from the Candle to the Still. Some Bodies heated by Motion or Fermentation, if the heat grow in- renfe, fume copioufly, and if the heat be great enough the Fumes will (liine and become Flame. Metals in fuflon do not flame for want of a co- pious Fume, except Spelter, which fumes co- pioufly, and thereby flames. All flaming Bo- dies, as Oil, Tallow, Wa"^, Wood, foffil Coals, Pitch, Sulphur, by flaming waflie and vanifli in- to burning Smoke, which Smoke, if the Flame be pur out, is very thick and vifible, and fome- times fmells ftrongly, but in the Flame lofes its
fmell
BOOK III. 317
fmell by burning, and according to the nature of the Smoke the Flame is of feveral Colours, as that of Sulphur blue, that of Copper open'd with fublimate green, that of Tallow yellow, that of Camphire white. Smoke paffing through Flame cannot but grow red hot , and red hot Smoke can have no other appearance than that of Flame. When Gun-powder takes fire, it goes away into flaming Smoke. For the Char- coal and Sulphur eafily take fire, and fet fire to the Nitre, and the Spirit of the Nitre being thereby rarified into Vapour , ruflies out with Explofion much after the manner that the Va- pour of Water rufhes out of an ^olipile^ the Sulphur alfo being volatile is converted into Vapour, and augments the Explofion. And the acid Vapour of the Sulphur (namely that which diftils under a Bell into Oil of Sulphur,) entring violently into the fix'd Body of the Ni- tre, fets loofe the Spirit of the Nitre, and ex- cites a great Fermentation, whereby the Heat is farther augmented, and the fix'd Body of the Nitre is alfo rarified into Fume, and the Explo- fion is thereby made more vehement and quick. For if Salt of Tartar be mix'd with Gun-pow- der, and that Mixture be warm'd till it takes fire, the Explofion will be more violent and quick than that of Gun-powder alone; which^ cannot proceed from any other caufe than the action of the Vapour of the Gun-powder upon the Salt of Tartar, whereby that Salt is rarified. The Explofion of Gun-powder arifes therefore from the violent aftion whereby all the Mixture being quickly and vehemently heated, is rarified
r and
3i8 O P T I C K S.
and converted into Fume and Vapour: which Vapour, by the violence of that adiion , be- coming fo hot as to fhine, appears in the form of Flame.
^. 1 1. Do not great Bodies conferve their heat the longeft, their parts heating one ano- ther, and may not great denfe and fix'd Bo- dies, when heated beyond a certain degree, e- mit Light fo copioufly, as by the Emilfion and Re-a6tion of its Light, and the Reflexions and Refradions of its Rays within its Pores to grow ilill hotter, till it comes to a certain period of heat, fuch as is that of the Sun ? And are not the Sun and fix'd Stars great Earths vehemently hot, whofe heat is conferved by the greatnef^ of the Bodies, and the mutual Adiion and Re- action between them, and the Light which they emit, and whofe parts are kept from fuming a- way, not only by their fixity, but alfo by the vaft weight and denfity of the Atmofpheres in- cumbent upon them ; and very ftrongly com- preffing them, and condenfing the Vapours and Exhalations which arife from them? For if Water be made warm in any pellucid Veflel emptied of Air, that Water in the Vacuum will bubble and boil as vehemently as it would in the open xAir in a Veffel fet upon the Fire till it conceives a much greater heat. For the weight of the incumbent Atmofphere keeps down the Vapours, and hinders the Water from boiling, until it grow much hotter than is re- quifite to make it boil in vacuo. Alfo a mix- ture of Tin and Lead being put upon a red hot Iron in vacuo emits a Fume and Flame^ but the 3 fame
BOOK III. 319
fame Mixture in the open Air, by reafon of the incumbent Atmofphere, does not fo much as e- mit any Fume which can be perceived by Sight. In like manner the great weight of the Atmo- fphere which lies upon the Globe of the Sun may hinder Bqdies there from riling up and going away from the Sun in the form of Va- pours and Fumes, unlefs by means of a far greater heat than that which on the Surface of our Earth would very eafily turn them into Va- pours and Fumes. And the fime great weight may condenfe thofe Vapours and Exhalations as foon as they fliall at any time begin to afcend from the Sun, and make them prefently fall back again into him, and by that adion increafe his Pleat much after the manner that in our Earth the Air increafes the Heat of a culinary Fire. And the fame weight may hinder the Globe of the Sun from being diminifh'd, unlefs by the Emiflion of Light, and a very fmall quan- tity of Vapours and Exhalations.
%/. 12. Do not the Rays of Light in falling upon the bottom of the Eye excite Vibrations in the Tunica Retina? Which Vibrations, be- ing propagated along the folid Fibres of the op- tick Nerves into the Brain, caufe the Senfe of feeing. For becaufe denfe Bodies conferve their Heat a long time, and the denfeft Bodies con- ferve their Heat the longeft, the Vibrations of their parts are of a lalling nature, and there- fore may be propagated along folid Fibres of uniform denfe Matter to a great diftance, for conveying into the Brain the impreffions made upon all the Organs of Senfe. For that Motion
which
320 O P T I C K S.
which can continue long in one and the fame part of a Body, can be propagated a long way from one part to another, fuppofing the Body homo- geneal, fo that the Motion may not be refleded, reffaded, interrupted or diforder'd by any un- evennefs of the Body.
^. 13. Do not feveral forts of Rays make Vibrations of feveral |)ignefres, which according to their bignelfes excite Senfations of feveral Co- lours, much after the manner that the Vibrations of the Air, according to their feveral bignelfes excite Senfations of feveral Sounds ? And parti- cularly do not the moft refrangible Rays excite the fhorteft Vibrations for making a Senfation of deep violet, the leafl refrangible the largeft for making a Senfation of deep red, and the feveral intermediate forts of Rays, Vibrations of feveral intermediate bigneffes to make Senfations of the feveral intermediate Colours ?
^. 14. May not the harmony and difcord of Colours arife from the proportions of the Vibra- tions propagated through the Fibres of the op- tick Nerves into the Brain, as the harmony and difcord of Sounds arife from the proportions of the Vibrations of the Air? For fome Colours, if they be view'd together, are agreeable to one another, as thofe of Gold and Indigo, and others difagree.
^i. 15. Are not the Species of Objedls feen with both Eyes united where the optick Nerves meet before they come into the Brain, the Fi- bres on the right fide of both Nerves uniting there, and after union going thence into the Brain in the Nerve whicji is on the right fide of
thq
BOOK III. .21
the Head, and the Fibres on the left fide of both Nerves uniting in the fame place, and af- ter union going into the Brain in the Nerve which is on the left fide of the Head, and thefe tw^o Nerves meeting in the Brain in fuch a man- ner that their Fibres make but one entire Spe- cies or Pidure, half of which on the right fide of the Senforium comes from the right fide of both Eyes through the right fide of both op- tick Nerves to the place where the Nerves meet, end from thence on the right fide of the Head into the Brain, and the other half on the left fide of the Senforium comes in like manner from the left fide of both Eyes. For the op tick Nerves of fuch Animals as look the fame way with both Eyes (as of Men, Dogs, Sheep, Oxen, &c\) meet before they come into the Brain, but the optick Nerves of fuch Animals as do not look the fame way with both Eyes (as of Fifiics, and of the Chameleon,) do not meet, if I am rightly inform'd.
^. 1 6. When a Man in the dark prefTes either corner of his Eye with his Finger, and turns his Eye away from his Finger, he will fee a Circle of Colours like thofe in the Feather of a Pea- cock's Tail. If the Eye and the Finger remain quiet thefe Colours vanifh in a fecond Minute of Time, but if the Finger be moved with a qua- vering Motion they appear again. Do not thefe Colours arife from fuch Motions excited in the bottom of the Eye by the PrelTure and Motion of the Finger, as at other times are excited there by Light for caufing Vifion ? And do not the Motions once excited continue about a Se-
,y cond
322 O P T I C K S.
cond of Time before they ceafe ? And when a Man by a ftroke upon his Eye fees a flafh of Light, are not the Hke Motions excited in the Retina by the ftroke ? And when a Coal of Fire moved nimbly in the circumference of a Cir- cle, makes the whole circumference appear like a Circle of Fire ; is it not becaufe the Motions excited in the bottom of the Eye by the Rays of Light are of a lafting nature, and continue till the Coal of Fire in going round returns to its former place ? And confidering the lafting- nefs of the Motions excited in the bottom of the Eye by Light, are they not of a vibrating nature ?
%/. 17. If a Stone be thrown into ftagnating Water, the Waves excited thereby continue- fome time to arife in the place where the Stone fell into the Water, and are propagated from thence in concentrick Circles upon the Surface of the Water to great diftances. And the Vi- brations or Tremors excited in the Air by per- cuffion, continue a little time to move from the place of percufTion in concentrick Spheres to great diftances. And in like manner, when a Ray of Light falls upon the Surface of any pellucid Body, and is there refra(fted or reflected, may not Waves of Vibrations, or Tremors, be thereby excited in the refracting or reflecfling Medium at the point of Incidence, and continue to arife there, and to be propagated from thence as long as they continue to arife and be propagated, when they are excited in the bottom of the Eye by the Prellure or Motion of the Finger, or by the Light which comes from the Coal of Fire in the Ex- periments.
B o o ic in. 323
perimetits abovemention'd ? and are not thefa Vibrations propagated from the point of Inci- dence to great diltances ? And do they not over- take the Rays of Light, and by overtaking them fucceffively, do they not put them into the Fits of eafy Reflex io.^. and eafy Tranfmiinon defcribed above? For if the Rays endeavour to recede from the denfeft part of the Vibration, they may be ahernately accelerated and retarded by the Vi- brations overtaking them.
%. 18. If in two large tall cylindrical Vef-* fels of Glafs inverted, two little Thermometers be fufpended fo as not to touch the Veffels, and the Air be drawn out of one of thefe Veffels, and thefe Veffels thus prepared be carried out of a cold place into a warm one; the Thermo- meter ift 'Vacuo will grov/ warm as much, and almoft as foon as the Thermometer which is not in vacuo. And when the Veffels are carri- ed back into the cold place, the Thermometer in vacuo will grow cold almofi: as foon as the other Thermometer. Is not th^e Heat of the warm Room convey'd through the Vacuum by the Vibrations of a much fubriler Medium than Air, which after the Air was drawn out remain- ed in the Vacuum f And is not this Medium the fame with that Medium by which Light is re- fracted and refleded, and bv whofe Vibrations Light communicates Heat to Bodies, and is put into Fits of eafy Reflexion and eafy Tranf- miffion ? And do not the Vibrations of this Me-* dium in hot Bodies contribute to the intenfenefs and duration of their Heat ? And do not hot Bodies communicate their Heat to contiguous
y 3 cdld
324 O P T I C K S.
cold ones, by the Vibrations of this Medium propagated from them into the cold ones ? And is not this Medium exceedingly more rare and fubtile than the Air, and exceedingly more ela- ftick and adlive? And doth it not readily per- vade all Bodies? And is it not ( by its elaftick force) expanded through all the Heavens ? .
^. 19. Doth not the Refradtion of Light proceed from the different denfity of this JEzhe- real Medium in different places, the Light re- ceding always from the denfer parts of the Me- dium? And is not the denfity thereof greater in free and open Spaces void of Air and other groffer Bodies, than vi^ithin tjie Pores of Wa- ter,' Glafs, Cryflal, Gems, and other compacfl Bodies? For w^hen Light paffes through Glafs or Cryflal, and falling very obliquely upon the farther Surface thereof is totally refleded, the total Reflexion ought to proceed rather from the denfity and vigour of the Medium w^ithout and beyond the Glafs, than from the rarity and w^eak- nefs thereof
^. 20. Doth not this Ethereal Medium in paffing out of Water, Glafs, Cryflal, and other compad: and denfe Bodies into empty Spaces, grov^ denfer and denfer by degrees, and by that means refraft the Rays of Light nor in a point, but by bending them gradually in curve Lines ? And doth not the gradual condcnfation of this Medium extend to fome diflance from the Bo- dies, and thereby caufe the Inflexions of the Rays of Light, which pafs by the edges of denfe Bodies, at fome diflance from the Bodies ?
^.
BOOK III. 325
^. 21. Is not this Medium much rarer with- in the denfe Bodies of the Sun, Stars, Planets and Comets, than in the empty celeftial Spaces between them ? And in pafling from them to great diftances , doth it not grow denfer and denfer perpetually, and thereby caufe the gra- vity of thofe great Bodies towards one another, and of their parts towards the Bodies; every Body endeavouring to go from the denfer parts of the Medium towards the rarer ? For if this Medium be rarer within the Sun's Body than at its Surface, and rarer there than at the hun- dredth part of an Inch from Its Body, and ra- rer there than at the fiftieth part of an Inch ftom its Body, and rarer there than at the Orb of Saturn, I fee no reafon why the Increafe of denfity fhould flop any where, and not rather be continued through all diftances from the Sun to Saturn^ and beyond. And though this In- creafe of denfity may at great diftances be ex- ceeding flow, yet if the elaftick force of this Medium be exceeding great, it may fufhce to impel Bodies from the denfer parts of the Me- dium towards the rarer , with all that power which we call Gravity. And that the elaflick force of this Medium is exceeding great, may be gather'd from the fwiftnefs of its Vibrations. Sounds move about 1 140 EnMh Feet in a fe- cond Minute of Time, and in feven or eight Minutes of Time they move about one hundred Englijlo Miles. Light moves from t':e Sun to us in about feven or eight Minutes f Time, which diflance is about 70000000 Eng jh Miles, fuppofing the horizontal Parallax of tiic Sun to
Y 3 be
3^6 O P T I C K S,
be about 12". And the Vibrations or Pulfes of this Medium, that they may caufe the akernatc Fits of eafy TraDfiriillion and eafy Reflexion, . muft be fwlJtcr th; n Light, and by confequencc above 700000 amL?. fwiirer.than Sounds. And therefore the eUitick force of this Medium, in proportion to its denfiiy, muft be above 70000Q X 700000 (that is, above 490000000000) times greater than the elaftick force of the Air is in proportion to its deufity. For the Velocities of the Puh'es of ehifticiv Mediums are in a fubdupU^ cate Ratio of the Hlailiciries and the Rarities of the Mediums taken together.
As Attraction is ilronger in fmall Magnets than in great ones in proportion to their Bulk, and Gravity is greater in the Surfaces of fmall Planets than in thofe of great ones in propor- tion to their bulk, and fmall Bodies are agita- ted much more by eledric attradion than great ones J fo the fmallnefs of the Rays of Light may contribute very much to the power of the Agent by which they are refraded. And fo if any one fhould fuppofe that Mther ( like our Air) may contain Particles which endeavour to recede from one another ( for J do not know what this Mther is) and that its Particles are exceedingly fmaller than thofe of Air, or even than thofe of Light: The exceeding fmallnefs of its Particles may contribute to the greatnefs of the force by which thofe Particles may re-, cede from one anqther, and thereby make that Medium exceedingly more rare and elaftick than Air, and by confequence exceedingly lefs able to refift the motions of Projediles, and
exceed-
BOOK III. 327
exceedingly more able to prefs upon grofs Bodies, by endeavouring to expand it lelf.
^/. 22. May not Planets and Comets, and all grofs Bodies, perform their Motions more freely, and with lefs refiftance in this ^Ethereal Medium than in any Fluid, which fills all Space ade- quately without leaving any Pores, and by confe- quence is much denfer than Quick'-lilver or Gold? And may not its refiftance be fo fmall, as to be inconfiderable ? Forinftance; 1£ this Mther (for fo I will call it ) fhould be - fuppofed 700000 times more elaftick than our Air, and above 700000 times more rare j its refiftance would be above 600000000 times lefs than that of Wa- ter. And fo fmall a refiftance would fcarce make any fenfible alteration in the Motions of the Planets in ten thoufand Years. If any one would ask how a Medium can be fo rare, let him tell me how the Air, in the upper parts of the Atmofphere, Qin be above an hundred thou- fand thoufand times rarer than Gold. Let him alfo tell me, how an eledtrick Body can by Fri- ction emit an Exhalation fo rare and fubtile, and yet fo potent, as by its Emiflion to caufe no fenftble Diminution of the weight of the de- rrick Body, and to be expanded through a Sphere, whofe Diameter is above two Feet, and yet to be able to agitate and carry up Leaf Cop- per, or Leaf Gold, at the diftance of above a Foot from the eledrick Body? And how the Effluvia of a Magnet can be fo rare and fubtile, as to pafs through a Plate of Glafs without any Reii- ftance or Diminution of their Force, and vet fo potent as to turn a magnetick Needle beyond the Glafs? y 4 ^,
328 0 P T I C K S.
^/. 23. Is not Vifion perform'd chiefly by the Vibrations of this Medium, excited in, the bot- tom of the Eye by the Rays of Light, and pro- pagated through the folid, pellucid and uniform Capillamenta of the optick Nerves into the place of Senfaticn ? And is not Hearing perform'd by the Vibrations either of this or fome other Medi- um, excited in the auditory Nerves by the Tre- mors of the Air, and propagated through the fo- lid, pellucid and uniform Capillamenta of thofe Nerves into the place of Senfatiofi ? And fo of the other Senfes.
^. 24. Is not Animal Motion perform'd by the Vibrations of this Medium, excited in the Brain by the power of the Will, and propaga- ted from thence through the folid, pellucid and uniform Capillamenta of the Nerves into the Mufcles, for contrad:ing and dilating them ? I fuppofe that the Capillamenta of the Nerves are each of them folid and uniform, that the vibra- ting Motion of the iEthereal Medium may be propagated along them from one e;id to the other uniformly, and w^ithout interruption: For Ob- ftrudions in the Nerves create Palfies. And that they may be Sufficiently uniform , I fuppofe them to be pellucid when view'd fmgly, tho' the Reflexions in their cylindrical Surfaces may make the whole Nerve ( compofed of many Capilla- menta) appear opake and white. For opacity .arifes from reflecting Surfaces, fuch as may di- fturb and interrupt the Motions of this Medium.
^/. 25. Are there not other original Proper- ties of the Rays of Light, befides thofe alrea- dy defcribed ? An inftance of another original
Fro-
BOOK III. 329
Property we have in the Refradion of Illand Cryftal , defcribed firft by Erajmm Bartholine^ and afterwards more exadly by Hugeniin^ in his Book De la Lumiere, This Gryftal is a pel- kicid fiffile Stone, clear as Water or Cryftal of the Rock, and without Colour j enduring a red Heat without lofing its tranfparency, and in a very ftrong Heat calcining without Fufion. Steep'd a Day or two in Water, it lofes its na- tural Polifh. Being rubb'd on Cloth, it attracfls pieces of Straws and other light things, like Am- bar or Glafs; and with Aqua Jortis it makes an Ebullition. It feems to be a fort of Talk, and is found in form of an oblique Parallelopiped, with lix parallelogram Sides and eight folid An- gles. The obtule Angles of the Parallelograms are each of them 10 1 Degrees, and 52 Minutes; the acute ones 78 Degrees and 8 Minutes. Two of the folid Angles oppofite to one another, as C and E, are compalTed each of them with three of thefe obtufe ^'* '/£""" Angles, and each of the other fix with one obtufe and two acute ones. It cleaves eaiily in planes parallel to any of its Sides, and not in any other Planes. It cleaves with a glofly polite Surface not perfectly plane, but with fome little unevennefs. It is eafily fcratch'd, and by reafon of its foftnefs it takes a Polifh very difficultly. It polifhes better upon polifh'd Looking-glafs than upon Metal, and perhaps better upon Pitch, Leather or Parch- ment. Afterwards it muft be rubb'd with a lit- tle Oil or white of an Egg, to fill up its Scratches; whereby it will become very tranfparent and po- lite.
330
O P T I C K S.
lite. But for feveral Experiments, it is not necef- fary to polifh it. If a piece of this cryflalline Stone be laid upon a Book, every Letter of the Book feen through it will appear double, by means of a double Refracflion. And if any beam of Light falls either perpendicularly, or in any oblique Angle upon any Surface of this Cryftal, it becomes divided into two beams by means of, the fame double Refraction. Which beams are of the fame Colour with the incident beam of Light, and feem equal to one another in the quantity of their Light, or very nearly equal. One of thefe Refra<flions is perform'd by the ufual Rule of Op- ticks, the Sine of Incidence out of Air into this Cryftal being to the Sine of Refradion, as five to three. The other Refra(5tion, which may be cal- led the unufual Refraction, is perform'd by the following Rule.
5\
H ^
Let ADBC reprefent the refrading Surface
of \
BOOK III. 331
of the Cryftal, C the biggeft folid Angle at that Surface, GEHF the oppofite Surface, and CK a perpendicular on that Surface. This perpen- dicular makes with the edge of the Cryftal C F, an Angle of 19 Degr. 3'. Join KF, and in it take KL, fo that the Angle KCL be 6 Degr. 40'. and the Angle LCF 12 Degr. 23'. And if ST reprefent any beam of Light incident at T in any Angle upon the refracfting Surface AD B C, let TV be the refradted beam determin'd by the given Portion of the Sines 5 to 3, according to the ufual Rule of Opticks. Draw V X parallel and equal to KL. Draw it the fame way from V in which L liethfromK; and joining TX, this line T X fhall be the other refracted beam carried from T to X, by the unufual Refra- d;ion,
If therefore the incident beam S T be perpen- dicular to the refra(5ling Surface, the two beams TV and TX, into which it fhall become di- vided, fliall be parallel to the lines CK and CL ; one of thofe beams going through the Cryftal perpendicularly, as it ought to do by the ufual Laws of Opticks, and the other T X by an unu- fual Refradion diverging from the perpendicular, and making with it an Angle V T X of about 6 1 Degrees, as is found by Experience. And hence, the Plane VTX, and fuch like Planes which are parallel to the Plane C F K, may be called the Planes of perpendicular Refradion. And the Coaft towards which the lines KL and VX are drawn, may be call'd the Coaft of unu- fual Refraction.
In like manner Cryftal of the Hock has a 5 double
332 O P T I C K S.
double Refra(5tion : But the difference of tl^ two Refradions is not fo great and manifefl as in Ifland Cryftal.
When the beam S T incident on Ifland Cry- ftal is divided into two beams T V and T X, and thefe two beams arrive at the farther Surface of the Giafs ; the beam T V, which was refra- cted at the firfl Surface after the ufual manner, Ihall be again refracted entirely after the ufual manner at the fecond Surface ; and the beam T X, which was refracted after the unufual manner in the firft Surface, lliall be again refradlied entirely after the unufual manner in the fecond Surface ; fo that both thefe beams fliall emerge out of the lecond Surface in lines parallel to the firft incident beam S T.
And if two pieces of Ifland Cryftal be pla- ced one after another, in fuch manner that all the Surfaces of the latter be parallel to all the correfponding Surfaces of the former: The Rays which are refradted after the ufual man- ner in the flrft Surface of the firft Cryftal, ftiall be reflated after the ufual manner in all the following Surliices j and the Rays which are re- fraded alter the unufual manner in the firft Sur- face, fhaii be relradted after the unufual manner in all tlie following Surfaces. And the fame thing happens, though the Surfaces of the Cryftals be any ways inclined to one another, provided that their Planes of perpendicular Refradlion be pa- rallel to ope another.
And therefore there is an original difterencc
an the Rays of Light, by means of which fome
Rays are m this Experiment conftantly refra(S-
k.' ed
BOOK m. 333
cd after the ufual manner, and others conftant- ly after the unufual manner : For if the diffe- rence be not original, but arifes from new Mo- difications imprefs'd on the Rays at their firft Refrad:ion, it would be aker'd by new Modi- fications in the three following Refractions; whereas it fuffers no alteration, but is conftant, and has the fame effed upon the Rays in all the Refractions. The unufual Refraction is there- fore perform'd by an original property of the Rays. And it remains to be enquired, whether the Rays have not more original Properties than are yet difcover'd.
^. 26. Have not the Rays of Light feveral fides, endued with feveral original Properties ? For if the Planes of perpendicular Refradtion of the fecond Cryftal be at right Angles with the Planes of perpendicular RefraCtion of the firft Cryftal, the Rays which are refradted after the ufual manner in paffing through the firft Cryftal, will be all of them refradted after the unufual manner in pafling through the fecond Cryftal; and the Rays which are refradted af- ter the unufual manner in paffing through the firft Cryftal, will be all of them refradted after the ufual manner in paffing through the fecond Cryftal. And therefore there are not two forts of Rays differing in their nature from one ano- ther, one of which is conftantly and in all Po- fitions refradted after the ufual manner, and the other conftantly and in all Pofitions after the unufual manner. The difference between the two forts of Rays in the Experiment mention'd in the 25th Queftion, was only in the Pofitions
I ©f
334 O P T I C K S.
of the Sides of the Rays to the Planes of pef<» pendicular Refrad:ion. For one and the fame Ray is here refraded fometimes after the ufual, and fometimes after the unufual manner, ac- cording to the Polition which its Sides have to the Cryflals. If the Sides of the Ray are poii- ted the fame way to both Cryflals, it is refra^ fted after the fame manner in them both : But if that fide of the Ray which looks towards the Coaft of the unufual Refradion of the iirft Cryftal, be 90 Degrees from that fide of the fame Ray which looks toward the Coaft of the unufual Refradion of the fecond Cryltal, (which may be effected by varying the Pofition of the fecond Cryftal to the firft, and by confequence to the Rays of Light, ) the Ray {hall be refraded after feveral manners in the feveral Cryflals. There is nothing more required to determine whether the Rays of Light which fall upon the fecond Cryflal fhall be refraded after the ufual or after the unufual manner, but to turn about this Cryflal, fo that the Coafl of this Cryflal's unufual Refradion may be orf this or on that fide of the Ray. And therefore every Ray may be confider'd as having four Sides or Quarters, two of which oppofite to one another incline the Ray to be refradled after the unufual man- ner, as often as either of them are turn'd to- wards the Coafl of unufuil Refradion j and the other two, whenever either of them are turn'd towards the Coafl of unufual Refradion, do not incline it to be otherwife refracted than after the ufual manner. The two iirfl may there- fore be call'd the Sides of unufual Refradion-
And
BOOK in. 335
And fince thefe DifpofitioRS were in the Rays before their Incidence on the fecond, third, and fourth Surfaces of the two Cryflals, and fuffer- ed no alteration ( fo far as appears, ) by the Re- fra(flion of the Rays in their paflilge through thofe Surfaces, and the Rays v/ere refrad:ed by the fame Laws in all the four Surfaces ; it ap- pears that thofe Difpofitions were in the Rays originally, and fufier'd no alteration by the firil Refradion, and that by means of thofe Difpofi- tions the Rays -were refradied at their Incidence on the firft Surface of the firfh Cryilal, fome of them after the ufual, and fome of them after the unufual manner, accordingly as their Sides of vinufual Refradion were then turn'd towards the Coaft of the unufual Refradion of that Cryilal, or lideways from it.
Every Ray of Light has therefore two oppo- fite Sides, originally endued with a Property on which the unufual Refradion depends, and the other two oppofite Sides not endued with that Property. And it remains to be enquired, whe- ther there are not more Properties of Light by which the Sides of the Rays differ, ani are di- ftinguifh'd from one another.
In explaining the difference of the Sides of the Rays above mention'd, I have fuppofed that the Rays fall perpendicularly on the firfl Cry- ftal. But if they falK obliquely on it, the Suc- cefs is the fame. Thofe Rays which are refra- ded after the ufual manner in the firfl Cryflal, will be refraded after the unufual manner in the fecond Cryflal, fuppoiing the Planes of perpen- dicular
336 O P T I C K a
dicular Refradtion to be at right Angles with one another, as above j and on the contrary.
If the Planes of the perpendicular Refraction of the two Cryflals be neither parallel nor per- pendicular to one another, but contain an acute Angle : The two beams of Light which emerge out of the firfl Cryftal, will be each of them di- vided into two more at their Incidence on the fe- cond Cryftal. For in this cafe the Rays in each of the two beams will fome of them have their . Sides of unufual Refradlion, and fome of them their other Sides turn'd towards the Coaft of the unufual Refradtion of the fecond Cryftal.
^/. 27. Are not all Hypothefes erroneous which have hitherto been invented for explain- ing the Phaenomena of Light, by new Modifica- tions of the Rays ? For thofe Phaenomena de- pend not upon new Modifications, a§ has been fuppofed, but upon the original and unchange- able Properties of the Rays.
^. 28. Are not all Hypothefes erroneous, in which Light is fuppofed to confift in Pref- lion or Motion, propagated through a fluid Me- dium ? For in all thefe Hypothefes the Phaeno- mena of Light have been hitherto explain'd by fuppofing that they arife from new Modifica- tions of the Rays j which is an erroneous Sup- pofition.
If Light confifted only in PreiTion propaga- ted without adhial Motion, it would not be a- ble to agitate and heat the Bodies which refrad: and refledl it. If it confifted in Motion propa- gated to all diftances in an inftant, it would re- quire an infinite force every moment, in every
fhining
BOOK IIL 337
fhinlng Particle, to generate that Motion. And if it confiiled in Preflion or Motion, propaga- ted either in an inftant or in time, it would bend into the Shadow.' For Preffion or Motion cannot be propagated in a Fluid in right Lines, beyond an Obitacle which ftops part of the Mo- tion, but will bend and fpread every way into the quiefcent Medium which lies beyond the Obftacle. Gravity tends downwards, but the PrelTure of Water arifnig from Gravity tends every way with equal Force, and is propagated as readily, and with as much force lideways as downwards, and through crooked paflages as through ftaait ones. The Waves on the Surface of ftagnating Water, paffing by the fides of a broad Obftacle which Itops part of them, bend afterwards and dilate themfelves gradually into the quiet Water behind the Obftacle. The Waves, Pulfes or Vibrations of the Air, where- in Sounds confift, bend manifeftly, though not fo much as the Waves of Water. For a Bell or a Cannon may be heard beyond a Hill which intercepts the fight of the founding Body, and Sounds are propagated as readily through crook- ed Pipes as through ftreight ones. But Light is never known to follow crooked Paftages nor to bend into the Shadow. For the fix'd Stars by the Interpofition of any of the Planets ceafe to be fien. And fo do the Parts of the Sun by the Interpofition of the Moon, Mercury or Venm. The Rays which pafs very near to the edges of any Body, are bent a little by the adion of the Body, as we ftiew'd above j but this bending is not towards but from the Shaiow,
Z and
338 O P T I C K S.
and is perform'd only in the paffage of the Ray by the Body, and at a very fmall diftance from it* So foon as the Ray is pafl the Body, it goes right on.
To explain the unufual Refra^ion of Ifland Cryftal by PreiTion or Motion propagated, has not hitherto been attempted ( to my knowledge) except by Huygms^ who for that end fuppofed two feveral vibrating Mediums within that Cry- ftal. But when he tried the Refradions in two fucceffive pieces of that Cryftal , and found them fuch as is mention'd above; he confef- fed himfelf at a lofs for explaining them. For PrefTions or Motions, propagated from a Ihining Body through an uniform Medium, muft be on all fides alike j whereas by thofe Experi- ments it appears, that the Rays of Light have different Properties in their different Sides. He fufpeded that the Pulfes of /Ether in pafling through the firft Cryftal might receive certain new Modifications, which might determine them to be propagated in this or that Medium within the fecond Cryftal, according to tht
Pofition of that Cryftal. M^is tour dirt comment But what Modifications
ceU fe fait, je nay rlen ^l^^fg might be he COuld trove jufqu id qui me fa- r. ^ i • i r
tisfaje. c. H. de la iumi- Hot lay, nor think of any ere. c. 5. p. 91. thing fatisfadory in that
Point. And if he had knov^n that the unufual Refradlion depends not on new Modifications, but on the original and unchangeable Difpofitionsof theRays, he would have found it as difficult to explain how thofe Pifpofitions which he fuppofed to be imprefs'd
_ on
BOOK IIL 339
on the Rays by the firft Cryftal, could be in them before their Incidence on that Cryftal, and in general, how all Rays emitted by £hi- ning Bodies, can have thpfe Difpofitions in them from the beginning. To me , at leafl:, this feems inexplicable ,. if Light be nothing elfe than Preffion or Motion propagated through Mther,
And it is as difficult to explain by thefe Hy- pothefes, how Rays can be alternately in Fits of eafy Reflexion and eafy Tranfmiffion j unlefs perhaps one might fuppofe that there are in all Space two ^Ethereal vibrating Mediums, and that the Vibrations of one of them conftitute Light, and the Vibrations of the other are fwift- er, and as often as they overtake the Vibrations of the firft, put them into thofe Fits. But how two Mthers can be diffufed through all Space, one of which ads upon the other, and by con- fequence is re-a<5led upon, without retarding, fliattering, difperling and confounding one an- others Motions, is inconceivable. And againft filling the Heavens with fluid Mediums, unlefs they be exceeding rare, a great Objedion arifes from the regular and very lafting Motions of the Planets and Comets in all manner of Courfes through the Heavens. For thence it is mani- feft, that the Heavens are void of all fenfible Refiftance, and by confequence of all fenfible Matter.
For the refifling Power of fluid Mediums a- rifes partly from the Attrition of the Parts of the Medium, and partly from the Vis inertia of the Matter. That part of the Refiftance of
Z 2 afphe-
340 O P T I C K S.
a fpherical Body which arifes from the Attrition of the Parts of the Medium is very nearly as the Diameter, or, at the moft, as the FaSfum of the Diameter, and the Velocity of the fpherical Bo- dy together. And that part of the Reliflance which arifes from the Vis inertia of the Matter, is as the Square of that FaBiim. And by this difference the two forts of Refiftance may be di- flinguifh'd from one another in any Medium; and thefe being diftinguifh'd, it will be found that almoft all the Refiftance of Bodies of a com- petent Magnitude moving-in Air, Water, Quick- filver, and fuch like Fluids with a competent Ve- locity, arifes from the Vis inertice of the Parts of the Fluid.
Now that part of the refifting Power of any Medium which arifes from the Tenacity, Fri- ction or Attrition of the Parts of the Medium, may be dimini(h'd by dividing the Matter into fmaller Parts, and making the Parts more fmooth and flippery: But that part of the Refiftance which arifes from the Vis inerti(X, is proportio- nal to the Denfity of the Mattel, and cannot be diminifh'd by dividing the Matter into fmaller Parts, nor by any other means than by decrea- iing the Denlity of the Medium. And for thefe Reafons the Denlity of fluid Mediums is very nearly proportional to their Refiftance. Li- quors which differ not much in Denfity, as Wa- ter, Spirit of Wine, Spirit of Turpentine, hot Oil, differ not much in Refiftance. Water is thirteen or fourteen times lighter than Quick- . iilver, and by confequence thirteen or fourteen times rarer, and its Refiftance is lefs than that
of
BOOK III. 341
of Quick-filver in the fame Proportion, or there- abouts, as I have found by Experiments made with Pendulums. The open Air in which we breathe is eight or nine hundred times lighter than Water, and by confequence eight or nine hundred times rarer, and accordingly its Refi- ftance is lefs than that of Water -in the fame Proportion, or thereabouts j as I have alfo found by Experiments made with Pendulums. And in thinner Air the Reiiftance is ftill lefs, and at length, by ratifying the Air, becomes infenfi- ble. For fmall Feathers falling in the open Air meet with great Refiftance, but in a tall Glafs well emptied of Air, they fall as fail as Lead or Gold, as I have feen tried feveral times. Whence the Refiftance feems ftill to decreafe in propor- tion to the Denlity of the Fluid. For I do not find by any Experiments, that Bodies moving in Quick-filver, Water or Air, meet with any oaher fenfible Refiftance than what arifes from the Denfity and Tenacity of thofe fenfible Flu- ids, as they would do if the Pores of thofe Flu- ids, and all other Spaces, were filled with a denfe and fubtile Fluid. Now if the Refiftance in a Veffel well emptied of Air, was but an hundred times lefs than in the open Air, it would be about a million of times lefs than in Quick- filver. But it feems to be much lefs in fuch a Veffel, and. ftill much lefs in the Hea- vens, at the height of three or four hundred Miles from the Earth, or above. For Mr. Boyle has fliew'd that Air may be rarified above ten thoufand times in VefTels of Glafs j and the Heavens are much emptier of Air than any Va-^
23. cuiim
342 O P T I C K S.
cuum we can make below. For fmce the Air is comprefs'd by the Weight of the incumbent Atmoiphere., and the Denfity of Air is propor- tional to the Force compreffing it, it follows by Computation, that at the lieight of about fe- ven and a half Engliflj Miles from the Earth, the Air is four times rra-er than at the Surface of the Earth J and at the height of 15 Miles it is fix- teen times rarer than that at the Surface of the Earth J and at the height of 22^, 30, or 38 Miles, it is refpedively 64, 256, or 1024 times rarer, or thereabouts J and at the height of 76, 152, 228 Miles, it is about loooooo, 1 000000000000, or loooGOOoooooooooooo times rarer j and fo on.
Heat promotes Fluidity very much, by dimi- nifliing the Tenacity of Bodies. It makes ma- ny Bodies fluid which are not fluid in cold, and increafes the Fluidity of tenacious Liquids, as of Oil, Balfam, and Honey, and thereby de- creafes their Refiftance. But it decreafes not the Refiftance of Water confiderably, as it would do if any confiderable part of the Refiftance of Water arofe from the Attrition or Tenacity of its Parts. And therefore the Refiftance of Wa- ter arifes principally and almoft entirely from the Vis inertice of its Matter j and by confe- quence, if the Heavens were as denfe as War» ter, they would not have much lefs Refiftance than Water J if as denfe as Quick-filver, they would not have much lefs Refiftance than Quicks filver; if abfolutely denfe, or full of Matter without any Vacimm^ let the Matter be never fo fubtil and fluid, they would have a greater
Refiftance
BOOK m. 343
Refiftance than Qulck-filver. A folid Globe in fuch a Medium would lofe above half its Mo- tion in moving three times the length of its Diameter, and a Globe not folid ( fuch as are the Planets, ) would be retarded fooner. And therefore to make way for the regular and lad- ing Motions of the Planets and Comets,- it's ne- ceffary to empty the Pleavens of all Matter, ex% cept perhaps fome very thin Vapours, Steams, or Effluvia, arifmg from the Atmofpheres of the Earth, Planets, and Comets, and from fuch an exceedingly rare ;^thereal Medium as we de- fcribed above. A denfe Fluid can be of no ufe foi- explaining the Phaenomena of Nature, the Motions of the Planets and Comets being better explain'd without it. It ferves only to difturb and' retard the Motions of thofe great Bodies, and make the Frame of Nature languifh : And in the Pores of Bodies, it ferves only to ftop the vibrating Motions of their Parts, wherein their Heat and A<fl:ivity conlifts. And as it is of no ufe, and hinders the Operations of Na- ture, and makes her languifn, fo there is no e- vidence for its Exiftence, and therefore it oueht to be rejected. And if it be rejeded, the Hy- pothefes that Light confiils in Preffion or Mo- tion, propagated through fuch a Medium, are rejeded with it.
And for rejeding fuch a Medium, we have the Authority of thofe the oldeft and moll ce- lebrated Philofophers -of Greece and Phcenkiay who made a Vacuum^ and Atoms, and the Gra- vity of Atoms, the firft Principles of their Phi- lofophyj tacitly attributing Gravity to fo.Ec- o-
Z 4 thci
344- O P T I C K S.
ther Caufe than denfe Matter. Later Philofo- phers baniili the Confi deration of fuch a Caufe out of natural Philofophy, feigning Hypothefes for explaining all things mechanically, and re- ferring other Caufes to Metaphylicks : Whereas the main Bufniefs of natural Philofophy is to argue from Phcenomena without feigning Hy- pothefes, and to deduce Caufes from Effects, till we come to the very firft Caufe, which cer- tainly is not mechanical ; and not only to un- fold the Mechanifm of the World, but chiefly to refolve thefe and fuch like Queftions. What is there in places almofl empty of Matter, and whence is it that the Sun and Planets gravitate towards one another, without denfe Matter be- tween them ? Whence is it that Nature doth nothing in vain ; and whence arifes all that Or- der and Beauty which we fee in the World ? To what end are Comets, and whence is it that Planets move all one and the fame way in Orbs concentrick, while Comets move all manner of ways in Orbs very excentrick ; and what hinders the fix'd Stars from falling upon one another ? How came the Bodies of Animals to be contri- ved with fo much Art, and for what ends were their feveral Parts ? Was the Eye contrived without Skill in Opticks, and the Ear without Knowledge of Sounds ? Plow do the Motions of the Body follow from the Will, and whence is the Inftindt in Animals ? Is not the Senfory of Animals that place to which the fenfitive Sub- itance is prefent, and into which the fenfible Species of Things ap carried through jthe Nerves and Brain, that there they may be perceived
BOOK III. 345
by their immediate prefence to that Scbftancc ? And thefe things being rightly difpatch'd, does it not appear from Plia^nomena that there is a Being incorporeal, living, intelligent, omnipre- fent, who in infinite Space, as it were in his Sen- fory, fees the things themfelves intimately, and throughly perceives them, and comprehends them wholly by their immediate prefence to himfelf : Of which things the Images only car- ried through the Organs of Senfe into pur little Senforiums, are there feen and beheld by that which in us perceives and thinks. And though every true Step made in this Philofophy brings us not immediately to the Knowledge of the firll Caufe, yet it brings us nearer to it, and on that account is to be highly valued.
^. 29. Are not the Rays of Light very fmall Bodies emitted from lliining Subllances ? For fuch Bodies will pafs through uniform Me- diums in right Lines without bending into the Shadow, which is the Nature of the Rays of Light. They will alfo be capable of feveral Properties, and be able to conferve their Pro- perties unchanged in paffing through feveral Mediums, which is another Condition of thq Rays of Light. Pellucid Subllauces a6t upon the Rays of Light at a diftance in refracting-, re- flecting, and inflecting them, and the Rays m.u- tually agitate the Parts of thofe Subfl:ances at ^a difl:arce for heating them i and this ACtion and Re-aUion at a difl:ance very much refembles an attractive Force between Bodies. If RefraCtion be perform'd by Attraction of the Rays, the Sines of Incidencs muft be to the Sines of Re- fraCtion
346 O P T I C K S.
fraftion in a given Proportion, as we {hew'd in our Principles of Philofophy : And this Rule is true by Experience. The Rays of Light in going out of Giafs into a Vacuum^ are bent to- wards the Glafs ; and if they fall too obliquely on the Vacuum^ they are bent backwards into the Glafs, and totally reflected j and ^ this Refle- xion cannot be afcribed to the Refiftance of an abfolute Vacuum^ but muft be caufed by the Power of the Glafs attracting the Rays at their going out of it into the Vacuum^ and bringing them back. For if the farther Surface of the Glafs be moiflen'd with Water or clear Oil, or liquid and clear Honey, the Rays which would otherwife be refleded will go into the Water, Oil, or Honey ; and therefore are not refle(5ted before they arrive at the farther Surface of the Glafs, and begin to go out of it. If they go out of it into the Water, Oil, or Honey, they go on, becaufe the Attraction of the Glafs is almoft balanced and rendered ineffectual by the contrary Attraction of the .Liquor. But if they go out of it into a Vacuum which has no Attraction to balance that of the Glals, the At- traction of the Glafs either bends and refraCts them, or brings them back and reflects them.- And this is ftill more evident by laying together two Prifms of Glafs, or two ObjeCt-glaSes of very long Telefcopes, the one plane, the o- ther a little convex, and fo compreffing them that they do not fully touch, nor are too far a- funder. For the Light which falls upon the farther Surface of the firfl Glafs where the In- terval between the Glaffes is not above the ten
hundred
BOOK III. 347
hundred thoufandrh Part of an Inch, will go through that Surface, and through tbe Air or Vacuum between the GlaiTes, and enter into the fecondGlafs, as was explain'd in the firft, fourth, and eighth Obfervations of the firft Part of the fecond Book. But, if the fecond Glafs be taken away, the Light which goes out of the fecond Surface of the. firft Glafs into the Air or Va- cuum^ will not go on forwards, but turns back into the firft Glafs, and is reflecftcd ; and there- fore it is drawn back by the Power of the firft Glafs, there being nothing elfe to turn it back. Nothing more is requifite for producing all the variety of Colours, and degrees of Refrangibi- lity, than that the Rays of Light be Bodies of different Sizes, the leaft of which may take violet the weakeft and darkeft of the Colours, and be more cafily diverted by refrad:ing Sur- faces from the right Courfe ; and the reft as they are bigger and bigger, may make tlie ftronger and more lucid Colours, blue, green, yellow, and red, and be more and more diHi- cultly diverted. Nothing more is requifite for putting the Rays of Light into Fits of eafy Re- flexion and eafy Tranfmiffion, than that they be fmall Bocjies which by their attractive Powers, or fome other Force, ftir up Vibrations in what they ad; upon, which Vibrations being fwifter than the Rays, overtake them fucceftively, and agitate them fo as by turns to increafe and de- creafe their Velocities, and thereby put them into thofe Fits. And laftly, the unufual Refra- (ftion of Ifland-Cryftal looks very much as if it were perform'd by fome kind of attractive vir- tue
348 O P T I C K S.
tue lodged in certain Sides both of the Rays, and of the Particles of the Cryftal. For were it not for* fome kind of Difpofition or Virtue lodged in fome Sides of the Particles of the Cryflal, and not in their other Sides, and which inclines and bends the Rays towards the Coafl of unufual Refraction, the Rays which fall per- pendicularly on the Cryllal, would not be re- fraded towards that Coafl rather than towards any other Coaft, both at their Incidence and at their Emergence, fo as to emerge perpendicu- larly by a contrary Situation of the Coaft of unufual Refradion at the fecond Surface ; the Cryftal acting upon the Rays after they have ■pafs'd through it, and are emerging into the Air; or, if you pieafe, into a V aciium' And lince the Cryftal by this Difpofition or Virtue does not ad: upon the Rays, unlefs when one of their Sides of unufual Refradion looks to- wards that Coaft, this argues a Virtue or Difpo- fition in thofe Sides of the Rays, which an- fwers to, and fympathizes with that Virtue or Difpofition of the Cryftal, as the Poles of two Magnets anfwer to one another. And as Mag- netifm may be intended and remitted, and is found only in the Magnet 2nd in Iron : So this Virtue of refrading the perpendicular Rays is greater in Ifland-Cryftal, lefs- in Cryftal of the Rock, and is not yet found in other Bodies. I do not fay that this Virtue is magnetical : It feems to be of another kind. I only fay, that wnatever it be, it's difficult to conceive how the Rays of Light, unlefs they be Bodies, can have a permanent Virtue in two of their Sides I which
BOOK III. 349
which is not in their other Sides, and this without any regard to their PoUtion to the Space or Me- dium through which they pafs.
What I mean in this Queftion by a Vacuum^ and by the Attradions of the Rays of Light to- wards Giafs or Cryftal, may be undcrftood ' by what was faid in the i8th, 19th, and 20th Que- ftions.
^eji. 30. Are not grofs Bodies and Light con- vertible into one another, and may not Bodies re- ceive much of their A(^l:ivity from the Particles of Light which enter their Compofition? For all fix'd Bodies being heated emit Light fo long as they continue fufficiently hot, and Light mutually flops in Bodies as often as its Rays ftrike upon their Parts, as we fliew'd above. I know no Body lefs apt to fliine than Water; and yet Wa- ter by frequent Diftillations changes into fix'd Earth, as Mr.Boy/e^ has try'd ; and then this Earth being enabled to endure a fufficient Heat, {hines by Heat like other Bodies.
The changing of Bodies into Light, and Light into Bodies, is very conformable to the Courfe of Nature, which feems delighted with Tranf- mutations. Water, which is a very fluid taflelefs Salt, fhe changes by Heat into Vapour, which is a fort of Air, and by Cold into Ice, which is a hard, pellucid, brittle, fufible Stone ; and this Stone returns into Water by Heat, and Vapour returns into Water by Cold. Earth by Heat be- comes Fire, and by Cold returns into Earth. Denfe Bodies by Fermentation rarify into feve- ral forts of Air, and this Air by Fermentation, and fometimes without it, returns into denfe
Bodies.
350 O P T I C K S.
Bodies. Mercury appears fometimes in the form of a fluid Metal, fometimes in the form of a hard brittle Metal, fometimes in the form of a corro- live pellucid Salt call'd Sublimate, fometimes in the form of a taftelefs, pellucid, volatile white Earth, call'd Mercip^ius Dulcis j or in that of a red opake volatile Earth, call'd Cinnaber j or in that of a red or vv^hite Precipitate, or in that of a fluid Salt ; and in Diftillation it turns into Vapour, and being .agitated i?i VaciiOj it fhines like Fire. And after all thefe Changes it re- turns again into its firfl: form of Mercury. Eggs grow from infenfible Magnitudes, and change into Animals j Tadpoles into Frogs ; and Worms into Flies. All Birds, Beaflis and Fifhes, Infers, Trees, and other Vegetables, with their feveral Parts, grow out of Water and watry Tinctures and Salts, and by Putre- fadtion return again into watry Subftances. And Water ftanding a few Days in the open Air, yields aTindurc, which (like that of Malt) by ftanding longer yields a Sediment and a Spi- rit, but before Putrefaction is fit Nourifhment for Animals and Vegetables. And among fuch various- and fl:range Tranfmutations, why may not Nature change Bodies into Light, and Light into Bodies ?
^leji. 3 1. Have not the fmall Particles of Bo- dies certain Powers, Virtues, or Forces, by which they adt at a diftance, not only upon the Rays of Light for reflecting, refra(fling, and inflect- ing them, but alio upon one another for pro- ducing a great Part of the Phaenomena of Na- ture ? For it's well known, that Bodies ad:
one
BOOK TIL 351
one upon anotlier by the Attradions of Gravity, Magnetifm, and Eledtricity j and thefe Inftances ihew the Tenor and Courfe of Nature, and make it not improbable but that there may be more at- tradlive Powers than thefe. For Nature is very confonant and conformable to her felf How thefe Attradtions may be perform'd, I do not here confider. What I call Attraction may be per- form'd by impulfe, or by fome other means un- known to me. I ufe that Word here to fignify only in general any Force by which Bodies tend towards one another, whatfoever be the Caufe. For we muft learn from the Phcenomena of Nature what Bodies attradt one another, and what are the Laws and Properties of the At- traction, before we enquire the Caufe by which the Attraction is perform'd. . The Attractions of Gravity, Magnetifm, and EleCtricity, reach to very fenfible diflances, and fo have been obferved by vulgar Eyes, and there may be others which reach to fo fmall diflances as hitherto efcape Ob- fervation j and perhaps eleCtrical Attraction may reach to fuch fmall diftances, even without being excited by FriCtion.
For when Salt of Tartar runs per IDeliquium, is not this done by an Attraction between the Particles of the Salt of Tartar, and the Parti- cles of the Water which float in the Air in the form of Vapours ? And why does not common Salt, or Salt-petre, or Vitriol, run per Deliqimirn^ but for want of fuch an Attraction ? Or why docs not -Salt of Tartar drav^^ more Water out of the Air than in a certain Proportion to its quantity, but for want of an attractive Force 2 after
^52 O P T I C K S.
after it is fatiated with Water ? And whence is it but from this attractive Power that Water which alone diftils with a gentle luke-warm Heat, will not diftil from Salt of Tartar with- out a great Heat ? And is it not from the like attractive Power between the Particles of Oil of Vitriol and the Particles of Water, that Oil of Vitriol draws to it a good quantity of Water out of the Air, and after it is fatiated draws no more, and in Diftillation lets go the Water very difficultly ? And when Water and Oil of Vi- triol poured fucceffively into the fame Veffel grow very hot in the mixing, does not this Heat argue a great Motion in the Parts of the Liquors ? And does not this Motion argue, that - the Parts of the two Liquors in mixing coa- lefce with Violence, and by confequence rufli to- wards one another with an accelerated Mo- tion ? And when Aqua fortis, or Spirit of Vi- triol poured upon Filings of Iron, dilTolves the Filings with a great Heat and Ebullition, is not this Heat and Ebullition effected by a violent Motion of the Parts, and does' not that Motion argue that the acid Parts of the Liquor rufh to- wards the Parts of the Metal with violence, and run forcibly into its Pores till they get be- tween its outmoft Particles, and the main Mafs of the Metal, and furrounding thofe Particles loofen them from the main Mafs, and fet them at liberty to float off into the Water ? And when the acid Particles, which alone would diftil with an eafy Heat, will not feparate from the Particles of the Metal without a very vio- lent
BOOK III. 353
lent Heat, does not this confirm the Attradtioa between them ?
When Spirit of Vitriol poured upon com- mon Salt or Salt-petre makes, an Ebulhtion with the Salt, and unites wich it, and in Diftillatian ' the Spirit of the common Salt 'or Salt-petre comes over much eafier than it would do be- fore, and the acid part of the Spirit of Vitriol ilays behind j does not this argue that the fi:<'d Alcaly of the Salt attrads the acid Spirit ot the Vitriol more ftrongly than its own Spirit, and not being able to hold them both, lets go its own? And when Oil of Vitriol is draw^n off from its weight of Nitre j and from both the Ingredients a compound Spirit of Nitre is diflil- led, and two parts of this Spirit are poured on one part of Oil of Cloves or Carraway Seeds, or. of any ponderous Oil of vegetable or animal Sub- ftanCes, or Oil of Turpentine thicken'd with a little Balfam of Sulphur, and the Liquors grow fo very hot in mixing, as prefently to fend up a burn- ing Flame ; does not this very great and fudden Heat argue that the two Liquors mix with vio- lence, and that their Parts in mixing run to- wards one another with an accelerated Motion, and cla(h with the greateft Force ? And is it not for the fame reafon that well redlified Spi- rit of Wine poured on the fame compound Spi- rit fla{hes*f and that the Piilvis fuUninam, com- pofed of Sulphur, Nitre, and Salt of Tartar, goes off with a more fudden and violent Ex- plofion than Gun-powder, the acid Spirits of the Sulphur and Nitre ruihing towards one an- other, and towards the Salt of Tartar, with fo
A a great
354- O P T I C K S.
great a violence, as by the (hock to turn the whole at once into Vapour and Flame ? Where the DilTolution is flow, it makes a flow Ebulli- tion and a gentle Heat j and where it is quick- er:, it makes a greater Ebullition with more heat ; and where it is done at once, the Ebul- lition is contraded into a fudden Blaft or vio- lent Explofion, with a heat equal to that of Fire and Flame. So when a Drachm of the a- bove-mention'd compound Spirit of Nitre was poured upon half a Drachm of Oil of Carraway Seeds i?i vaciio^ the Mixture immediately made a flafh like Gun-powder, and burll the ex- haufted Receiver, which was a Glafs fix Inches wide, and eight Inches deep. And even the grofs Body of Sulphur powder'd, and with an equal weight of Iron Filings and a little Water made into Pafte, ads upon the Iron,* and in five or fix hours grows too hot to be touch'd, and emits a Flame, And by thefe Experiments com- pared with the great quantity of Sulphur with which the Earth abounds, and the warmth of the interior Parts of the Earth, and hot Springs, and burning Mountains, and with Damps, mi- neral Corufcations, Earthquakes, hot fuffoca- ting Exhalations, Flurricanes, and Spouts; we may learn, that fulphureous Steams abound in the Bowels of the Earth and ferment with Mi- nerals, and fomietim^es take fire with a fudden Corufcatlon and Explofion; and if pent up in fubterraneous Caverns, burfl the Caverns with a great {baking of the Earth, as in fpringing of a Mine. And then the Vapour generated by the Explofion, expiring through the Fores of the
3 Earth,
BOOK III. 355
Earth, feels hot and fuffocateSj and iiiakes Tem-« pefls and Hurricanes, and fometimes caufes the" Land to Hide, or the Sea to boil, and carries up the Water thereof in Drop3, which by their weight fall down again in Spouts, ^xlfo fome fulphureous Steams, at all times when the Earth is dry, afcending into the Air, ferment there with nitrous Acids^ and fometimes taking fire caufe Lightning and Thunder, and fiery Me- teors. For the Air abounds with acid Vapours fit to promote Fermentations, as appears by the- rufling of Iron and Copper in it, the kindling of Fire by blowing, and the beating of the Heart by means of Refpiration. Now the a- bove-mention'd Motions are fo great and violent as to fhew t]iat in Fermentations the Particles of Bodies which almofi: reft, are put into new Mo- tions by a very potent Principle, w^hich ad:s up- on them only when they approach one another, and caufes them to meet and clafh with 2;reat vi* olence, and grow hot with the motion, and dafli one another into pieces, and vapifli into Air, and Vapour, and Flame.
When Salt of Tartar per deliqiiium^ being poured into the Solution of any Metal, preci- pitates the Metal, and makes it fail down to the bottom of the Liquor in the form of Mud: Does not this argue tliat the acid Particles are attracted more ftrong-ly by the Salt of Tartar than by the Metal, and by the ftronger Attra- d:ion go from the Metal to the Salt of Tartar ? And fo when a Solution of Iron in Anna forth diffolves the Lapis Calciminarh^ and lets go the Iron, or a Solution of Copper difiblves Iron im-
A a 2 merfed
356 O P T I C K S.
irierfed in it and lets go the Copper, or a So- '4ution of Silver difTolves Copper and lets go the Silver, or a Solution of Mercury in Aquafortis being poured upon Iron, Copper, Tin, or Lead, difTolves the Metal and lets go the Mercury ; does not this argue that the acid Particles of the Aqua fortis are attracted more ftrongly by the Lapis Calamniaris than by Iron, and more flrongly by Iron than by Copper, and more ftrongly by Copper than by Silver j and more ftrongly by Iron, Copper, Tin, and Lead, than by Mercury ? And is it not for the fame reafon that Iron requires more Aqua fortis to dilTolve it than Copper, and Copper more than the other Metals ; and that of all Metals, Iron is dilTolved moft eafily, and is mofi: apt to ruft ; and next af- ter Iron, Copper?
When Oil of Vitriol is mix'd w^ith a little Water, or is run per deliquiuni^ and in Diftil- lation the Water afcends difficultly, and brings over v^rith it fome part of the Oil of Vitriol in the form of Spirit of Vitriol, and this Spirit be- ing poured upon Iron, Copper,' or Salt of Tar- tar, unites with the Body and lets go the Wa- ter 'j doth not this fliew that the acid Spirit is at- ■ traded by the Water, and more attracted by the fix'd Body than by the Water, and there- fore lets go the Water to clofe v^ith the fix'd Body ? And is it not for the fame reafon that the Water and acid Spirits which are mix'd to- gether in Vinegar, Aqua fortis^ and Spirit of Salt, cohere and rife together in Diftillation ; but if the Mejiftruum be poured on Salt of Tar- tar, or on Lead, or Iron, or any fix'd Body
which
BOOK III. 357
which it can diflblve, the Acid by a fironger At- traction adheres to the Body, and lets go ths Water ? And is it not alfo from a mutual At- tracftion that the Spirits o£ Soot and Sea-Sak unite and compofe the Panicles of Sal-armo- niac, which are lefs volatile than before, be- caufe grofler and frc€r from Water ; and that the Particles of Sal-armoniac in Sublimation car- ry up the Particles of Antimony, which will not fublime alone ; and that the Particles of Mer- cury uniting with the acid Particles of Spirit of Salt compofe Mercury fublimate, and with the Particles of Sulphur, compofe Cinnaber; and that the Particles of Spirit of Wine and Spirit of Urine well redlitied unite, and letting go the Water which dillblved them, compofe a confident Body; and that in fubliming Cinna- ber from Salt of Tartar, or from quick Lime, the Sulphur by a ftronger Attraftion of the Salt or Lime lets go the Mercury, and flays with the fix'd Body ; and that when Mercury fubli- mate is fublimed from Antimony, or from Re- gulus of Antimony, the Spirit of Salt lets go the Mercury, and unites with the antimonial Me- tal which attracts it more ftrongly, and ftays with it till the Heat be great enough to make them both afcend together, 'and then carries up the Metal with it in the form of a very fu^ fible Salt, called Butter of Antimony, although the Spirit of Salt alone be almoft as volatile as Water, and the Antimony alone as fix'd as Lead ?
When yi^ua fortis diffolves Silver and not Gold, and Aqua regia diffolves Gold and not
A a 3 Silver,
35^
O P T I C K S.
Silver, may it not be faid that Aqua forth is fubtil enough to penetrate Gold as well as Sil- ver, but wants the attracflive Force to give it Entrance j and that Aqua regia is fubtil enough to penetrate Silver as v/ell as Gold, but wants the attractive Force to give it Entrance ? For Aqua rcgia is nothing elfe than Aqua fortis mix'd v/ith fome Spirit of Salt, or with Sal-ar- moniac J and even common Salt diiTolved in A-^ qua fcrtis^ en.ibies the Metijiruwrn to dilfolve Gold, though the Salt be a grofs Body. When therefore Spirit of Snlt precipitates Silver out of Aqua fortis^ is it not done by attrading and jnixing with the Aqua Jortisy and not attrad:- jng, or perhaps repelling Silver? And when Water precipitates Antimony out of the Subli- mate of Antimony and Sal-armoniac, or out of putter of Antimony, is it not done by its dif^ folving, mixing with, and weakening the Sal^ grmoniac or Spirit of Salt, and its not attract- ing, or perhaps repelling the Antimony ? And is it not for want of an attradive virtue be- tween the Parts of Water and Oil, of Quick-^ lilver and Antimony, of Lead and Iron, that thefe Subllances do not mixj .and by a weak Attradion, that Quick-filver and Copper mix difiicultly j and fi'om a flrong one, that Quick- filver. and Tin, Antimony and Iron, Water and Salts, mix readily? And in general, is it not from the fame Principle that Heat congregates; homogeneal Bodies, and feparates heterogeneal ones?
When Arfenick with Soap gives a Regulus^
and with Mercury fublimate a volatile fufible
^ ■ Salt,
BOOK III. 359
Salt, like Butter of. Antimony, doth not this lliew that Arfenick, which is a Subftance totally volatile, is compounded of fix'd and volatile Parts, ftrongly cohering by a mutual Attradion, fo that the volatile will not afcend without car- rying up the fixed ? And fo, when an equal weight of Spirit of Wine and Oil of Vitriol are digefted together, and in Diftillation yield two fragrant and volatile Spirits which will not mix with one another, and a fix'd black Earth remains behind ; doth not this fliew that Oil of Vitriol is compofed of volatile and fix'd Parts ftrongly united by Attradion, fo as to afcend to- gether in form of a volatile, acid, fluid Salt, until the Spirit of Wine attrads and feparates the volatile Parts from the fixed ? And there- fore, fince Oil of Sulphur per Campcmam is of the fame Nature with Oil of Vitriol, may it not be inferred, that Sulphur is alfo a mixture of volatile and fix'd Parts fo ftrongly cohering by Attradion, as to afcend together in Sublima- tion. By diflblving Flowers of Sulphur in Oil of Turpentine, and diftilling the Solution, it is found that Sulphur is compofed of an inflama- ble thick Oil or fat Bitumen, an acid Salt, a very fix'd Earth, and a little Metal. The three firfl were found not much unequal to one another, the fourth in fo fmall a quantity as fcarce to be worth confidering. The acid Salt difix)lved in Water, is the fame with Oil of Sul- phur per Campanam, arid abounding .much in the Bowels of the Earth, and particularly in Markafites, unites it felf to the other Ingredi- ents of the Markafite, which are. Bitumen, I-
A a 4 ron,
360 O P T I C K S.
ron. Copper, and Earth, acid with them corn- pounds Alkim, Vitriol, and Sulphur. With the Earth alone it compounds AUum ; with the Me- tal alone, or Metal and Earth together, it com- pounds Vitriol; and with the Bitumen and Earth it compounds Sulphur. Whence it comes to pafs that Markances abound v/ith thofe three Mi- nerals. And is it not from the mutual Attradtior^ of the Ingredients that they ftick together for ccmpoundins; thefe Minerals, and that the Bitu- men carries up the other Ingredients of the Sul- phur, which without it would not fublime ? And the fame Queftion may be* put concerning all, or almofc all the grofs Bodies in Nature. For all the Parts of Animals and Vegetables are com- pofed of Subftances volatile and fix'd, fluid and folid, as appears by their Analyfis ; and fo are Salts and Minerals, fo far as Chymifls have been hitherto abl? to examine their Compofi- tion.
When Mercury fublimate is re-fublimed with frefh Mercury, and becomes Mercurius Dulcis^ which is a white taftelefs Earth fcarce dilTolva- ble in Water, and Mercurius Dulcis re-fublimed with Spirit of Salt returns into Mercury fubli- mate ; and when Metals corrpded with a little acid turn into ruft, which is an Earth taftelefs and indiffolvable in Water, and this Earth im- bibed with more acid becomes • a metallick Salt ; and when fome Stones, as Spar of Lead, diifolv^d in proper M^nfiruums become Salts ; do not thef.:; tilings fhew that Salts are dry Earth and watry Acid united by Attradion, and that the Earth \\all not become a Salt without fq
muql^
BOOK III. 361
much acid as makes it diffolvable in Water ? Do not the {harp and pungent Taftes of Acids arife from the ftrong Attradtion whereby the acid Particles rufli upon and agitate the Par- ticles of the Tongue ? And when Metals are dif- folved in acid MenJi?'immSy and the Acids in conjunction with the Metal ad after a different manner, fo that the Compound has a different Tafte much milder than before, and fometimes a fweet one j is it not becaufe the Acids ad-, here to the metallick Particles, and thereby lofe much of their Aftivity ? And if the Acid be in too fmall a Proportion to make the Com- pound diffolvable in Water, will it not by ad- hering flrongly to the Metal become unadive and lofe its Tafle, and the Compound be a taflelefs Earth ? For fuch things as are not diffolvable by the Moiflure of the Tongue, ad not upon the Tafle.
As Gravity makes the Sea flow round the deafer and weightier Parts of the Globe of the Earth, fo the Attraction may make the watry Acid flow round the denfer and compader Par- ticles of Earth for compofing the Particles of Salt. For otherwife the Acid would not do the Ofhce of a Medium between the Earth and common Water, for making Salts diffolvable in the Water j nor would Salt of Tartar readily draw off the Acid from diffolved Metals, nor Metals the Acid from Mercury. Now, as in the great Globe of the Earth and Sea, the denfefl Bodies by their Gravity fink down in Water, ^nd always endeavour to go towards the Cen- ter of the 'Globe; fo in Particles of Salt, the
denfefl
362 O P T I C K S.
denfcft Matter may always endeavour to approach the Center of the Particle : So that a Particle of Salt may be compared to a Chaos ; being denfe, hard, diy, and earthy in the Center j and rare, foft, moift, and watry -in the Circumference. And hence it feems to be that Salts are of a lafting Nature, bejng fcarce dellroy'd, unlefs by drawing away their watry Parts by violence, or by letting them foak into the Pores of the central Earth by a gentle Heat in Putrefa- ction, until the Earth be diflblved by the Wa- ter, and feparated into fmaller Particles, which by reafon of their Smallnefs make the rotten Compound appear of a black Colour. Hence ilfo It may be, that the Parts of Animals and "Vegetables preferve their feveral Forms, and affimilate their Nouriihment j the foft and moift Nourifhment eafily changing its Texture by a gentle Heat and Motion, till it becomes like the denfe, hard, dry, and durable Earth in the Cen- ter of each Particle. But when the Nourilh- ment grows unfit to be allimilated, or the cen- tral Earth grows too feeble to affimilate it, the Motion ends in Confufion, Putrefacftion, and Death.
If a very fmall quantity of any Salt or Vitriol be dilfolved in a great quantity of Water, the. particles of the Salt or Vitriol will not fmk to the bottom, though they be heavier in Specie than the Water, but will eveidy diffufe them- felves into all the Water, fo as to make it as fa- line at the top as at the bottom. And does not this imply that the Parts of the Salt or Vitriol recede from one another, and endeavour to ex- pand
BOOK III. 363
pand themfelves, and get as far afunder as the quantity of Water in which they float, will al- low ? And does not this Endeavour imply that they have a repulfive Force by which they fly from one another, or at leaft, that they attrad: the Water more llrongly than they do one ano- ther ? For as all things afcend in Water which are lefs attraded than Water, by the gravitating Power of the Earth j fo all the Particles of Salt which float in Water, and are lefs attraded than Water by any one Particle of Salt, muil recede from that Particle, and give way to the more at- traded V/ater.
When any faline Liquor is evaporated to aCu- ticle and let cool, the Salt concretes in regular Figures j which argues, that the Particles of the Salt before they concreted, floated in the Liquor ^t equal difl:ances in rank and file, and by confe- quence that they aded upon one another by fome Power which at equal diilances is equal, at une- qual diftances unequal. For by fuch a Power they will range themfelves uniformly, and with- out it they will float irregularly, and come to- gether as irregularly. And fmce the Particles of Ifland-Cryftal ad all the fame way upon the Rays of Light for caufing the unufual Re- fradion, may it not be fuppofed that in the For- mation of this Cryfl:al, the Particles not only ranged themfelves in rank and file for concreting in regular Figures, but alfo by fome kind of po- lar Virtue turned their homogeneal Sides the fame way.
The Parts of all homogeneal hard Bodies which fully touch one another, flick together
N'ery
364 OPTIC K S.
very ftrongly. And for explaining how this may be, fome have invented hooked Atoms, which is begging the Queftion^ and others tell us that Bodies are glued together by reft, that is, by an occult Quf.lity, or rather by nothing; and others, that they flick together by confpi- ring Motions, that is, by relative reft . amongft themfelves. I had rather infer from their Co- hefion, that their Particles attrad: one another by fbme Force , which in immediate Contaft is ex- ceeding ftrong, at fmall diftances performs the chymical Operations above-mention'd , and reaches not far from the Particles with any fenfi- ble -Effea.
All Bodies fcem to be compofed of hard Par- ticles : For otherwife Fluids would not congeal 5 as Water, Oils, Vinegar , and Spirit or Oil of Vitriol do by freezing ; Mercury by Fumes of Lead; Spirit of Nitre and Mercury, by diflbl- ving the Mercury and evaporating the Flegm ; Spirit of Wine and Spirit of Urine, by deflegm- ing and mixing them; and Spirit of Urine and Spirit of Salt, by fubliming them together to make Sal-armoniac. Even the Rays of Light feem to be hard Bodies ; for otherwife they would not retain different Properties in their different Sides, And therefore Hardnefs may be reckon'd the Property of all uncompounded Matter. At leaft, this feems to be as evident as the univerfal Impenetrability of Matter. For all Bodies, fo far as Experience reaches, are ei- ther hard, or may be harden'd; and we have no other Evidence of univerfal Impenetrability, befides a large Experience without an experi- mental
BOOK III. 365
mental Exception. Now if compound Bodies are fo very hard as we find fome of them to be, and yet are very porous, and confift of Parts which are only laid together j the fimple Par- ticles which are void of Pores, and were never yet divided, muft be much harder. For fuch hard Particles being heaped up together, can fcarce touch one another in more than a few Points, and therefore muft be feparable %by much lefs Force than is requifite to break a fo~ lid Particle, whofe Parts touch in all the Space between them, without any Pores or Interftices to weaken their Cohelion. And how fuch ve- ry hard Particles which are only laid together and touch only .in a few Points, can flick toge- ther, and that (b firmly as they do, without the a{rifi;ance of fomething which caufes them to be attracted or prefs'd towards one another, is very difficult to conceive.
The fame thing I infer alfo from the cohe- ring of two polifh'd Marbles in vacuo^ and from tlie llanding of Quick-filver in the Barometer at the height of 50, 60 or 70 Inches, or above, when ever it is well-purged of Air and careful- ly poured in, fo that its Parts be every where contiguous both to one another and to the Glais. The Atmofphere by its weight prefles the Quick-filver into the Glafs, to the height of 29 or 30 Inches. And fome other Agent railes it higher, not by preihng it into the Glafs, but by making its Parts flick to the Glafs, and to one another. For upon any difcontinuation of Parts, made either by Bubbles or by fhaking the
Glafs,
366 O P T I C K S.
Glafs, the whole Mercury falls down to the height of 29 or 30 Inches.
And of the fame kind with thefe Experi- ments are thofe that follow. If two plane po- lifh'd Plates of Glafs ( fuppofe two pieces of a polifh'd Looking-glafs ) be laid together, fo that their fides be parallel and at a very fmall di- ftance from one another, and then their lower edggs be dipped into Water, the Water will rife up between them. And the lei's the di- ftance of the Glaffes is, the greater will be the height to which the Water will rife. If the diftance be about the hundredth part of an Inch, the Water will rife to the height of about an Inch J and if the diilance be greater or lefs in any Proportion, the height will be reciprocally proportional to the diftance very nearly. For the attractive Force of the Glaffes is the fame, whether the diftance between them be greater or lefsi and the weight of tlie Water drawn up is the fame, if the height of it be recipro- cally proportional to the diftance of the Glaffes. And in like manner , Water afcends between two Marbles polifti'd plane, when their poliftied lides are parallel, and at a very little diftance from one another. And if flender Pipes of Glafs be dipped at one end into ftagnating Wa- ter, the Water will rife up within the Pipe, and the height to which it riles will be reciprocally proportional to the Diameter of the Cavity of the Pipe, and will equal the height to which it rifes between two Planes of Glafs, if the Semir- diameter of the Cavity of the Pipe be equal to the diftance betv/een the Planes, or thereabouts.
And
BOOK IIL 367
An.d thefe Experiments fucceed after the fame manner in 'vacuo as in the open Air, (as hath been tried before the Royal Society, ) and there- fore are not influenced by the Weight or Pref- fiire of t!^e Atmofphere.
And if a large Pipe of Giafs be fiiied with fifted Afhes well preffed together in the Glafs, .and one end of the Pipe be dipped into ftagna- ting Water, the Water will rife up flowly^ in the Afhes, fo as in the fpace of a Week or Fort- night to reach up within the Glafs, to the height of 30 or 40 Inches above the ftagnating Water. And the Water rifes up to this height by the Action only of thofc Particles of the Aihes which are upon the Surface of the elevated Water; the Particles which are within the Water, at- tra6ting or repelling it as much downwards as upwards. And therefore the Action of the Par- ticles is very ftrong. But the Particles of the Alhes being not lb denfe and clofe together as rhofe of Glafs, their Action is not fo flrong as that of Glafs, which keeps Quick- fiiver fuf- pended to the height of 60 or 70 Inches, and therefore a6ls with a Force which would keep Water fufpcnded to the height of above 60 Feet.
By the fame Principle, a Sponge fucks in Water, and the Glands in the Bodies of Ani- mals, according to their feveral Natures and Difpofitions, fuck in various Juices from the Blood. . ■ -
If two plane polifh'd Plates of Gafs three or four Inches broad, and twenty or twenty five long, be laid one of them parallel to the Ho- rizon,
368 O P T I C K S.
1-izon, the other upon the firft, fo as at one of their ends to touch one another, and contain an Angle of about lo or 15 Minutes, and the fame be firft moiften'd on their inward fides with a Glean Cloth dipp'd into Oil of Oranges or Spirit of Turpentine, and a Drop or two of the Oil or Spirit be let fall upon the lower Glafs at thei. other end j fo foon as the upper Glafs is laid • down upon the lower, fo as to touch it at one end as above, and to touch the Drop at the other end, making with the lower Glafs an Angle of about 10 or 15 Minutes; the Drop will begin to move towards the Concourfe of the GlalTes, and will continue to move with an accelerated Mo- tion, till it arrives at that Concourfe of the Glailes. For the two Glaffes attradt the Drop, and make it run that way towards which the At-^ tradlions . incline. And if when the Drop is in motion you lift up that end of the Glaffes where they meet, and towards which the Drop moves, the Drop will afcend between the Glaffes, and therefore is attracted. And as you lift up the Glaffes more and more, the Drop will afcend flower and flower, and at length reit, being then carried downward by its Weight, as much as up- wards by the Attraction. And by this means you may know the Force by which the Drop is attracted at all diftances from the Concourfe of the Glaffes. ^
Now by fome Experiments of this kind, (made by Mr. Hauksbee) it has been found that the Attraction is almofl reciprocally in a dupli- cate Proportion of the diflance of the middle of the Drop from the Concourfe of the Glaffes,
viz.
BOOK III. 369
1/2;. reciprocally in a limple Propoition, by rea- fon of the fpreading of the Drop, and its touch- ing each Glafs in a larger Surface; and again re- ciprocally in a fimple Proportion, by* reaibn of the Attradions growing ftronger within the fame quantity of attracting Surface. The At- traction therefore within the fame quantity of attrading Surface, is reciprocally as the diftance between the Glaiies. And therefore where the diftance is exceeding fmall, the Attraction muft be exceeding great. By the Table in the fe- cond Part of the fecond Book, wherein the thicknefles of colour'd Plates of Water be- tween two Glafles are fet down, the thicknefs of the Plate where it appears very black, is three eighths of the ten hundred thoufandth part of an Inch. And where the Oil of O- ranges between the Glafles is of this thicknefs, the Attraction coUeCled by the foregoing Rule, feems to be fo ftrong, as within a Circle of an Inch in diam.eter, to fuffice to hold up a Weight equal to that of a Cylinder of Water of an Inch in diameter, and two or three Fur- longs in length. And where it is of a lefs thicknefs the Attraction mny be proportionally greater, and continue to increafe, until the thicknefs do not* exceed that of a iinglc Par- ticle of the Oil. There are therefore Agents in Nature able to make the Particles of Bo- dies ftick together by very ftrong Attractions. And it is the Bufinefs o£ experimental Philofophy to find them out.
B b ^ . Now
370 O P T I C K S.
fjow the fmalleft Particles of Matter may co- here by the ftrongeil Attra61:ions, and compofe bigger Particles of weaker Virtue ; and many of thele may* cohere and compofe bigger Particles whofe Virtue is flill weaker, and fo on for divers Succeffions, until the Progrellion end in the big- geft Particles on which the Operations in Chymi- Itry, and the Colours of natural Bodies depend, and which by cohering compofe Bodies of a fen- fible Magnitude. If the Body is compact, and bends or yields inward to Preflion without any Hiding of its Parts, it is hard and elaftick, re- turning to 'its Figure with a Force riling from the mutual AttracCtion of its Parts. If the Parts flide upon one another, the Body is mal- leable or foft. If they flip eafily, and are of a fit Size to be agitated by Heat, and the Heat is big enough to keep them in Agitation, the Body is fluid ; and if it be apt to flick to things, it is humid ; and the Drops of every fluid affed a round Figure by the mutual Attradiion of their Parts, as the Globe of the Earth and Sea affedrs a round Figure by the mutual Attraction of its Parts by Gravity,
Since Metals difTolved in Acids attradt but a fniall quantity of the Acid, their attradiive Force can reach but to a fmall diftance from them. And as in Algebra, where affirmative Quanti- ties vanifli and ceafe, there negative ones be- gin J fo in Mechanicks, where Attradion cea- fes, there a repulfive Virtue ought to fucceed. And that there is fuch a Virtue, feems to fol- low from the Reflexions and Inticxions of the I Rays
BOOK III. 371
Rays of Light. For the Rays are repelled by Bodies in both thefe Cafes, without the imme- diate Contad; of the reflecting or inflecting Bo- dy. It feems alfo to follow from the Emillion of Light ; the Ray fo foon as it is ihaken off from a fhining Body by the vibrating Motion of the Parts of the Body, and gets beyond the reach of Attraction, being driven away with ex- ceeding great Velocity. For that Force which is fufficient to turn it back in Reflexion, may be fufficient to emit it. It feems alfo to fol- low from the Produdion of Air and Vapour. The Particles when they are fjjaken off from Bodies by Heat or Fermentation, fo foon as they are beyond the reach of the Attradion of the Body, receding from it, and alfo from one another with great Strength, and keeping at a diftance, fo as fometimcs to take up above a Million of Times more fpace than they did be- fore in the form of a denfe Body. WliicJi vafh Contradion and Expanfion feems unintelligible, by feigning the Particles of Air to be fpringy and ramous, or rolled up like Hoops, or by any other means than a repulfive Power. The Particles of Fluids which do not cohere 100 ftrongly, and are of fuch a Smallncfs as renders them mofl: fufceptibk of thofe Agitations which keep Liquors \n a Fluor, are mofl: eafily fepa- rated and rarifled into Vapour, and in the Lan- guage of the Chymifl:s, they are volatile, rari- fying with an eafy Heat, and condenfing with Cold. But thofe which are groffer, and fo lefs ibfceptible of Agitationj or cohere by a flironger B b 2 Attradion,
372 O P T I C K S.
Attradlon, are not feparated without 'a fironger Pleat, or perhaps not without Fermentation. And thefe iaft are the Bodies which Chymifls call fix'd, and being rarified by Fermentation, become true permanent Air j thofe Particles re- ceding from one another with the greateft Force, and being moft difficultly brought toge- ther, which upon Conrad: cohere moft ftrongly. And becaufe the Particles of permanent Air are grofter, and arife from denfer Subftances than thofe of Vapours, thence it is that true Air is more ponderous than Vapour, and that a moift Atmofphere is lighter than a dry one, quantity for quantity. From the fame repelling Power it feems to be that Flies walk, upon the Wa- ter -without wetting their Feet ; and that the Obje<5t-giaiTes of long Telefcopes lie upon one another without touching j and that dry Pow- ders are difficultly made to touch one ano- ther fo as to ftick together, unlefs by melting them, or wetting them with Water, which by exhaling may bring them together ; and that two poliih'd Marbles, which by immediate Con- tad ftick together, are difficultly brought fo clofe together as to ftick.
And thus Nature will be very conformable to herfelf and very fimple, performing all the great Motions of the heavenly Bodies by the Attradion of Gravity which intercedes thofe Bodies, and almoft^U the fmall ones of their Particles by fome other attractive and repelling Powers which intercede the Particles. The Vis inertias is a paffive Principle by which Bo- dies
BOOK III. 373
dies perfift in their Motion or Reft, receive Mo- tion in proportion to the Force kiiprefTing it, and refift as much as they are itfifted. By this Principle alone there never could Ivxvq been any Motion in the World. Some other Principle was neceffary for putting Bodies into Motion ; and now they are in Motion, fome other Prin- ciple is neceflary for conferving the Motion. For from the various Compofition of two Mo- tions, 'tis very certain that there is not always the fame quantity of Motion in the World. For if two Globes joined by a Ilendtr Rod, revolve • about their common Center of Gravity with an uniform Motion, while that Center moves on uniformly in a right Line drawn in the Plane of their circular Motion j the Sum of the Motions of the two Globes, as often as the Globes are in the right Line defcribed by their common Center of Gravity, will be bigger than the Sum of their Motions, when they are in a Line perpendicular to that right Line. By this Liftance it appears that Motion may be got or loft. But by reafon of the Tenacity of Fluids, and Attrition of their Parts, and the Weakneli of Elafticity in Solids, Motion is much more apt to be loft than got, and is always -upon the Decay. For Bodies which are either abfolutely hard, or fo foft as to be void of Elafticity, will not rebound from one another. Impene- trability makes them only ftop. If two equal Bodies meet diredly t^i 'vacuo, they will by the Laws of Motion ftop where they meet, and lofe all their Motion, and remain in reft, unlefs
B b 3 they
374 O P T I C K S.
they be elafcick, and receive new Motion froi^ their Spring. If they have lb much Elafticit] aSifuffices to make them re- bound with a quar- ter, or half, or three quarters of tlie Force with which they come together, they will lofe three quarters, or half, or a quarter of their Motion. And this may be try'd, by letting two equal Pendulums fall againft one another from equal heights. If the Pendulums be of Lead or foft Clay, they will lofe all or almoft all tlieir Mo- tions: If of elaftick Bodies they will lofe all but what they recover from their Elafticity. If it be faid, that they can lofe no Motion but what . they communicate to other Bodies, the confe- quence l;, that i?t vacuo they can lofe no Mo- tion, but when they meet they muft go on and penetrate one another's Dimenlions. If three equal round Veffels be filled, the one with Wa- ter, the other with Oil, the third with molten Pitch, and the Liquors be ftirred about alike to give them a vortical Motion j the Pitch by its Tenacity will lofe its Motion quickly, the Oil being lefs tenacious will keep i^ longer, and the Water being lefs tenacious will keep it long- eft, but yet will lofe it in a fliort time. Whence it is eafy to underftand, that if many contiguous Vortices of molten Pitch were each of them as large as thofe which fome fuppofe to revolve about the Sun and fix'd Stars, yet thefe and all their Parts would, by their Tenacity and Stiffnefs, communicate their Motion to one another till they all refted among themfelves. Vortices of Oil or Water, or fome fluider Matter, might
continue
BOOK III. 375
continue longer in Motion ; but unlefs the Mat- ter were void of all Tenacity and Attrition of Parts, and Communication of Motion, (which is not to be fuppofed,) the Motion v/ould con- ftantly decay. Seeing therefore the variety of Motion which we find in the World is ahvays decreafing, there is a neceflity of confer ving and recruiting it by adive Principles, fuch as are the caufe of Gravity, by which Planets and Comets keep their Motions in their Orbs, and Bodies acquire great Motion in falling; ai>d the caufe of Fermentation, by which the Heart and Blood of Animals are kept in perpetual Motion and Heat; the inward Parts of the Earth are conftantly warm'd, and in fome places grow very hot; Bodies burn and fhine. Mountain^ take Fire, the Caverns of the Earth are blown up, and the Sun continues violently hot and lucid, and warms all things by his Light. For we meet with very little Motion in the World, befides what is owing to thefe ad:ive Principles. And if it were not for thefe Principles, the Bo- dies of the Earth, Planets, Comets, Sun, and all things in them, would grow cold and freeze, and become inadtive Mafles ; and all Putrefadi- on, Generation, Vegetation and Life would ceafe, and the Planets and Comets would not remain in their Orbs.
All thefe things being confider'd, it feems pro- bable to me, that God in the Beginning form'd Matter in folid, mafly, hard, impenetrable, move- able Particles, of fuch Sizes and Figures, and with fuch other Properties, and in fuch Proportion
B b 4 to
376 OPTIC K S.
to Space, as moft conduced to the End £o\ which he form'd them j and that thefe primi-) tive Particles being Solids, are incomparably harder than any porous Bodies compounded of them J even lb very hard, as never to v^^ear or break in pieces ; no ordinary Pov^er being able to divide what God himfelf made one in the jErft Creation. While the Particles continue entire, they may compofe Bodies of one and the fame Nature and Texture in all Ages : But fhould they wear away, or break in pieces, the Nature of Things depending on them, would be chan- ged. Water and Earth, compofed of old worn Particles and Fragments of Particles, would not be of the fame Nature and Texture now, with Water and Earth compofed of entire Particles in the Beginning. And therefore, that Nature may be lafting, the Changes of corporeal Things are to be placed only in the various Separations and new Aflbciations and Motions of thefe per- manent Particles j compound Bjodies being apt to break, not in the midfi of fclid Particles, but where thofe Particles are laid together, and only touch in a few Points.
It feems to me farther, that thefe Particles have not only a Vis i?ierticej accompanied with fuch paffive Laws of Motion as naturally refult from that Force, but alfo that they are moved by certain adive Principles, fuch as is that of Gravity, and that which caufes Fermentation, and the Cohefion of Bodies. Thefe Principles I confider, not as occult Qualities, fuppofed to refult from the fpeciiick Forms of Things, but
as
BOOK in. 377
PS general Laws of Nature, by which the Things themfelves are form'd; their Truth appearing to us by Phenomena, though their Caufes be not yet difcover'd. For theie are manifeil Qua- lities, and their Caufes only are occult. iVud the Arijloteiians gave the Name of occult Qua- lities, not to manifeil Qualities, but to iuch Qualities only as they fuppofed to lie hid im Bodies, and to be the unknown Caufes of ma- nifeft Effeds : Such as would be the Caufes of Gravity, and of m.agnetick and eledrick At- tradtions, and of Fermentations, if we fliould fuppofe that thefe Forces or Adions arofc from Qucilities unknov/n to us, and uncapable of be- ing difcovered and made manifeil. Such oc- cult Qualities put a Hop to the Improvement of natural Philofophy, and therefore of. late Years have been rcjedled. To tell us that e-r very Species of Thii^gs is endow'd with an oc- cult fpecifick Quality by which it ads and pro- v duces manifefl Etfeds, is to tell us nothing: But to derive two or three general Principles of Mo- tion from Phaenomena, and afterwards to tell us how the Properues and Adions of ail corporeal Things follow from thofe manifeil Principles, would be a very great ilep in Philofophy, though the Caufes of thofe Principles were not yet dif- cover'd : And therefore I fcruple not to propbfe the Principles of Motion above-mention'd, they being of very general Extent, and leave tl^ir* Caufes to be found out.
Now by the help of thefe Principles, all ma- terial Things feern to have been comoofed of
the
378 O P T I C'k S.
the hard and folid Particles above-mention'! varioufly aiTociated in the iirfl Creation By th) Counfel of an intelligent Agent. For it beeame) him who created them to fet them in order. And if he did fo, it's unphilofophical to feek for any other Origin of the World, or to pre- tend that it might arife out of a Chaos by the mere Laws of Nature j though being once form'd, it may continue by thofe Laws for ma- ny Ages. For while Comets move in very ex- centrick Orbs in all manner of Pofitions, blind Fate could never make all the Planets move one and the fame way in Orbs concentrick, fome inconfiderable Irregularities excepted, which may have rifen from the mutual Ad:ions of Comets and Planets upon one another, and which will be apt to increafe, till this Syflem wants a Reformation. Such a wonderful Uni- formity in the Planetary Syflem mufl be allow- ed the Effect of Choice. And fo muft the Uniformity in the Bodies of Animals, they ha- ving generally a right and a left fide fhaped a- like, and on either fide of theii: Bodies two Legs behind, and either two • Arms, or two Legs, or two Wings before upon their Shoul- ders, and between their Shoulders a Neck run- ning down into a Back-bone, and a Head up- on it J and in the Head two Ears, two Eyes, a Nofe, a Mouth, and a Tongue, alike fituated. •Alfo the firfl Contrivance of thofe very artifi- cial Parts of Animals, the Eyes, Ears, Brain, Mufcles, Heart, Lungs, Midriff, Glands, La- rynx, Hands, Wings, fwimming Bladders, na- tural
BOOK III. 379
. nral Spedlacles, and other Organs of Senfe and Motion J and the Inftin(!^ of Brutes and Infeds, can be the effed of nothing elfe than the Wif- dom and Skill of a powerful ever-living Agent, who being in all Places, is more able by his Will to niove the Bodies within his bound- lefs uniform Senforium, and thereby to form and reform the Parts of the Univerfe, than we are by our Will to move the Parts of our own Bodies. And yet we are not to confider the World as the Body of God, or the feveral Parts thereof, as tlie Parts of God. He is an uni- form Being, void of Organs, Members or Parts, and they are his Creatures fubordinate to him, and fubiervient to his Will j and he is no more the Soul of them, than the Soul of Man is the Soul of the Species of Things carried through the Organs of Senfe into the place of its Sen- fation, where it perceives them by means of its immediate Prefence, without the Intervention of any third thing. The Organs of Scnic are not for enabling the Soul to perceive the Spe- cies of Things in its Senforium, but only for conveying them thither j and God has no need of fuch Organs, he being every where prefent to the Things themfelves. And fince Space is divifible in injimtum^ and Matter is not necef- farily in all places, it may be, alfo allow'd that God is able to create Particles of Matter of fe- veral Sizes and Figures, and in feveral Propor- . tions to Space, and perhaps of different Denli- ties and Forces, and theieby to vary the Laws of Nature, and make Worlds of feveral forts in
feveral
380 O P T I C K S.
feveral Parts of the Univerfe. At leafl, I fee i^j- thiiig of Contradidiion in all this.
As in Mathematicks, fo in Natural Philofo- phy, the Inveftigation of difficult Things by the\ Method of Analyfis, ought ever to precede the Method of Compofition. This Analylis con- fifts in making Experiments and Obfervations, and in drawing general Concluiions from them by Induction, and admitting of no Objections againft the Conclufions, but fuch as are taken from Experiments , or other certain Truths. For Hypothefes are not to be regarded in ex- perimental Philofophy. And although the ar- guing from Experiments and Obfervations by Induction be no Demonftration of general Con- clufions ; yet it is the befl way of arguing which the Nature of Things admits of, and may be looked upon as fo much the flronger, by how much the Induction is more general. And if no Exception occur from Phaenomena, the Con- clufion may be pronounced generally. But if at any time afterwards any Exception fliall oc- cur from Experiments, it may then begin to be pronounced with fuch Exceptions as occur. By this way of Analylis we may proceed from Com- pounds to Ingredients, and from Motions to the Forces producing them j and in general, from Effeds to their Caufes , and from particular Cauies to more general ones, till the Argument end in the moll general. This is the Method of Analyfis : And the Synthefis coniifls in af- fuming the Caufes difcover'd, and eftablifh'd as Principles, and by them explaining the Phae-
nomena
{ BOO K III. 381
noraena proceeding from them, and proving the Explanations."
In the two firfl -Books of thefe Opticks, I . proceeded by this Analyfis to difcover and prove ' the original Differences of the Rays of Light in refped: of Refrangibility, Reflexibility, and Co- lour, and their alternate Fits of eafy Reflexion and eafy Tranfmiffion, and the Properties of Bodies, both opake and pellucid, on which their Reflexions and Colours depend. And thefe Difcoveries being proved, may be alTumed in the Method of Compofition for explaining the Phzenomena arifmg from them: An In- ftance of which Method I gave in the End of the firft Book. In this third Book I have only begun the Analyfis of what remains to be dif- cover'd about Light and its Eflfcdts upon the Frame of Nature, hinting feveral things about it, and leaving the Hints to be examin'd and improv'd by the farther Experiments and Ob- fervations of fuch as are inquifitive. And if natural Philofophy in all its Parts, by purfuing this Method, Ihall at length be perfedied, the Bounds of Moral Philofophy will be alfo enlar- ged. For fo far as we can know by natural Philofophy what is the firlt Caufe, what Power he has over us, and what Benefits we receive from him, fo far our Duty towards him, as well as that towards one another, will appear to us by the Light of Nature. And no doubt, if the Worlhip of falfe Gods had not blinded the Hea*- then, their moral Pmioibphy would have gone farther than to the four Cardinal Virtues j and
infi:ead
382
O P T I C K S.
infteadof teaching the Tranfmigration of Souls, and to worfhip the Sun and Moon, and dead Heroes, they would have tajught us to worfhip our true Author and Benefactor, as their Ance- ftors did under the Government of Noah and his Sons before they corrupted themfelves.
FINIS.
BOOKS printed for William Innys.
Is A A CI Newtoni, Equ. Aur. in Academia Cantabrigienfi Ma- thefeos olim Profeflbris Lucafiani Leftiones opiicae. 4/0. 1729.
The fame in Englijh. %vo. 1728.
Univerfal Arithmctick. By Sir Ifaac Newton. The Second E- dition. %vo. 1728.
Opticas : Sive de Reflexionibus, Refraflionibus, Inflexionibus & Coloribus Lucis Libri ties, Authore Ifaaco Newton, Equite Au- rato. Latine reddidit Samuel Clarke, S. T. P. Editio fecunda, auftior. 8cff. 1719-
Philofophise Naturalis Principia Mathcmatica. Authore Ifaaco Newton, Equ. Aur. Editio tertia, aufta ^ emendata. \to. 1726.
The Method of Fluxions both Direft and Inverfe : The former being a Tranllation from the Marquis de V Hofpital, and the latter fupplied by the Tranflator, E. Stone, F. R. S. Jn two Volumes. %vo. 1730. _ /
Epiilola ad amicum de Cotelii Inventis Ciirvarum ratione, ^V. \to. 1722.
An Analytick Treatife of Conic Sedlions. By E. Stone. \t9.
Mathematical Elements of Natural Phiiofophy confirm'd by Ex- periments : Or an Introduftion to Sir Ij'aac Newton's Phiiofophy. By1V.J.'sGravefandt,hL.D. In two Vols. 8:/^. The Third Edition. 1726.
Phyfico-Theology : Or a Demonftration of the Being and Attri- butes of God, from his Works of Creation ; with large Notes and many curious Obfervations. By IV. Derham, Canon of WindjoTy and F. R. S. The Seventh Edition. %vo. 1727.
Mr. Derhani's Allro-ThcoJogy : Or a Demonftration of the Be- ing and Attributes of Gc I from a Survey of the Heavens; with Cuts. The Fifth Edition. Sr-a. 1726.
Philofophical Letters between the la:e Learned Mr. Ray and fe- veral of his Ingenipus Correfpendents, Natives and Foreigners. To which are added thofe of fra^icis Wiiloughby, Efq; The whole confining of many curious Difcoverics and Improvements in the Hii^ory of Quadrupeds, Birds, Fifr.es, Infefts, Plants, Fofiils, Fountains, idc. Publifhed by Mr. Dcrhatn. Zvo.
Mr. Ray\ Three Phyiico-Theologlcal Difcourfes, concerning I. The primitive Chaos, and Creation of the World. II. The general Deluge, its Caufes artd EfFedls. III. The DilTolution of the World and future Conflagration, l^c. Illuftrated with Copper- Plates. The fourth Edition, with Additions. %vo.
His Wifdom of God in the Works of the Creation. The
Ninth Edition. %vo. 1727.
Mr. Ronayne\ Treatile of Algebra. The Second Edition, with Additions. Sec. 1727
Geometria Organica : Sive Defcriptio Linearum Curvarum uni- verfilis. Auftore Colino Mac Laurin, Math. Col. Abred. Prof. & R. S. S. 4/(?. 1720.
Aa
BOOKS printed for W. I n N y s. •
An Introduftion to Natural Philofophy : Or PhiJorophrcal Le- £lures read in the Univerfity of Oxford, A. D. 1 700. To which zre added, The DcmonHrations of Mr. Huyge?;is Theorems, con- cerning Force and circular Motion. By yo/:?n Kei'/, M. D. Sav. Prof, of Allronomy, and F. R. S. The Second Edition. Svff.
PhilofophicrJ Tranfaclinns, giving fome Account of the prefent "Ehidertakings, Studies and Labours of the Ingenious, in many con- fiderable Parts of the World. Vol. 36. Continued and publifh'd by JV. Rr/ity, M. D. and Reg. Soc. Seer. 4/1?. 1730.
The Lives of the French, Italian and Gerjnaii Philofophers, late Members of the Royal Academy of Sciences in Paris. Together with Abftracls of the chqicefl Pieces communicated by them to that Tlluftrious Society. To which is added, the Preface of the Ingeni- ous Monfieur Fonicnelie, Sccretgry and Author of the Hiilory of the faid x'\cademy, ^vo.
\Leonaidi Plukeneti'. M. D. Opera omnia Botanica in fex Tomoe divifa,. viz. I. II. III. Phytographise. IV. Almageftum Botani- <wm. V. Almagefti Botanici MantifTa. VI. Amaltheum Botani- cum in quibus Stirpes illuftriores minus cognitae, exoticae, Rarioref- due novjffime detcftae ad plures Chiliadas defcribuntur. Turn ionibus Tabulis JEntis CCCCLIV. fumma cura depiftis Figu- fintur.
I Methodus Incrementorum direfla & univerfa. Auftore Brook Taylor, L. L. D. & Reg. Soc. Seer. 4/^. 171 7. i The Pollhumous Works of Dr. Robert Hcoke; in which, I. The j^refcnt Deficiency of natural Philofophy is difcourfed of, with tiie Methods of rendring it more certain and beneficial. II. Of the Nature, Motion and Effedls of Light, particularly that of the Sun and Comets. III. An hypothetical Explication of Memory ; how the Organs made ufe of by the Mind in its Operation may be inechanically underftood. IV. An Hypothefis and Explication of ^e Cauie of Gravity, or Gravitation, Maignetifm, iffc. V. Dif- courfes of Earthquakes, their Caufes and Effects, and Hiftories of fcveral : To which are annex'd, Phyfical Explicntions of feveral of the Fables in Oviifs Metamorphofis, very difisrent from other Mythologick Interpreters. VI. Ledures for improving Navi- gation and Aftronomy, with the Defcriptions of feveral new and ufeful Inlh-uments-, illuftrated with Sculptures To thefe Dif- courfes is prefix'd the Author's Life. By Richard IVttller, R. S. Seer. Folio.
Synopfis Univerfa Medicina TraFltca : Sive doftiffimorum vi- rorum de Morbis eorumque Caufis ac Rem.ediis judicia. Accefle- runt nunc demum cafus nonnulli oppido rari. Authorc J. Allen, M.D. Editio tertia;, prioribus, triente plus, auftior. In 2 Vol. 'ivo. 1729.
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