,:jr;»^ ',— :^- i\ n -fk ■n^ THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES GIFT Dr. K. N. Beigelman jt" •^^IL- ' • t,^/9''77tieifpoJition 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 refradion of thofe Rays to be the bending or breaking of thofe lines in their [3 ] their pading out of one Medium into another. And thus may Rays and Refradions be confi- dered, if Light be propagated in an inftant. But by an Argument taken from the JEquz^ tions of the times of the Edipfes of Ji^piter's Satellites it Teems that Light is propagated in time, {pending in its pallage from the Sun to us ifpofition to be refleiiedor turned back into the fame Medium from any other Medium up07i whofe Surface they fall. And Rays are more or lefs re flexible^ which are turned back more or lefs eafily. As if Light pafs out of Glafs into Air, and by being inchned more and more to the common Surface of the Glafs and Air, begins at length to be totally re- lleded by that Surface ; thofe forts of Rays which at like Incidences are refleded moll co- pioufly, or by inclining the Rays begin fooneft to be totally refleded, are moft reflexible. D E F I N. IV. The Angle of Incidence is that Angle, which the Line defcribed by the incident Ray contains with the Perpendicular to the refleBing or re- fradiing Surface at the Toint of Incidence. B X D E F I N. C 4 ] D E F I N. V. The Angle of Reflexion or Refradiion^ is the Angle which the line defer ibed by the refleE^ed cr refraCied Ray containeth with the 'Perpendi- cular to the refleBing or refraUing Surface at the Toint of Incidence. D E F I N. VI. The Sines of Incidence, Refle:}iion, and Re fra- il ion, are the Sines of the Angles of Incidence^ Reflexion, and Refra^ion. D E F I N. VII. The Light whofe Rays are all alike Refran- gible, I call Simple , Homogeneal and Similar ; and that whofe Rays are feme more Refrangible than others, I call compound, Heterogeneal and 'Difflmilar. The former Light I call Homoge- neal, not becaufe I would affirm it fo in all re- fpeds ; 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- mary, Homogeneal and Simple, and thofe of Heterogeneal Lights, Heterogeneal and Com- pound. For thefe are always compounded of the colours of Homogeneal Lights ; as will ap* pear in the following Difcourfe. AXIOMS. [5] AXIOMS. A X. I. THE Angles- of Reflexion^ and RefraUton^ lie hi one and the fame Tlane with the Angle of Incidence. A X. II. The Angle of Reflexion is equal to the Angle of Incidence, A X. III. If the RefraBed Ray be returned diredily back to the Toint of Incidence ., it fhall be re- framed into the Line before defer ibed by the iu' cident Ray. A X. IV. Refra5fion out of the rarer Medium into the denfer, is made towards the Perpendicular^ that is., fo that the Angle of Refraction be lefs than the Angle of Incidence, A X. V. The Sine of Incidence is either accurately or very nearly in a given Ratio to the Sine of Re- fradi'ton. Whence if that Proportion be known in any one Inclination of the incident Ray, 'tis known in all the Inclinations, and thereby the Refra- ftion in all cafes of Incidence on the fame refra- fting Body may be determined. Thus if the B 3 B.efra^ 1^1 -Refradion be made out of Air into Water, the Sine of Incidence of the red Light is to the Sine of its Refraction as 4 to 3. If out of Air into Gkfs, the Sines are as 17 to n. In Light of other Colours the Sines have other Proportions : but the difference is fo httle that it need feldom be confidered. Suppofe therefore, that RS [in Fig. i.] repre- fents the Surface of llagnating 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 relieved or refrafted, and I would. know whither this Ray fhall go after Reflexion or Refradion : I eredt upon the Surface of the Water from the point of Incidence the Perpendicular C P and produce it downwards to Q, and conclude by the firfl Axiom , that the Ray after Reflexion and Re- fradion, lliall be found fomewhere in the Plane of the Angle of Incidence AC P produced. I let fall therefore* upon the Perpendicular C P the Sine of Incidence AD; and if the refleded Ray be defired , I produce AD to B f o that DB be equal to AD, and draw C B. For this Line CB Ihall be the refleded Ray ; the Angle of Reflexion BCPand its Sine BD being e- qual to the Angle and Sine of Incidence, as they ought to be by the fecond Axiom. But if the' refraded 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 ACP with the Radius C A defcribing a Circle A BE, I draw Parallel to the Perpendicular C P Q, the Line H E cutting the Circum- C7] Circumference in E, and joyningCE, this Line C E iliall be the Line of the refrafted Ray. For if E F be let fall perpendicularly on the Line PQ, this Line EF fliall be the Sine of Re- fraction of the Ray CE, the Angle ofRefradtion being E C Q ; and this Sine E F is equal to D H, and confequently in Proportion to the Sine of Incidence A D 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 poliflied 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 paffing crofs this Prifm be defired : Let ACB [in Fi^. i.] reprefent a Plane cutting this Prifm tranveruy to its three Parallel lines or edges there where the Light pafleth through it, and let D E be the Ray inci- dent upon the firlt lide of the Prifm AC where the Light goes into the Glafs ; and by putting the Proportion of the Sine of Incidence to the Sine of Refradion as 17 to 11 find EF the firii refracted Ray. Then taking this Ray for the Incident Ray upon the fecond fide of the Glaf? B C where the Light goes out, find the next refra6led Ray EG by putting the Proportion of the Sine of Incidence to the Sine of Re- fraftion as 11 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 mud on the contrary be to the Sine of Refradion as 11 to 17, by the third! Axiom. B 4 Much [8] Much after the fame manner, if ACBD [in Fig. 3.'] reprefcnt a Glafs fpherically Convex on both fides (ufually called a Lefis, fuch as is a Burn- ing-glafs, or Spedacle glafs, or an Objed glafs of a Telefcope) and it be required to know how Light falling upon it from any lucid point Q fliall be refraded, let Q M reprefent a Ray falling upon any point M of its firll fpherical Surface A C B, and by ere61jng a Perpendicular to the Glafs at the point M, find the firft re- frafted 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 ^ by the Proporti- on of the Sines 11 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. TJomogeneal Rays which flow from fever al "Joints of any ObjeBy and fall perpendicularly or almoft perpendicularly on any reflecting or refr ail- ing ^lane or fpherical Surface^ Jhall afterwards diverge fromfo many other Toints, or be Parallel to fo many other Lines y or converge to fomojiy other T'oints, either accurately or without any fenfible Error. And the fame thing will happen^ if the Rays be reflected or refradted fucceflively by two or three or more ^lane 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- ven, that of the refleded or refraded ones may be en be found by finding the Rcfra^lion of any two Rays, as above; or more readily thus. Caf. !.• Let A C B [in Fig. 4.] be a receding or refracting Plane, and Q the Focus of the incident Rays, and Q ^ Ca perpendicular to that Plane. And if this perpendicular be produced to ^, fo that ^ C be equal to Q C, the point q, fliall . be the Focus of the refleded Rays. Or if f G be taken on the fame fide of the Plane with Q C and in Proportion to Q C as the Sine of Incidence to the Sine of Rcfra6tion, the point q fliall be the Focus of the refraded Rays. Caf. 2. Let AC B [in Fig. 5-.] be the refleding Surface of any Sphere whofe Center is E. Bi- feft any Radius thereof (fuppofe EC.) in T, and if in that Radius on the fame fide the poinc T you take the Points Q and ^, fo that TQ, TE, and T ^, be continual Proportionals, and the point Q be the Focus'of the incident Rays, the pointy lliall be the Focus of the refleded ones. Caf I. Let ACB [in Fig. 6.] be the refrading Surface of any Sphere whofe Center is E. In any Radii^s 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 leder of the Sines of Incidence and Re- fradion hath to the difference of thofe Sines. And then if in the fame Line you find any two Points Q and q, fo that TQ be to ET as E t to t q^ taking t q the contrary way from t which TQ lieth from T, and if the Point Q be the Focus of any incident Rays, the Point q fliiill be the Focus of the refraded ones. And 3 [lO] And by the fame means the Focus of the Rays after two or more Reflexions or Refrac- tions may be found. Caf.^. Let ACBD [in Fig. 7.] be any refrac- ting Lens, fpherically Convex or Concave or Plane on either fide, and let CD be its Axis (that is the Line which cuts both its Surfaces perpendicularly, and palTes through the Centers , of the Spheres, ) and in this Axis produced let F and/be the Foci of the refraded Rays found as above, when the incident Rays on both fides the Lens are Parallel to the fame Axis ; and upon the Diameter F/bifeded in L, defcribe a Circle. Suppofe now that any Point Q be the Focus of any incident Rays. Draw Q E cutting the faid Circle in T and t, and therein take t q in fuch Proportion to ^ E as ^^ E or T E hath to T Q. Let t q lye the contrary way from t which TQ doth from T, and q fhall be the Focus of the refrafted Rays without any fenfible Error, pro- vided the Point Q be not fo remote from the Axis, nor the Lens fo broad as to make any of the Rays fall too obliquely on the refratling Surfaces. And by the like Operations may the refleding or refrading Surfaces be found when the two Foci are given, and thereby a Lens be formed, which fhall make the Ravs flow towards or from what place you pleafe. 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 ihall after R«- fiexion or Refradion flow from or towards the Point [ " ] Point q found by the foregoing Rules. And if the incident Rays flow from or towards feveral points Q, the refleded or refraded Rays ihall flow from or towards fo many other Points q found by the fame Rules. Whether the reflect- ed and refraded Rays flow from or towards the Point q is eafily known by the fituation of that Point. For if that Point be on the fame fide of the refle61ing or refrading Surface or Lens with the Point Q, and the incident Rays flow from the Point Q, the refleded flow towards the Point q and the refraded from it ; "and if the incident Rays flow towards Q, the reflected flow from q^ and the refraded to'wards it. And the contrary happens when q is on the other fide of that Surface. A X. VII. Wherever the Rays which come from all the Joints of any Obje£i meet again in fo many Totnts after they have been made to converge by Reflexion or RefraBion, there they will make a TiBure of the Object 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-fliut of a dark Chamber, where- by the Rays that come from any Point Q of that Objeft are made to converge* and meet a- gain in the Pointy; and if a Sheet of white Pa- per be held at q for the Light there to fall up- on it: the Pidure of that Objed PR will ap- pear upon the Paper in its proper lliape and Co- lours. C 12 ] lours. For as the Light which comes from the Point Q goes to the Point ^, fo the Light which comes from other Points P and R of the Objeft, will go to fo many other correfpondent Points / and r (as is manifell by the fixth Axiom ;) fo that every Point of the Objed fhall illuminate a coirefpondent Point of the Pidure, and there- by make a Pidure like the Objed in Shape and Colour, this only excepted, that the Pidure fhall be inverted. And this is the reafon of that vulgar Experiment of calling the Species of Ob- jcds from abroad upon a Wall or Sheet of white Paper in a dark Room. In like manner, when a Man views any Objeft PQR, [in Fig.. 8.] the Light which comes from the feveral Points of the Objeft is fo refraded by the tranfparent skins and humours of the Eye, (that is by the outward coat EFG called the Tunica Cornea^ and by the cryflalline hu- mour A B which is beyond the Pupil m k) as to converge and meet again at fo many Points in the bottom of the Eye, and there to paint the Pidure of the Objed upon that skin (called the Tunica Retina) with which the bottorn of the Eye is covered. For Anatomifts when they have taken off from the bottom of the Eye that out* ward and moil thick Coat called the T)ura Ma- ter, can then fee through the thinner Coats, the Piftures of Objeds Hvely painted there- on. And thefe Pidures propagated by Mo- tion along the Fibres of the Optick Nerves in- to the Brain, are the caufe of Vifion. For ac- cordingly as thefe Piftures are perfed or im- perfed, the Objed is feen perfedly or imperfed- I 13 ] ly. If the Eye be tinged with any colour (as in the Difeafe of the Jaund'tfe) {o as to tinge the Figures 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 Ihrinking to make the Cornea and Coat of the Cryfialline humour grow flatter than before, the Light will not be re- fracted enough, and for want of a fuHicient Re- fra61ion 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 Pidure, and according to the indiflind- nefs of this Pidure the Objed will appear con- fufed. This is the reafon of the decay of fight in old Men, and iliews why their Sight is mend- ed by Spedacles. For thofe Convex glafles fup- ply the defed of plumpnefs in the Eye, and by encreafmg 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 diitind, unlefs the Objed be brought fo near the Eye as that the 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 Refradi- ons diminiflied by a Concave-glafs of a due de- gree of Concavity, or laftlv that by Age the Eye C 14] Eye grow flatter till it come to a due Figure: For ihort-fighted Men fee remote Objeds beft in Old Age, and therefore they are accounted to have the moit lading Eyes. A X.. VIIL An ObjeEi feen by Reflexion or RefraBton.^ af fears in that place from whence the Rays af- ter their laft Reflexion or RefraBion diverge in- falling on the SpeEiators Eye. If the Objed A [in Fig. 9.] be feen by Reflexion of a Looking-glafs m n^ it Ihall 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 thefe Rays do make the fame Pidure 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 ihape of that Pidure. In like manner the Obje6l D [in Fig. x.] 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 ^. And fo the Objed Q [in Fig. 10.] feen through the Lens AB, appears at the place q from whence the Rays diverge in pafling from the Lens to the F/ye. Now it is to be noted, that the Image of the C 15] the Objeft at q is fo much bigger or leiTer than the Object it felf at Q, as the diibnce of the Image at q from' the Lens A B is bigger or lefs than the ditlance of the Objedl at Q from the. fame Lens. And if the Objed be feen through two or more fuch Convex or Concave-glalTes, every Glafs fliall make a new Image, and the Objed lliall appear in the place and of the big- nefs of the lalt Image. Which confideration un- folds the Theory of Microfcopes and Telefcopes. For that Theory confifts in almoft nothing elfe than the defcribing fuch GlaHes as fhall make the laft Image of any Objedt as diitind and large and luminous as it can conveniently be made. I have now given in Axioms and their Ex- plications the fumm of what hath hitherto been treated of in Opticks. For what hath been ge- nerally agreed on I content my felf to alTume under the notion of Principles, in order to what I have farther to write. And this may fuffice for an Introduction to Readers of quick Wit and good Underltanding not yet verfed in Op- ticks : Although thofe who are already acquain- ted with this Science, and have handled GlafTes, will more readily apprehend what followeth. TROTO' [ I«] L PROPOSITIONS. TROT. I. Theor. I. IGHTS 'uuhkh differ in Colour ^ differ alfi 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 bide to the other, diflinguiOied it into two e- qiial Parts. One of thefe parts I painted with a red colour and the other with a blew. The Paper was very black, and the Colours intenfe and thickly laid on , that the Phsenomenon might be more confpicuous. This Paper I view'd through a Prifm of folid Glafs, whofe two Sides through which the Light paifed to the Eye were plane and well poliilied, 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 witn the fame Paper [ 17 .] Paper by the Light reflefted from it to theE^^e, 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 refledkd from thence, which in palhng by the edges of the Paper to the Eye, might mingle it felf with the Light of the Paper, and obfcure the Phsenomenon there- of . Thefe things being thus ordered, I ^ound that if the refrafting Angle of the Prifm be turned upwards, fo that the Paper may feem td be lifted upwards by the Refradion, its blue half will be lifted higher by the Refraction than its red half But if the refrading Angle of the Prifm be turned downward , fo that the Paper may feem to be carried lower by the Refra- dion, its blue half, will be carried fomething lower thereby than its red half Wherefore iri both cafes the Light which comes from the blue half of the Paper through the Prifm to the Eye, does in like Circumllances fuffer a greater Refradion than the Light which comes from the red half, and by- contequence is more refrangible. llluftration. In the eleventh Figure, M-N reprefents the Window, and DE the Paper terminated with parallel Sides DJ and HE, and by the tranfverfe Line FG diftinguiCied into two halfs , the one D G of an intenfely blue Colour, the other FE of an intenfely red. And B A C f ^ ^ reprefents the Prifm whofe refrading Planes K^ b a, and h.C c a meet in the edge of the refrading Angle A ^?, This edge A a being upward^ is parallel both lo G the [i8] 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. Av\di d e reprelents the Image of the Paper feen hy Hefi'a(^ion upwards in fuch manner that the blue half DG is carried higher to ^^ than the red half F E is to fe, and therefore fuffers a greater Fvefradion. If the edge of the refradl- ing Angle be turned downward, the Image of the Paper will be refraded downward , fuppofe to ^ £, and the blue half will *be refraded lower to «^>' than the red half is to cp g. Exper. z. About the aforelaid Paper, whofe two halfs were painted over with red and blue, and which was lliff like thin Paltboard, I lapped feveral times a flender thred of very black Silk, in fuch manner that the feveral ' rts of the thred might appear upon the Colours like fo many black Lines drawn over them, or like long and llender dark Shadows call: 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 Hand 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 Itrong- 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 ereded a glafs Lens four Inches and a quarter broad, which r 1^3 which might colleft 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 I- mage of the coloured Paper upon a white Pa- per placed there, after the fame manner that a Lens at a hole in a Window cafts the Images of Objeds abroad upon a Sheet of white Paper in a dark Room. The aforefaid white Paper, e- reeled perpendicular 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 moff diftinc^t. 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 {lender Lines (which by reafon of their blacknefs were Hke Shadows on the Colours) were confufed and fcarce vifi- ble, unlefs when the Colours on either fide of each Line were terminated mofl diflindly. No- ting therefore , as diligently as I could , the places where the Images of the red and blue halfs of the coloured Paper appeared moft di- ftind:, I found that where the red half of the Paper appeared diflindl, 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 moft diflinft, the red half appeared confufed , fo that the black Lines upon it were fcarce vilible. And between the two places where thele Images appeared C 2. diflina F 20 ] diftin^t there was the diftance of an Inch and a half: the diftance of the white Paper from the Lens, when the Image of the red half of the coloured Paper appeared mod diftind, being greater by an Inch and an half than the diitance of the fame white Paper from the Lens, when the Image of the blue half appeared moft di- ftin^l. In like Incidences therefore of the blue and red upon the Lens, the blue was refrafted more by the Lens than the red, fo as to con- vefge fooner by an Inch and a half, and there- fore is more refrangible. Illuftrat'ton. In the twelfth Figure, D E fig- nifies the coloured Paper, DG the blue half, FE the red half, MN the Lens, HJ the white Paper in that place where the red half with its black Lines appeared diltindl, and h i the fame Paper in that place where the blue half appear- ed dillind:. The place h i was nearer to the Lens MN than the place H J by an Inch and an half. Scholium. The fame things fucceed, notwith- flanding that fome of the Circumitances be va- ried : as in the firil 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 Circumitances by which either the PhaB- 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. [21 ] faffice. Now from thefe Experiments it fol- lows not that all the Light of the blue is more Refrangible than all the Light of the red : For both Lights are mixed of Rays diiierently Re- frangible, fo that in the red there are i'ome Hays not lefs Pvcfrangible than thofe of the blue, and in the blue there are fome Rays not more Re- frangible than thofe of the red : But thefe Rays in proportion to the whole Light are but few, and ferve to diminifh the Event of the Expe- riment, but are not able to deilroy it. For if the red and blue Colours were more dilute and weak, the diftance of the Images would be lefs than an Inch and a half ; and if they were more intenfe and full, that didance would be greater, as will appear hereafter. Thefe Experiments may fuffice for. the Colours of Natural Bodies. For in the Colours made by the Rerraftion of Prifms this Propofition will appear by the Ex- periments which are now to follow in the next Proportion. T ROTAl. Theor.il The Light of the Sun conjifts of Rays differently Refrangible, The Proof by Experiments. Ex{er. 3. TN a very dark Chamber at a round X. hole about one third part of an Inch broad, made in the Shut of a Windoiv I placed a Glafs Prifm, whereby the Beam of the Sun's Light which came in at that hole might C 3 be [ 22 ] be refrafled upwards toward the oppofite Wall of the Chamber, and there form a colour'd I- mage of the Sun. The Axis of the Prifm (that is the Line palling through the middle of the Prifm from one end of it to the other end pa- rallel to the edge of the Refrafting Angle) was in this and the following Experiments perpen- dicular to the incident Rays. About this Axis I turned the Prifm llowly, and faw the refra- &d Light on the Wall or coloured Image of the [Sun firit 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 pollute, that it fliould be moved no more. For in that poflure the Re- fractions of the Light at the two fides of the lefrafting 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 alfoin other Experiments, as often as I would have the Re- fradions on both fides the Prifm to be equal to one another, I noted the place where the Image of the Sun formed by the refraded Light flood Hill between its two contrary Motions, in the common Period of its progrefs andregrefs; and when the Image fell upon that place, I made fall the Prifm. And in this Polture, as the molt convenient, it is to be underllood that all the Prifms are placed in the following Experiments, unlefs where fome other poflure is defcribed. The Prifm therefore being placed in this po- flure, I let the refrafted Light fall perpendicu- larly upon a Sheet of white Paper at the oppo- |ite Wall of the Chamber, and obferved the Fi- gur§ [23 3 gure and Dimenfions of the Solar Image form- ed on the Paper by that Light. This Image was Oblong and not Oval, but terminated with two Reftilinear and Parallel Sides, and two Se- micircular Ends. On its Sides it was bounded pretty dillinftly, but on its Ends very confufed- ly and indiftinftly , the Light there decaying and vanifliing by degrees. The breadth of this Image anfvvered to the Sun's Diameter, and was about two Inches and the eighth part of an Inch, including the Penumbra. For the Image was eighteen Feet and an half diitant from the Prifm, and at this diflance that breadth if di- miniflied by the Diameter of the hole in the Window- fliut, 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 the Image was about ten Inches and a quarter, and the length of the Re- dilinear 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 refradling Surface of the Prifm, the Imnge foon became an Inch or two longer, or more ; and if the Prifm was turned about the contrary way, fo as to make the Rays fall more oblique- ly on the firll refrading Surface, the Image foon became an Inch or two fliorter. And there- fore in tr} ing this Experiment, I was as curi- ous as I could be in placing the Prifm by the C 4 above- [ 24] above-mention'd Rule exadlly in fuch a poijure 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- fe6l in increafing the length of- the coloured Spedlrum. For I tried the fame Experiment V/ith other Prifms with the fame Succefs. And particularly with a Prifm which feemed free from fuch Veins, and whofe refrafting Angle was 62,4 Degrees, I found the length of the Irpage 9-+- or 10 Inches at the diftance of 18 4- Feet from the Prifm, the breadth of the hole in the Window-iliut being i of an Inch, as be- fore. And becaufe it is eafy to commit a mi- itake in placing the Prifm in its due poilure, 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 Pohili, which feem- ed free from Veins, and whofe refra<^ling Angle was 63 4 Degrees , the length of this Image at the fame diliance of 18 4 Feet was alfo about 10 Inches, or ro4. Beyond thefe Meafures for about a 7 or 7 of an Inch at either end of the Spe- «ftrum the Light of the Clouds feemed to be a little tinged with red and violet, but fo very faintly, that I fufpec^ted that tincture might ei- ther wholly or in great meafure arife from fome Rays of the Spe61rum fcarrered irregularly by fome inequalities in the Su!.>ltaace and poliih of the Glafsj- and therefore I did not include it in ' ' . • thefe [25] thefe Meafures. Now the different Magnitude of the hole in the Window- Ihut, and different thicknefs of the Prifm where the Rays paffed through it, and different inchnations 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 Vcffel made of poliilied Plates of Glafs cemented together in the lhap& of a Prifm and filled with Water, there is the like Succefs of the Experiment according to the quantity of the Refraftion. , It is farther to be obferved, that the Rays went on in right Lines from the Prifm to the Image, and therefore at their ve- ■ ry 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 [in Fig. 13.'] re- prefent the Window-fliut, Fthe hole made there- m 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 tranfverily through the middle of the Light. Or if you pleafe, let ABC reprefent the Prifm it felf, looking 4i- redly towards the Speftator's-Eye with its near- er end: And let XY be the Sun, MN the Pa- per upon which the Solar Image or Speftrum is caft, and PT the Image it felf whofe fides to- . wards v and w are Redilinear and Parallel, and ends towards P and T Semicircular. YKHP and [20 and X L J T are two Rays, the firfl 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 refradled at L and J. Since the Refradions on both fides the Prifm are e- qual to one another, that is the Refradion at K equal to the Refradion at J, and the Refra- ftion 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 IncUnation 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 v w, and therefore the Image would be round. Thus it would be were the two Rays X L J T and Y K H P, and all the reft which fprip the Image V w T v, 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 go-^ ing to the upper end P of the Image fufFer the* greateft [ 27 3 greatefl Refra6lion, mufl be more refrangible than thofe which go to the lower end T, un- lefs the inequality of Refradion be cafual. This Image or Speftrum P T was coloured, being red at its leall refraded end T, and vio- let at its moft refraded end P, and yellow green and blue in the intermediate Spaces. Which agrees with the firit Propofition, that Lights which differ in Colour do alfo differ in Refrangibility. The length of the Image in the foregoing Experiments I meafured from the fainted and outmoft red- at one end, to the faintelt and outmod 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-fliut, at the dillance -of fome Feet from the hole, I held the Prifm in fuch a po-» dure 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 make the Image of the hole afcend and defcend, when between its two contrary Motions it feemed Stationary, I llopp'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 Prifm 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 moft refraded part thereof appeared violetj the leaft refraded red, ■' ^ • . the. E 28 ] 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 (hining by the Light of the Clouds beyond it. And yet if the Refraftion were done regularly according to one certain Proportion of the Sines of Inci- dence and Refradion as is vulgarly fuppofed , the refradted Image ought to have appeared round. So then, bythefe two Experiments it appears that in equal Incidences there is a confiderable inequality of Refraftions. But whence this in- equaUty arifes, whether it be that fome of the incident Rays are refraded more and others lefs, conftantly, or by chance, or that one and the fame Ray is by Refradion difturbed, fliatrer'd, dilated , and as it were fplit and fpread into many diverging Rays, as Grimaldo fuppofes, *does not yet appear by thefe Experiments, but will appear by thofe that follow. Exper. s- Confidering therefore, that if in the third Experiment the Image of the Sun fliould be drawn out into an oblong form, ei- ther by a Dilatation of every Ray, oc 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 Reffadions fide- ways, I tried what would be the efFeds of fuch a fecond Refradion. For-tliis end I ordered . all things as in the third Experiment, and then placed a fecond Prifm immediately after the firft C 29 ] firft in a crofs Pofition to it, that it might again refraft the beam of the Sun's Light which came to it through the firll Prifm. In the fiiit Prifm this beam was refraded upwards, and in the fecond Tideways. And I found that by the Re- fr^idion of the fecond Prifm the breadth of the Image was not increafed , but its fuperior part which in the firfl Prifm fufFered the greater Refradion and appeared violet and blue, did again in the fecond Prifm fuffer a greater Re- fradion than its inferior part, which appeared red and yellow, and this without any Dilatation of the Image in breadth. Illuftrat'ion. .Let S [in Ftg. 14.] reprefent the Sun, F the hole in the Window, ABC the firll Prifm, D H the fecond Prifm, Y the round Image of the Sun made by a direft beam of Light when the Prifms are taken away, PT the oblong Image of the Sun made by that beam pafRng through the firft 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 Refradion of the firft Prifm, fo that they fliould not any lon- ger go in fmgle Lines to fmgle Points, but that every Ray being fplit, fhattered, and changed from a Linear Ray to a Superficies of Rays di- verging from the Point of Refradion, land ly- ing in the Plane of the Angles of Incidence and Refradion, they fhould go in thofe Planes to fo many Lines reaching almoft from one end of the Image P T to the other, and if that Image fliouid [30] 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 fideways by the tranfverfe Refradion of the fecond Prifm, fo as to com- . pofe a four fquare Image, fuch as is reprefent- ed at TT^. For the better underllanding of which, let the Image P T be diltinguiflied into five e- qual parts PQK, KQRL, LRSM, MSVN, K V T. 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 PQK which takes up a fpace of the fame length and breadth with the Light Y ought to be by the Refradion of the fecond Prifm dilated and drawn out into the long Image -n- qkp^ and the Light KQR L in- to the long Image kqr I, and the Lights LRSM, MSVN, NVT, into fo many other long I- mages Irsm, tnsvn^ nvf\\ and all thefe long Images would compofe the four fquare Image 5r7. Thus it ought to be were every Ray dila- ted by Refraflion, and fpread into a triangular Superficies of Rays diverging from the Point of Refradfion. 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 refradfed more than others. But the Event is otherwife. 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 th^ [ 31 3 the Refraftion tranflated to 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 refrafted in the fecond Prifm thaji the Light which tended towards the lower end T, that is the blue and violet, than the red and yellow ; and therefore was more refrangible. The fame Light was by the Refradion of the firfl Prifm tranflated far- ther from the place Y to which it tended before Refradion ; and therefore fuffered as well in the firlt Prifm as in the fecond a greater Refra- ftion than the reft of the Light, and by con- fequence was more refrangible than the refl, 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 refrafted than the reft in the firft Prifm were alfo more refra£led in all the reft, and that without any Dilatation of the Image fideways : and therefore thofe Rays for their conftancy of a greater Refradion are defervedly reputed more refrangible. But that the meaning of this Experiment may more clearly appear, it is to be confidered 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 perfe6t geo- metrical Circle, but any orbicular Figure whofe length is equal to its breadth, and which, as to fenfe, may feem circular. Let therefore A G 6 [in [ 32 ] [in Fig. If.] reprefent the Circle which all the moil refrangible Rays propagated from the whole Difque of the Sun, would illuminate and paint upon the oppofite \yall if they were a- lone ; E L the Circle which all the leaft refran- gible Rays would in like rnanner illuminate and paint if they were alone; B H, C J, D K, the Circles which fo many intermediate forts of Rays would fucceffively paint upon the Wall, if they were fmgly propagated from the Sun in fucceffive order, the reft being always in- tercepted ; and conceive that there are other intermediate 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 Speftrum P T is . compofed which I de- fcribed 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 Dilatation of the fmgle Rays, or by any other irregularity in the Refradion of the firlt Prifm , converted into the oblong Speftrum , FT: then ought every Circle AG, BH, CJ^ ^c. in that Spedrum, by the crofs Refraftion of the fecond Prifm again dilating or otherwife fcattering the Rays as before, to be in Hke man- ner drawn out and transformed into an oblong Figure, and thereby the breadth of the Image FT r 33 3 P T would be now as much augmented as the length of the Image Y was before by the Refra- dion of the firil Prifm ; and thus by the Refra- dions of both Prifms together would be form- ed a four fquare Figure/ tt t% as I defcribed a- bove. Wherefore lince the breadth of the Spe- drum P T is not increafed by the Refraflion Tideways, it is certain that the Rays are not fplit or dilated, or otherways irregularly fcat- ter'd by that Refradion , but that every Circle is by a regular and uniform Refraftion tranfla- ted entire into another place , as the Circle A G by the greateft Refradion into the place a gy the Circle B H by a lefs Refradion into the place b h, the Circle C J by a Refradion ftill lefs into the place c /', 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 mull be of the fame bignefs with the former, becaufe the breadths of all the Spedrums Y, P T and p t 2X equal diflances from the Prifms are equal. I conlidered farther, that 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 p t. I placed there- fore at that hole a Lens or Objed-glafs of a Te- lefcope which 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 / ^ was D alfo [ 34.] alfo thereby taken away, fo that thofe Sides ap- peared as diftinftly defined as did the Circum- ference of the firlt Image Y. Thus it happens if the Glafs of the Priims be free from Veins, and their Sides be accurately plane and well poUfhed without thofe numberlefs Waves or Curies which ufually arife from Sand-holes a little fmoothed in polifhing with Putty. If the Glafs be only well poHfhed and free from Veins and the Sides not accurately plane but a little Convex or Concave , as it frequently happens ; yet may the three Spedrums Y , P T and / t want Penumbras, but not in equal diftances from the Prifms. Now from this want of Pen- umbras, I knew more certainly that every one of the Circles was refrafted according to fome moil regular, uniform, and conitant law. For if there were any irregularity in the Refraclion, the right Lines A E and G L which all the Cir- cles in the Spedrum P T do touch, could not by that Refraftion be tranflated into the Lines a e and j: / as diftinft and ftraight as they were before, but there would arife in thofe tranflated . Lines fome Penumbra or Crookednefs or Un- dulation, or other fenfible Perturbation con- trary to what is found by Experience. What- foever Penumbra or Perturbation fhould be made in the Circles by the crofs Refradion of the fecond Prifm, all that Penumbra or Pertur- bation would be confpicuous in the right Lines a e and g I which touch thofe Circles. And therefore iince there is no fuch Penumbra or Perturbation in thofe right Lines there mud be none in the Circles. Since the diltahce between thofe [ 35 ] thofe Tangents or breadth of the Speftrum is not increased by the Refradions, the Diameters of the Circles are not increafed thereby. Since thofe Tangents continue to be right Lines, e- very Circle which in the firft Prifm is more or lefs refraded , is exadly in the fame propor- tion more or lefs refradted in the fecond. And feeing all thefe things continue to fucceed af- ter the fame manner when the Rays are again in a third Prifm, and again in a fourth refrad- ed fideways, it is evident that the Rays of one and the fame Circle, as to their degree of Re- frangibility continue always uniform and ho- mogeneal to one another, and that thofe of fe- veral Circles do differ in degree of Refrangibi- lity, and that in fome certain and conllant pro» portion. Which is the thing I was to prove. There is yet another Circumitance or two of this Experiment by which it becomes itill more plain and convincing. Let the fecond Prifm D H [in Fig. i(5.] be placed not im- mediately after the firlt, but at fome diflance from it ; fuppofe in the mid- way between it and the Wall on which the oblong Spedrum P T is cait, fo that the Light from the firil Prifm may fall upon it in the form of an oblong Spedrum tt? parallel to this fecond Prifm, and be refraded fideways to form the oblong . .Spedrum / t upon the Wall. And you will find as before, that this Speftrum / r is inclined to that Spedrum P T, which the firfl Prifm forms"alone without the fecond; theblue ends P and/ being farther diftant from one another" than the red ones T and ^, and by confequence D 2. that c sn that the Rays which go to the blue end ^r of the Image tt? and which therefore futfer the greateft Refraftion in the firlt Prifm, are again in the lecond Prifm more refraded than the reft. The fame thing I try'd alfo by letting the Sun's Light into a dark Room through two ht- tle round holes F and (p [in Fig. 17.] made in the Window, and with two parallel Prifms ABC and ci/Sy placed at thofe holes (one at each) refrading thofe two beams of Light to the oppofite Wall of the Chamber, in fuch man- ner that the two colour'd hnages P T and MN which they there painted were joined end to end and lay in one ftraight Line, the red end T of the one touching the blue end M of the o- ther. For if thefe two refraded Beams were again by a third Prifm D H placed crofs to the two firit, refraded Tideways, and the Spedrums .thereby tranflated to fome other part of the Wall of the Chamber, fuppofe the Speftrum FT to pt and the Spedrum MN to ;i^ Ji, thefe tranflated Spedrums J^f and mn would not lie in one Itraight Line with their ends contiguous as before, but be broken off from, one another and become parallel, the blue end m of the I- niage mn being by a greater Refradion tran- flated farther from its former place MT, than the red end f of the other Image / t from the fame place M T; which* puts the Propofition pafl difpute. And this happens whether the third Prifm D H be placed immediately after the two firft, .or at a great diflance from them, fo that the Light refraded in the two firit [37] firft Prifms be either white and circular, or cq- loured and oblong when it falls on the third. Exper. 6. In the middle of two thin Boards I made round holes a third part of an Inch in diameter, and in the Window -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 refrad it towards the oppofite Wall, 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 reit be intercepted by the Board. Then at the dillance of about twelve Feet from the firit Board I fixed the other Board in fuch man- ner that the middle of the refraded Light which came through the hole in the firft Board and fell upon the oppofite Wall might pafs through the hole in this oiher Board, and the reit 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 re- fract the Light .which came through the hole. Then I returned fpeedily to the firlt Prifm, and by turning it flowly 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 Refradion in the fecond Prifm did pafs ; and by the difference of the places I found that the Light which being mod refraded in the Da • M :^- [ 38 ] firft 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 v/ell the firlt Pro- portion as the fecond. And this happened whether the Axis of the two Prifms were pa- rallel, or inclined to one another and to the Horizon in any given Angles. • Ilhiftratmt. Let F [in Fig. i8.] be the wide hole in the Window (liut, through which the Sun lliines upon the firil Prifm ABC, and let the refrafted Light fall upon the middle of the Board DE, and the middle part of that Light upon the hole G made in the middle of that Board. Let this trajeded part of the 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- ly to and fro about its Axis this Image will be made to move up and down the Board d e^ and by this means all -its parts from one end. to the other may be made to pafs fucceflively through the hole g which is made in the mid- dle of that Board. In the mean while another Prifm ^ ^ r is to be fixed next after that hole g to refrad the trajeded Light a fecond time. And thefe things being thus ordered, I marked the places M and N of the oppofite Wall upon which the refrafted Light fell, and found that whilit the two Boards and fecond Prifm re- mained unmoved, thofe places by turning the firil Prifm about its Axis were changed perpe- a tually. For when the lower part of the Light * which C 39 3 which fell upon the fecond Board d e was caft 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 g^ it went , . to a higher place N on the Wall, and when a- ny intermediate part of the Light was cafl through that hole it went to fome place on the Wall between M and N. The unchanged Po- fition of the Holes in the Boards, made the In- cidence of the Rays upon the fecond Prifm to be the fame in all cafes. And yet in that com- mon Incidence fome of the Rays were more re- fracted and others lefs. And thofe were more refrafted in this Prifm which by a greater Re- fra6lion in the firlt Prifm were more turned out of the way, and therefore for their con- ftancy of being mxore refraded are defervedly called more refrangible. Exper. 7. At two holes. made near one ano- ther in my Windovv-fiiut I placed two Prifms, one at each, which might cad upon the oppo- *fite Wall (after the manner of the third Expe- riment ) two oblong coloured Images of the Sun. And at a little diflance from the Wall I placed a long flender Paper with flraight and parallel edges, and ordered the Prifms and Pa- .per fo, that the red Colour of one Image might fall diredtly upon one half of the Paper, and the violet Colour of. the other Image upon the o- ther 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 firit and fecond Experiments. Then with a black Cloth I covered the Wall behind D 4 the [40 ] the Paper ; that no Light might be reflefled from it to didurb the Experiment, and view- ing the Paper through a third Prifm held pa- rallel to it, I favv that half of it which was il- luminated by the violet Light to be divided from the other half by a greater Refradion, e- • fpecially 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 conti- guous at one of their Angles like the painted Paper in the firlt Experiment. Which alfo happened when the Paper was too broad, Sometimes inilead 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 e d f g are the parts of the Thred feen by Refraction. If one half of the Thred be con- Itantly illuminated with red, and the other half be illuminated with all the Colours fuccellively, (which may be done by caufmg one of the Prifms to be turned about its Axis whiht the other remains unmoved) this other half in view- ing the Thred through the Prifm, will appear in a continued right Line with the firfl half when ' illuminated with red , and begin to be a little divided from it when illuminated with orange*, and remove farther from it when illuminated with yellow, and itill farther when with green, and farther when with blue, and go yet farther off when illuminated with indigo, and fartheft when [41 ] when with deep violet. Which plainly fliews, that the Lights of feveral Colours are more and more refrangible one than another, in this or- der of their Colom's, red, orange, yellow, green, blue, indigo, deep violet ; and fo proves as well the firlt Propofition as the fecond. I caufed alfo the coloured Speftrums P T [in Fig. 17.] and MN made in a dark Cham- ber by the Refradions of two Prifms to lye 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 mji, the violet end m of the Spedrum m n being by a greater Refra- ction tranflated farther from its former place M T than the red end t of the other Spedrum I farther caufed thofe two Spedrums PT [in Fig. xo.] 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 0- ther, as they are reprefented in the oblong Fi- gure P T M N ; and then viewing them through a Prifm DH held parallel to their lengtih, they appeared not co-incident as when view'd with the naked Eye, but in the form of two diftind Spedrums f t and m n croffing one another in the middle after the manner of the letter X. Which (hews that the red of the one Spedrum and violet of the other, which were co-incident at P N and M T, being parted from one another by a greater Refradion of the violet to f and m ' than C 42 ]. then of the red to n and t^ do differ in degrees of Refrangibility. I illuminated alfo a little circular piece of white Paper all over with the Lights of both Prifms intermixed, and when it was illumina- ted with the *red of one Spe6lrum 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 dillance, and then at a greater, through a third Prifm ; and as I went from the Paper, the refrafted Image there- of became more and more divided by the une- qual Refradion of the two mixed Colours^ and at length parted into two dillin6l Images, a red one and a violet one, whereof the violet was fartheit from the Paper, and therefore fuffered the greateit Refradion. And when that Prifm at the V/indow which call the violet on the Pa- per was taken away, the violet Image difap- peared ; but when the other Prifm was taken away the red vaniflied: which fliews 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, fuppofe that which caft the violet on the Paper, was turned about its Axis to make all the Colours in this order, vio- let, indigo, blue, green, yellow, orange, red, fall fucceiiively on the Paper from that Prifm, the violet Image changed Colour accordingly, turning fucceiiively to indigo, blue, green, yel- low [43 ] low and red, and in changing Colour came nearer and nearer to "the red Image made by the other Prilm, until when it was alfo red both Images became fully co-incident. • I placed alfo two 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 them an Inch in dia- meter, and behind them the Wall was dark that the Experiment might not be dilturbed by any Light coming from thence. Thefe Circles thus illuminated , I viewed through a Prifm fo held that the Refraftion might be made towards the red Circle, and as I went from them they came nearer and nearer together, and at length be- came CO incident ; and afterwards when I went IHll farther off, they parted agam in a contrary order, the violet by a greater Refradion being carried beyond the red. Exfer, 8. In Summer when the Sun's Light ufes to be (trongeft, I placed a Prifm at the hole of the Window-ihut, 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 refrafted Light, I placed an open Book. Then going fix Feet and two In- ches from the Book, I placed there the above- mentioned Lens, by which the Light refledted 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 llieet of white Pa- per much after the m.anner of the fecond , Ex- periment. The Book and Lens being made faft, Ino- [44 3 I noted the place where the Paper was, when the Letters of the Book, illuminated by the fulleft red Light of the folar Image falling up- on it, did cait their Species on that Paper moil diltindly : And then I flay'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; and when thofe Letters were illuminated by that blue, I noted again the place of the Pa- per when they caft their Species moil diftindlly upon it : And I found that this lail 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 makp it. For if thefe Colours be diluted and Weak- ned by the mixture of any adventitious Light, the diflance between the Places of the Paper will not be fo great. This diliance 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. Here in the Colours of the Prifm , which are manifeltly more full, intenfe, and live- ly than thofe of natural Bodies, the diltance is two Inches and three quarters. And were the Colours' Hill more full, I queftion not but that the diftance would be confiderably greater. For the coloured Light of the Prifm, by the interr fering'of the Circles defcribed in the fecond Figure t45] Figure of the fifth Experiment, and alfo by the Li'ght of the very bright Clouds next the Sun's Body intermixing with thefe Colours, and by the Light fcattered by the inequalities in the Polifli of the Prifm, was fp very much com- pounded, that the Species which' thofe faint and dark Colours, the indigo and violet, caft upon the Paper were not diitinft enough to be well obferved. Exfer. 9. 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-fliut as in the third Experiment. And turning the Prifm flowly about its Axis until all the Light which went through one of its Angles and was refra- cted by it began to be refleded by its Bafe, at which till then it wxnt out of the Glafs, I ob- ferved that thofe Rays which had fufFered the greateit Refraftion were fooner refleded than the reft. I conceived therefore that thofe Rays of the refle^fted Light, which were molt re- frangible , did firft of all by a total Reflexion become more copious in that Light than the reft, and that afterwards the reft alfo, by a to- tal Reflexion, became as copious as thefe. To try this, I made the reflefted Light pafs through another Prifm, and being refracted by it to fall afterwards upon a fheet of white Paper placed at fome diflance behind it, and there by that Refraction to paint the ufual Colours of the Prifm. And then caufing the firft Prifm to be turned about its Axis as above, I obferved that when [4^ ] when thofe Rays which in this Prifm had fuf- fered the greateit Refraction and appeared of a blue and violet Colour began to be totally* re- fleded, the blue- and violet Light on the Paper which was moil refrafted in the fecond Prifm received a fenfible increafe above that of the red and yellow, which was leait refraded ; 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 refleded 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 differently refrangible. And that all fuch reflefted Light is of the fame na- tiire with the Sun's Light before its Incidence on the Bafe of the Prifm, no Man ever doubt- ed : it being generally allowed, that Light by fuch Reflexions fufTers no alteration in its Mo- difications and Properties. I do not here take notice of any Refractions made in the fides of the firft Prifm, becaufe the Light enters it per- pendicularly at the firft fide , and goes out per- pendicularly at the fecond fide, and therefore fufFers none. So then, the Sun's incident Light being of the fame Temper and Conftitution with his emergent Light, and the laft being compounded of Rays differently refrangible, the firft mufl be in like manner compounded. Illuflration. In the twenty firft Figure, ABC is the firft Prifm, B C its Bafe, B and C its equal [47 ] equal Angles at the Bafe, each of 4^ Degrees, A its re&ngular Vertex,- F M a beam of the Sun's Light let into a dark Room through a hole F one third part of an Inch broad, M its Incidence on the Bafe of the Prifm, MG a lefs refrafted Ray, MH a more refraded Ray, MN the beam of Light refleded from the Bafe, V X Y the fecond Prifm by which this beam in pafling through it is refrafted, N t the lefs re- fraded Light of this beam, and N / the more refrafted part thereof. When the firft Prifm ABC 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 firft Prifm, the Rays M G are alfo refleded to N and increafe the number of the Rays N t. 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 FM, the Reflexion of the fpecular Bafe B C caufmg no alteration therein. Exfer. 10. Two Prifms, which were alike in fliape, I tied fo together, that their Axes and oppofite Sides being parallel, they compofed a Parallelopiped. And, the Sun Hiining into my dark Chamber through a little hole in the Win- dow-lhut, I placed that Parallelopiped in his beam at fome diftance from the hole, in fuch a poiiure 3 [48 ] poftiire that the Axe§ of the Prifms might be perpendicular to the incident Rays , and that thofe 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 lalt Side of the fecond Prifm. This Side being parallel to the firlt Side of the firil 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 Refradion cafl the ufual Colours of the Prifm upon the oppofite Wall, or upon a ilieet of white Paper held at a convenient diftance behind the Prifm for that refraded 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 becam.e fo oblique to the inci- dent Rays that thofe Rays began all of them to be reflected , thofe Rays which in the third Prifm had fuffered the greateft Refradion and painted the Paper with violet and blue, were ^ firit of all by a total Reflexion taken out of the 1 tranfmitted Light, the reft remaining and oa 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 refl: of the Rays alfo by a total Reflexion vanifhed in order, according to their degrees of Refrangibility. The Light therefore which emerged out of the two Prifms is conipound- ed of Rays differently refrangible , feeing the more refrangible Rays may be taken out of it while the lefs refrangible remain. But this Light [ 49 ] Light being trajedled only through the parallel Superficies of the two Prifms, if it fuffer'd any change by the Refraftion of one Superficies it loll that impreflion by the contrary 'Refracaon of the other Superficies, and fo being reflor'd to its priftine Conititution became of tl>e fame nature and condition as at firfl before its Inci- dence on thofe Prifms; and therefore, before its Incidence, was as much compounded of Rays differently refrangible; as afterwards. Illnftration. In the twenty fecond Figure ABC and BCD are the two Prilms tied toge- ther in the form of a Parallelepiped, their Sides B C and C B being contiguous, and their Sides A B and CD parallel. And HJK is the third Prifm, by which the Sun's Light propagated through the hole F into' the dark Chamber, and there pafTmg through thofe fides of the Prifms AB, BC, CB and CD, is refra^ed at O to the white Paper P T, falling there partly upon P by a greater Refradtion, partly upon T by a lefs Refradion, and partly upon R and other in- termediate places by intermediate Refradions. By turning the Parallelepiped ACBD about its Axis, according to the order of the Letters A, C, D, B> at length when the contiguous Planes B Cand C B become fufliciently oblique to the Rays F M, which are incident upon them at M, there will vanifli totally out of the refrafted Light OPT, firfl of all the mofl refrafted Rays O P, (the refl O R and O T remaining as be- fore) then the Rays O R and other intermedi- ate ones, and laftly, the leaft refradled RaysOT, For when the Plane B C becomes fuiiiciently E oblique C 50] oblique to the Rays incident upon it, thofe Rays will begin to be totally refleded by it to- wards N ; and firll the moft refrangible Rays will be totally reflefted (as was explained in the preceding Experiment) and by confeqUence mutt fiiit dilappear at P, and afterwards the reft as they are in order totally refleded to N, they mutt difappear in the fame order at R and T. So then the Rays which at O fuf- fer the greateft Refradion, may be taken out of the Light M O whilll the retl 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 Refradions dettroy one anothers Ef- feds, the incident Light F M mult be of the fame kind and nature with the emergent Light M O, and therefore doth alfo confitt of Rays differently refrangible. Thefe two Lights F M and M O, before the mott refrangible Rays are feparated out of the emergent Light M O, a- gree in colour, and in all other properties fo far as my obfervation reaches, and therefore are defervedly reputed of the fame nature and contlitution , and by confequence the one is compounded as well as the other. But after the moft refrangible Rays begin to be totally retledted, 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 Ked fuccef- fively and then " totally vaniilies. For after the mott refrangible Rays which paint the Paper at P with. [51.] P with a purple Colour, are by a total Refle- xion taken out of the beam of Light M O, the relt of the Colours which appear on the Paper at R and T being mix'd in the Light 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 rell which appear between R and T (that is the yel- low, orange, red and a little green) being mix- ed in the beam M O compound there an orange ; and when all the Rays are by Reliexion taken out of the beam M O, except the Icalt" 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 Refraftion of the Prifm HJ K ferving only to feparate the differently refran- gible Rays, without making any alteration in their Colours, as lliall be more fully proved hereafter. All which confirms as well the firlt Propofition as the fecond. Scholium. If this Experiment and the former be conjoined and made one by applying a fourth Prifm VXY [in Fig. 22.] to refrad the refled:- ed beam MN towards /^/, the conclufion will be clearer. For then the Light N p which in the fourth Prifm is more refraded, will become fuller and flronger when the Light O P, which in the third Prifm H J K is more refraded, va- nifties at P ; and afterwards when the lefs re- fraded Light O T vanillies at T, the lefs re- fraded Light N t will become encreafed whilft. the more refraded Light at p receives no far- ther encreafe. And as the trajeded beam M O in vaniihing is always of fuch a Colour as ought Ex to C.52] to refult from the mixture of the Colours which fall upon the Paper P T, fo is the reflecSted beam MN 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 moft 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 refleded Light, does not only make the violet, indigo and blue at p more full, but alfa. makes the beam MN change from the yellowifli Colour of the Sun's Light, to a pale white in- clining to blue, and afterward recover its yel- lovvifn Colour again, fo foon as all the reft of the tranfmitted Light MOT is refleded- Now feeing that in all this variety of Expe- riments, whether the Trial be made in Light reflected, and that either from natural Bodies, as in the firlt and fecond Experiment, or fpe- cular, as in the ninth ; or in Light refraded, and that either before the unequally refraded Rays are by diverging feparated from one an- other, and lofing their whitenefs which they have altogether, appear feverally of feveral Co- lours, as in the fifth Experiment ; or after they are ieparated from one another, and appear co- lour'd as in the fixth, feventh, and eighth Ex- periments ; or in Light trajeded through paral- lel Superficies, deftroying each others ElFefts, as in the tenth Experiment ; there are always .found Rays, which at equal Incidences on the fame Medium fuffer unequal Refraffions, and that without any fplitting or dilating of fingle Rays, or contingence in the inequality of the Refra« C 53 ] Refraflions, as is proved in the fifth and fixth Experiments. And feeing the Rays wliich dif- fer in Refrangibility may be parted and forted from one another, and that either by Refra- ction as in the third Experiment , or by Re- flexion as in the tenth, and then the feveral forts apart at equal Incidences fuffer unequal Refractions, and thofe forts are more refrafted than others after feparation, which were more refrafted before ir, as in the fixth and folio w- iing Experiments, and if the Sun's Light be tra- ijefted through three or more crofs Prifms fuc- [ceffively, thofe Rays which in the^firfl Prifiu iare refraCled more than others, are in all the following Prifms refracted more than others *iii the fame rate and proportion, as appears by ithe fifth Experiment ; it's manifeil that the iSun's Light is an htrerogeneous mixture of jRays^ fome of which are conltantly more re- frangible than others, as was propofcd. 'P ROT. III. Theor. III. The Suits Light confifls of Rays differing hi Re- Jiexibility^ and thofe Rays are 7nore reflexible than others ijuhich are more refrangible. HIS is manifefl 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 refraCled by its Bafe, became fo ^oblique to that Bafe, as to begin to be totally E 3 reflected [54] refleded thereby; thofe Rays became firft of all totally refleded, which before at equal In- cidences with the reft had fuffered the greateft Refradion. And the fame thing happens in the Reflexion made by the common Bafe of the two Prifms in the tenth Experiment. TROT.W, Pro B.I. To fe^arate from one another the heterogeneous' Rays of compound Light. ' I ^ H E heterogeneous Rays are in fome mea- j fure feparated from one another jby the Retradion of the Prifm in the third Experi- ment, and in the fifth Experiment by taking a- way the Penumbra from the redilinear fides of the coloured Image, that feparation in thofe ve- , ry redilinear fides 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 fumciently compound. But if thefe Circles, whilft their centers keep their diftances and pofitions, could be made lefs in diameter, their interfering on0!| with another and by confequence the mixture of the heterogeneous Rays would be propor- tionally diminilh'd. In the twenty third Figure let A G, B H, C J, D K, E L, F M be the Cir- cles which fo many forts of Rays flowing froni C 55] the fame difque of the Sun, do in the third Experiment illuminate ; of all which and in- numerable other intermediate ones lying in a continual Series between the two reftilinear and parallel edges of the Sun's oblong Image PT, that Image is compos'd as was explained in the fifth Experiment. And let a g-i b h, c /, d'k^ e /, fm be fo many lefs Circles lying in a like continual Series between two parallel right Lines ^/and g m with the fame diitances be- tween their centers , and illuminated by the fame forts of Rays, that is the Circle a g with the fame fort by which the correfponding Cir- cle A G was illuminated , and the Circle b h with the fame fort by which the correfponding Circle BH was illuminated, and the relt of the Circles f /, d k^ e I, f m refpeftively, with the fame forts of Rays by which the feveral corre- fponding Circles C J, D K, EL, F M were il- lutainated. In the Figure P T compofed of the greater Circles, three of thofe Circles A G, B H, CJ, are fo expanded into one another, that the three forts of Rays by which thole Circles are illuminated, together with other innumerable forts of intermediate Rays, are mixed at Q R in the middle of the Circle B H. A-nd the like mixture happens throughout almoll: the whole length of the Figure P T. But in the Figure / t compofed of the lefs Circles, the three lefs Circles ag^ bh, ci, which anfwer to thofe three greater, do not extend into one another ; nor are there any where mingled fo much as any two of the three forts of Rays by which thofe E 4 ' Circles I S6-\ Circles are illuminated, and which in the Figure P T are all of them intermingled at B H. Now he that ihall thus confider it, will eafily underftand 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 V T will be* to their mixture in the lefs p t^ as the Latitude of the greater Fi- gure is to the Latitude of the lefs. For the Latitudes of thefe Figures are equal to the Di- ameters of their Circles. And hence it eafily follows, that the mixture of the Rays in the re- frafted Spectrum / ^ 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 qf the fame Speftrum. So then, if we would diminifh the mixture of the Rays, we are to diminifli the Diameters of the Circles. Now thefe would be diminifli- ' 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 diltance from the Prifm towards the Sun, lome opake Body were placed, with a round hole in the middle of it, to intercept all the Sun's Light, excepting fo much as coming from the middle of his Body could pafs througl [57] that hole to the Prifm. For fo the Circles A G, BH and the reft, would not any longer anlVer 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 appa- rent magnitude of that hole view'd from the Prifm. But that thefe Circles niay anfwer more diftinftly to that hole, a Lens is to be placed by the Prifm to caft the Image of the hole, (that is, every one of the Circles A G, B H, &c.) di- {lindly upon the Paper at P T, after fuch a manner as by a Lens placed at a Window the Species of Objects abroad are caft diftinftly up- on a Paper within the Room, and the redili- near Sides of the oblong folar Image in the fifth Experiment became diftinft without any Pen- umbra. . If this be done it will not be necelfa- ry to place that hole very far off, no not beyond the Window. And therefore inftead of «that hole, I ufed the hole in the Window-fhut as follows. Exper. II. In the Sun's Light let into my darkned Chamber through a fmall round hole in my Window-lhut, at about ten or twelve Feet from the Window, I placed a Lens, by which the Image of the hole might be diitinc^t- ly caft upon a Sheet of white Paper, placed at the diftance of fix, eight, ten or twelve Feet from the Lens. For according to the diife- 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 refraded either upwards or fideways^ and there^ ■ ' ■ ' ' by C 58 ] l)y 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 diitance from the Prifm as before, moving the Paper either towards the Prifm or from it, until I found the juft diftance where the redilinear Sides of the Image became moft diitind:. For in this cafe the circular Images of the hole which compofe that Image after the fame manner that the Cir- cles a g^ b h, c i, 8cc. do the Figure /> f [in Fig. 23.] were terminated moll diitindly without any Penumbra, and therefore extended into one another the lealt that they could, and by confequence the mixture of the heterogeneous Rays was now the leait of all. By this means I ufedto form an oblong Image (fuch as is/ t) lin-Fig. 13, and 24.] of circular Images of the hole (fuch as are a g, b h^ c i, &c.) and by u- fmg a greater or lefs hole in the Window-fliut, I made the circular Images ag^ b hi ^ /, &c. of which it was formed, to become greater or lefs at pleafure, and thereby the mixture of the Rays in the Image/ 1 to be as much or as little as I defired- Illuftration. In the twenty fourth Figure, F reprefents the circular hole in the Window- fhut, M N the Lens whereby the Image or Spe- cies of that hole is caft diilindly upon a Paper at'J, ABC the Prifm whereby the Rays are at their emerging out of the Lens refracted from J towards another Paper at / t, and the round Image at J is turned iato an oblong Image / t falling C 59 ] falling on that other Paper. This Image/ t con- fifls of Circles placed one. after another in a re- dilinear order, as was fufficiently explained in the fifth Experiment ; and thefe Circles are e- qual to the Circle J , and confequently anfwer in magnitude to the hole F ; and therefore by diminifhing that hole they may be at pleafure diminifhed, whilft their Centers remain in their places. By this means I made the breadth of the Image / ^ to be forty times, and fometimes fixty or feventy times lefs than its length. As for inflance, if the breadth of the hole F be one tenth of an Inch, and M F the diftance of the Lens from the hole be 12 Feet ; and if/ B or/ M the di- Itance of the Image / t from the Prifm or Lens be 10 Feet, and the refradling Angle of the Prifm be 61 Degrees, the breadth of the I- mage / t will be one twelfth of an Inch and the length about fix Inches, and therefore the length to the breadth as 71 to i, and by confe- quence the Light of this Image 71 times lefs compound than the Siin's dired Light. And Light thus far fimple and homogeneal, is fuffi- cient for trying all the Experiments in this Book about fimple Light. For the compofition of heterogeneal Rays is in this Light fo little that jt is fcarce to be difcovered and perceiv'd by Senfe, except perhaps in the indigo and vio- let. For thefe being dark Colours, do eafily fuffer a fenfible allay by that little fcattering Light which ufes to be refraded irregularly by the inecjualities of the Prifm. Yet inttead of the circular hole F, 'tis better to fubititute an oblong hole fhap^ like a long Paral- I 60 1 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 : the Light of the Image / t will be as fimple as before, or fimpler, and the Image will become much broader, and therefore more fit to have Experiments tried in its Light than before. Inltead of this parallelogram hole may be fub- ftituted a triangular one of equal Sides, whofe Bafe for initance 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 £t [in Fig. 15-.] will now be form'd of equi- crural Triangles a g, bhy c i^ dk, e /, fm^ &c. and innumerable other intermediate ones an- fwering to the triangular hole in Ihape and big- nefs, and lying one after another in a continual Series between two parallel Lines a f and g m, Thefe Triangles are a little intermingled at their Bafes but not at their Vertices, and therefore the Light on the brighter fide /?/of the Image where the Bafes of the Triangles are, is a little compounded, but on the darker fide gm is al- together uncompounded , and in all places be- tween the fides the Compofition is proportio- nal to the diflances of the places from that ob- fcurer fide g m. And having a Spedrum / t of fuch a Compofition, we may try Experiments either in its flronger and lefs fimple Light near the fide ^/, or in its weaker and fimpler Light pear the other fide g nty as it Ihall feem mofl convenient. • But [61 ] But in 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/r, and render it com- pound ; efpecially if we would try Experiments in the more fimple Light next the fide g m of the Spedrum ; 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 Httle convex or concave, as ufually happens, but truly plane, and its Polifli elaborate, as in working Optick-glalTes, and not fuch as is ufually vi^roughc with Putty, whereby the edges of the Sand- holes being worn away, there are left all over the Glafs a numberlefs cornpany of very little convex polite Rifmgs like Waves, The edges alfo of the Prifm and Lens fo far as they may make any irregular Refradion, muft be covered with a black Paper glewed on. And 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 with black Pa- per or other black Obftacles. For otherwife the ufelefs Light being reflec^ted every way in the Chamber, will mix with the oblong Spe- ftrum and help to difturb it. In trying thefe' things fo much diligence is not altogether ne- cellary, but it will promote the fuccefs of the Expe- 162 ] Experiments, and by a very fcrupulous Examin- er of things deferves to be applied. It's difficult to get Glafs Prifms fit for this purpofe, and therefore I ufed fometimes prifmatick VefTels made with pieces of broken Looking-glafTes, and filled with Rain Water. And to increafe the Refraftion, I fometimes impregnated the Water itrongly with S ace bar urn Saturnt. T ROT.Y. Theor.IV. Homogeneal Light is refracted regularly with" out any dilatation fplitting or /battering 'of the Rays^ and the confufed Vifion of Objedis feen through re framing Bodies by heterogeneal Light arijes from the different Refrangibility of fever al forts of Rays. THE firfl 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, II. 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 Speftrum of homogeneal Light defcribed in the former Propofition, fo to fall, that fome part of the Light might pafs through the hole of the Paper. This tranfmitted part of the Light I refrafted with a Prifm placed behind the Paper, and letting this refrafted Light fall perpendicularly upon a white Paper two or three Feet dillant from the Prifm, I found that the C ^3 3 the Speftrum formed on the Paper by this Light was not oblong, as when 'tis made (in the third Experiment) by refrading the Sun's compound Light, but was (fo far as I could judge by my Eye) perfectly circular, the length being no greater than the breadth. "Which fliews that this Light is refraded regularly without any Di- latation of the Rays. Exper. 13. In the homogeneal Light I placed . a Paper Circle of a quarter of an Inch in diameter, and in the Sun's unrefrafted heterogeneal white Light I placed another Paper Circle of the fame bignefs. And going from the Papers to the diltance of fome Feet, I viewed both Circles through a Prifm. The Circle illuminated by the Sun's heterogeneal Light appeared very ob- long as in the fourth Experiment, the length being many times greater than the breadth ; but the other Circle illuminated with homogeneal Light appeared circular and didindly defined as when 'tis view'd with the naked Eye. Which proves the whole Propofition. Exper. 14. In the homogeneal Light I placed Flies and fuch like minute Objeds, and view- ing them through a Prifm, I faw their parts as diltindly defined as if I had viewed them with the naked Eye. The fame Objefts placed in the Sun's unrefraded heterogeneal Light which was white I viewed alfo through a Prifm, and faw them molt confufedly defined, fo that I could not diltinguifli 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] through a Prifm, they appeared in the latter cafe fo confufed and indillinft that I could not read them ; but in the former they appeared fo diitind that I could read readily, and thought I favv them as diflin^l 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 fitua- tion. There was no difference but in the Light by which the Objefts were illuminated, and which in one cafe was limple and in the other compound, and therefore the diftinft 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 Pro- pofition. And in thefe three Experiments it is farther very remarkable, that the Colour of homoge- neal Light was never changed by the Refra- dion. T ROT. VL Theor.V. The Sine of Incidence of every Ray conjidered a* party is to its Sine of Refra5iion in a gtveti Ratio, "^H AT every Ray confider'd apan*t is con- llant to it felf in fome degree of Refran-^ gibility, is fufficiently manifell out of what has been laid. Thofe Rays which in the firft Re- fraftion are at equal Incidences moft refrafted,^ are alfo in the following Refradions at equa! Inci- r<^5] Incidences tnofl refrafted ; and fo of the leaft refrangible, and the reft which have any mean degree of Refrangibility, as is manifeft by the fifth, fixth, feventh, and eighth, and ninth Ex- periments. And thofe which the firft time at like Incidences are equally refrafted, are again at like Incidences equally and uniformly refra- ded , and that whether they be refradled be- fore they be feparated from one another as in the fifth Experiment, or whether they be re- fraded apart, as in the twelfth, thirteenth and fourteenth Experiments. The Refradion there- fore of every Ray apart is regular* and what Rule that Refradtion obferves we are now to iliew. 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 Initruments fit- ted for meafuring of Refradions, or otherwife experimentally examining this Proportion, do acquaint us that they have found it accurate. But whillt they , not underftanding the diffe- rent Refrangibility of feveral Rays, conceived them all to be refrafted according to one and the fame Proportion, 'tis to be prefumed that they adapted their meafures only to the middle of the refraded Light ; fo that from their mea- fures we may conclude only that the Rays which have a mean degree of Refrangibility, that is thofe which when feparated from the reft appear green, are refraded according to a given Proportion of their Sines. And there- fore we are now to fhew that the like given F Pro- c ^o Proportions obtain in all the refl. That it fhould be fo is very realbnable, Nature being ever conformable to her felf: but an experi- mental Proof, is defired. And fuch a Proof will be had if we can fliew that the Sines of Refraction of Rays differently refrangible are one to another in a given Proportion when their Sines of Incidence are equal. For if the Sines of Refraction of all the Rays are in given Proportions to the Sine of Refradion of a Ray which has a mean degree of Refrangibility, and this Sine is in a given Proportion to the equal Sines of Incidence, thofe other Sines of Refra- dion will alfo be in given Proportions to the equal Sines of Incidence. Now when the Sines of Incidence are equal; it will appear by the following Experiment that the Sines of Refra- dion are in a given Proportion to one ano- ther. E^per. II). The Sun fhining into a dark Charnber through a little round hole in the Window-fliut, let S [in Fig. 26.] reprefent his round white Image painted on the oppofite Wall by his diredt Light, P T his oblong co- loured Image made by refrading that Light with a Prifm placed at the Window; and p t, orzpzt, or 3 Z' 3 t, his oblong colour'd Image made by refrading again the fame Light fide- ways with- a fecond Prifm placed immediately after the firft in a crofs pofition to it , as was explained in the fifth Experiment : that is to fay, / t when the Refradion of the fecond Prifm is fmall ^ z p 1 t when its Refraftion is ' greater, and ip i t when it is greateft. For fuch [ ^7 ] fuch will be the diverfity of the Reflations if the refrading Angle of the fecond Prifm be of various magnitudes ; fuppofe of fifteen or twen- ty Degrees to make the Image/ t^ of thirty or forty to make the Image x/' 1 1, and of fixty to make the Image 3/ 3 /^. But for want of folid Glafs Prifms with Angles of convenient big- nefles, there may be VefTels made of poliilied Plates of Glafs cemented together in the form of Prifms and filled with Water. Thefe things being thus ordered, I obferved that all the fo- lar Images or coloured Spedrums P T, / ^ ^ / nt, 3 / 3 r 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 Speftrum P T, that is the Line drawn through the middle of it parallel to its re^ilinear Sides, did when produced pafs exadly through ths middle of that white round Image S. And when the Refraftion of the fecond Prifm was equal to the Refradion of the firft, the refrading An- gles of them both being about 60 Degrees, the I Axis of the Speftrum 3/ 3 ^ made by that Re- ! fraftion, did when produced pafs alfo through the middle of the fame white round Image S. '■ But when the Refraction of the fecond Prifm was lefs than that of the firft , the produced Axes of the Speftrums r/ ox 'l t x p made by that Refraftion did cut the produced Axis of the Speftrum T P in the points m and ;/, 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 [ ^8 ] the Proportion of x^ T to x/P, and this Pro- portion a Uttle greater than that of ^ T to /> P. Now when the Light of the Spedrum P T falls perpendicularly upon the Wall, thofe Lines 3 2f T, 3 Z' Pj and x /f T, 2 /> P and t T, p P, are the Tangents of the Refraftions, and therefore by this Experiment the Proportions of the Tan- gents of the Refra61ions are obtained, from whence the Proportions of the Sines being de- rived, they come out equal, fo far as by view- ing the Spedrums and ufing fome mathemati- cal Reafoning I could eitimate. For I did not make an accurate Computatioji. So then the Proportion holds true in every Ray apart, fo far as appears by Experiment. And that it is accurately true, may be demonftrated upon this Suppofition. That Bodies refratl Light hy a^l- ing upon its Rays in Lines perpendicular to their Surfaces. But in order to this Demon- flration, I mull diltinguifli the Motion of every Ray into two Motions, the one perpendicular to the refracting Surface, the other parallel to it , and concerning the perpendicular Motion lay down the following Propofition. If any Motion or moving thing whatfoever be incident with any velocity on any broad and thin fpace terminated on both fides by two pa- rallel Planes, and in its paffage through that fpace be urged perpendiciilarly towards the far- ther Plane by any force which at given diltances from the Plane is of given quantities; the per- pendicular velocity of that Motion or Thing, at its emerging out of that fpace, fliali be al- ways equal to the fquare Root of the fum of the. [ 69 3 the fquare of the perpendicular velocity of that Motion or Thing at its Incidence on that fpace ; and of the fquare of the perpendicular velocity which that Motion or Thing would have at its Emergence, if at its Incidence its perpendicu- lar velocity was infinitely little. And the fame Propofition holds true of any Motion or Thing perpendicularly retarded in its pafTage through that fpace, if inftead of the fum of the two Squares you take their diffe- rence. The demonitration Mathematicians will eafily find out, and therefore I fhall not trouble the Reader with it. Suppofe now that a Ray coming mofl oblique- ly in the LineM C [in Fig. i.] be refracted at C by the Plane R S into the Line C M, and if it be. required to find the Line C E, into which any other Ray AC fliall be refra^led; let MC, AD, be the Sines of Incidence of the two Rays, and N G, E F, their Sines of Refradion, and let the equal Motions of the incident Rays bd reprefented by the equal Lines M C and AC, and the Motion M C being ccnfidered as paral- lel to the refrafting Plane, let the other Motion A C be diftinguilhed into two Motions A D and DC, one of which A D is parallel, and the other D C perpendicular to the refrading Sur- face. In Hke manner, let the Motions of the emerging Rays be diilinguifli'd into two, whereof the perpendicular ones are ~ C G and ~ C F. And if the force of the refrading Plane begins to aft upon the Rays either in that Plane or at a certain diitance from it on the one fide, and ends at a certain diftance from it on the other F 3 iide [ 70 ] fide, and in all places between thofe two limits adts upon the Rays in Lines perpendicular to that refrading Plane, and the Adions upon the Rays at equal diflances from the refrafting Plane be equal, and at unequal ones either equal or unequal according to any rate whatever ; that Motion of the Ray which is parallel to the re- frafting Plane will fuffer no Alteration by that force ; 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 — C G as above, then the perpendi- cular velocity of any other emerging Ray C E which was — r C F, will be equal to the fquare Root of C D ^ 4- ^^^ C G f . And by fquaring thefe Equals, and adding to them the Equals; A D ^ and M C ^ — C D f, and dividing the Sums by the Equals C F ^ -f EF ^ and C G ^ -^-j NG^, you will have ^-~ equal to^^\ Whence A D, the Sine of Incidence, is to E F the Sine of RefradHon, as MC to N G, that is, in a given ratio. And this Demonltration being general, without determining what Light is, or by what kind of force it is refrafted, or alTuming any thing farther than that the refrafting Body adls upon the Rays in Lines perpendicular to its Surface ; I take it to be a very convincing Argu- ment of the full truth of this Propofition. So then, if the rafio of the Sines of Inci- dence and Refraction of any fort of Rays be found C 71 3 found in any one cafe,/tis given in all cafes; and this may be readily found by the method in the following Propoiition. T R OT.yW, Theor.VI. The TerfeBton of Telefeopes is impeded by the different Refrangibitity of the Rays of Light. ' I ^ H E Imperfeftion of Telefeopes is, vul- JL garly attributed to the fpherical Figures ot the Glafles, and therefore Mathematicians have propounded to figure them by the coni- cal Sedions. To fliew that they are miflaken, I have inferted this Propofition ; the truth of which will appear by the meafures of the Re- fraftions of the feveral forts of Rays ; and thefe meafures I thus determine. In the third Experiment of the firft Book, where the refracting Angle of the Prifm was 61-;: Degrees, the half of that Angle 31 deg. 15' min. is the Angle of Incidence of the Rays at their going out of the Glafs into the Air ; and the Sine of this Angle is 5188, the Radius being 1 0000. When the Axis of this Prifm was pa- rallel to the Horizon, and the Refradion . of the Rays at their Incidence on this Prifm equal to that at their Emergence out of it, I obferved with a Quadrant the Angle which the mean re- frangible Rays (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 Angle which the eniergent Rays contained with F 4 the [72 ] the incident to be 44 deg. and 40 min. and the half of this Angle added to the Angle of Inci- dence 31 deg. 15" min. makes the Angle of Re- fraftion, which is therefore 5-3 deg. 35- min. and its Sine 8047. Thefe are the Sines of Incidence and Refradion of the mean refrangible Rays, and their proportion in round numbers is zo to 31. 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 refrading Angle 634 Degrees. The Angle which the emergent Rays contained, with the incident 45 deg. 50 min. The Sine of half the firll An- gle 5^6l. The Sine of half the fum of the An- gles 8157. And their proportion in rotmd num- bers 20 to 31, as before. From the length of the Image, which was about 9-1 or 10 Inches, fubdud: its breadth, which was 24 Inches, and the remainder 7-I Inches would be the length of the Image were the Sun but a point, and therefore fubtends the Angle which the moft and leaft refrangible Rays, when incident on the Prifm in the fame Lines, do contain with one another after their Emergence, Whence this Angle is 2 deg. o'. 7'^. For the diltance between the Image and the Prifm where this Angle is made, was 184 Feet, and at that diftance the Chord 7^ Inches fubtends an Angle of x deg. o'. y^\ Now half this Angle is the Angle which thefe emergent Rays con- tain with the emergent mean refrangible Rays, and a quarter thereof, that is 30^. x^\ may be accounted the Angle which they would contain with the fame emergent mean refrangible Rays, were [73 ] were they co-incident to them within the Glafs and fuffered no other Refraclion than that at their Emergence. For if two equal" Refradiions, the one at the Incidence of the Rays on the Prifm, the other at their Emergence, make half the Angle % deg. o^. 7'^. then one of thofe Re- fractions'will make about a quarter of that An- gle, and this quarter added to and fubdufted from the Angle of Refraftion of the mean re- frangible Rays, which was 5-3 deg. 35^ gives the Angles of Refraction of the molt and lead refrangible Rays 54 deg. 5^ -l^^ and 53 deg. 4^ 5-8^'', whofe Sines are 8099 and 7995", the common Angle of Incidence being 31 deg. if^ and its Sine 5-188; and thefe Sines in the leaft round numbers are in proportion to one another, as 78 and yy to 5-0. Now if you fubdu(?c the common Sine of In- cidence 50 from the Sines of Refradion 77 and 78, the remainders ly and x8 ihew that in fmall Refractions the RefraCtion of the leaft refran- ^ gible Rays is to the RefraCtion of the moil re- frangible ones as 27 to 28 very nearly, and that the difference of the Refractions of the leaft re- frangible and moit refrangible Rays is about the Z74th part of the whole RefraCtion of the mean refrangible Rays. Whence they that are skilled in Opticks will eafily underftand, that the breadth of the leall circular fpace into which ObjeCt glaffes of Te- lefcopes can colleCt all forts of parallel Rays, is about the 274th part of half the Aperture of the Glafs, or 5fth part of the whole Aperture ; and tjiat the Focus of the molt refrangible Rays is • ^ ■ ■ ' nearer [74] nearer to the Objeft-glafs than the Focus of the Jeaft refrangible ones, by about the 174th part of the diftance between the Objeft-'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 Refraction of the Lens to con- verge to points not too remote from the Lens, the Focus of the mod refrangible Rays iliall be nearer to the Lens than ihe Focus of the leafl refrangible ones, by a diftance which is to the xy-irth part of the diftance of the Focus of the mean refrangible Rays from the Lens as the di- ftance between that Focus and the lucid point from whence the Rays flow , is to the diftance between that lucid point and the Lens very nearly. Now to examine whether the difference be- tween the Refradions which the moft refrangi- ble and the leaft refrangible Rays flowing from the. fame point fuffer in the Objeft-glalFes of Telefcopes and fuch like GlalTes, be fo great as is here described, I contrived the following Ex- periment. Exfer. 16. The Lens which I ufed in the fe- cond and eighth Experiments, being placed fix Feet and an Inch diftant from any Objedt, col- lefted the Species of that Objed by the mean refrangible Rays at the diftance of fix Feet and an Inch from the Lens onthe other fide. And therefore by the foregoing Rule it ought to col- led the Species of that Objeft by the leaft re- frangible Rays at the diftance of fix Feet and 37 Inches from the Lens, and by the moft re- frangible [ 75] frangible ones at the diftance of five Feet and 104 Inches from it: So that between the two places where thefe lead and mdft refrangible Rays colleft the Species, there may be the di-- fiance of about $j Inches. For by that Rule, as fix Feet and an Inch (the diftance of the Lens from the lucid Objeft) is to twelve Feet and two Inches (the diftance of the lucid Objeft from the Focus of the mean refrangible Rays ) that is, as one is to two, fo is the zyith 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 5-4.4 Inches, that is very near- ly 57 Inches. Now to know whether this mea- fure was true, I repeated the fecond and eighth Experiment with coloured Light, which was lefs compounded than that I there made ufe of : For I now feparated the heterogeneous Rays from one another by the method I de- fcribed in the eleventh Experiment , fo as to make a coloured Spedrum about twelve or fif- teen times longer than broad. This Speftrum I caft on a printed Book, and placing the above- mentioned Lens at the diftance of fix Feet and an Inch from this Speftrum to colled the Spe- cies of the illuminated Letters at the fame di- ftance on the other fide , I found that the Spe- cies of the Letters illuminated with blue were nearer to the Lens than thofe illuminated with deep red by about three Inches or three and a quarter : but the Species of the Letters illumi- nated with indigo and violet appeared fo con- fufed c in fufed and indiflinft, that I could not read them : Whereupon viewing the Prifm, I found it was full\)f Veins Tunning from one end of the Glafs to the other ; fo that the Refradion could not be regular. I took another Prifm therefore which was free from Veins, and inltead of the Letters I ufed two or three parallel black Lines a little broader than the flroaks 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 Spedriim to the other, I found that the Focus where the indigo, or confine of this Colour and violet cait the Species of the black Lines moil diftindly , to be about four Inches or 4^ nearer to the Lens than the Focus where the deepeft red call the Species of the fame black Lines moil di{lin6l- ]y. The violet was fo faint and dark, that I could not difcern the Species of the Lines di- Itindly by that Colour ; 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 ftreams of faint Light lliooting out from both ends of the Colours, which made me con- clude that fomething was amifs ; and viewing the Prifm, I found two or three httle bubbles in the Glafs which refrafted the Light irregu- larly. Wherefore I covered that part of the Glafs with black Paper, and letting the Light' pafs through another part of it which was free from fuch bubbles, the Speftrum of Colours became free from thofe irregular Streanps of Light, and was [77] Was now fuch as I defired. 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 deepeil part of it, which was next the end of the Speftrum. I fufpeded therefore that this faint and dark Colour might be allayed by that fcattering Light which was refraded , and reflefted irregularly, partly by fome very fmall bubbles in the Glalfes, and partly by the inequalities of their Polifli : which Light, tho' it was but little, yet it being of a white Colour, might fuffice to affed: the Senfe fo llrongly as to diiturb 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 confid of a fenfible mixture of heteroge- neous Rays, but found it did not. Nor did the Refraftions caufe any other fenfible Colour than violet to emerge out of this Light , as they would have done out of white Light, and by confequence out of this violet Light had it been fenfibly compounded with white Light. And therefore I concluded , that the realbn why I could not fee the Species of the Lines diftinft- ly by this Colour, was only the darknefs of this Colour and thinnefs of its Light, and its di- Itance from the Axis of the Lens ; I divided therefore thofe parallel black Lines into equal parts, by which I might readily know the di- llances of the Colours in the Speftrum from one another, and noted the diltances of the Lens from the Foci of fuch Colours as caft the Species of the Lines diltindly, and then confi- fidered [ 78 ] dered whether the difference of thofe diftances bear fuch proportion to si Inches, the greateft difference of the diftances which the Foci of the deepeit red and violet ought to have from the Lens, as the diftance of the obferved Go- lours from one another in the Spedrum bear to the greatefl diftance of the deepefl red and violet meafured in the reftilinear fides 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 deepeft fenfible red, and the Colour in the Confine of green and blue, which at the redilinear Sides of the Spedrum was diftant from it half the length of thofe Sides, the Focus where the Con- fine of green and blue caft the Species of the Lines diltindly on the Paper, was nearer to the Lens than the Focus where the red cafl thofe Lines ditiindly on it by about x^ or i4 Inches. For fometimes the Meafures were a little great- er," fometimes a little lefs, but feldom varied from one another above i of an Inch. For it was very difficult to define the places of the Foci, without fome little Errors. Now if the Colours diftant half the length of the Image, (meafured at its reftilinear Sides) give Zt or 2-| difference of the diftances of their Foci from the Lens, then the Colours diftant the whole length ought to give s or 5^ Inches difference of thofe diftances. But here it's to be noted, that I could not fee the red to the full end of the Spedrum , but [79] but only to the center of the Semicircle which bounded that end , or a Uttle farther ; and therefore I compared this red not with that Colour which was exadly in the middle of the Speftrum, or Confine of green and blue, but with that which verged a Uttle 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 Spedlrum, but the length of its rectilinear Sides, fo completing the femicircu- lar Ends into Circles, when either of the ob- ferved Colours fell within thofe Circles, I mea- fured the diftance of that Colour from the fe- micircular end of the Spectrum , and fubduft- ing half this diftance from the meafured di- ftance of the two Colours, I took the remain- der for their corre(5led diftance ; and in thefe Obfervations fet down this corrected diftance for the difference of the diftances of their Foci from the Lens. For as the length of the refti- linear Sides of the Spedrum would be the whole length of all the Colours, were the Circles of which (as we ihewed) that Spedrum confifts contraded and reduced to phylical Points, fo in that cafe this corrected diltance would be the real diftance of the two obferved Colours. When therefore I farther obferved the deep- eft fenfible red, and that blue whofe correded diftance from it was -t parts of the length of the reftilinear Sides of the Spedrum, the dif- ference of the diftances of their Foci from the Lens was about 3-^ Inches, and as 7 to iz fo is 3 -T to 55. When 3 [80 ] When I obferved the deepeft fenfible red, and that indigo whofe correded diflance was TT or 4 of the length of the redilinear Sides of the Spedrum, the difference of the diltances of their Foci from the Lens, was about 34 Inches, and as ^ to 3 fo is 34 to 5-4. When I obferved the deepefl fenfible red, and that deep indigo whofe correded diflance from one another was -% or -| of the length of the redilinear Sides of the Spedrum, the dif- ference of the diilances of their Foci from the Lens was about 4 Inches ; and as 3 to 4 fo is 4 to 5-4.. When I obferved the deepeft fenfible red, and that part of the violet next the indigo, whofe corredied diftan'ce from the red was 44 or 4 of the length of the reftilinear Sides of the Speftrum., the difference of the diftances of their Foci from the Lens was about 44 Inches, and as 5 to 6, fo is 44 to 5-4. For fometimes when the Lens was advantagioufly placed, fo that its Axis refpefted the blue, and all things elfe were well ordered, and the Sun fhone clear, and I held my Eye -very near to the Paper on which the Lens caft the Species of the Lines, I could fee pretty diftinflly the Species of thofe Lines by that part of the violet which was next the indigo ; 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 diftindiy ; and then the red ap- peared r 8i ] peared much lefs dillinft than before. Where- fore I contrived to make the Spe(^trum of Co- lom's fhorter than before, fo that both its ends might be nearer to the Axis of the Lens. And now its length was about 24 Inches and breadth about 4 or 4 of an hich. Alfo inftead of the black Lines on which the SpeArum was caft, I made one black Line broader than thofe, that I might fee its Species more eafily ; and this Line I divided by Ihort crofs Lines into equal parts, for meafuring the diftances of the obfer- ved Colours. And now I could fometimes fee the Species of this Line with its divifions al- moft as far as the center of the femicircular violet end of the Spedrum, and made thefe farther Obfervations. When I obferved the deepefl fenfible red, and that part of the violet whofe correfted diftance from it was about -I parts of the redilinear fides of the Spedrum the difference of the diftances of the Foci of thofe Colours from the Lens, was one time 44, another time 4-I, another time 4-r Inches, and as 8 to 9, fo are 47, 4-^-, 44, to 54, 544 5I4 refpedively. When I obferved the deepeft fenfible red, land deepeft fenfible violet, (the correfted di- iftance of which Colours when all things were ■ordered to the beft advantage, and the Sun jflione very clear, was about 44 or 44 parts of Sthe length of the redilinear Sides of the co- iloured Speftrum ) I found the difference of the jdiftances of their Foci from the Lens fometimes 1 44 fometimes 54, and for the moft part 5- In- * G ches [ 82 ] ches or thereabouts: and as ii to ix or 15- to 16, fo is f Inches to 54 or Si Inches. And by this progreilion of Experiments I fa- tisiied my felf, that had the Light at the very ends of the Speflrum been lirong enough to make the Species of the black Lines appear plainly on the Paper, the Focus of the deepeft violet would have been found nearer to the Lens, than the Focus of the d^epefl red, by about si Inches at lead. And this is a farther evidence, that the Sines of Incidence and Re- fradion of the feveral forts of Rays, hold the fame proportion to one another in the fmalleft Refradions which they do in the greateft. My progrefs in making this nice and trouble- fome Experiment I have fet down more at large, that they that Ihall try it after me may be aware of the circumfpedion requifite to make it fuc- ceed well. And if they cannot make it fuc- ceed fo well as I did, they may notwithftand- ing collect by the proportion of the diftance of the Colours of the Spedrum, to the difference pf the diflances of their Foci from the Lens, what would be the fuccefs in the more diitant Colours by a better trial. And yet if they ufe a broader Lens than I did, and tix it to a long Itraight Staff by means of which it may be rea- dily and truly dire61ed to the Colour whofe Fo- v cus is defired, I quellion not but the Experi- ment will fucceed better with them than it did i with me. For I direded the Axis as nearly as I could to the middle of the Colours, and then the faint ends of the Spedrum being remote from the Axis, call their Species lefs diflindly * on [83 ] on the Paper than they would have done had the Axis been fucceflively dire6led to them. Now by what has been faid, it's certain that the Rays which differ in RefrangibiUty do not converge to the fame Focus, 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 refrangible Rays iliall be nearer to the Lens than that of the leaft refrangible, by above the fourteenth part of the whole diltance : and if they flow from a lucid point, fo very re- mote from the Lens that before their Incidence they may be accounted parallel, the Focus of the moft refrangible Rays iliall be nearer to the Lens than the Focus of the lead refrangible, by about the x7th or i8th part of their whole diftance from it. And the diameter of the Cir- cle in the middle fpace between thofe two Fo- ci 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 5-5th part of the diameter of the Aperture of the Glafs. So that 'tis a won- der that Telefcopes reprefent Objefts fo diftind as they do. But were all the Rays of Light equally refrangible, the Error arifing only from the fphericalnefs of the Figures of Glaffes would be many hundred times lefs. For if the Obje^l- glafs of a Telefcope be Plano-convex, and the Plane fide be turned towards the Objeft, and the diameter- of the Sphere whereof this Glafs is a fegment be called D, and the femidiame- ter of the Aperture of the Glafs be called S, and the Sine of Incidence out of Glafs into Air, G z be [ 84 ] be to the Sine of Refradion as I to R : the Rays which come parallel to the Axis of the Glafs, fliall in the place where the Image of the Objed is mofl diilinftly made, be fcattered all over a little Circle whofe diameter is -j^ x 5-^ very nearly, as I gather by computing the Errors of the Rays by the method of infinite Series, and ^ rejedting the Terms whofe Quantities are in- confiderable. As for inftance, if the Sine of Incidence I, be to the Sine of Refradion R, as 20 to 31, 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 femidia- meter of the Aperture be two Inches, the dia- meter of the little Circle (that is ^"^ \ "* ' will be ^' * ^^ ''^' — Cor ' "^^^ parts of an Inch. iO X lo X I ICO X 12,00 ^ 7ZOOOOUO *■ But the diameter of the little Circle through which thefe Rays are fcattered by unequal Re- frangibility, will be about the 5- 5th part of the Aperture of the Objed glafs which here is four Inches. And therefore the Error arifmg from the fpherical Figure of the Glafs, is to the Er- ror arifmg from the different Refrangibility of the Rays, as to — that is as i to 5449 : •' 7ioooooo 55: y I ly 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 Obje61s appear through Telefcopes fo diilindt as they do ? I anfwer, 'tis i becaufe [ 85 ] becaufe the erring Rays are not fcattered uni- formly over all that circular fpace, but colled- ed infinitely more denfely in the center than in any other part of the Circle, and in the way from .the center to the circumference, grow continually rarer and rarer, fo as at the circum- ference to become infinitely rare ; and by rea- fon of their rarity are not ftrong enough to be vifible, unlefs in the center and very near it. Let A D E [in Fig. 27.] reprelent one of thofe Circles defcribed with the Center C and Semi- diameter A C, and let B F G be a fmaller Circle ^ concentrick to the former, cutting with its cir- ' ^ cumference the Diameter A C in B, and bifed ^ 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 lefTer Circle BFG, will be to the whole Light within the greater A ED, as the Excefs of the Square of AC above the Square of AB, is to the Square of A C. As if BC be the fifth part of AC, the Light will be four times den- 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, mull: ftrike the Senfe much more flrongly, 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 mod lu- minous of the prifmatick Colours are the yel- low and orange. Thefe affedl the Senfes more ftrongly than all the reft together, and next to G 3 thefe I 8^ ] thefe in ftrength are the red and green. The blue compared with thefe is a faint and dark Colour, and the indigo and violet are much darker and fainter, fo that thefe compared with the Itronger Colours are little to be regarded. The Images of Obje61s 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 Ra57s which are in the middle of the orange and yellow ; there where the Colour is moll luminous and fulgent, that is in the brighteit yellow, that yellow which inclines more to orange than to green. And by the Refradion of thefe Rays (whofe Sines of Incidence and Refradion in Glafs are as 17 and 11) the Refradion of Glafs and Cryftal for op- tical Ufes is to be meafured. Let us therefore place the Image of the Object in the Focus of thefe Rays, and all the yellow and orange will fall within a Circle, whofe diameter is about the 150th 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 Colours will fall within the fame Circle, and' two fifth parts will fall without it round about ; and that which falls without will be fpread through almoft as much more fpace as that which falls within, and fo in the grofs be almofl three times rarer. Of the other half of the red and green, (that is of the deep dark red and willow green) about one quarter will fall within this Circle, and three [ 87 ] three " quarters without , and that which falls without will be fpread through about four or 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 15 times rarer than all that taken in the grofs ; or rather more than 30 or 40 times ra- rer, becaufe the deep red in the end of the Speftrum 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 affect the Senfe, efpecially fmce the deep red and willow green of this Light, are much darker Colours than the refl. And for the fame reafon the blue and violet being much darker Colours than thefe, and much more rarified, may be neglefted. 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 a^oth part of the diameter of the Aperture of the Objeft-glafs of a good Telefcope, or not much broader, if you except a faint and dark mif- ty Light round about it, which a Spectator will fcarce regard. And therefore in a Telefcope whofe aperture is four Inches, and length an hundred Feet, it exceeds notx^'45"'^',or i'^ . And in a Telefcope whofe aperture is two Inches, and length lo or 30 Feet, it may be 5-^^ or 6" and fcarce above. And this aiifwers well 10 G 4 expe- [ 88 ] experience : For fome Aftronomers have found the Diameters of the fix'd Stars, in Telefcopes of between lo and 60 'Feet in length, to be about 5" or 6'\ or at moll %'^ or \o'^ in diame- ter. But if the Eye-Glafs be tinfted faintly with the fmoke of a Lamp or Torch , t o ob- fcure the Light of the Star, the fainter Light in the circumference of the Star ceafes to be vilible, and the Star (if the Glafs be fufficient- ly foiled with fmoke ) appears fomething more like a mathematical Point. And for the fame reafon, the enormous part of thfe Light in the circumference of every lucid Point ought to be lefs difcernible in iliorter Telefcopes than in longer, becaufe the fliorter tranfmit lefs Light to the Eye. Now that the fix'd Stars, by reafon of their immenfe diftance, appear like Points, unlefs fo far as their Light is dilated by Refradion, may appear from hence ; that when the Moon paf- fes over them and Qclipfes them, their Light vanilhes, not gradually like that of the Planets, but all at once ; and in the end of the EcHpfe it returns into Sight all at once, or certainly in . lefs time than the fecond of a Minute ; the Re- fradion of the Moon's Atmofphere a little pro- trading the time in which the Light of the Star firlt vanifhes, and afterwards returns into Sight. Now if we fuppofe the fenfible Image of a lu- cid point, to be even x5"o times narrower than the aperture of the Glafs : yet this Image would be ftill much greater than if it were only from the fpherical Figure of the Glafs. For were it not for tlie different Refrangibility of the Rays, C 85 ] Rays, its breadth in an 100 Foot Telefcope whofe aperture is 4 Inches would be but- 961 72.0C0000 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 arifing from the different Refrangibility of the Rays as —^-^^^ — to— at mofl, that is only •' 710C0000 250 J as I to 12-00. And this fufKciently Hiews that it is not the fpherical Figures of GlafFes but the different RefrangibiUty of the Rays which hin- ders the perfedion of Telefcopes. There is another Argument by which it may appear that the different Refrangibility of Rays, is the true caufe of the iraperfedion of Tele- fcopes. For the Errors of the Rays arifmg from the fpherical Figures of Objeft-glafTes, are as the Cubes of the Apertures of the Obje6l- glalTes ; and thence to make Telefcopes of va- rious lengths, magnify with equal diflindnefs, the Apertures of the Objed-glafTes , and the Charges or magnifying Powers, ought to be as the Cubes of the fquare Roots of their lengths ; which doth not anlwer to experience. But the Errors of the Rays arifmg from the different Refrangibilty, are as the Apertures of the Ob- jedt-glafTes, and thence to make Telefcopes of various lengths, magnify with equal diftindnefs, their Apertures and Charges ought to be as the fquare Roots of their lengths ; and this anfwers to experience, as is well known. For inflance, a Telefcope of 64 Feet in length, within Aper- ture C 50 ] ture of i-f Inches, magnifies about 120 times, with as much diftinftnefs as one of a Foot in length, with 7 of an Inch aperture, magnifies 15: times. Now were it not for this different Refrangi- bility of Rays, Telefcopes might be brought to a greater perfedion than we have yet defcrib'd, by compofmg the Objeft-Glafs of two GlafTes with Water between them. Let ADFC [in Fig, ^8.] reprefent the Objed-glafs compofed of two GlalTes ABED and BEFC, alilie convex on the outfides AGD and CHF, and alike concave on the infides B M E, BNE, with Water in the concavity B MEN. 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 T 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 RK— RI: and the Refraftions on the concave fides of the GlafTes, 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 fufficient per- fedion, were it not 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 Refraftions alone than that of increanng their lengths, for which end the late Contrivance of Hugeniits [ 91 ] Hugenins feems well accommodated. For ve- ry long Tubes are cumberfome, and fcarce to be readily managed, and by reafon of their length are very apt to bend, and Ihake by bend- ing fo as to caule a continual trembling in the Objeds, whereby it becomes difficult to fee them dillindly : whereas by his contrivance the Glafles are readily manageable, and the Objedt- glafs being fix'd upon a Itrong upright Pole- be- comes more ileady. Seeing therefore the Improvement of Tele- fcopes of given lengths by Refradions is defpe- rate ; I contrived heretofore a Perfpec^ive by Reflexion, ufmg initead of an Objed-glafs a concave Metal. The diameter of the Sphere- to which the Metal was ground concave was a- bout 25- Englifli Inches, and by confequence the length of the Inilrument about fix Inches and a quarter. The Eye-glafs was Plano-con- vex, and the diameter of the Sphere to which the convex fide was ground was about 4 of an Inch, or a little lefs, and by confequence it magnified 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 hmited 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 , llopp'd much of the erroneous Light, which otherwife would have diilurbed the C 92 ] the Vifion. By comparing it with a pretty good Perfpedive of four Feet in length, made with a concave Eye-glafs, I could read at a greater diftance with my own Inflrument than with the Glafs. Yet Objedls appeared much darker in it than in the Glafs, and that partly becaufe more Light was loft by Reflexion in the Metal, than by Refradion in the GJafs, and partly be- caufe my Inllrument was overcharged. Had it magnified but 30 or 25 times it would have made the Objeft appear more brisk and plea» fant. Two of thefe I made about 16 Years a- go, and have one of them Hill by me by which I can prove the truth of what I write. Yet it .is not fo good as at the firlt. For the concave has been divers times tarnillied and cleared a- gain, by rubbing it with very fofc Leather. When I made thefe, an Artifl in London undertook to imitate it ; but ufmg another way of polifliing them than I did, he fell much ihort of what I had attained to, as I afterwards underflood by difcourfing the under Workman he had em- ployed. The Polilli I ufed was in this man- ner. I had two round Copper Plates each fix Inches in diameter, the one convex the o- ther concave, ground very true to one another. On the convex I ground the Objeft-Metal or Concave which was to be polifh'd, till it had taken the Figure of the Convex and was ready for a Polifh. 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 whetted to make it fpread eavenly all over the convex. Thus [ 93 ] Thus by working it well I made it as thin as a Groat, and after the convex was cold I ground it again to give it as true a Figure as I could. Then I took Putty which I had made very fine by wafliing it from all its groffer Particles, and laying a little of this upon the Pitch, I ground it upon the Pitch with the concave Copper till it had done making a 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 frefli Putty upon the Pitch and ground it again till it dad done making a noife, and afterwards ground the Objeft-Metal upon it as before. And this Work I repeated till the Metal was poHilied, grinding it the lail time with all my Itrength for a good while together, and. frequently breathing upon the Pitch to keep it moitt with- out laying on any more frefli Putty. The Ob- jedt-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 polifhed them both I tried which was bed, 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- lifliing, till I made thofe two refleding Perfpe- ftives I fpake of above. For this Art of po- hfliing will be better learn'd by repeated Pra- ftice than by my defcription. Before I ground the Obje6t-Metal on the Pitch, I always ground the Putty on it with 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 [94 ] to flick fafl in the Pitch, they would by rolling up and down grate and fret the Objeft-Metal and fill it full of little holes. But becaufe Metal is more difficult to polifh than Glafs , and is afterwards very apt to be fpoiled by tarnifliing and refleds not fo much Light as Glafs quick-filver'd over does : I would propound to ufe inltead 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 muft be every where of the fame thicknefs exadly. O- therwife it will make Objefts look colour'd and indiftindl. By fuch a Glafs I tried about five or fix Years ago to make a refleding Telefcope of four Feet in length to magnify about 15-0 times, and I fatisfied my felf that there wants nothing but a good Artiit to bring the Defign to perfe- ftion. For the Glafs being wrought by one of our London Artiits after fuch a manner as they grind GlalTes for Telefcopes, tho' it feemed as well wrought as the obje^t-glalTes 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- jedfs appeared indiftindl in this Inftrument. For the Errors of reflecSted Rays caufed by any In- equality of the Glafs, are about fix times great- er than the Errors of refraded Rays caul'ed 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 diilurb the Vifion, did no fenfible prejudice to it, and by confequence that nothing is wanting to [95] to perfeft thefe Telefcopes, but good Work- men who can grind and polifti Glafles truly fpherical. An Objed-gla.fs of a fourteen Foot Telefcope, made by an Artificer at London^ I once mended confiderably, by grinding it on Pitch with Putty, and leaning very eafily on it in the grinding, left the Putty fliould fcratch it. Whether this way may not do well enough for poliihing thefe refleding GlafTes, I have not yet tried. But he that fliall try either this or any other way of pohfliing which he may think bet- ter, may do well to make his GlalTes ready for polifhing by grinding them without that vio- lence, wherewith our London Workmen prefs their GlafTes in grinding. For by fuch violent prefTure, GlafTes are apt to bend a Httle in the grinding, and fuch bending will certainly fpoil their Figure. To recommend therefore the confideration of thefe reflecting Glaffes, to fuch Artifts as are curious in figuring GlafTes, I fhall defcribe this optical Inllrument in the following Propofition. TROT, WW. Prob.il To jhorte7t Telefcopes. LET A B D C [in Fig. 29.] 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 Objeds appear colour'd and indi- C 96 ] ihdiflin(3:, and let it be very truly wrought and quick filver'd over on the back- fide ; and fet in the Tube V X Y Z which mufl be very black within. Let E F G 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 F GK, to the end of which made flat it is cemented. Let this Prifrn 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 lides F E and G E be fquare, and by confequence the third fide F G a re- ftangular Parallelogram, whofe length is to its breadth in a fubduplicate proportion of two to one. Let it be fo placed in the Tube, that the Axis of the Speculum may pafs through the middle of the fquare fide E F perpendicularly, and by confequence through the middle of the fide F G at an Angle of 45 Degrees, and let the fide EF 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 E F, and be reflefted by the fide F G, and thence go out of it through the fide G E, to the point T which mult 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 the Rays at their coming out of the Glafs pafs through a fmall round hole, or aperture made in a lit- tle plate of Lead, Brafs or Silver, wherewith the (911 the Glafs is to be covered, which hole mufl be ho bigger than is necefTary for Light enough to pais through. For fo it will render the Ob- jeft diflinft, the Plate in which 'tis made inter- cepting all the erroneous part of the Light which comes from the verges of the Speculum AB. Such an Inilrument well made, if it be fix Foot long, (reckoning the length from the Speculum- to the Prifm, and thence to the Fo- cus 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 Inilrument be made longer or morter, the aper- ture mull be in proportion as the Cube of the fquare-fquare Root of the length, and the mag- nifying as the aperture. But it's convenient that the Speculum be an Inch or two broader than the aperture at the leatl, and that the Glafs of the Speculum be thick, that it bend not in the working. The Prifm EFG mull be no bigger than is neceifary , and its back fide F G rhuft not be quick-filver'd over. For without quick- filver it will refleft all the Light incident on it ft'om the Speculum. In this Inftrument the Objedl will be invert* ed, but may be ereded by making the fquare fides EF and E G bf the Prifm E F G not plane but fpherically convex, that the RayS may crofs as well before they come at it as afterwards between it and the Eye- glafs. If it- be defired that the Inilrument bear a larger aperture, that H may [98 ] may be alfo done by compofing the Speculum of two GlaiTes with Water between them. If the Theory of making Telefcopes could at lengrh be fully brought into pradice, 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 perpe- tual Tremor ; as may be feen by the tremulous Motion of Shadows call from high. Towers, and by the twinkling of the fix'd Stars. But thefe Stars do not twinkle when view'd through Telefcopes which have large apertures. For the Rays of Light which pafs through divers parts of the aperture, tremble each of them a- part, and by means of their various and fome- times contrary Tremors, fall at one and the fame time upon different 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, compofed of thofe many trembling Points confufedly and infenfibly mix- ed with one another by very fliort 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 Ob- jeds to appear brighter and larger than ibort ones can do, but they cannot be fo formed as to take away that confufion of the Rays which arifes from the Tremors of the Atmofphere. The only remedy is a molt-ferene and quiet Air, fuch as may perhaps be found on the tops of the higheil Mountains above the grolTer. Clouds. THE THE FIRST BOOK O F TICKS. P A R T II. TROT. I. Theor. I. The Thanomena of Colours in refraBed or re* JleBed Light are not caufed by new Modifi- cations of the Light varioujly imprejs'd, ac* cording to the various Terminations of ths Light and Shadow. The Proof by Experiments. Exfer.i. ^^^|OR if the Sun iliine into a ^^tf?rTr^I| ^gj.y j^j.|, (^}-,^j^-5[^(^j^. through g an oblong hole F, [in Fig. i.] ^ whofe breadth is the lixth or eigth part of an Inch, or fomething lefs ; and his beam F H do afterwards pals firit through a H 2. very C too ] very large Prifm ABC, diftant about ^o Feet from the hole, and parallel to it, and then (with its white part) through an oblong hole H, whofe breadth is about the fortieth or fixtieth part of an Inch, and which is made in a black opake ^ Body G I, and placed at the diilance of 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 / 1, placed after that hole H, at the diftance of three. or four Feet from it, and there paint the ufual Colours of the Prifm , fuppofe red at ?, yellow at s, green at r, blue at ^, and violet ^t/; 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, /, m, n or o^ take away any one of the Colours at t^ s, r, q or/, whilfl the other Colours remain upon the Paper as before ; or with an Obftacle fomething bigger you may take 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 outmolt in the Confine of the Shadow towards /, and any one of them as w^ell as red may be- come outmoll in the Confine of the Shadow towards t, 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 toany Confines of Sha- dow, [ ,o, ] 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 Philofophers. 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 diminilhed, but that the Colours at /> ^ be fufliciently vifible. To procure a Prifm of folid Glafs large enough for this Experiment will be" difificult, and therefore a prifmatick VeiTel mult be made of poliili'd Glafs Plates cemented together, and filled with fait Water or clear Oil. Exper. z. The Sun's Light let into a dark Chamber through the round hole F, [in Fig. z.] 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 diftant 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 DE. If that Paper was perpendicular to that Light incident upon it, as 'tis reprefented in the pofture 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 njuch incli- ned to the Light as 'tis reprefented in the Po- rtions de and h\ the fame Light in the one cafe appeared yellow and red, in the other blue. H 3 Her« [ I02 ] Here one and the fame part of the Light in one and the fame place, according to the va- rious Inclinations of the Paper, appeared in one cafe white, in another yellow or red, in a third blue, whillt the Confine of Light and Shadow, and the Refractions of the Priim in all thefe ca- fes remained the fame. Exper. 3. Such another Experiment may be more eafily tried as follows. Let a broad beam of the Sun*s Light coming into a dark Cham- ber through a hole in the Window-diut be re- fraded by a large Prifm ABC, [in Fig. 3.] whofe refrading Angle C is more than 60 De- grees, and fo foon as it comes out of the Prilm let it fall upon the white Paper D E glewed up- on a ftiff Plane"; and this Light, when the Pa- per is perpendicular to it, as 'tis reprefented in D E., will appear perfectly white upon the Pa7 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, tlie 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 pollure de^ or into blue and violet, as in the pofture ^i. And if the Light before it fall upon the Paper be twice refraCled 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- iour'd all over with one uniform Colour, the Golgur being always the fame in the middle of the I 103 ] the Paper as at the edges, and this Colour chan- ged according to the various obhquity of the refleding Paper^ without any change in the Re- fradions 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 asked, What then is their Caufe ? I anfwer, That the Paper in the polture de, be- ing more oblique to the more refrangible Rays than to the leis refrangible ones, is more Itrong- ly illuminated by the latter than by the. former, and therefore the lels refrangible Rays are pre- dominant in the refleded Light. And whcre- ever they are predominant in any Light they tinge it with red or yellow, as may in fome mea- fure appear by the tirlt Propofition of the firft Book, and will more fully appear hereafter. And the contrary happens in the poflure of the Paper ^g, 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 of 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 llowly 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 aril'e from fome regular H 4 caufe C 104 ] Caufe which depends not on any Confine of Shadow. What this Caufe is will be iliewed in the next Book. To thefe Experiments may be added the tenth Experiment of the firll Book, where the Sun's Light in a dark Room being trajeded through the parallel Superficies .of two Prifms tied together in the form of a Parallelopipede, became totally of one uniform yellow or red Colour, at its emerging out of the Prifms. Here, in the produdion of thefe Colours, the Confine of Shadow can have nothing to do. For the Light changes from white to yellow, orange and red fucceffively, without any alte- ration of the Confine of Shadow : And at both edges of the emerging Light where rhe con- trary Confines of Shadow ought to produce different Effe61s, the Colour is one and the fame, whether it be white, yellow, orange or red : And iq the middle of the emerging Light, where there is no Confine of Shadow at all, th^ Colour is the very fame as at the edges, the whole Light at its very firfl 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 work in refrafted Light after its Emergence. Nei- ther can thefe Colours arife from any new Mo- difications of the Light by Refradions, becaufe they change fucceffively from white to .yellow, orange and red, while the Refradions remain the fame, and alfo becaufe the Refradions are ip^ade contr^ary v>'ays by parallel Superficies which deflroy C I05] deftroy one anothers EfFeds. They arife not therefore from any Modifications of Light made by Refradions and Shadows, but have fome other Caufe. What that Cajife is we fhewed 'above in this tenth Experiment, and need not here repeat it. There is yet another material circumftance of this Experiment. For this emerging Light be^ ing by a third Prifm HIK [in Fig. tl-l. Tart i.] refracted towards the Paper FT, and there paint- ing the ufual Colours of the Prifm, red, yellow, green, blue, violet : If thefe Colours arole from the Refradions of that Prifm modifying the Light , they would not be in the L ight before its Incidence on that Prifm. And yet in that Experiment we found that when by turning the two firfl Prifms about their common Axis all the Colours were made to vaniili but the red ; the Light which makes that red being left alone, appeared of the very fame red Co^ lour before its Incidence on the third Prifm. And in general we find by other Experiments that when the Rays which differ in Refrangibi- lity are feparated from one another, and any one fort of them is conCdered apart, the Co- lour of the Light which they compofe cannot be changed by any Refradion or Reflexion whatever, as it ought to be were Colours no- thing elfe than Modifications of Light caufed by Refraftions, and Reflexions, and Shadows. This unchangeablenefs of Colour I am now to defcribe in the following Propofition. TROT, C 106 ] T R OTAl. Theor. II. ^11 homogeneal Light has its f roper Colour an- fwering to its degree of Refrangibility^ and. that Colour cannot be changed by Reflexions and Refr anions. IN the Experiments of the fourth Propofition of the firfl: Book, when I had feparated the heterogeneous Rays from one another, the Spe- ftrum / 1 formed by the feparated Rays, did in the progrefs from its end />, on which the mofl refrangible Rays fell, unto its other end ty on which the leafl reh'angible Rays fell, appear tinged vv^ith this feries of Colours, violet, indi- go, blue, green, yellow, orange, red, together with all their intermediate degrees in a con- tinual Succeflion perpetually varying. So that there appeared as many degrees of Colours, as there were forts of Rays differing in Refran- gibility. Exper. 5". Now that thefe Colours could not be changed by Refra^ion, I knew by refrading with a Prifm fometimes one very little part of this Light, fometimes another very little part, as is defcribed in the twelfth Experiment of the firft Book. For by this Refradion the Co- lour of the Light was never changed in the Icaft. If any part of the red Light was refradkd, it remained totally of the fame red Colour as be- fore. No orange, no yellow, no green or blue, , no other new Colour was produced by that Refradion. Neither did the Colour any ways change by repeated Refradions, but continued always [ »07 ] always the fame red entirely as at firft. The like conibncy and immutability I found alfo in the blue, green, and other Colours. So alfo if I looked through a Prifm upon any Body illu- minated with any part of this homogeneal Light, as in the fourteenth Experiment of the firft Book is delcribed ; I could not perceive any new Co- lour generated this "way. All Bodies illumina- ted vvith 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 iefs diitin^l:, nor otherwife coloured, than when viewed with the naked Eyes. Their Colours were not in the leatl changed by the Refradion of the interpofed Prifm. I fpeak here ol a fenfible change of Colour : For the Light whicli I here call homogeneal, being not ablolutely homogeneal, there ought to arife fome httle 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 RefraCdons, fo neither were they by Reflexions. For all white, grey, red, yel- low, green, blue, violet Bodies, as Paper, Aflies, red Lead, Orpiment, Indigo, Bife, Gold, Sil- ver, Copper, Grafs, blue Flowers, Violets, Bubbles of Water tinged wixh various Colours, peacock's Feathers, the Tindure of Lignum C io8 ] Nephriticum^ and fuch like, in red homogeneal Light appeared totally red, in blue Light to- tally blue, in green Light totally green , and fo of other Colours. In the homogeneal Light of any Colour they all appeared totally of that fame Colour, with this only difference, that fome of them refleded that Light more ftrong- ly, others more faintly. I never yet found any fiody which by refleding homogeneal Light could fenfibly change its Colour. From all which it is manifelt, that if the Sun's Light confifted of but one fort of Rays, there would be but one Colour in the whole World, nor would it be pofTible to produce any new Colour by Reflexions and Refracfiions, and by confequence that the variety of Colours depends upon the compofition of Light. T>EFINlTtON. TH E homogeneal Light and Rays which appear red, or rather make Objefts ap- pear fo, I call Rubrific or Red- making ; thofe which make Objeds appear yellow, green, blue and violet, I call Yellow-making, Green-ma- king, 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 woijld be underftood to fpeak not philofo- phicaliy^id properly, but grollly, and accor- dingly 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 nQthing elfe than a certain [ I09 ] certain power and difpofition to flir up a Sen- fation of this or that Colour. For as Sound iti a Bell or mufical String or other founding Bo- dy, is nothing but a trembling Motion, and in the Air nothing but that Motion propagated from the ObjeS, and in the Senforium 'tis a Senfe of that Motion under the form of Sound; fo Colours in the Objed: are nothing but a Dif- pofition to refledl this or that fort of Rays more copioufly than the reft; in the Rays they are nothing but their Difpofitions to propagate this or that Motion into the Senforium, and in the Senforium they are Senfations of thofe Motions under the forms of Colours. TROT. III. Prob. I. To define the Refrangib'tUty of the fever al forts of homogeneal Light anfwermg to the feve^ ral Colours. FOR determining this Problem,! made the following Experiment. Exper. 7. When I had caufed the redili- near fides A F, G M, [in Fig. 4.] of the Spe- drum of Colours made by the Prifm to be di- ftindly defined , as in the fifth Experiment of the firft Part is defcribed, there were found in it all the homogeneal Colours in the fame or- der and fituation one among another as in the Spe6lrum of fimple Light, defcribed in the fourth Propofition of that Part. For the Cir- cles of which the Spedrum of compound Light PT [ no ] PTis compofed, and which in the middle parts of the Speftrum interfere and are intermixed with one another, are not intermixed in their GUtmolt parts where they touch thofe redili- near fides A F and G M. And therefore in thofe re6^ilinear fides when dillindly defined, there is no new Colour generated by Refra- dion. I obferved alfo , that if any where be- tween the two outmod Circles T M F and P G A a right Line, as y ^, was crofs to the Spedrum, fo as at both ends to fall perpendi- cularly upon its redlilinear fides, there appear- ed one and the fame Colour and degree of Co- lour from one end of this Line to the other. I delineated therefore in a Paper the perimeter of the Spedrum F A P G M T, and in trying the third Experiment of the firlt Book, I held the Paper fo that the Spedrum might fall upon this delineated Figure, and agree wdth it exact- ly, whillt an Aiiiltant whofe Eyes for diilinguifh- ing Colours were more critical than mine, did by right Lines a, 13, y^^e t, &c. drawn crofs the Spec^trum, note the Confines of the Colours,* that is of the red M ci/3 F, of the orange cty ^(3, of the yellow y s^^, of the green iv^ ^y of the blue }] iic9, of the indigo * a /* z, and of the vio- let A G A=/tA. And this Operation being divers times repeated both in the fame and in feveral Papers, I found that the Oblervations agreed well ehough with one another, and that the redilinear fides M G and F A were by the faid crofs Lines divided after the manner of a mu- fical Chord. Let G M be produced to X, that M X may be equal to G M, and conceive GX, C HI ] GX, aX, ;X, ^X, eX, yX, ^X, MX, to be in proportion to one another, as the numbers, I, V, 4, 4, T> T. tI, 4, and fo to reprefent the Chords of the Key, and of a Tone, a third Mi- nor, a fourth, a fifth, a fixth Major , a feventh and an eighth above that Key: And the inter- vals Met, ay, ye, sf}-, >? *. ^ ^y and A G, will be the Species which the feveral Colours (red, o- range, yellow, green, blue, indigo, violet) take up. Now thefe Intervals or Spaces fubtending the differences of the Refradions of the Rays go- ing to the Umits of thofe Colours, that is, to the Points M, ct, y, £, tj, ;, a, G, may without any fenfible Error be accounted proportional to the differences of the Sines of Refradion of thofe Rays having one common Sine of Inci- dence, and therefore lince the common Sine of Incidence of the moil and lead refrangible Rays out of Glafs into Air was (by a method df^fcri- bed above) found in proportion to their Sines of Refradion, as 50 to yy and 78, divide the dif- •ference between the Sines of RefracStion 77 and 78, as the Line G M is divided by thofe Inter- vals, and you will have 77, 774, 77t, 77i^ n-\y 77t» 774, 7^? the Sines of Refradion of thofe Rays out of Glafs into Air, their common Sine of Incidence being 5-0. 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- 5-0 to 77^ nor lefs than 50 to 77^^ but they varied from one ano- ther according to all intermediate proportions. And the Sines of the Incidences of the green- making [ ii^ 3 Jiiaking Rays were, to the Sines of their Refra° flions in all proportions from that of 50 to 77-f, unto that of 50 to 'jj^. And by the like limits abovementioned were the Refradions of the Rays belonging to the reit of the Colours de- fined, the Sines of the red-making Rays extend- ing from "jj to 'j'j^'i thofe of the orange- making from ^-j^ to yj^^ thofe of the yellow-making from -j-j^ to 'jj^^ , thofe of the green making from y-j^ to yy^^ thofe of the blue making from 774 to 77t, thofe of the indigo-making from 774 to yyi , and thofe of the violet from yy~ to 78. Thefe are the Laws of the Refradiohs made out of Glafs into Air, and thence by the third Axiom of the firft part of this Book, the Laws of the Refradions made out of Air into Glafs are eafily derived. Expr. 8. I found moreover that when Light goes out of Air through feVeral contiguous re- frading 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 Refradions '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 whitenefs of the emerging Light will by degrees in palling on from the place of E- mergence, become • tinged in its edges with Colours. This I tryed by refrading Light with Prifms of Glafs placed within a prifmatick Vef- fel of Water. Now thofe Colours argue a di- verging r "3 ] verging and feparation of the heterogeneous Rays from one another by means of their une- qual Refradions, as in what follows will more fully appear. And on the contrary, the per- manent whitenefs argues, that in like Inciden- ces of the Rays there is no fuch feparation of the emerging Rays, and by confequence no in- equality of their whole Refraftions. Whence I feem to gather the two following Theorems. I. The ExcelTes of the Sines of Refraftion of feveral forts of Rays above their common Sine of Incidence when the Refractions are made out of divers denier Mediums immedi- ately into one and the fame rarer Medium, fup- pofe of Air, are to one another in a given Pro- portion. ^. The Proportion of the Sine of Incidence to the Sine of Refradion 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 Refradion out of the firlt Medium into any third Medium, and of the .Proportion of the Sine of Incidence to the Sine of Refradion out of that third Medium into the fecond Medium. By the firft Theorem the Refractions of the Rays of every fort made out of any Medium in- to Air are known by having the Refraction of the Rays of any one fort. As for inftance, if the Refractions 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 I fubduCted 4 C "4 ] fubdufled from the Sines of Refradlion, and the ExcelTes will' be x/, 274, x74, 2,7-7, 274, . 2-77* '^lif 2-8. Suppofe now that the Sine of Incidence of the leail refrangible Rays be to their Sine of Refradion out of Rain-water in- to Air as 3 to 4, and fay as i the difference of thofe Sines is to 3 the Sine of Incidence, fo is 17 the leaft of the ExcefTes above-mentioned to a fourth number 81 ; and 81 will be the common. Sine of Incidence out of Rainwater into Air, to which Sine if you add all the a- bovementioned ExcefTes you will have the de- fired Sines of the Refradions 108, 1084, 1084, 1084, 1084, 1084, 1084, 109. By the latter Theorem the Refradion out of one Medium into another is gathered as often as you have the Refradions out of them both into any third Medium. As if the Sine of In- cidence of any Ray out of Glafs into Air be to its Sine of Rerradion as 1.0 to 31, and the Sine of Incidence of the fame Ray out of Air into Water, be to its Sine of Refradion as 4 to 3 ; the Sine of Incidence of that Ray out of Glafs into Water will be to its Sine of Refradion as io to 31 and 4 to 3 jointly, that is, as the Fa- ftum of 20 and 4 to the Fadrum of 31 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; not only by teaching thofe things which tend ro the perfedion of Vifion, but alfo by determining mathematically all kinds of Phae- nomena of Colours which could be produced Jl by I [ 115 ] by Refra61ions. For to do this, there is tio» thing elfe requifite than to find out the Separa- tions 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 necefTary to the Argument; and by the fuccelTes I met with in the Trials, I dare promife, that to him who fhall argue tru- ly, and then try all things with good Glafles and fuflRcient Circumfpcdion, the expefted E- vent will not be wanting. But he is firlt to know what Colours will arife from any others mix'd in any ailigned Proportion. TROT. IV. Theor.III. Colours may be produced by Compojition 'which jhall be like to the Colours of homogeneal Light as to the Appearance of Colour^ but not as to the Immutability of Colour and Conftitution of Light. And thofe Colours by how much they are more compounded by fo much are they lefs fill and intenfe^ and by too much Compo- Jition they may be diluted and weaken d till they ceafe^ and the Mixture becomes white or grey. There may be alfo Colours produced by Compojition, which are not fully like any of the Colours of homogeneal Light, FOR a Mixture of homogeneal red and yel- low compounds an orange, like in appear- ance of Colour to that orange which in the I ^. feries [ iiO feries of unmixed prifmatick Colours lies be- tween them ; but the Light of one orange is homogeneal as to Refrangibility , that of the other is heterogeneal , and the Colour of the one, if viewed through a Prifm, remains un- changed , that of the other is changed and re- folved into its component Colours red and yel- low. And after the fame manner other neigh- bouring homogeneal Colours may compound new Colours, like the intermediate homoge- neal ones, as yellow and green, the Colour be- tween them both, and afterwards, if blue be ad- ded, there will be made a green the middle Co- lour of the three which enter the Compofition : For the yellow and blue on either hand, if they are equal in quantity they draw the intermedi- ate green equally towards themfelves in Com- pofition, and fo keep it as it were in i5iquilibrio, that it verge not more to the yellow on the one hand, than to the blue on the other, but by their mix'd Adions remain ftill a middle Colour. To this mix'd green there may be farther ad- ded fome red and violet, and yet the green will not prefently ceafe but only grow lefs full and vivid , and by increafing the red and vio- let it will grow more and more dilute, until by the prevalence of the added Colours it be over- come and turned into whitenefs, or fome other Colour. So if to the Colour of any homoge- neal Light, the Sun's white Light compofed of all forts of Rays be added, that Colour will not vanidi, or change its Species but be diluted, and by adding more and more white it will be diluted more and more perpetually. Laltly, if red [ 117 ] red and violet be mingled, there will be gene- rated according to their various Proportions various Purples, fach as are not like in appear- ance to the Colour of any homogeneal Light, and of thefe Purples mix'd with yellow and blue may be made other new Colours. • "PRGT.V. Theor. IV. IFh'ttenefs and all grey Colours between white and blacky ?nay be compounded of Colours^ and the whitenefs of the Sun's Light is compound- ed of all the primary Colours mix'd in a due proportion. The Proof by Experiments. Exper.^. 'I ^ H E Sun lliining into a dark \ Chamber through a Uttle round hole in the Window-lhut, and his Light being there refraded by a Prifm to call his coloured Image PT [in Fig. 5.] upon the oppofite Wall : I held a white Paper V to that Image in fuch man- ner that it might be illuminated by the colour'd Light refledled from thence, and yet not inter- cept any part of that Light in its palTage from the Prifm to the Speflrum. And I found that when the Paper was held nearer to any Colour than to the reft, it appeared of that Colour 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 wer^ I 3 inte^- [ ii8 ] intercepted, the Paper loft its white Colour, and appeared of the Colour of the rell 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 reflefted thence to the Eye; lb that if it had been either alone (the reft of the Light being intercepted) or if it had a- hounded moft and been predominant in the Light reflefted from the Paper, it would have tinged the Paper with its own Colour ; and yet being mixed with the reft of the Colours in a due proportion, it made the Paper look white, and therefore by a Compofition with the reft produced that Colour. The feveral parts of the coloured Light refleded from the Spedrum, whilft they ar^ propagated from thence through the Air, do perpetually retain their proper Co- lours, becauie wherever they fall upon the Eyes of an)rSpedator, they make the feveral parts of the SpeArum to appear under their proper Co- lours. They retain therefore their proper Co- lours when they fall upon the Paper V, and fo by the confufion and perfeft mixture of thofe Colours compound the whitenefs of the Light reflefted from thence. Exper. TO. Let that Speftrum or folar Image P T. [in Fig. 6.] fall now upon the Lens M N above four Inches broad, and about fix Feet di- ftant from the Prifm ABC, and fo figured that it may caufe the coloured Light which diverg- eth from the Prifm to converge and meet again at [ II? 3 at its Focus G, about fix or eight Feet diftant from the Lens, and there to fall perpendicular- ly upon a white Paper D E. And if you move this Paper to and fro, you will perceive that near the Lens, as at d e, the whole folar Image (fuppofe at / t J 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 perfeft mixture they will wholly vanifli 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 ap- pear again, but yet in a contrary order ; fup- pofe at ^i^ where the red t is now above which before was below, and the violet / is below which before was above. Let us now Hop 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 ^ reftpre [ I20 ] redore the vvhitenefs. So if the violet, blue and green be intercepted, the remaining yel- low, orange and red will compound upon the Paper an orange, and then if the intercepted Colours be let pafs they will fall upon this com- pounded orange, and together with it decom- pound a white. So alfo if the red and violet be intercepted, the remaining yellow, green and blue, will compound a green upon the Pa- per, and then the red and violet being let pafs will fall upon this green, and together with it decompound a white. And that in this Com- pofition 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 ^£y and then the red Colour at the Lens be alternately intercepted, and let pafs a- gain, the violet Colour on the Paper will not fuffer any Change thereby, as it ought to do if the feveral forts of Rays afted upon one ano- ther in the Focus G, where they crofs Nei- ther will the red upon the Paper be changed by any alternate {lopping, and letting pafs the violet which crofleth it. And if the Paper be placed at the Focus G, and the white round Image at G be viewed through the Prifm HIK, and by the Refradion of that Prifm be tranflated to the place r v, and there appear tinged with various Colours, name- ly, the violet at v and red at r, and others be- tween, and then the red Colour at the Lens be [ 121 ] be often ftopp'd and let pafs by turns, the red at r will accordingly disappear and return as often, but the violet at v will not thereby fuf- fer any Change. And fo by Hopping and letting pafs alternately the blue at the Lens, the blue at r will accordingly difappear and return, with- out any change made in the red at r. The red therefore depends on one fort of Rays, and the blue on another fort, which in the Focus G where they are commix'd do not a6l on one another. And there is the fame reafon of the other Colours. I confidered farther, that when the moil re- frangible Rays P/, and the lead refrangible ones T^, are by converging inclined to one another, 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 refleded Light would be tinged in that Focus with the Colour of the pre- dominant Rays, provided thofe Rays feverally retained their Colours or colorific Qualities in the Compofition of white made by them in that Focus. But if they did not retain them in that w^hite, but became all of them feverally endued there with a difpoficion to itrike 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 ob- liquely, as in the fecond Experiment of this Book, that the molt refrangible Rays might be more copioufly refleded than the reft, and the whitenefs at length changed fucceffively into blue, indigo and violet. Then I inclined it the [ 122 ] the contrary way, that the lead refrangible Rays might be more copious in • the refleded Light than the refi:, and the whitenefs turned fuc- ceffively 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 fucceflively the Teeth of this Initrument near the Lens, I in- tercepted 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 folar Image. But the Paper I had tirft placed fo, that the Image might appear white as often as the Comb was taken away ; and then the Comb being as was faid in- terpofed, that whitenefs by realbn 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, yellow, green, blue and purple, did always fuc- ceed one another. I caufed therefore all the Teeth to pafs fucceflively over the Lens, and when the Motion was flow, there appeared a perpetual fucceflion of the Colours upon the Paper : But if I fo much accelerated the Mo- tion, that the Colours by reafon of their quick fucceflion could not be diftinguifhed from one another , the appearance of the fingle Colours ceafed. There was no red, no yellow, no green. [ 123 ] green, no blue, nor purple to be feen any lon- ger, but from a confufion of them 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 llrike the Senfori- um. If the Impreilions follow one another flowly, fo that they may be feverally perceived, there is nlade a dilHnft Senfation of all the Co- lours one after another in a continual fuccef- fion. But if the Impreflions 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 Succef- fions 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 feveral 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 ImprefTion of every Co- lour remains in the Senforium, until a revolu- tion of all the Colours be compleated, and that firft Colour return again. The Impreffions there- fore of all the fucceffive Colours are at once in the C '24 ] the Senforium, and jointly ftir up a Senfation of them all ; and fo it is manifelt by this Expe- riment, that the commix'd ImprefKons of all the Colours do flir 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 aU the Colours may at once pafs from the Lens to the Paper, and be there intermixed, and to- gether reflected thence to the Spedators Eyes ; their Impreflions on the Senforium being now more fubtilly and perfectly commixed there, ought much more to Itir up a Senfation of whitenefs. You may inflead of the Lens ufe two Prifms HIK and LMN, which by refrafting the co- loured Light the contrary way to that of the firft Refradion, may make the diverging Rays converge and meet again in G; as you lee re- prefented in the feventb Figure. For where they meet and mix they will cpmpofe a white Light, as when a Lens is ufed. Exper. II. Let the Sun's coloured Image PT [ii)/%.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 abc^ held parallel to the Prifm ABC, by whofe Refradion 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 Image P T, the Speftrum S will appear oblong and coloured Hke the Image PT; but if you recede from it, the Colours of the Spedrum S will be contraded more and more, and [ 125 ] and at length vanifh, that Speflrum S becoming perfedly round and white ; and if you recede yet farther, the Colours will emerge again, but in a contrary order. Now that Spedrum S ap- pears white in that cafe when the Rays of fe- veral forts which converge from the feveral parts of the Image P T, to the Prifm abc^ are fo refrafted unequally by it, that in their paf- fage from the Prifm to the Eye, they may di- verge from one and the fame point of the Spe- drum 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 P T may be fucceflively intercepted ; the Spe- drum S when the Comb is moved flowly will be perpetually tinged with fucceflive Colours : But when by accelerating the motion of the Comb, the fucceflion of the Colours is fo quick that they cannot be feverally feen, that Spe- drum S, by a confufed and mix'd Senfation of them all, will appear white. Exper. \-L. The Sun fhining through a large Prifm ABC [in Fig. 9] upon a Comb XY, placed immediately behind the Prifm, his Light which palTed through the Interllices of the Teeth fell upon a white Paper DE. The breadths of the Teeth were equal to their In- terftices, and feven Teeth together with 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 Interltices painted fo many [ »2^ ] many ranges of Colours, kl^ m ;/, of^ q r, &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 mo- ved continually up and down with a receiprocal motion, afcended and defcended in the Paper, and when the motion of the Comb was fo quick, that the Colours could not be dillinguiflied 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 feveral ranges of Colours will be dilated and expanded into one another more and more, and by mixing their Colours will dilute one another , and at length , when the diilance of the Paper from the Comb is about a Foot, or a little more (fuppofe in the place ^DzE) they will fo far dilute one another as to become white. With any obilacle let all the Light be now ftopp'd which pafles through any one interval 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 ta- ken away, and there to be coloured. Let the intercepted range pafs on as before, and its Colours falling upon the Colours of the other ranges, and mixing with them, will reftore the whitenefs. Let the Paper i D i E be now very much in- clined to the Rays, fo that the moft refrangible Rays [ 127 3 Rays may be more copioufly refleded than the reil, 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 refleded than the reil, and by their Excefs the white- nefs will be changed into yellow and red. The leveral Rays therefore in that white Light do retain their colorific quaUties, by which thofe of any fort, when-ever they become more co- pious than the reit, do by their Excefs and Pre- dominance caufe their proper Colour to ap- pear. And by the fame way of arguing, applied to the third Experiment of this Book, it may be concluded, that the white Colour of all refra- fted 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- ducing the Phsenomenon 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 ufmg only three Prifms, as alfo by ufing only two as follows. Let two Prifms ABC and abc^ [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 CB and € b^ at which the Rays emerge, may lie in Di- redum. C 128 ] redum. Then let the Light trajeded through them fall upon the Paper MN, diflant about 8 or II 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 Prifm is rellored to its place again, fo that its Colours may there fall upon the Colours of the other, the mixture of them both will rellore the whitenefs. This Experiment fucceeds alfo, as I have tri- ed, when the Angle b of the lower Prifm, is a little greater than the Angle B of the upper, and between the interior Angles B and r, there intercedes fome fpace B c^ as is reprefented in the Figure, aud the refrading Planes B C and bcy are neither in diredum nor parallel to one another. For there is nothing more requifite to the fuccefs of this F,xperiment, than that, the Rays of all forts may be uniformly mixed upon the Paper in the place P T. If the molt refrangible Rays coming from the fuperior Prifm take up all the fpace 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 fpace from thence towards N. If the leait refrangible Rays coming from the fuperior Prifm take up the fpace MT, the Rays of the fame kind which come from the other Prifm ought to begin at T, and take up the remaining fpace T N. If one fort of the Rays which have intermediate degrees of Re- frangibility. frahgibility, and come from the fuperior Prifrri be extended through the fpace MQ, and an- other fort of thofe Rays through the fpace MR^ and a third fort of them through the fpace M Sj the fame forts of Rays coming from the Idwer Prifm, ought to illuminate the remaining fpaces Q N, R N, S N, refpeftively. And the fame is to be underitood of all the othei* forts of Rays. For thus the Rays of every fort will be fcattered uniformly and eavenly thro' the whole fpace M N, and fo being every where mix'd ill the fame proportion, they mud every where produce the fame Colours. And therefore iince by this mixture they produce white in the ex- terior fpaces M P and T N, they muft alfo pro- duce white in the interior fpace P T. This is the reafon of the compofition by which white- nefs was produced in this Experiment, and by what other way foever I made the like compofi- tion the refult was whitenefs. Laftly, If with the Teeth of a Comb of a due fize, the colour'd Lights of the two Prifms which fall upon the fpace P T be alternately intercepted, that fpace 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 fucceflive Colours calnnot be diftinguifli'd from one another, it will appear while 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; . agitiited to raife a Froth, and after that Froth K has [ no ] has flood a little, there will appear to one that iliall view it intently various Colours every where in the Surfaces of the feveral Bubbles ; but to one that fliall go fo far off that he cannot di- ftinguilh the Colours from one another, the whole Froth will grow white with a perfed whiten efs. Exper. If. Laitly, in attempting to com- pound a white by mixing the coloured Powders w^iich Painters ufe, I confider'd that all co- lour'd Powders do fupprefs and Hop in them a very confiderable part of the Light by which they are illuminated. For they become colour'd by refleding the Light of their own Colours more copiouily, and that of all other Colours more fparingly, and yet they do not reflect the Light of their own Colours fo copiouily as white Bodies do. If red Lead, for initance, and a white Paper, be placed in the red Light of the colour'd Spedrum made in a dark Cham- ber by the Refradion of a Prifm, as is defcri- bed in the third Experiment of the firil Book ; the Paper will appear more lucid than the red Lead, and therefore refleds the red-making Rays more copiouily than red Lead doth. And if they be held in the Light of any other Co- lour, the Light refle61ed by the Paper will ex- ceed the Light refleded by the red Lead in a much greater proportion. And the like hap- pens in Powders of other Colours. And there- fore by mixing fuch Powders we are not to ex- ped a ib'ong and full white, fuch as is that of Paper, but fome dusky obfcure one, fuch as might arife from a mixture of light and dark- nefs, t 131 ] hefs, or from white and black, that is, a grey, or dun, or rufTet brown, fuch as are the Co- lours of a Man's Nail, of a Moufej of Allies^ of ordinary Stones, 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 Powders. For thus one part of red Lead, and five parts of V'tride JEar'tL, compo- fed a dun Colour like that of a Moufe. For thefe two Colours were feverally fo compound- ed of others, that in both together were mix*- ture of all Colours ; and there was lefs red Lead ufed than Viride Mris^ becaufe of the fulnefs of its Colour. Again, one part of red Lead, and four parts of blue Bife, compofed a dun Colour verging a little to purple, and by ad- ding to this a certain mixture of Orpiment and Vtr'tde Mrts in a due proportion , the mixture loft its purple tindure, and became perfeAly dun. But the Experiment fucceeded beft with- out Minium 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 diluted that red by adding a little Viride M- rif, and a little more blue Bife than Viride M- ris, until 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 e- ' qual in whitenefs to that of Afhes or of Wood ' newly cut, or of a Man's Skin. The Orpiment ! refleded more Light than did any other of the Powders, and therefore conduced more to ihs whitenefs of the compounded Colour than they. K * Tq [ 132 ] To aflign the Proportions accurately may be difficult, by reafon of the different goodnefs of Powders of the fame kind. Accordingly as the Colour of any Powder is more or lefs full and luminous, it ought to be ufed in a lefs or greater proportion. Now confidering that thefe grey and dun Co- lours may i)e alfo produced by mixing whites and blacks, and by confequence differ from perfe6l whites not in fpecies of Colours but on- ly in degree of Luminoufnefs , it is manifeft that there is nothing more requilite to make them perfedly white than to increafe their Light fufficiently; and, on the contrary, if by increa- fmg their Light they can be brought to perfed whitenefs, it will thence alfo follow, that they are of the fame fpecies of Colour with the belt whites, and differ from them only in the quan- tity of Light. And this I tried as follows. I took the third of the abovemention'd grey Mixtures (that which was compounded of Orpiment, Pur- ple, Bife, and FiridejEris) and rubbed it thick- ly upon the Floor of my Chamber, where the Sun flione upon it through the opened Cafe- ment ; and by it, in the fhadow, I laid a piece of white Paper of the fame bignefs. Then going from them to the dillance of ix or i8 Feet, fo that I could not difcern the uneavennefs of the Surface of the Powder, nor the little ihadows let fall from the gritty Particles thereof; the Powder appeared intenfely white, fo as to tran- fcend even the Paper it felf in whitenefs, efpe- cially if the Paper were a little iliaded from the Light of the Clouds, and then the Paper com- pared [ 133 ] pared with the Powder appeared of fuch a grey Colour as the Powder had done before. But by laying the Paper where the Sun (hines thro' the Glafs of the Window, or by fliutting the Window that the Sun might fhine through the Glafs upon the Powder, and by fuch oihcr fit means of increafing or decreafing the Lights wherewith the Powder and Paper were illumi- nated, the Light wherewith the Powder is illu- minated may be made ftronger in fuch a due proportion than the Light wherewith the Paper is illuminated, that they Ihall both appear ex- aftly alike in whitenefs. For when I was try- ing this, a Friend coming to vifit me, I llopp'd him at the Door, and before I told him what the Colours were, or what I was doing ; I ask- ed him, Which of the two Whites were the bell, and wherein they differed ? And after he had at that diftance viewed them well, he an- fwer'd, That they were both good Whites, and that he could not fay which was bell, nor wherein their Colours differed. Now if you confider, that this white of the Powder in the Sun- fhine was compounded of the Colours which the component Powders (Orpiment, Purple, Bife, and Viride Mr'ts) have in the fame San- Ihine, you mull acknowledge by this Experi- ment, as well as by the former, that perfed' whitenefs may be compounded of Colours. From what has been faid it is alfo evident, that the whitenefs of the Sun's Light is com- pounded of all the Colours wherewith the fe- veral forts of Rays whereof that Light confifts, when by their feveral Refrangibilities they are K 5 fepa' [ 134- ] feparated from one another, do tinge Paper or any other white Body whereon they fall. For thofe Colours by Trop./L. are unchangeable, and whenever all thofe Rays with thofe their Colours are mix'd again, they reproduce the fame white Light as before. TROT. VI. Prob. IL In a mixture of primary Colours, the quantity and quality of each being given^ to know the Colour of the Com_pound. WI T H the Center O [in Fig. 1 1 .] and Ra- dius O D defcribe a Circle ADF, and dillinguifli its circumference into feven parts DE, EF, FG, GA, AB, BC, CD, propor- tional ,ta the feven mufical Tones or Intervals of the eight Sounds, Sol., la, fa, fol, la, mi, fa^ fol, contained in an eight, that is, proportiorKal to the number 4, tV, tV, 4, tV, tV, -i-. Let the firfl part D E reprefent a red Colour, the fe- cond E F orange, the third F G yellow, the fourth C A green, the fifth A B blue, the fixth BC indigo, and the feventh CD violet. And conceive that thefe are all the Colours of un- compounded Light gradually palling into one another, as they do when made byPrifms; the circumference DEFGABCD, reprefenting the whole feries 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 t^e mean Colour between red and orange, from E toF to F all degrees of orange, at F the mean be- tween orange and yellow, from F to G all de- grees of yellow, and fo on. Let / be the cen- ter of gravity of the Arch D E, and q^ r, j-, t^ u, AT, the centers of gravity of the Arches E F, FG, GA, AB, BC and C D refpedively, and about thofe centers of gravity let Circles pro- portional to the number of Rays of each Co- lour 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- Idng Rays in the Mixture, and fo of the reit. Find the common center of gravity of all thofe Circles />, ^, r, j, t, Uy 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 lliall fliew the Colour ariling from the compofition of all the Colours in the given Mixture, and the Line OZ ihall be pro- portional to the fulnefs or intenfenefs of the Colour, that is, to its diitance from whitenefs. As if Y fall in the middle between F and G, the compounded Colour lliall be the bed yel- low ; if Y verge from the middle towards F or G, the compound Colour lliall accordingly be a yellow% verging towards orange or green. If Z fall upon the circumference the Colour fliall be intenfe and florid in the higheft degree ; if it fall in the mid way between the circum- ference and center, it Ihall be but half fo intenfe, that is, it Ihall be fuch a Colour as would be made by diluting the mtenfell yellow K 4 with C 13^ ] with an equal quantity of whitenefs ; and if it fall uppn 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 O P, the main ingredients being the red and violet, the Colour compounded fliall 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 Una t> O 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 oppofite to one another be mixed in an equal proportion, the point Z lliall fall upon the cen- ter O, and yet the Colour compounded of thofe two iliall not be perfectly white, but fome faint anonymous Colour. For I could never yet by mixing only two primary Colours pro- duce a perfed 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 ofUttle or no moment to the underftanding 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 compoiition of all Colours. To give an inflance of this Rule ; fuppofe a Colour is compounded of thefe homogeneal Colours, of violet one part, of indigo one part, of blue two parts, of green three parts, of yel- low five pans, of orange fix parts, and of red teu C 137 ] ten parts. Proportional to thefe parrs defcribe the Circles a;, v^ ^ j, r, q, /, refpecftively, that is, fp that if the Circle x be one, the Circle 'u may be one, the Circle t 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 • O Y, the Point Y falls upon the circumference between E and F, fome thing nearer to E than to F, and thence I conclude, that the Colon? compounded of thefe Ingredients will be an o- range, verging a Uttle more to red than to yel- ^ low. Alfo I find that O Z is a little lefs than one half of O Y, and thence I conclude, that this orange hath a little lefs than half the ful- nefs or intenfenefs of an uncompounded o- range ; that is to fay, that it is fuch an orange as may be made by mixing an homogeneal o- range with a good white in the proportion of the Line O Z- to the Line Z Y, this Proportion being not of the quantities of mixed orange and white Powders , but of the quantities of the Lights reflefted from them. This Rule I conceive accurate enough for ■ praftice , though not mathematically accurate ; and the truth of it may be fufficiently proved to Senfe, by flopping any of the Colours at the Lens in the tenth Experiment of this Book. For the reft of the Colours which are not ftopp'd, but pafs on to the Focus of the Lens, will there compound either accurately or very nearly fuch a Colour as by this Rule ought to refult from dieir mixture. , TROT. C 138 ] T R OT.\ni. Theor. V. ^11 the Colours in the 1)niverfe which are made by Lights and depend not on the ^ower of /- magination, are either the Colours of homoge- neal Lights, or compounded of thefe, and that either accurately or very nearly^ according to the Rule of the foregoing Problem. XT' OR it has been proved (in Trop. i. Tart.z.) P that the changes of Colours made by Re- fraftions do not arife from any new Modifica- tions of the Rays imprefs'd by thofe Refradions, and by the various Terminations of Light and Shadow, as has been the condant and general Opinion of Philofophers. It has alfo been pro- ved that the feveral Colours of the homogeneal Rays do conftantly anfwer to their degrees of Refrangibility, (Trop. i. Tart i. and ^rop. z, IPart Z.J and that their degrees of Refrangibi- lity cannot be changed by Refradions and Re- flexions, (Trop.x. Tarti.J and by confequence that thofe their Colours are likewife immuta- ble. It has alfo been proved direftly by refra- fting and refleding homogeneal Lights apart, that their Colours cannot be changed, (Trop. 2. Tart Z.J It has been proved alfo, that when the feveral forts of Rays are mixed, and in crof- fmg pafs through the fame fpace, they do not ad: on one another fo as to change each others colorific qualities. (Exper. 10. Tart zj but by mixing their Adions in the. Senforium beget a Senfation differing from what either would do apart, that is a Senfation of a mean Colour be- tween [ ^39 I tween their proper Colours ; 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 P.ays would have apart, (Trop. f. Tarn. J The Rays in that mixture do not lofe or alter their feveral colorific qualities, but by all their various kinds of Anions mix'd in the Senfori- urn, beget a Senfation of a middling Colour between all their Colours, which is whitenefs. For whitenefs is a mean between all Colours, having it felf indifferently to them all, 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 prefently 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 fliewed alfo, that as the Sun*s Light is mix'd of all forts of Rays, {b its whitenefs is a mixture of the Colours of all forts of Rays ; thofe Rays having from the beginning their feveral colorific qua- lities as well as their feveral Refrangibilities, and retaining them perpetually unchanged not- withflanding any Refraftions 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. 9. and 10. Tart 1. or by Refraftion as happens in all Refraftions) fepa- rated from the relf, they then manifelt their proper Colours. Thefe things have been prov'd, and the fum of all this amounts to the Propofi- tion here to be proved.. For if the Sun's Light ifr^ [ HO 3 is mix'd of feveral forts of Rays, each of which have originally their feveral Refrangibilities and colorific Qualities, and notwithftanding their Refra(^tions and Reflexions , and their various Separations or Mixtures, keep thofe their ori- ginal Properties perpetually the fame without alteration; then all the Colours in the World muft be fuch as conflantly ought to arife from the original colorific qualities of the Rays where- of the Lights confift by which thofe Colours are feen. And therefore if the reafon of any Colour whatever be required, we have nothing elfe to do than to confider how the Rays in the Sun's Light have by Reflexions or Refradions, or other caufes been parted from one another, or mixed together ; or otherwife to find out what forts of Rnys are in the Light by which that Colour is made, and in what proportion ; and then by the lalt Problem to learn the Co- lour 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 Caufes, as when by the power of Phantafy we fee Colours in a dream, or a mad IVlan fees things before him which arediot there; or when we fee Fire by llriking the Eye, or fee Colours like the Eye of a Peacock's Feather, by preffing our Eyes in either corner whild w^e look the other w^ay. Where thefe and fuch like Caufes interpofe not, the Colour always anfwers to the fort or forts of the Rays whereof the Light confifls, as I have conilantly found in whatever Phsenomena of Colours I have hitherto been able to exa- mine. r HI 1 ^' mine. I fliall in the following Propofitions give inftances of this in the Phaenomena of chiefell note. TROT.Vm. Prob.III. By the d'tfcovered Troferttes of Light to ex* flatn the Colours made by ^rijms, LET A B C [in Fig. 12.] reprefent a Prifm refrafting the Light of the Sun, which comes into a dark Chamber through a hole F (p almolt as broad as the Prifm, and let M N re- prefent a white Paper on which the refrafted Light is cafl, and fuppofe the moll refrangible or deepeft violet -making Rays fall upon the Space P TT, the lead refrangible or deeped red- making Rays upon the fpace T7j the middle fort between the indigo making and blue- ma- king Rays upon the Space Q x^ the middle fort of the green-making Rays upon the fpace R ^, the middle fort between the yellow-making and orange- making Ra}js upon the fpace S o-, and o- ther intermediate forts upon intermediate Spa- ces. For fo the Spaces upon wnich the feveral forts adequately fall will by reafon of the dif- ferent Refrangibility of thofe forts be one lower than another. Now if the Paper MN be fo near the Prifm that the Spaces P T and cr7 do not interfere with one another, the diftance be- tween them T tt will be illuminated by all the forts of Rays in that proportion to one another which they have at their very firit coming out of C 142 ] of the Prifm, and confequently be white. But the Spaces PT and ^7 on either hand, will not be illuminated by them all, and therefore will appear coloured. And particularly at P, where the outmoft violet-making Rays fall alone, the Colour mufl be the deepelt violet. At Q where the violet-making and indigo-making Rays are mixed, it mull be a violet incHning much to indigo. At R where the violet-making, indi- go-making, blue-making, and one half of the green- making Rays are mixed, their Colours mult (by the conttru^lion of the fecond Pro- blem ) compound a middle Colour between in- digo and blue. At S where all the Rays are mixed except the red-making and orange-mak- ing, their Coloitrs 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 lead refrangible or utmoll red-mak- ing Rays are alone, the Colour mult be the deepelt red. At , that is, between / and B, and can by reflexion come from thence to the Eye, will be reflerted thither, but every where between p and r, mnny of thefe Rays will get through the Bafe and be refraded ; and the fame is to be underftood of the meanly refrangible Rays on either iide of the Point r. Whence it follows, that the Bafe of the Prifm muft 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 / and C, by reafon of the tranfmiflion of many Rays of every fort, look more pale , obfcure and dark. But at r, and in other places between / and t^ where all the more refrangible Rays are refleded to the Eye, and many of the lei's refrangible are tranf- mitted, the Excefs of the molt; refrangible in the refleded Light will tinge that Light with their Colour , which is violet and blue. And ;his t 147 ] this happens by taking the Line Cp r t E anf where between the ends of the Prifm H G and E I. TROT. IX. Prob. IV. By the difcovered Troperties of Light to explain the Colours of the Rain-bow, HIS Bow never appears but where it rains in the Sun-fhine, and may be made artiricially by fpouting up Water which may break aloft, and fcatter into drops, and fall down like Rain. For the Sun lliining upon thefe drops certainly caufes the Bow to appear to a Spectator Handing in a due pofition to the Rain and Sun. And hence it is now agreed upon, that this Bow is made by refraftion of the Sun's Light in drops of falling Rain. This was uri- derilood by fome of the Ancients, and of late more fully difcover'd and explain'd by the fa- mous Antonius de T)om'mis Archbiihop of Spa- lato, in his Book De Radiis Visits & Lucis, pub- liihed by his Friend Bartolus at Venice^ in the Year 161 1, and written above 20 Years before. For he teaches there how the interior Bow is made in round drops of Rain by two Rerra- (Sions of the Sun's Light, and one Reflexion between them, and the exterior by two Refra- ^ions and two forts of Reflexions between them in each drop of Water, and proves his Explications by Experiments made with a Phial full of Water, and with Globes of Glafs. filled L % witb [148] with Water, and placed in the Sun to make the Colours of the two Bows appear in them. The fame Explication T>es - Cartes hath purfued in his Meteors, and mended that of the exterior Bow. But whilft they underftood not the true origin of Colour's, it's necefTary^to purfue it here a little farther. For underllanding there- fore how the Bow is made, let a drop of Rain or any other fpherical tranfparent Body be repre- fented by the Sphere BNFG, [in Ftg, 14] de- fcribed with the center C, and femi-diameter C N. And let A N be one of the Sun's Rays incident upon it at N, and thence refraded to F, where let it either go out of the Sphere by Refraftion towards V, or be refleAed to G; and at G let it either go out by Refradion to R, or be refledted to H ; and at H let it go out by Refradion 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 perpen- diculars C D and CE, and produce CD till it fall upon the circumference at L. Parallel to the incident Ray A N draw the diameter B Q, and let the Sine of Incidence out of Air into Water be to the Sine of Refraftion 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 QF will firll increafe and then decreafe, and fo will the Angle A X R which the Rays A N and G R contain ; and the Arch Q F and Angle A X R will be biggelt when N D is to C N asVji-RR to -/ 3 RR, in which cafe N E will be to N D as i R to I. Al- fo the Angle AYS which the Rays AN and HS contain [ H9 ] contain will firft decreafe, and then increafe and grow lead when N D is to C N as Vii- kk to 1/ 8 RR, in which cafe NE will be to N D as 3 R to I. And fo the Angle which the next emergent Ray (that is, the emergent Ray after three Reflexions) contains with the incident Ray AN will come to its limit when ND is to CN as v'li-KK to V 15- RR, in which caJe NE will be to ND 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 C N as v/u -kk to 1/ 14 RR, in which cafe N E will be to N D as 5- R to I ; and fo on infinitely, the numbers 3, 8, 15-, 14, ^c. being gather'd by continual addition of the terms of the arithmetical Progreflion 3» f* 7j 9j ^^- The truth of all this Mathematicians will eafily ex- amine. Now it is to be obferved, that as when the Sun comes to his Tropicks, Days increafe and decreafe but a very little for a great while to- gether ; fo when by increafing the diitance C D, thefe Angels come to their limits, they vary their quantity but very httle for fome time to- gether, and therefore a far greater number of the Rays which fall upon all the Points N in the Quadrant B L, ihall emerge in the Hmits of thefe Angles, than in any other IncUnations. And farther it is to be obferved, that the Rays which differ in Refrangibility will have diffe- rent limits of their Angles of Emergence, and by confequence according to their different de- gree? of Refrangibility emerge mofi: copioufly L 3 in [ i5o] in different Angles, and being feparated froni one another appear each in their proper Co- lours. And what thofe Angles are may be ea- fily gather'd from the foregoing Theorem by computation. For in the leait refrangible Rays the Sines I and R (as was found above) are io8 and 8i, and thence by computation the greateit Angle A X R will be found 4x Degrees and i Minutes and the lead Angle AY S, 5-0 Degrees and 57 Minutes. And in the moll; refrangible Rays the Sines I and R are 109 and 81, and thence by computation the greatell Angle A X R will be found 40 Degrees and 17 Minutes, and the leait Angle AYS 54 Degrees and 7 Minutes. Suppofe now that O [in Fig. 15-.] is the Spe- iftator's Eye, and OP a Line drawn parallel to the Sun's Rays, and let P O E, P O F, P O G, POH, be Angles of 40 Degr. 17. Min. 4x. Degr. i Min. 5-0 Degr. 57 Min. and 5-4 Degr. 7 Min. refpedively, and thefe Angels turned about their common Side O P, fliall with their other Sides OE, OF ; OG, OH, defcribe the Verges of two Rain.bows AF BE and CH DG. For 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 Deg. 17 Min. lliall be the greateit Angle in which the moit refrangible Rays can after one Reflexion be re- fracted to the -Eye, and therefore all the drops in the Line OE ihall fend the moit refrangible Rays moit copioufiy to the Eye, and thereby \ ' ftrike r 151 3 ftrike the Senfes with the deepefl violet Colour in that Region. And in like manner the Angle SFO being equal to the Angle POF, or 41 Degr. 2, Min. Ihall be the greatell in which the lealt refrangible Rays after one Reflexion can emerge out of the drops, and therefore thofe Rays fliall come molt copioufly to the Eye from the drops in the Line O F, and ftrike the Senfes with the deepeft red Colour in that Region. And by the fame Argument, the Rays which have intermediate degrees of RefrangibUty iliall come mod copioufly from drops between E and F, and Itrike the Senfes with the intermediate Colours in the order which their degrees of RefrangibiUty require, that is in the progrefs from E to F, or from the infide of the Bow to the outfide in this order, violet, indigo, blue, green, yellow, orange, red. But the violet, by the mixture of the white Light of the Clouds, will appear faint and incline to purple. Again, the Angle SGO being equal to the Angle POG, or 50 Gr. fi Min. fliall be the leafl Angle in which the lealt refrangible Rays can after two Reflexions emerge out of the drops, and therefore the lealt refrangible Rays fhail come moft copioufly to the Eye from the drops in the Line O G, and Itrike the Senfe with the deepeft red in that Region. And the Angle SHO being equal to the Angle POHor 5-4 Gr, 7 Min. fhall be the lealt Angle in which the moit refrangible Rays after two Reflexions can e- merge out of the drops, and therefore thofe Rays fliall come moft copioufly to the Eye from the drops in the Line OH, and ftrike the Senfes . L 4 witfe C ^52 ] with the deepelt violet in that Region/ And by the fame Argument, the drops in the Re- gions between G and H fhall ftrike the Senfe with the intermediate Colours in the order which their degrees of Refrangibihty require, that is, in the progrefs from G to H, or from the infideofthe Bow to the outfide in this or- der, red, orange, yellow, green, blue, indigo, violet. And lince thefe four Lines OE, OF, OG, OH, may be fituatcd any where in the abovemention'd conical Superficies, what is faid of the Drops and Colours in thefe Lines is to be underflood of the Drops and Colours every where in thofe Superficies. Thus ihall there be made two Bows of Co- lours, an interior and ilronger, by one Reflexion in the drops, and an exrerior and fainter by two ; for the Light becomes fainter by every Reflexion. And their Colours iliaii lie in a con- trary order to one another, the red of both Bovvs bordering upon the Space G F which is between the Bows. The breadth of the inte- rior Bow EOF meafured crofs the Colours Ihall be i Degr. 45- Min. and the breadth of the exterior GOH Ihall be 3 Degr. 10 Min. and the diftance between them GOF ihall be 8 Gr. 15: Min. the greatell Semi-diameter of the inner- moft, that is, the Angle P O F being 41 Gr. % Min. and the leafl: Semi- diameter of the outer- molt P O G, being 50 Gr, 5-7 Min. Thefe are the Meafures of the Bows, as they would be were the Sun but a point; for by the breadth pf his Body the breadth of the Bows will be in- ^reafed" and their diitance decreafed by half a Degree, C 153 ] Degree, and fo the breadth of the interior Iris will be X Degr. 1$ Min. that of the exterior 3 begr. 40 Min. their diitance 8 Degr. 15- Min. the greateft Semi-diameter of the interior Bow 42 Degr. 17 Min. and the lealt of the exterior 50 Degr. 41 Min. And fuch are the Dimenfions of the Bows in the Heavens found to be very nearly, when their Colours appear ftrong and perfect. For once, by fuch means as I then had, I meafuredthe greateit Semi-diameter of the interior Iris about 41 Degrees, and the breadth of the red, yellow and green in that Iris 6} 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 befides the violet, which was fo much obfcu- red by the brightnefs of the Clouds, that I could not meafure its breadth. But fuppofmg 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 z^ De- grees, as above. The leaft diitance between this Iris and the exterior Iris was about 8 De-. grees and 30 Minutes. The exterior Iris was broader than the interior, but fo faint, efpeci- ally on the blue fide, that I could not meafure its breadth dillindly. At another time when both Bows appeared more diiHn(51, I meafured the breadth of the interior Iris x 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 C 154- 1 This Explication of the Rain-bow is yet far- ther confirmed by the known Experiment (made hyAntonius de 'Domt7iis 'iiwd IDes-Cartes ) of hanging up any where in the Sun fliine a Glafs Globe filled with Water, and viewing it in fuch- a pollure that the Rays which come from the Globe to the Eye may contain with the Sun's Rays an Angle of either 41 or 5*0 Degrees. For if the Angle be about 41 or 43 Degrees, the Spedator (fuppofe at O) fliall fee a full red 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 deprefling the Globe to E) there will appear other Colours, yellow, green and blue fucceffively in the fame fide of the Globe. But if the Angle be made about $0 Degrees (fuppofe by lifting up the Globe to G) there will appear a red Colour in that fide of the Globe towards the Sun, and if the An- gle be made greater (fuppofe by lifting up the Globe to H) the red will turn fucceiiively to the other Colours, yellow, green and blue. The fame thing I have tried by letting a Globe reft, and raifing or depreffiug the Eye, or o- therwife mo^ing it to make the Angle of a jail magnitude. 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 Spectator iliall fee red in the Prifm, and when the red falls upon the Eye he fliall fee blue; and if this were certain, the Colours of the Globe and Rain-bow ought to appear in a con- trary order to what we find. But the Colours. of [ '55 ] of the Candle being very faint, the miilake feems to arife from the difficulty of difcerning what Colours fall on the Eye. For, on the con- trary, I have fomtimes had occafion to ob- ferve in the Sun's Light refraded by a Prifm, that the Spectator 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 flowly from the Line which is drawn diredly from the Candle to the Eye, the red appears firft in the Prifm and then the blue, and therefore each of them is i^een when it falls upon the Eye. For the red palTes over the Eye firlt, and then the blue. The Light which comes through drops of Rain by two Refradions without any Reflexion, ought to appear llrongefl at the diilance of a- bout 26. Degrees from the Sun, and to decay gradually both ways as the diilance from him increafes and decreafes. And the fame is to be underltood of Light tranfmitted through fpherical Hail-flones. And if the Hail be a lit« tie flatted, as it often is, the Light tranfmitted may grow fo ftrong at a little lefs diilance than that of 26 Degrees, as to form a Halo about the Sun or Moon ; which Flalo, as often as the Hail-itones are duly figured may be colour'd, and then it mult be red within by the leail re- frangible Rays , and blue without by the moft refrangible ones, efpecially if the Hnil-ilones have opake Globules of Snow in their center to intercept the Light within the Halo (as ////- gefji7is has obferv'd) and make the infide there- of more diltindly, defined than it would other- ' wife C 15^ ] wife be. For fuch Hail-llones, though fphe- rical, 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 ufe to be. For of thofe Rays which pafs clofe by the Snow the Rubriform will be lead refraded, and fo come to the Eye in the diredelt Lines. The Light which paiTes through a drop of Rain after two Refradions, and three or more Reflexions , is fcarce Itrong enough to caufe a fenfible Bow ; but in thofe Cylinders of Ice by which Hugenms explains the Tarhelia^ it may perhaps be fenfible. T R O T.X. Prob. V. By the d'tfcovered ^roferties of Light to ex- plain the permanent Colours of Natural BO' dies. 'THHESE Colours arife from hence, that jl fome natural Bodies refled fome forts of Jtays, others other forts more copioufly than the reft. Minium refle6ls the leall refrangible or red making Rays moft copioufly, and thence appears red. Violets refled: the moft refrangi- ble, moft copioufly, and thence have their Co- lour, and fo of other Bodies. Every Body re- fle(^ts the Rays of its own Colour more copi- oufly than the reft, and from their excefs and predominance in the refleded Light has its Colour. Ex^er^ [ 157 ] Exfer. 17. For if in the homogeneal Lights obtained by the folution of the Problem pro- pofed in the fourth Proportion of the firft Part you place Bodies of feveral Colours, you will find, as I have done, that every Body looks moft fplendid and luminous in the Light of its own Colour. Cinnaber in the homogeneal red Light is moft refplendent, in the green Light it is manifeftly lefs refplendent, and in the blue Light ftill lefs. Indigo in the violet blue Light is moft refplendent, and its fplendor is gradu- ally diminilh'd as it is removed thence by de- grees through the green and yellow Light to the red. By a Leek the green Light, and next that the blue and yellow which compound green^ are more ftrongly reflefted than the other Co- lours red and violet, and fo of the reft. But to make thefe Experiments the more manifeit, fuch Bodies ought to be chofen as have the fuUeft and moft vivid Colours, and two of thofe Bodies are to be compared together. Thus, for in- ftance, if Cinnaber and ultra-mznne 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 lu- minous and refplendent red, and the ftUra-m^L" 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 tiUra- 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 refledls the red Light much more copioufly than the ultra m^r'me doth, and the t 158 ] the uUra-mmne reflefts the blue Light much more copioufly than the Cinnaber 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 different itrength or weaknefs of their Co- lour and Light. And as the reafon of the Colours of natural Bodies is evident by thefe Experiments , fo it is farther confirmed and put palt difpute by the two firfl Experiments of the firlt Part, where- by 'twas proved in fuch Bodies that the reflect- ed Lights which differ in Colours do differ alfo in degrees of Refrangibility. , For thence it's certain, that fome Bodies refleft the more re- frangible, others the lefs refrangible Rays more copioufly. And that this is not only a triie reafon of thefe Colours, but even the only reafon may ap- pear farther from this coniideration , that the Colour of homogeneal Light cannot be chan- ged by the Reflexion of natural Bodies. For if Bodies by Reflexion cannot in the leaft change the Colour of any one fort of Rays, they cannot appear colour'd by any other means than by refleding 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 call: on them, but of fome [ i?9 ] fome 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 illu- minated 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 Ex- cefs of the yellow-making, green-making and blue-making Rays in the incident green Light, will caufe thofe Rays to abound fo much in the retleded Light as to draw the Colour from red towards their Colour. And becaufe the red Lead reflefts 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 refleded Light will be more in proportion to the Light than they were in the incident green Light, and there- by will draw the retleded Light from green to- wards their Colour. 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 w^here 'tis thin, and a little higher where 'tis thicker grows orange, and where 'tis Hill thicker becomes red, and where 'tis thickeft the 4 t 1^0 ] the red is deepell and darkeft. For it is to be conceiv'd that fuch a Liquor flops the indigo- making and violet-making Rays molt eafily, the blue-making Rays more dii^cultly, the green- Jnaking Rays Hill more difficultly, and the red- making moil 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 Trop. 6. Tart i.) 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 fome of the green-making, the reft muft compound an orange ; 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 reft muft begin to com- pound 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 in- creafmg the thicknefs of the Liquor, fo that i^"^ 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 Veflel, found in a clear Sun-fliine Day^ that when he was funk many Fathoms deep into the Water, the upper part of his Hand on which the Sun ilione diredly through the Water and through a fmallGlafs Window in the VeiTelj appeared of a red Colour like that of a Damask Rofe, and the Water below and the under part of his Hand illuminated by Light refleded from the Water Water below look'd green. For thence it may be gather'd, that the Sea Water retleCh back the violet and blue-making Rays molt eailly, and lets the red-making Rays pafs moll freely and copioufly to great depths. For thereby the Sun's dired: Light at all great depths, by reafon of the predominating red-making Rays, mud ap- pear red ; and the greater the depth is, the ful- ler and intenfer mult that red be. And at fuch depths as the violet-making Rays fcarce pene- trate unto, the blue-making, green-making and yellow- making Rays being refleded from be- low more copioully than the red-making ones, mull compound a green. Now if there be two Liquors of full Colours, ftippofe a red iind a blue, and both of them fo thick as fuffices to make their Colours fuffici- ently full ; though either Liquor be fufficient- ly tranfparent apart, yet will you not be able to fee through both together. For if only the red-making Rays pafs through one Liquor, and only the blue-making through the other, no Rays can pais through both. This Mr. Hook tried eafually with Glafs Wedges filled with red and blue Liquors, and was furprized at the unex- pedted event, the reafon of it being then un- known ; which makes me trull the riiore to his Experiment, though I have not tried it my lelf. But he that would repeat it mull take care the Liquors be of very good and full Colours. Now whilil Bodies become coloured by re Heal- ing or tranfmitting this or that fort of Rays more copioully than the refl, it is to be conceived that they ilop and flifle in themfelves the Rays M which [ 1^2 ] which they do not refled or tranfmit. For if Gold be foliated and held between your Eye and the Light, the Light looks of a greenifli blue, and therefore mafly Gold lets into its Body the blue making Rays to be refleded to and fro within it till they be flopp'd and flifled, whilit it refleds the yellow-making outwards, and thereby looks yellow. And much after the fame manner that Leaf Gold is yellow by re- fledted, and blue by tranfmitted Light, and maf- fy Gold is yellow in all Pofitions of the Eye ; there are fome Liquors , as the Tinfture of Lignum Nephriticum^ and fome forts ofGlafs which tranfmit one fort of Light moll copiouf- ly, and refled another fort, and thereby look 6f feveral Colours, according to the pofition of the Eye to the Light. But if thefe Liquors or Glades were fo thick and mafly that no Light could get through them , I queltion not but they would like all other opake Bodies appear of one and the fame Colour in all Pofitions of the Eye, though this I cannot yet affirm by ex- perience. For all colour'd Bodies, fo far as my Obfervation reaches, may be feen through if made fuiiiciently thin, and therefore are in fome meafure tranfparent, and differ only in degrees of Tranfparency from tinged tranfparent Li- quors ; thefe Liquors, as well as thole Bodies, by a fuliicient thicknefs becoming opake. A tranfparent Body which looks of any Colour by tranfmitted Light, may alfo look of the fame ( -olour by refleded Light, the Light of that Colour being reflet^led by the farther Surface of the Body, or by the Air beyond it. And then [ '^3 ] then the refle^ /:>, and thereby caft the ufual prif- matick Colours PQ R S T upon the Paper LV placed behind. And then by Hopping any of the Colours/, q, r, s, r, at the Lens, I found that the fame Colour would vanifh at the Pa- per. So if the purple / was llopp'd at the Lens, the purple P upon the Paper would va- ni(h, and the rell of the Colours would remain unalter'd, unlefs perhaps the blue, fo far as fome purple latent in it at the Lens might be feparated from it by the following Refradions. And fo by intercepting the green upon the Lens, the green R upon the Paper would vanifh, and fo of the relt ; which plainly fliews, that as the white beam of Light X Y was compounded of feveral Lights varioufly colour'd at the Lens, fo the Colours which afterwards emerge out of it by new Refradions are no other than thofe of which it§ whitenefs was compounded. The M 3 Refra- [ I^^ ] Reflation of the Prifm HlKkh generates the Colours P Q R S T upon the Paper , not by changing the colorific qualities of the Rays, but by feparating the Rays which had the very fame colorific quaUties before they enter'd the Com- pofition of the refrafted 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 examin the reafon of the Co- lours of natural Bodies, I placed fuch Bodies in the Beam of Light X Y, and found that they all appeared there of thofe their own Colours which they have in Day light, and that thofe Colours depend upon theRays which had the fame Colours at the Lens before they enter'd the jGompofition of that beam. Thus, for in- fiance, Cinilaber illuminated by this beam ap- pears of the fame red Colour as in Day-light ; and if at the Lens you intercept the green-ma- king and blue-making Rays, its rednefs will be- come more full and lively : But if you there in- tercept the red-making Rays, it will not any longer appear red, but become yellow or green, or of fome other Colour, according to the forts of Rays which you do not intercept. So Gold in this Light X Y 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 fhews that its yellownefs arifes from the Excefs of the intercepted Rays tinging that whitenefs with their Colour when they are let pafs. So the infufion of Lignum Nephritz- cum cum (as I have alb tried) when held in this beam of Light X Y, looks blue by the refleft' ed part of the Light, and red by the tranimit. ted part of it, as when 'tis view'd in Day- light, but if you intercept the blue at the Lens the infufion will lofe its refleded blue Colour, whillt its tranfmitted red remains perfeft 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 re- main and become more full and perfed. Which fhews, that the Infufion does not tinge the Rays with blue and red, but only tranfmit thofe moft copioufly which were red-making before, and reflects thofe moft copioully which were blue- making before. And after the fame man- ner may the Reafons of other Phaenomena be examined, by trying them in this artificial beam of Light XY. M THE [ 1^8 ] T H E J ^"^^ O F o CKS. PART I. ^ Obfervatioiis 'concerning the Reflexions^ Refror Bionsy and Colours of thin tranjparent Bo- dies, IT has been obferved by others, that p traiifparent Subftances, as Glafs, Wa- I ter, Air, ^c. when made very thin by ^"- being blown into Bubbles., or other wife formed into Plates, do exhibit various Colours according to their various thinnefs, although at a greater- C 1^9 ] a greater thicknefs they appear very clear and colourlefs. In the former Book I forbore to treat of thefe Colours, becaufe they feemed of a more difficult Confideration, and were not neceflaryfor eltabliihing the Properties of Light there difcourfed of But becaufe they may con- duce to farther Difcoveries for compleating the Theory of Light, efpecially as to the conftitu- tion of the parts of natural Bodies, on which their Colours or Tranfparency depend ; I have here fet down an account of them. To render this Difcourfe fhort and diltinft, I have firfl de- fcribed the principal of my Obfervations , and then confider'd and made ufe of them. The Obfervations are thefe. Obf.x. Comprefling 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 reflefted ; it feemed in that place of contad: to be wholly tranfmitted, infomuch that when look'd upon, it appeared like a black or dark fpot, by reafon that Uttle or no fenfible Light was refleded from thence, as from other places ; and when looked through it feemed (as it were) a hole in that Air which was formed into a thin Plate, by being comprefs'd between the GlalTes. And through this hole Objeds that were beyond might be feen dittiiidly, which could not at all be feen through other parrs of th.j [ '70 ] . ^ the GlafTes where the Air was interjacent. AW , though the Glaffes were a little convex, yet this- ' tranfparent 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 prelTure. For they prefling them very hard together it wouM^ - become much broader than otherwife. 0^/2. When the Plate of Air, by turning the Prifms about their common Axis, became fo little inclined to the incident Rays, that fome of them began to be tranfmitted , there arofe in it many (lender Arcs of Colours which at firfl were fhaped almoft like the Conchoid , as you fee them delineated in the firit Figure. And by continuing the Motion of the Prifms, thefe Arcs increafed and bended more and more a- bout the faid tranfparent fpot , till they were completed into Circles or Rings incompaffing it, and afterwards continually grew more aM more con traded. ' .•^. Thefe Arcs at their firlt appearance were of ' a violet and blue Colour, and between therri were white Arcs of Circles, which prefentt\^ by continuing the Motion of the Prifms becanfe a little tinged in 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 ; black, red, orange, yellow, white, blue, violet, ^c. But the yel- low and red were much fainter than the blue and violet. ' ■ ■ The [ '71 ] The Motion of the Prifms about their Axis being continued, thefe Colours contraded more and more, Shrinking towards the whitenefs on either fide of it, until they totally vaniflied in- to it. And then the Circles in thofe parts ap- pear'd black and white, without any other Co^ lours intermix'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 yellow. So that now their order from the cen- tral Spot was white, yellow, red, black, vio- let, blue, white, yellow, red, &c. contrary to what it was before. O^f 3. When the Rings or fome parts of them appeared only black and white, they were very dillindt and well defined, and the black-^ nefs 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 diiiinft, which made them vifible to a very great multitude. I have fometimes number'd above thirty Succeflions (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 m^any Colours, I could not diftinguilh 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- flinft, and without any other Colour than black and white, I found it necelfary to hold my Eye at C 172 ] ^t a good diftance from them. For by ap- proaching nearer, although in the fame inclina- tion of my Eye to the Plane of the Rings, there emerged a blueifti Colour out of the white, which by dilating it felf more and more into the black, render'd the Circles lefs diilind:, and left the white a little tinged with red and yel- low. I found alfo by looking through a flit or oblong bole, which was narrower than the Pu- pil of my Eye, and held clofe to it parallel to the Prifms, 1 could fee the Circles much di- itinfter and vifible to a far greater number than otherwife, Obf. 4. To obferve more nicely the order of the Colours which arofe out of the white Circles as the Rays became lefs and lefs incli- ned to the Plate of Air ; I took two Objeft- glafles, the one a Plano-convex for a fourteen Foot Telefcope, and the other a large double Convex for one of about fifty Foot ; and upon this, laying the other with its plane fide down- wards, I prelTed them (lowly together, to make the Colours fucceffively emerge in the middle of the Circles, and then flowly lifted the upper Glafs from the lower to make them fucceflive- ly vanifli again in the fame place. The Colour, w^hich by prefling the GlalTes together emerged laft in the middle of the other Colours, would upon its firit appearance look like a Circle of a Colour almoft uniform from the circumference to the center, and by comprefling the Glalles Hill more, grow continually broader until a new Co- lour emerged in its center, and thereby it became a Ring encoinpalTuig that new Colour. And by com- [ 173 ] comprefling the GlafTes 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 fucceffively emer- ged there, and became Rings encompailing the innermoft Colour , the laft of which was the black Spot. And, on the contrary, by lifting up the upper Glafs from the lower, the diame- ter of the Rings would decreafe, and the breadth of their Orbit increafe, until their Colours reach- ed fucceffively to the center; and then they being of a confiderable breadth, I could more eafily difcern and diftinguifli their Species than before. And by this means I obferv'd their Suc- ceffion and Quantity to be as followeth. Next to the pellucid central Spot made by the contaft of tne Glafles fucceeded blue, white, yellow, and red. The blue was fo little in quan- tity that I could not difcern it in the Circles made by the Prifms, nor could I well diftinguifli 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 encompaffing 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 C 174 ] ^rder was purple, blue, green, yellow, and red ; in which the purple feemed more reddifli than the violet in the former Circuit, and the green was much more confpicuousj being as brisk and copious as any of the other Colours, except the yellow ; but the red began to be a little 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 fide to blue, and on the other fide to yellow. But in this fourth Circuit there was neither violet, blue, nor yel- low, and the red was very imperfeft and dir- ty. Alfo the fucceeding Colours became more and more imperfed and dilute, till after three or four revolutions they ended in perfeft whitenefs. Their form, when the Glafles were molt comprefs'd fo as to make the black Spot appear in the center , is delineated in the fe- . cond Figure ; where a^ b, c, d^ e: f^ g, h, /, k : /, my fty Oy f : q, r : s, t : v, x : j, 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: greeniih blue, red: greeniih blue, pale red: greenifli blue, reddiHi white. Obf. 5". To determine the interval of the Glafles, or thicknefs of the interjacent Air, by which each Colour was produced, I meafured the Diameters of the firit fix Rings at the moft lucid part of their Orbits, and fquaring them, I found their Squares to be in the arithmetical ProgrefTion of the odd Numbers, i, 3, 5-, 7, 9, 11. And C 175 ] And fmce one of thefe GlafTes was plane, and the other fpherical, their Intervals at thofe Rings mull be in the fame Progreflion. I meafured alfo the Diameters of the dark or faint Rings between the more lucid Colours , and found their Squares to be in the arithmetical Progref- lion of the even Numbers, x, 4, 6, 8, lo, iz. And it being very niCe and difficult to take thefe meafures exadly ; I repeated them divers times at divers parts of the GlaiTes, that by their Agreement I might be confirmed in them. And the fame method I ufed in determining fome others of the following Obfervations. Olff. 6. The Diameter of the fixth Ring at the molt lucid part of its Orbit was ^ parts of an Inch, and the Diameter of the Sphere on which the double convex Objeft-glafs was ground was about lox Feet, and hence I ga* thered the thicknefs of the Air or Aereal Inter- val of the GlafTes at that Ring. But fome time after, fufpefting that in making this Obfervation I had not determined the Diameter of the Sphere with fufficient accuratenefs, and being uncertain whether the Piano convex Glafs was truly plane, and not fomething concave or con- vex on that lide which I accounted plane ; and whether I had not prelTed the GlaiTes together, as I often did, to make them touch ; (For by prelling fuch GlaiTes together their parts eafily vield inwards , and the Rmgs thereby become ienfibly broader than they would be, did the GlaiTes keep their Figures.) I repeated the Experiment , and found the Diameter of the fixth t n^ ] fixth lucid Ring about ^ parts of an Inch. I repeated the Experiment alfo with fuch an Ob- jeft-glals of another Telefcope 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 diilantfrom it 834 Inches. And thence, if the Sines of Incidence and Refradion of the bright yellow Light be alTumed in proportion as II to 17, the Diameter of the Sphere to which the Glafs was figured will by computa- tion be found i8i 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 ndw 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 points of a pair of CompafTes on the upper Surface on the upper Glafs, and my Eye was about eight or nine Inches diftant from the Glafs, almoft perpendicularly over it, and the Glafs was i of an Inch thick, and thence it is eafy to colled: that the true Diameter of the Ring be- tween the GlafTes was greater than its meafur'd Diameter above the Glafles in the Proportion of 80 to 79, or thereabouts, and by confequence equal to ■— part of an Inch, and its true Semi- diameter equal to ~ parts. Now as the Dia- meter of the Sphere (i8x Inches) is to the Se- mi-diameter of this fifth dark Ring (-^ parts of an Inch) fo is this Semi-diameter to the thick- nefs of the Air at this fifth dark Ring 5 which is there- r ill ] therefore — — r: or -- — - parts of an IncH ; and S^79jI 17/47^4 ^ the fifth part thereof, viz. the ^— - part of art Inch, is the thicknefs of the Air at the firft of thefe dark Rings. The fame Experiment I repeated with ano- ther double convex Objed-glais ground on both fides to one and the lame Sphere. Its Focus was diilant from it 1684 Inches, and therefore the Diameter of that Sphere was 184 Inches. The Glafs being laid upon the fame plain Glafs, the Diameter of the tifth of the dark Rings, when the black Spot in their center appear'd plainly without prefling the Glaffes, was by the meafure of the Compaires upon the upper Glafs ^^ parts of an Inch, and by confequence be- tween the Glaffes ft was g^ For the upper Glafs was 4 of an Inch thick, and my Eye was diltant from it 8 Inches. And a third propor- tional to half this from the Diameter of the Sphere is ^^^ parts of an Inch. This is there- fore the thicknefs of the Air at this Ring, and a fifth part thereof, viz. the ^-^th part of an Inch is the thicknefs thereof at the firft of the Rings, as above. I tried the fame thing by laying thefe Ob- jeft-glafTes upon flat pieces of a broken Look- ing-glafs, and found the fame Meafures of the Rings : Which makes me rely upon them till N they [ 178 ] they can be determin'd more accurately by Glailes ground to larger Spheres, though in fuch GlaiFes greater care mult be taken of a true Plane. Thefe Dimenfions were taken when my Eye was placed almoit perpendicularly over the GlalTes, being about an Inch, or an Inch and a quarter, diilant from the incident Rays, and eight Inches diltant from the Giafs ; fo that the Rays were inclined to the Glafs in an Angle of about four Degrees. Whence by the following Obfervation you will underiland, that had the Rays been perpendicular to the Glailes, the thicknefs of the Air at thefe Fungs would have been lefs in the proportion of the Radius to the Secant of four Degrees , that is of looco to 10024. Let the thicknefles found be therefore diminifli'd in this Proportion, and they will be- come 57^ and r-^ or (to ufe the nearefi: round number ) the ~— th part of an Inch. ^ 09000 ^ This is the thicknefs of the Air at the darkeft part of the firll dark Ring made by perpendi- cular Rays, and half this thickneis multiplied by the Progreilion, i, 3, 5", 7? 9? n? ^c. gives the thicknelTes of the Air at the moll luminous parts of all the brighteil Rings, viz,. 17^000 ^c. their arithmetical l7booo? 1 7 800C;, ,17^000' Means —r~-> —0^9 -^y ^^- being its "**^ 178000' 178000' i/»ooo' c> thicknefles at the darkeil parts of all the dark ones. OH. [ 179 j t)bj. 7. The Rings were leaft when my Ey^ Was placed perpendicularly over the GlalFes in the Axis of the Rings : And when I view'd them obliquely they became bigger, continual- ly fwelling as I removed my Eye farther from the Axis. And partly by meafuring the Diame- ter of the fame Circle at feveral Obliquities of my Eye, partly by other means, as alfo by ma- king ufe of the two Prifms for very great Obli- quities, I found its Diameter, and confequenc- ly the thicknefs of the Air at its Perimeter in all thofe' Obliquities to be very nearly m the Pro- portions exprefs'd in this Table. Angle of In- Angle of Re- '^Diameter Thicknefs cidence on fra^ion in- of the of the the Air. to the Air. Ring. Air. Degr. Min. 00 00 00 00 10 10 06 a6 10 00 IOt't ' • IOtV IX 4f 2o 00 lOf 10^ 18 49 30 00 IOt 114 24 30 40 00 I It 13 29 37 50 00 124 ■1)4 33 5S 60 GO 14 20 IS 47 6$ GO 15-^ 2^3^ 11 19 70 00 i6| ^^. 38 33 75" 00 19^ 37 39 2.7 80 GO 22j 5^-4 40 00 85- GO ^9 84VT 40 II 90 00 35" 12X4 Na %. [ i8o] Fn the two firft Columns are exprefs'd the Obliquities of the incident and emergent Rays to the Plate of the Air, that is, their Angles of Incidence and Refradtion. In the third Column the Diameter of any colour'd Ring at thofe Ob- liquities is exprelTed in parts, of which ten con- Ititute that Diameter when the Rays are per- pendicular. And in the fourth Column the thicknefs of the Air at the circumference of that Ring is exprefTed in parts of which alfo ten conftitute its thicknefs when the Rays are perpendicular. And from thefe Meafures I feem to gather this Rule : That the thicknefs of the Air is proportional to the fecant of an Angle, whofe Sine is a certain mean Proportional between the Sines of Incidence and Refradion. And that mean Proportional, fo far as by thefe Meafures I. can determine it, is the firfl of an hundred and fix arithmetical mean Proportionals be- tween thofCiSines counted from the bigger Sine,' that is, from the Sine of Refradion when the Refradion is made out of the Glafs into the Plate of Air, or from the Sine of Incidence when the Refradion is made out of the Plate of Air into the Glafs. Obf.%. The dark Spot in the middle of the Rings increafed alfo by the Obliquation of the Eye, although almoit infenfibly. But if infte^ of the Objed'glaiTes the Prifms were made ufe of, its Increafe was more manifeft when view- ed fo obliquely that no Colours appear'd aboiit it. It was lead when the Rays were incident molt obliquely on the interjacent Air, and as the [ i8i ] the obliquity dccreafed it increafed more and more until the colour'd Rings appear'd, and then decreafed again, but not lb much as it in- creafed before. And hence it is evident, that the Tranfparency was not only at the abfolute Contaft of the GlalTes, but alfo where 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 firfl Cir- cuit or Revolution of Colours when view'd al- moll perpendicularly ; whereas when view'd ob- liquely it hath wholly vanifh'd and become opake and white like the other parts of the Glafs ; whence it may be collefted that the GlalTes did then fcarcely, or not at all, touch one another, and that their hiterval at the perimeter of that Spot when view'd perpendicularly was about a fifth or fixth part of their Interval at the cir- cumference of the faid red. Obf. 9. By looking through the two conti- guous Objeft glailes , I found that the interja- cent Air exhibited Rings of Colours, as well by tranfmitting Light as by refledfing it. The central Spot was now white, and from it the order of the Colours were yellowilli 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 trajedted very obliquely through the GlalTes : For by that means they became pretty vivid. Only the firlt yellowilli red, like the blue in the fourth Obfervation, was fo little and faint as fcarcely to be difcern'd. Comparing N 3 thp .:;;:#'■ [ 182 ] the colour'd Rings made by Reflexion, with thefe made by tranfmiffion of the Light ; 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 , thofe parts of the Glafs were black when looked through, which when looked upon appear'd white, and on the contrary. And fo thofe which in one cafe ex- hibited 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 AB, CD, are the Surfaces of the Glaf- {cs contiguous at E, and the black Lines be- tween them are their Diitances in arithmetical Progreilion, and the Colours written above are feen by refleLled Light, and thofe below by Light tranfmitted. . O^/ 10. Wetting the Objeft - glalTes a little at ^ their edges, the Water crept in llowly 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 firil: arrived would appear broken off from th^ other half, and contracted into a lefs Room. By meafuring them I found the Pro- portions otNheir Diameters to the Diameters of the like Circles made by Air to be about feven to eight, and confequently the Intervals of the Glades 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 caufed thereby v^ill be to their Intervals [ 183 ] Intervals caufed by interjacent Air, as the Sines are which meafure the Refradion made out of that Medium into Air. Obf.w. When the Water was between the GlalTes, if I preifed the upper Glafs varioufly 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 vanifli. Its appearance w^as 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 vanilh. The Refle- xion muft have rather been caufed by a fubtiier Medium, which could recede through the GlalTes at the creeping in of the Water. Obf. 11.. Thefe Obfervations were made in the open Air. But farther to examine the Ef- feds of colour'd Light falling on the Glailes, I darken'd the Room, and view'd them by Re- flexion of the Colours of a Prifm call on a Sheet of white Paper, my Eye being fo placed that I could fee the colour'd Paper by Reflexion in the GlalTes, as in a Looking-glafs. And by this means the Rings became dillinfter 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 dif- cern above eight or nine. Obf. 13. Appointing an Alliltant to move the Prifm to and fro about its Axis, that all the Colours might fuccellively fall on that part of the Paper which I faw by Reflexion from thar N 4 pari [ '84 ] Part of the GlafTes, where the Circles appear 'd, fo that all the Colours might be fuccefTively re- fleded from the Circles to my E3^e whilll I held it immoveable, I found the Circles which the red Light made to be manifellly bigger than thofe which were made by the blue and violet. And it was very pleafant to fee them gradually fvvell or contraft 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 the utmoil red Light, was to their Interval at the fame Ring when made by the utmofl violet, gre::iter than as 3 to 2, and lefs than as 13 to 8. By the moil of my Obfervations it was as 14 to 9. And this Proportion fcem'd very nearly the fame in all Obliquities of my Eye ; unleis when two Prifms were made ufe of in- ftead of the Objeft-glalTes. For then at a cer- tain great obliquity of my Eye, the Rings made by the feverai Colours feem'd equal, and at a greater obliquity thofe made by the violet would be greater than the fame Rings made by the red : the RefradUon of the Prifm in this cafe caufing the moll refrangible Rays to fall more obliquely on that plate of the Air than the leaft refrangi- ble ones. Thus the Experiment fucceeded in the colour'd Light, which was fufficiently flrong and copious to make the Ritigs fenfible. And thence it may be gathered, that if the moft re- frangible and leail refrangible Rays had been co- pious enough to make the Rings fenfible with- out the mixture of other Rays, the Proportion \vhich here was 14 to 9 would have been a little greater, fuppofe 14^^ or 147 to 9, - , . Qbf. C 185 ] Ohf. 14. Whilft the Prifm was turn'd about its Axis with an uniform Motion, to make all the feveral Colours fall fuccefTively upon the Objed- glafTes, and thereby to make the Rings contrad and dilate : The Contraction or Dila- tation of each Ring thus made by the variation of its Colour was fwifteft in the red, and flow- eil in the violet, and in the intermediate Colours it had intermediate degrees of Celerity. Com- paring the quantity of Contrac^tion and Dilata- tion made by all the degrees of each Colour, I found that it was greatell in the red ; lefs in the yellow, flill lefs in the blue, and lead in the violet. And to make as juif an Eilim.ation as I could of the Proportions of their Contradions or Dilatations, I obferv'd that the whole Con- tradion 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 outmolt red, and the lead Diameter thereof made by the outmofl violet ; contrary to what happens in the Colours of the oblong Spedrum made by the Refradion of a Prifm, where the red is mod contraded, the violet mod expanded, and in the midd of all the Colours is the Corn- fine of green and blue. And hence I feem to colled that the thicknedes of the Air between the GlafTes there, where the Ring is fucceflive- 5y [ i80 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 neady as the fix lengths of a Chord which found the Notes in a fixth Major, fol^ la^ mt, fa, fol, la. But it agrees fomething better with the Obfer- vation to fa3^ that the thicknefTes of the Air between the GlafTes there, where the Rings are fucceffively 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 of a Chord, which found the Notes in an eighth, fil, la, fa, fol, la, mi, fa fol; that is, as the Cube Roots of the Squares of the Numbers, i, ■S 5 5 ' 5 _9 I :?? -K-y "+? 7) T5 xTJ 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 with which they wxre illuminated. And by projeding the prii'matick Colours immediately upon the GlafTes, I found that the Light which fell on the dark ^Spaces which were between the colour'd Rings, v/as 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 receded, and of the bignefs of their im- mediate Spaces. And from thence tlie origin of [ i87 ] of thefe Rings is manifefl; namely, that the Air between the Glafles, according to its vari- ous thicknefs, is difpofed in fome places to re^ fled:, and in others to tranfmit the Light of a- ny one Colour (as you may fee repreiented in the fourth Figure) and in the fame place to re- flect that of one Colour where it tranfmits that of another. Obf 1 6. The Squares of the Diameters of thefe Rings made by any prifmatick Colour were in arithmetical Progrellion, as in the fifth Ob- fervation. And the Diameter of the fixch Cir-» cle, when made by the citrine yellow, and viewed almoit 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 Medium, terminated by a denfer, fuch as was Air or Water comprefs'd between two GlalFes. 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 Subflances terminated on all iides with Air. Obf.ij. If a Bubble be blown with Water firlt made tenacious by dillblving 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 be- ing agitated by the external Air (whereby their Colours are irregularly moved one among ano- ther, fo that no accurate Obfervation can be inadc of them,) as foon as I had blown any of them [ m ] 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 vanifli'd fuc- ceffively. 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 tir(t Obfervation, which continually dilated it felf till it became fome- times more than 4 or 4 of an Inch in breadth before the Bubble broke. At firft I thought there had been no Light refle(^i:ed from the Wa- ter in that place, but obferving it more curi- oufly, I faw within it feveral fmaller round Spots, which appeared much blacker and dark- er than the reli:, whereby I knew that there was fome Reflexion at the other places which were not fo dark as thofe Spots. And by far- ther Tryal I found that I could fee the Images of fome things (as of a Candle or the Sun) ve- ry faintly retledted, not only from the great black Spot, but alfo from the little darker Spots which were within in it. Befides the aforefaid colour'd Rings there would often appear fmall Spots of Colours, af- eending 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 afcend [ '8^ ] afcend up to the larger black Spot at the top of the Bubble, and unite with it. Obf.i%. Becaufe the Colours of thefe Bubbles were more extended and lively than thofe oi the Air thinn'd between two GlalTes, and fo more eafy to be dillinguilli'd, I iliall 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 thefe, red, blue ; red, blue ; red, blue; red, green; red, yellow, green, blue, purpje ; red, yellow, green, blue, violet ; red, yellow, white, blue, black. The three firft Succeflions 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 and blue, only the blues (and principally the fecond blue) incUned a little to green. The fourth red was alfo dilute and dirty, but not fo much as the former three ; after that fucceeded 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 blueifh Colour ; but there fucceeded neither blue nor violet. The fifth red at firft inchned 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 changed 3 [ i^o ] chang'd to green : But that green was copious and fomething more pure, deep and lively, thait 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 inclin'd to red. The fixth red was at firfl of a very fair and lively Scarlet, 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 greenifh yelloWj and then to a greenifli blue; but the green between the yellow and the blue, was very little and dilute, leeming 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 ; and the violet was intenfe and deep with little or no rednefs in it. And lefs in quantity than the blue. In the lafl: red appeared a tindure of fcarlet next to violet, which foon changed to a bright- er Colour, inclining to an orange ; and the yel- low which followed was at firft pretty good and lively, but afterwards it grew more dilute, until by degrees it ended in perfeft whitenefs* And this whitenefs, if the Water was very te^ nacious and well tempered, would flow ly fpread and dilate it felf over the greater part of the Bubble; continually growing paler at the top, where at length it would crack in many places, and thofe cracks, as they dilated, would appear of C 191 ] of a pretty good, but yet obfcure and dark Sky- colour ; the white between the blue Spots diminifhing , untill 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 would 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 fometimes they would break forth within the precedent yellow, or red, or perhaps within the blue of the fecond order, before the inter- mediate Colours 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, al- though fet down in a contrary order, by reafon that they begin to appear when the Bubble is thickeft and are molt conveniently reckon'd from the lowelt and thickeft part of the Bubble upwards. Obf. 19. Viewing in feveral oblique Pofitions pf myEye the Rings of Colours emerging on the [ 152 ] 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 were dilated (o 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 appeared when viewed perpendicularly ; where- as in this cafe the thicknefs of the Water, at which they arriv'd when view'd molt obliquely, was to that thicknefs which exhibited them by perpendicular Rays, fomething lefs than as 8 to 5. By the bed of my Obfervations it was be- tween i^ and i5'4 to 10; an increafe about 14 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 Politions of the Eye. And then the Co- lours which were feen at its apparent circumfe- rence by the obliquelt Rays would be different from thofe that were feen in other places, by Rays lefs obUque to it. And divers Spedators 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 affiltance of the 4th, 14th, 1 6th and 18 th 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 r ^93 ] to be very nearly in the Proportion exprefled in this Table. Incidence on Refra^ion in- Thickiiefs of the JVater. to the Water. the Water. Dcgr. Min. Degr. Min. GO CO GO GO 10 15- 00 ii 11 lO:^ ^0 00 22 I 104 45" 00 32 2 114 60 00 40 30 13 IS 00 46 -Ly 144 90 00 48 35- TfT 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 diflblution of Soaps in the Water, may a little alter its refra(^Hve Virtue. In the third Column 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 welt with thefe Meafures, if duly apply'd ; namely, that the thicknefs of a Plate of Water rcquifite to exhibit one and the fame Colour at feveral Obhquities of the Eye, is proportional to the fecant of an Angle whofe Sine is the firfl: of an hundred and fix arithmetical mean Proportio- O nals C 194 ] nals between the Sines of Incidence 'and Refra- dion couiucd from the leflerSine, that is, from the Sine of Refradion when the Refradion is made out of Air into Water, otherwife from the Sine of Incidence. I have fometimes obferv'd, that the Colours which arife on poHlh'd Steel by heating it, or on Bell- metal, and fome other metalUne Sub- ftances, when melted and pour'd on the ground, where they may cool in the open Air, have, hke the Colours of Water- bubbles, been a little changed by viewing them at divers Obliquities, and particularly that a deep blue, or violet, when vievv'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 molt 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 glaffy Skin, caufes thefe Colours, is much denfer than Water ; and 1 find that the Change made by the Obliquation of the Eyes is leaft in Colours of the denfelt thin Subilances. Obf.ro. 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 refleded from it, feem'd red at its apparent circumference, if the Clouds at the fame time, or immediately after, wereview'd through it, the Colour at its circumference would be blue. And, on the ' contrary. [ 155 ] contrary, when by reflefted Light it appeared blue, it would appear red by tranfmitted Light. Obf.xi. By wetting very thin Plates of Muf- covy Glafs, whofe thinnefs made the Hke Co- lours appear, the Colours became more faint 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 denfity 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 Mufcovy Glafs, or other Subflances, have at any Colour produced by them. Obf. zz. 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 in the Air and Glafs. For blowing Glafs very thin at a Lamp Furnace, thofe Plates encompaiTed with Air did exhibit Colours much more vivid than thofe of Air made thin between two GlaiTes. Obf 13. Comparing the quantity of Light reflefted from the feveral Rings, I found that it was moll copious from the firft or inmoft, and in the exterior Rings became gradually lefs and lefs. Alfo the whitenefs of the firfl Ring was Itronger than that refleded from thofe parts of the thin Medium or Plate v.^hich were without the Rings; as I could manifeltly per- ceive by viewing at a diftance the Rings made O z by U^96 1 by the tu^o Objed-glafTes ; pr. by comparing two Bubbles of Water blown at diftant times , in the firft of which the whitenefs appear'd, which fucceeded all the Colours, and in the other, the whitenefs which preceded them all. Obf.i^. When the two Objed-glafTes were lay'd upon one another, fo as to make the Rin^s of the Colours appear, though with my nake^' Eye I could not difcern above eight or nine of thofe Rings, yet by viewing them through a Prifm I have feen a far greater multitude, info- much that I could number more than forty, be- fides many others, that were fo very fmall and clofe together, that I could not keep my Eye itea- dy on them feverally fo as to number them, but by their Extent I have fometimes eftimated them to be more than an hundred. And I believe the Experiment may be improved to the difcovery qf far greater Numbers. For they feem to be really unUmited, though vifible only fo far as they can be feparated by the Refraftion of this Prifm as I lliall hereafter explain. But it was but one fide of thefe Rings, name- ly, that towards which the Refradion was made, which by that Refradion was render'd dillinft, 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 couid difcern eight or nine with my naked Eye. And their Segments or Arcs, which on* the other fide appear'd fp numerous, for the moil part exceeded not the third part of a Cir- cle. If the Refradion, was very great, or the *-" '^' 4 Prifm [ '5>7 ] Prifm very diftant from the Objeff^-glafTes, the middle part of thofe Arcs became aUb confu- fed, fo as to difappear and conftitute an even whitenefs, whilit on either fide their ends, as alfo the whole Arcs fartheft from the center, became diftinfter than before, appearing in the form as you fee them defign'd in the fifth Fi- gure. The Arcs, where they feem'd diftin^iefl, were only white and black fucceffively, without any other Colours intermix'd. But in other places there appeared Colours, whofe order was in- verted by the Refradion in fuch manner, that if I firfl held the Prifm very near the Objed- glaffes, and then gradually removed it farther off towards my Eye, the Colours of the id, 3d, 4th, and following Rings fhrunk towards the white that emerged between them, until they wholly vanifli'd into it at the middle of the Arcs, and afterwards emerged again in a con- trary 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 Hke manner Plates of Mufcpvy Glafs, and Bubbles of Glafs blown at a Lamp Furnace, which were not fo thin as to exhibit any Colours to the naked Eye, have through the Prifm exhibited a great varie- ty of them ranged irregularly up and down in O 3 the [ '58 ] the form of Waves. And fo Bubbles of W^- ter, before they began to exhibit their Colours to the naked Eye of a By-ftander, have appear- ed through a Prifm, girded about with many parallel and horizontal Rings ; to produce which EfFeft, it was necelTary to hold the Prifm pa- rallel, or very nearly parallel to the Horizon^^ and to difpofe it fo that the Rays might be re-i fra(^ed upwards. THE C 199 ] THE SECOND BOOK O P TIC K S. P A R T II. , Remarks ufon the foregoing Obfervation^. A V IN G given my Obfervations of thefe Colours, before Lmake ufe of them to unfold the Caufes of the Colours of natural Bodies, it is convenient that by the fimpleft of them, fuch as are the 2d, 3d, 4th, 9th, 1 2th, 1 8th, 20th, and 24th, I firit ex- O 4 plain [ 200 ] pkin the more compounded. And firfl to fhew hovv^ the Colours in the fourth nnd eighteenth Obiervarions are produced, let there be taken in any right Line from the Point Y, [in Fig. 6.1 the lengths Y A, Y B, Y C, Y D, Y E, Y F, Y G, YK, in proportion to one another, as the Cube Roots of the Squares of the Numbers, 4, t«, t» 4, ^, 4, Tj i> whereby the lengths of a mufical Cnord to found all the Notes in an eighth are reprcfcnted ; that is, in the proportion of the Numbers 63C0, 6814, 71 14, 7631, Si^^, 885-5', 9143, loooo. And at the Points A, B, C, D, E, F, G, Fi, let perpendiculars A ct, B /3, ^c. be erected, by whofe Intervals the Extent of the feveral Colours fet underneath againft them, is to be reprefented. Then divide the Line A a. in fuch proportion as the Numbers i, 2, 3, 5-, 6, 7, 9, 10, II, ^c. fet at the Points of Divifion denote. And through thofe Divifions from Y draw Lines 1 1, 2 K, 3^,5- M, 6 N, 7 O, ^c. Now if A 2 be fuppofed to reprefent the thicknefs of any thin tranfparentBody, at which the outmofl violet is moil copiouily retlefted in the firit Ring, or Series of Colours, then by the 13th Obfervation, H K will reprefent its thicknefs, at which the utmoii: red is moil co- pioufly refledled in the fame Series. Alfo by the 5th and i6th Obfervations, A 6 and H N will denote the thicknelTes at which thofe ex- treme Colours are moft copiouily refleded in the fecond Series, arid A 10 and H Q the thick- nefles, at which they are moft copioufly reflect- ed in the third Series, and fo on. And the fhicknefs at which any of the intermediate Co- lours C 20I ] lours are reflefted moft copioully , will zccop{ ding to the 14th Obfervation, be defined by the diilance of the Line A H from the intermediate parts of. the Lines zK,' 6N, loQ, ^c. againd which the Names of thofe Colours are written .below, But farther, to define the Latitude of thefe Colours in each Ring or Series, let A i defign the leaft thicknefs, and A 3 the greatefl thick- nefs, at w^hich the extreme violet in the firll Series is reflefted, and let H I, and H L, de- fign the like limits for the extreme red, and let the intermediate Colours be limited by the in- termediate parts of the Lines i I, and 3 L, a- gainfl which the Names of thofe Colours are written, and fo on: But yet wath this caution, that the Reflexions be fuppofed ftrongeft at the intermediate Spaces, x K, 6 N, 10 Q, &c. and from thence to decreafe gradually towards thefe limits, I I, 3 L, s M, 7 O, &c. oh either fide ; where you muit not conceive them to be pre- cifely Umited, but to decay indefinitely. And whereas I have aflign'd the fame Latitude to e- very Series; I did it, becaufe although the Co- lours in the firll Series feem to be a little broad- er than the refl, by reafon of a ftronger Re- flexion there, yet that inequaUty is fo infen- fible as fcarcely to be determin'd by Obferva- tion. Now according to this Defcription, concei- ving that the Rays originally of feveral Colours are by turns refleded at the Spaces 1 1 L 3, 5 M O 7, 9 P R II, ^c. and tranfmitted at the Spaces AHIi, 3 l-^M 5", 7O P9, ^f. it is eafy to know what [ 202 ] what Colour mud in the open Air be exhi- bited at any thicknefs of a tranfparent thin Bo- dy. For if a Ruler be applied parallel to A H, at that diitance from it by which the thicknefs of the Body is reprefented the alternate Spaces iIL 3, s-MOy, &c. which it crofleth will de- note the refleded original Colours, of which the Colour exhibited in the open Air is com- pounded. Thus if the conftitution of the green in the third Series of Colours be defired, apply the Ruler as you fee at tt ^ crcp, and by its paf- fing through lome of the blue at t and yellow at