THE LIBRARY 
 
 OF 
 
 THE UNIVERSITY 
 
 OF CALIFORNIA 
 
 LOS ANGELES 
 
 GIFT 
 
 Dr. M. N. Beigelinan 
 
 \' ^ 
 
L / 
 
\ 
 
OPTICKS: 
 
 O R, A 
 
 TREATISE 
 
 O F T H E 
 
 Refledions , Refractions , 
 Inflexions and Colours 
 
 O F 
 
 LIGHT. 
 
 The Second Rditton^ with Addit'tons. 
 
 By Sir Isaac Newton, Knt. 
 
 LONDON: 
 
 Printed for W. and J. Innys, Printers to the 
 Royal Society, at the Prince' s-Jrms in St. PauVs 
 Church- Yard. 1718. 
 

Advertisement L 
 
 ART of the enfiiing Dif- 
 coiirje about Light was 
 written at the De/ire of 
 fome Gentlemen oftheKoyal So- 
 ciety, in the Tear i6is, ^^d then 
 fent to their Secretary, and read 
 at their Meetings, and the rejl 
 was added about twelveTears af- 
 ter to complete the Theory ; except 
 the Third Book, and the laft Oh 
 fervatton in the laft Part of the 
 Second, which were finceput to- 
 gether out of fcatterd Papers. To 
 amid being engaged in Difputes 
 
 A 2 about 
 
Advertifement. 
 
 dhont thefe Matters, I have hi- 
 therto delayed the printing, and 
 Jhotildftillhave delay edit, had not 
 the Importunity of Friends pre- 
 vailed upon ?ne. If any other Pa- 
 pers writ on this SiibjeB are got 
 out of my Hands they are imper- 
 fect, and were perhaps written 
 before I had tried all the Expe- 
 rhnents here fet down, and f idly 
 fatisfied my f elf alout the Laws 
 of Refractions and Compo/ition 
 of Colours. I have here pullijljd 
 ivhat I think proper to come A- 
 broad, xviJJnng that it may not he 
 trav fated into another Language 
 Without my Confent. 
 
 The Crowns of Colours, which 
 fometimes appear about the Sun 
 and Moon, I have endeavoured 
 to give an Account of-, but for 
 
 want 
 
Advertifement. 
 
 want of fi/fficient Olfervatiom 
 leave that Matter to he farther 
 examined. The Siihjecl of the 
 Third Book I have alfo left im- 
 perfect, not havifig tried all the 
 Experiments which I intended 
 when I was Soui^thcfe Matters, 
 nor repeated fonie of thofe which 
 I did try , until I had fatisfied 
 my felf ahoiit all their Circum- 
 fiances. To communicate what 
 I have tried, and leave the reft 
 to others for farther Enquiry , 
 is all ?ny De/ign in puUijlnng 
 thefe Papers. 
 
 In a Letter written to ]\ Ir. Lei b- 
 liitz /;; the Tear 1676, and pnh- 
 lified hy Dr Wallis, I inentiond 
 a Method l?y which I had found 
 fome general Theorems about 
 fquaring Curvilinear figures , 
 
 or 
 
Advertifemcnt. 
 
 or comparing them with the Co- 
 nic SeBions, or other the jimplefl 
 Figures with which they may he 
 compared. And fome Tears ago 
 I lent out a Manufcrtpt contain-' 
 ing fiich Theorems, and having 
 fince met with ^ome Things cop- 
 ed out of it, I have on this Occa- 
 fion made it piblick, prefixi.g to 
 it an Introdutlion, andfubjoin- 
 tng a Scholium concerning that 
 Method, And I have joined with 
 it another f mall Tract concerning 
 the Curvilinear Figures of the 
 Second Kind, which was alfo 
 written many Tears ago, and 
 made known to fome Friends , 
 who have folicited the inaking it 
 pulTick. 
 
 April I. T ]\I 
 
 1704. - ^' ^^' 
 
Advertisement IL 
 
 A^ tins Second Edition of 
 thefe Opticks I have o- 
 mitted the Mathematical 
 TraBs puMiJhed at the End of 
 the former Edition , as not be- 
 longing to the SnhjeEt. And at 
 the End of the Third Book I 
 have added fome ^/ejtions. And 
 to JJjew that I do not take Gra- 
 vity for an ejfential Property of 
 Bodies, I have added one ^le- 
 Jiion concerning its Caufe, chti- 
 fing to propoje it hy way of a 
 :^ie/iion, fecanfe I am not yet 
 fatisfied alout it for want of 
 J^xperiments. 
 
 I N. 
 
 July 16. 
 
 1717. 
 
^ jg IK « JK -K «»•« -K «•!• IS IK -K «*■«?«)«•«•« -S -K jK * 
 
 w'' X \ . ■ • • •■ 
 
 CORRIGENDA. 
 
 PAGE 3. line 17. read turned back., p. 7.. 1. ult. forF'^g. 5. r. Mucb. 
 p. 4c. l.io. r.de znd fg. p. 5-7. I'i.r.-wliole. p.9f. l.zj. r.PT{pP.VUl. 
 p.m. ].Z^. Intervab, andyou. p. i li. 1. Zf. r/jat »f ^»j*r- p.IJJ.l.li. 
 r. rt»(^ the breadth. p. 157. 1. 24.. Y.redhomogeneal Light, p. I^o. J. $Z. X.the VeJJel 
 appeared of a red Colour like. p. i(Sy. 1. 4. r. they entered, p. 19(3. 1,22. r. ff'"" «/ 
 thePnfin, on. p.204. 1. 27. r. ru'W *« Fx, F ,</. p. 212. l.T. r. {that is, in the 
 Cirtumfereme on one fide. p. 237. 1. 30. r. more ftrongly refleBing. p. 238. 1. 3. 
 T. invented by Ono GuCric, ""d improved and made ufeful by Mr. Boyie) p. 242. 
 Ll^.r. than. p. 244. 1. 19. r.^io. '/ p.z66. \. '^l- r. Colours. p.322. 1.31. 
 X. continue to arife and be propagated, -when p. 33^. i.zi. r. to the Power, p.334. 
 1. 6. r. 1^7. p. 336. 1. 22. r. to the dijlance of. 
 
 ^««*«rH!KrK««««-K^«JS««JKj^««»!««««»»jK3'« «■«•}•« 
 
[I] 
 
 THE 
 
 FIRST BOOK 
 
 OF 
 
 OPTICKS. 
 
 PART I. 
 
 Y Defign in this Book is not to ex- 
 plain the Properties of Light by Hy- 
 pothefes, but to propofe and prove 
 them by Reafon and Experiments: In 
 which I iliall premile the foUou^ing 
 
 order to wliich 1 liiall pi 
 Definitions and Axioms. 
 
 e 
 
 TfEFL 
 
[ ^ 1 
 
 DEFINITIONS. 
 DEFIN. I. 
 
 V i T the Rays of Light I under ft and Its leafl 
 \3 ^ aris;^ andthofi as well Succejjive in the 
 Jam^ lines as Contemporary in feveral lines. 
 For it li manifeit that Light confifls of parts 
 both bucceflive and Contemporary ; becaufe in 
 'tnefame place you may flop that which comes 
 one moment, and let pafs that which comes pre- 
 fentl)^ after ; and in the fame time you may 
 Hop it in any one place, and let it pafs in any 
 other. For that part of Light which is llopt 
 cannot be the fame with that which is let pais. 
 The leaft Light or part of Light,which may 
 be ftopt alone without the reft of the Light, or 
 propogated alone, or do or fuffer any thing alone 
 which the reft of the Light doth not or fuffers 
 not, I call a Ray of Light. 
 
 DEFIN. II. 
 
 Refrangibility of the Rays of Lights is their 
 'Dijpojition to be refra6ied or turned out of their 
 Way in puffing out of one tranjparent Body or 
 Medium into another. And a greater or lefs Re- 
 frangibility of Rays, is their 'Dijpojition to be 
 turned more or lejs out of their Way in like In- 
 cidences on the fame Medium. Mathematicians 
 ufually confider the Rays of Light to be Lines 
 reachmg from the luminous Body to the Body 
 illuminated, and the refraftion of thofe Rays to 
 be the bending or breaking of thofe lines in 
 
 their 
 
t3] 
 
 their pafling out of one Medium into another. 
 And thus may Rays and Refrac^tions be conli- 
 dered, if Light be propagated in ail inltant. 
 But by an Argument taken fi-om the /Equa- 
 tions of the times of the Ecfipfes oi Jupiter^ 
 Satellites it feems that Light is propagated in 
 time, fpending in its paflage from the Sun to us 
 about leven Minutes of time : And therefore 1 
 have chofen to define Rays and Refradions in 
 fuch general terms as-may agree to Light in both 
 cafes. 
 
 DEFINf. III. 
 
 Reflex ibiltty of Rays^ is their Difpofition to be 
 rvflettedor turned back into the fime Medium from 
 any other Medium upon whofe Surface they fall. 
 And Rays are more or lefs reflexible^ 'which are 
 returned 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- 
 flefted by that Surface; thofe forts of Kays 
 which at Hke Incidences are reflected moil co- 
 pioully, or by inclining the Rays begin foonelt 
 to be totally refleded, are moll reilexible. 
 
 DEFIN. IV. 
 
 The Angle of Incidence is that Angle-, which 
 the Line defcribed by the incident Ray contains 
 'with the Perpendicular to the refie^ling or re^ 
 framing Surface at the Toint of Incidence i 
 
 B 1 DEFIN; 
 
Ul 
 
 DEFIN. V. 
 
 The Angle of RefeBion or RefraEimh i^ ^he 
 Angle which the line defcribed hy the refleBed 
 or refradied Ray*contatneth with the Perpendi- 
 cular to the refle5ling or refradting Surface at 
 the ^oint of Incidence. 
 
 DEFIN. VI. 
 
 The Sines of Incidence^ Reflexion^ and Re fr a- 
 Bion^ are the Sines of the Angles of Incidence y 
 Reflexion^ and Refra^ion, 
 
 DEFIN. VII. 
 
 The Light whofe Rays are all alike Refrau" 
 gible-i I call Simple^ Homogeneal and Similiar ; 
 and that whofe Rays are fome more Refrangible 
 than others^ I call compound, Heterogenal and 
 *T>iffimilar. The former Light I call Homoge- 
 neal, not becaufe I would affirm it fo in all re- 
 fpefts ; but becaufe the Rays which agree in Re- 
 frangibility, agree at leafl in all thofe their other 
 Properties which I confider in the following 
 Difcourfe. 
 
 DEFIN. VIII. 
 
 The Colours of Homogeneal Lights, I call Tri- 
 mary, Homogeneal and Simple-, and thofe of 
 Heterogeneal Lights, Heterogeneal and Com- 
 ponnd. For thefe are always compounded of 
 the colours of Homogeneal Lights ; as will ap- 
 pear in the following Difcourfe- 
 
 AXIOMS. 
 
[5] 
 
 AXIO MS. 
 AX. I. 
 
 THE Angles of Reflexion, and Refra^iion^ 
 lie in one and the fame Tlane ijuitb the 
 jingle of Incidence. 
 
 AX. n. 
 
 The Angle of Reflexion is equal to the Angle 
 of Incidence. 
 
 AX. in. 
 
 If the Re framed Ray be returnea direBly 
 back to the ^oint of Incidence.^ it floall be re- 
 fratfed into the Line before defcribedby the in- 
 cident Ray, 
 
 AX. IV. 
 
 RefraBion out of the rarer Medium intothe 
 denfer, is made toijvards the "Perpendicular, that 
 is, fo that the Angle of Re f ration be lefs than 
 the Angle of Incidence. 
 
 AX. V. 
 
 The Sine of Incidence is either accurately or 
 very nearly in a given Ratio to the Sine of Re'- 
 fraction. 
 
 Whence if that Proportion be known in any 
 one Inclination of the incident Ray, 'tis known 
 in all the Inclinations, and thereby the Refra- 
 ^lon in all cafes of Incidence on the fame refra^ 
 ding Body may be determined. Thus if the 
 
 B 3 Refra- 
 
Rj2fra(^tion be made out of Air into Water, the 
 Sine 'of Incidence of the red Light is to the Sine 
 pfitsRefradionas 4to 3. If out of Air into Glafs, 
 the Sines are as 17 to 11. In Light of other 
 Colours the Sines have other Proportions : but 
 the difference is fo little that it need feldom be 
 confidered. 
 
 Snppofe therefore, that R S [mFig.i.^ repre- 
 fents the Surfaceof ftagnating Water, and that C 
 is, the point of Incidence in which any Ray coming 
 in the Air from A in the Line AC is retiedted or 
 reffraded, and I would know whither this Ray 
 fliall go after Reflexion or Refradion : I ereA 
 Vipon the Surface of the Water from the point 
 of Incidence the Perpendicular CP and produce 
 it downwards to Q, and conclude by the firft 
 Axiom., that the Ray after Reflexion and Re- 
 fraction, ihall be found fomewhere in the Plane 
 of the Angle of Incidence A CP produced. I let 
 fall therefore upon the Perpendicular CP the 
 Sine of Incidence AD; and if the refleded 
 Ray be defired, I produce AD to B fo that 
 DB be equal to AD, and draw CB. For this 
 Line C B iliall be the reflefted Ray ; the Angle 
 pf Reflexion BCP and its Sine BD being e- 
 qual to the Angle and Sine of Incidence, as they 
 ought to fcje by the fecond Axiom. But if the 
 refi'a6led Ray be defired, I produce AD to H, 
 fo that DH may be to AD as the Sine of Re- 
 iraftion 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 ABE I draw Parallel to the 
 Perpendicular C P Q, the Line H E cutting the 
 
 Cireum- 
 
[7] 
 
 Circumference inE, and joyningCE, this Line 
 CE ihall be the Line of the refraded Ray. 
 For if EF be let fall perpendicularly on the 
 Line PQ, this Line EF ihall be the Sine of Re- 
 fradion of the Ray C E, the Angle of Refradion 
 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 
 w^ell poliilied 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 theRefraftion of the Light in palling crofs this 
 Prifm be defired : Let AC B [in Fig. i.] reprefent 
 a Plane cutting this Prifm tranfverlly to its three 
 Parallel lines or edges there where the Light 
 paffeth through it, and let DE be the Ray inci- 
 dent upon the firit fide of the Prifm A C where 
 the Light goes into the Glafs ; and by putting 
 the Proportion of the Sine of Incidence to the 
 Sine of Refradion as 17 to 11 find EF the 
 firll refrafted Ray. Then taking this Ray for the 
 Incident Ray upon the fecond fide of the Glafs 
 BC where the Light goes out, tind the next 
 refraded R^y F G by putting the Proportion 
 of the Sine of Incidence to the Sine of Re- 
 fradion 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 muft on the contrary be to the 
 Sine of Refradion as 11 to 17, by the third 
 Axiom. 
 
 B 4 P^g'^^ 
 
[8] 
 
 Much after the fame manner, if ACBD [in 
 Fig. 3.] reprefent a Glafs fpherically Convex on 
 both fides (ufually called a Lens^ fuch as is a Birrn- 
 ing-glafs, or Spedacle-giafs, or an Objeft-glafs of 
 a Telefcope) and it be required to know how 
 Light falling upon it from any lucid point Q 
 iliall be relra(^ted, let QM reprefent a Ray 
 falling upon any point M of its firft fpherical 
 Surface A C B, and by ereft ing a Perpendicular 
 to the Glafs at the point M, find the firft re- 
 fra6fed Ray MN by the Proportion of the 
 Sines 17 to 11. Let that Ray in going out. of 
 the Glafs be incident upon N, and then find 
 the fecond refraded Ray N q by the Proporti- 
 on of the Sines 11 to 17, And after the fame 
 inanner may the Refraction 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 
 
 Hofnogeneal Rays <whtch flow from federal 
 joints of any Obje^^ and fall pcr.pendktilarly or 
 almo ft perpendicularly on any refleir'tng or refraEi- 
 ing Plane or fphertcal Surface^ jloall afterwards 
 diverge from fo many other Point s^ or be Parallel 
 tofo many other Lines, or converge tofo many other 
 Points J either accurately or without any fenfible 
 Error. And the fame thing will happen, if the 
 Rays be refieBed or refra6ledfucce£ively by twot 
 Qr three or mere Plane or Spherical Surfaces. 
 
 The Point from which Rays diverge or to 
 which they converge may be called their Focm. 
 And the Focus of the incident Rays being gi- 
 ven^ th^t of the rf fleded or refraded ones may 
 . be 
 
[9] 
 
 be found by finding the Refraftion of any two 
 Rays, as above ; or more readily thus. 
 
 Caf I. Let A C B [in Fig. 4.] be a reflecting or . 
 refrading Plane, and Q the Focus of the incident 
 Rays, and Q ^ C a perpendicular to that Plane. 
 And if this perpendicular be produced to ^, 
 fo that ^ C be equal to QC, the point q, Ihall 
 be the Yocus of the refleded Rays. Or if ^ C 
 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 Refradion, the point 
 ^ ihall be the Focus of the refraded Rays. 
 
 Cafz. Let A C B [in Fig. 5.] be the refleding 
 Surface of any Sphere whofe Center is E. .Bi- 
 {e&i any Radius thereof (fuppofe EC) in T, 
 and if in that Radius on the fame lide the 
 point T you take the Points Q and ^, fo that 
 T Q, TE, and T a, be continual Proportionals, 
 ^nd the point Q be the Focus of the incident 
 Rays, the point ^ Ihall be the Focus of the re- 
 flec^ted ones. 
 
 Ca/: 3. Let A C B [in Fig. 6.] be the refrading 
 Surface of any Sphere wnofe Center is E. In 
 any Radius thereof EC produced both ways 
 take E T and C f equal to one another and fe- 
 verally in fuch Proportion to that Radius as 
 the leffer 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 Ef 
 to f ^, taking /^ ^ the contrary way from ^ which 
 TQ lieth from T, and if the Point Q be the 
 Focus of any incident Rays, the Point ^ Ihall be 
 the Focus of the refraded ones. 
 
 And 
 
[lo] 
 
 And by the fame means the Focus of the 
 Rays after two or more Reflexions or Refrac- 
 tions may be found. 
 
 Caf. 4. Let AC B D [in Fig, 7.] be any refraft- 
 ing Lens, fpherically Convex or Concave or 
 Plane on either fide, and let C D be its Axis 
 (that is the Line which cuts both its Surfaces 
 perpendicularly, and palTes through the Centers 
 of the Spheres,) and in this Axis produced let 
 F and /be the Foci of the refracted 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 E, defcribe a Circle. 
 Suppofe now that any Point Q be the Focus of 
 any incident Rays. Draw QE cutting the faid 
 Circle in T and ^, and therein take ^ ^ in fuch 
 Proportion to /^ E as ^ E or TE hath to TO. 
 Let t q lye the contrary way from t which T Q 
 doth from T, and q fliall be the Focus of the 
 refra(^ted 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 oblicjuely on the refraaing 
 Surraces. 
 
 And by the like Operations may the refleft- 
 ing or refrafting Surfaces be found when the 
 two Foci are given, and thereby a Lens be form- 
 ed, which fhall make the Rays 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 fhall after Re- 
 flexion or Refradion flow from or tow^ards the 
 
 Point 
 
["] 
 
 Point q found by the foregoing Rules. And if 
 the incident Rays fiow from or towards feveral 
 points Q, the refleded or refraded Rays fliall 
 flow from or towards fo many other Points q 
 found by the fame Rules. Whether the rcfleft- 
 ed and refracted 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 reflecting 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 refrafted from it ; and if the 
 incident Rays flow towards Q, the refleded 
 flow from ^, and the refraded towards it. And 
 the contrary happens when q is on the other 
 fide of that Surface. 
 
 AX. VII. 
 
 Wherever the Rays "juhich come from all the 
 'Points of any Object meet- again in fo many 
 Joints after they have been made to converge 
 by Reflexion or RefraBion^ there they i2;ill make 
 a TiBtire of the Obje6f ufon any white Body 
 on which they fall. 
 
 So if P R [in Fig. 3 .] reprefent any Objeft with- 
 out Doors, and A B be a Lens placed at a hole 
 in the Window-ihut of a dark Chamber, where- 
 by the Rays that come from any Point Q of 
 that Objedf are made to converge and meet a- 
 gain in the Point q\ and if a Sheet of white Pa- 
 per be held at q for the Light there to fall up- 
 on it : the Picture of that Objed: PR will ap- 
 pear upon the Paper in its proper Ihape and Co- 
 lours 
 
[12] 
 
 lours. For as the Light which comes from the 
 Point Qgoes to the Point q^ 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 manifeit by the fixth Axiom ;) fo 
 that every Point of the Objeft fliall illuminate a 
 correfpondent Point of the Pidure, and there- 
 by make a Pidure like the Objed in Shape and 
 Colour, this only excepted that the Pidure 
 lliall be inverted . And this is the reafon of that 
 vulgar Experiment of caftingthe Species of Ol> 
 jeds from abroad upon a Wall or Sheet of white 
 Paper in a dark Room. 
 
 In Uke manner, when a Man views any Objed 
 PQR, [ini^i^,8.] the Light which comes from 
 the feveral Points of the Objed is fo refracted 
 by the tranfparent skins and humours of the 
 Eye, (that is by the outward coat EFG called 
 the Tunica Cornea^ and by the cryftalline hu- 
 mour A?j 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 
 Pidurc of the Objeft upon that skin (called the 
 Tunica Retina) with which the bottom of the 
 Eye is covered, For Anatomilts when they have 
 taken off from the bottom of the Eye thatout- 
 w^ard and moll thick' Coat called the 2)//r^ Ma- 
 ter^ can then fee through the thinner Coats, 
 the Pictures of Objeds lively painted there- 
 on. And thefe Pidures propagated by Mo- 
 tion along the Fibres of the Optick Nerves in- 
 to the Brain, arc the caufe of Vifion. For ac- 
 cordingly as thefe Pidures are perfed or im^ 
 perfed, the Objed is feen perfedly or imperfecl- 
 
[13] 
 
 ly. If the Eye be tinged with any colour (as in 
 the Difeafe of the JaundifeJ fo as to tinge the 
 Pidlures in the bottom of the Eye with that 
 Colour, then all Objects appear tinged with the 
 fame Colour. If the humours of the Eye by 
 old Age decay, fo as by flirinking to make the 
 Cornea and Coat of the Cryftalline htimoitr grow 
 flatter than before, the Light will not be re- 
 fraded enough, and fornvant of a fuiiicient Re- 
 fradion will not converge to the bottom of the 
 Eye but to fome place beyond it, and by con- 
 fequencc paint in the bottom of the Eye a con- 
 fuled Pidure, and according to the indiitind- 
 nefs of this Pidure the Objed will appear con- 
 fufcd. This is the reafon of the decay of fight 
 in old Men, and fhews why their Sight is mend- 
 ed by Spedacles. For thole Convex-glalFes fup- 
 ply the defed of plumpnefs in the Eye, and by 
 encreafmg the Refradion make the Rays con- 
 verge fooner fo as to convene diilindly at the 
 bottom of the Eye if the Glafs have a due de- 
 gree of convexity. And the contrary happens 
 in fliort-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 diflind, 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- 
 on s diminifhed by a Concave-glafs of a due de- 
 gree of Concavity, or laftly that by Age the 
 
 I Eye 
 
[14] 
 
 Eye gro'<^' flatter till it come to a due Figure : 
 For iliort-fighted Men fee remote Objeds befl 
 in Old Age, and therefore they are accounted 
 to have the moft laiting Eyes. 
 
 A X. VIII. 
 
 An Obje5f feen by Reflexion or RefraBton^ 
 nf fears in that flace from whence the Rays af- 
 ter their laft Reflexion or RefraSiion diverge in 
 falling on the SfeBator^s Eye. 
 
 If the Objeft A [in Fig, 9.] be feen by Reflexion 
 of a Looking-glafs m n, it fhall appear, not in its 
 proper place A, but behind the Glafs at a, from 
 whence anyRays 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 Speftator'sEyes. 
 For thefe Rays do make the fame Pi6lure in the 
 bottom of the Eyes as if they had come from 
 the Objeft really placed at a without the inter- 
 pofition of the Looking-glafs ; and all Villon is 
 made according to the place and fliape of that 
 Pidure. 
 
 In like manner the Objeft D [in Fig. 2.] feen 
 through a Prifm, appears not in its proper place 
 D, but is thence tranflated to fome other place 
 d fituated in the lait refraded Ray F G drawn 
 backward from F to ^. 
 
 And fo the Objeft Q [in Fig. 10.] feen through 
 the Lens AB, appears at the place q from whence 
 the Rays diverge in pafliingfrom the Lens to the 
 Eye. Now it is to be noted> that the Image of 
 
 the 
 
[»5] 
 
 the Objeft at q is fo much bigger or lefler than 
 the Objed: it felf at Q, as the diftance of the 
 Image at q from the Lens AB is bigger or lefs 
 than the dillance of the Objed at Q from the 
 fame Lens. And if the Objed be feen through 
 two or more fuch Convex or Concave-glilies, 
 every Glafs Ihall make a new Image, and the 
 Objed fliall appear in the place and of the big- 
 nefs of the lail Image. Which confideration un- 
 folds the Theory of Microfcopes and Telefcopes. 
 For that Theory confilh in almoft nothing elfe 
 than the defcribing fuch GlafTes as fliall make 
 the laft Image of any Objeft as diilinft 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. P'or 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 Introdudion to Readers of quick Wit 
 and good Underflanding not yet verled in Op- 
 ticks : Although thofe who are already acquain- 
 ted with this Science, and have handled GlaiTes, 
 will more readily apprehend what folio weth. 
 
 TROTO^ 
 
[•«] 
 
 L 
 
 PROPOSITIONS. 
 
 TROT.l The OR. I. 
 
 IG HTS which differ in Colour^ differ alfi 
 in T>egrees of Refrangihility, 
 
 The Proof by Experiments. 
 
 Exfer. I. I took a black oblong fliff Paper 
 terminated by Parallel Sides, and with a Per- 
 pendicular right Line drawn crofs from one 
 Side to the other, dillinguiflied it into two e- 
 quai 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 Phaenomenon 
 might be more confpicuous. This Paper I 
 view'd through a Prifm of folid Glafs, whofe 
 two Sides through which the Light palTed to the 
 Eye were plane and well polifhed , and contained 
 an Angle of about fixty degrees : which Angle 
 I call the refrafting Angle of the Prifm. And 
 whiKlI viewed it, I held it and the Prifm before 
 a Window infuch manner that the Sides of the 
 Paper were parallel to the Prifm, and both thofe 
 Sides and the Prifm were parallel to the Horizon, 
 and the crofs Line was alfo parallel to it ; and 
 that the Light which fell from the Window upon 
 the Paper made an Angle with the Paper, equal 
 to that Angle which was made with the fame 
 
 Papef 
 
[17] 
 
 Paper by the Light refle6ted from it to the Eye. 
 Beyond thePriim was the Wall of the Chamber* 
 under the Window covered over with black 
 Cloth, and the Cloth was involved in Darknei's 
 that no Light might be refleded from thence, 
 which in palling by the edges of the Paper to 
 the Eye, might mingle it felf with the Light of 
 the Paper, and obfcure the Phaenomenon there- 
 of Thefe things being thus ordered, I found 
 that if the- refradiing Angle of the Prifm be 
 turned upwards, fo that the Paper may feem to 
 be lifted upwards by the Refraction, its blue 
 half will be lifted higher by. the Refraclion 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 Re. ra- 
 tion, its blue half, will be carried fomething 
 lower thereby -than it^s red half W herefore in 
 both cafe? the Light which comes from the 
 blue half of the Paper through the Prii'm to 
 the Eye, does in like Circumltances futier a 
 greater Refradion than the Light which comes 
 from the red half, and by confcquence is more 
 refrangible. 
 
 Illtijtration. In the eleventh Figure, MN 
 reprefents^ the Window, and DE the Paper 
 terminate,d with parallel Sides DJ and HE, 
 and by the tranfverfe Line FG dilbnguifhed 
 into ;two halfs, .fhe one D G of an intenfely 
 blue Colour, the other FE of an intenfely 
 red. And B A C^ ^^ reprefents the Prifm 
 whofe refrafting Planes A B ^ ^ and A C ^ ^ 
 rneet in the edge of the refrading Angle A a. 
 This edge A.a being upward, is parallel both to 
 
 C thof 
 
I .8] 
 
 the Horizon and to the parallel edges of the 
 Paper DJ and HE, and the tranfverfe Line FG 
 is perpendicular to the Plane of the Window. 
 And de reprefents the Image of the Paper feen 
 by Refradion upwards in fuch manner that the 
 blue half D G is carried higher to dg than the 
 red half FE is to/^, and therefore fuffers a 
 greater Refradion. If the edge of the refraft- 
 ing Angle be turned downward, the Image of 
 the Paper will be refrafted downward, fuppofe 
 to <5^€, and the blue half will be refraded lower 
 to ly than the red half is to <p6. 
 
 Exper. 2. About the aforefaid Paper, whofe 
 two halfs were painted over with red and blue, 
 and which was IHfFlike thinPaftboard, I lapped 
 feveral times a flender thred of very black Silk, 
 in fuch manner that the feveral parts of the 
 thred might appear upon the Colours like fo 
 many black Lines drawn over them, or like 
 long and (lender dark Shadows 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 Hned 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 llrong- 
 ly : For the Experiment was tried in the Night. 
 The flame of the Candle reached up to the 
 lower ^dig^ 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 erefted 
 a glafs Lens four Inches and a quarter broad, 
 
 which 
 
[19] 
 
 whieh might colleft the Rays coming from the 
 fevcral Points of the Paper, and make them con- 
 verge towards fo many other Points at the fame 
 diflance of fix Feet and one or two hiches on 
 the other fide of the Lens, and fo form the I- 
 mage of the coloured Paper upon a white Pa- 
 
 Eer placed there, after the fame manner that a 
 iCns at a hole in a Window calls the Images of 
 Objeds abroad upon a Sheet of white Paper in 
 a dark Room. The aforefiiid white Paper, e- 
 refted 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 moll: diftinft. Thofe places I eafilyknew by 
 the Images of the black Lines which I had made 
 by winding the Silk about the Paper. For the 
 Images. of thole fine arid flender Lines (which 
 by rcafon of their blacknefs were like Shadows 
 on the Colours) were confufed and fcarce vili- 
 ble, unlels when the Colours on either fide of 
 each Line were terminated moll dillinctly. No- 
 ting therefore, as diligently as I could, the 
 places where the Images of the red and blue 
 halfs of the coloured Paper appeared moll di- 
 llinft, I found that where the red half of the 
 Paper appeared dillind, the blue half appeared 
 confufed , fo that the black Lines drawn upon 
 it could fcarce be feen ; and on the contrary, 
 where the blue half appeared mofl dillindl, the 
 red half appeared confufed , fo that the black 
 Lines upon it were fcarce vifible. And between 
 the two places where thefe Images appeared 
 
 C -L diflina 
 
[20] 
 
 diftin(f^ there was the diftance of an Inch and ^ 
 half: the diftance of the white Paper from the 
 Lens, when the Image of the red half of the 
 coloured Paper appeared moft diilincft, being 
 greater by an Inch and an half than the diflance 
 of the fame white Paper from the Lens when 
 the Image of the blue half appeared moft di- 
 flinft. 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- 
 verge fooner by an Inch and an half, and there- 
 fore is more refrangible. 
 
 Illuftration. In the twelfth Figure,. DE fig- 
 nifies the coloured Paper, DG theblue half, 
 FE the red half, MN the Lens, H J the white 
 Paper in that place 'where the red half with its 
 black Lines appeared diftind, and hi the fame 
 Paper in that place where the blue half appear- 
 ed diftinft. The place h t was nearer to the 
 Lens MN than the place HJ by an Inch and 
 an half, 
 
 Scholhim. The fame things fucceed notwith- 
 ftanding that fome of the Circumftances be va- 
 ried : as in the firft Experiment when the Prifm 
 and Paper are any ways inclined to the Hori- 
 zon, and in both when coloured Lines are 
 drawn upon very black Paper. But in the De- 
 fcription of thefe Experiments, I have fet down 
 fuch Circumftances by which either the Phse- 
 nomenon might be rendred 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 
 
 fuffice. 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 differently Re- 
 frangible, fo that in the red there are fome Rays 
 not lefs Refrangible 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 diminifli the Event of the.Experi- 
 ment, but are not able to deftroy it. For if 
 the red and blue Colours were more dilute and 
 weak, the diflance of the Images would be iefs 
 than an Inch and an half; and if they were more 
 intenfe and full, that diftancc would be greater, 
 as will appear hereafter. Thefe Experiments 
 may fuffice for the Colours of Natural Bodies. 
 For in the Colours made by the Refradion of 
 Prifms this Proportion will appear by the Ex- 
 periments which are now to follow in the next 
 Propofition. 
 
 TROT. n. Theor. II. 
 
 The Light of the Sun conjifts of Rays differently 
 Refrangible. 
 
 The Proof by Experiments. 
 
 Exper. a.TN a very dark Chamber at around 
 \^ hole about one third part of an 
 Inch broad made in the Shut of a Window 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 refracted 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 paffing through the middle of the 
 Prifm from one end of it to the other end pa- 
 rallel to the edge of the Refrading Angle) was 
 in this and the following Experiments perpen- 
 dicular to the incident Rays. About this Axis 
 I turned the Prifm flowly, and faw the refra- 
 &d Light on the Wall or coloured Image of 
 the Sun firll 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 pofturc, that it fliould be 
 moved no more. For in that pofture the Re- 
 fractions of the Light at the two fides of the 
 refrac^ting Angle, that is at the entrance of the 
 Rays into the Prifm, and at their going out of 
 it, were equal to one another. So alfo in other 
 Experiments, as often as I would have the Re- 
 fraftions on both fides the Prifm to be equal to 
 one another, I noted the place where the Image 
 of the Sun formed by the refrafted Light flood 
 Hill between its two contrary Motions, in the 
 common Period of its progrefs and regrefs ; and 
 when the Image fell upon that place, I made 
 fail the Prifm. And in this Pofture, as the mofl 
 convenient, it is to be underftood that all the 
 Prifms are placed in the following Esjg^riments, 
 unlefs where fome other pofture is defcribed. 
 The Prifm therefore being placed in this po- 
 fture, I let the refraded Light fall perpendicu- 
 larly upon a Sheet of white Paper at the oppo- 
 fite Wall of the Chamber, and obferved the Fi- 
 gure 
 
[23] 
 
 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 Redilinear and Parallel Sides, and two Se- 
 micircular Ends. On its Sides it was bounded 
 pretty diitindly, but on its Ends very confufed- 
 ly and indiilindly, the Light there decaying 
 and vanifhing by degrees. The breadth of this 
 Image anfwered 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 diftant from the 
 Prifm, and at this diftance that breadth if di- 
 minifhed by the Diameter of the hole in the 
 W' indow-ihut, 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- 
 6liUnear Sides about eight Inches ; and the re- 
 frading Angle of the Prifm whereby fo great a 
 length was made, was 64 degrees. W ith 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 
 refrafting Surface of the Prifm, the Image foon 
 became an Inch or two longer, or more ; and 
 if the Pi;ifm was turned about the contrary 
 way, fo as to make the Rays fall more oblique- 
 ly on the fii'it refrading Surface, the Image loon 
 became an Inch or two fliorter. And there- 
 fore in trying this Experiment, I was as curi- 
 ous as I could be in placing the Prifm by the 
 
 C 4 above- 
 
[24] 
 
 above-mentioned Rule exac^lly in fuch a pollure 
 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 fet^fible ef- 
 fed in encreafing the length of the coloured 
 Spedrum. For I tried the fame Experiment 
 with other Prifms with the fame Succefs. And 
 particularly with a Prifm which feemed free 
 from fuch Veins, and whofe refracting Angle 
 was 6i4 Degrees, I found the length of the 
 Image 94 or 10 Inches at the dillance of 184 
 Feet from the Prifm, the breadth of the hole 
 in the Window-iliut being ^ of an Inchj as be- 
 fore. And becaufe it is caiie to commit a mi- 
 flake in placing the Prifm in its due poliure, I 
 repeated the Experiment four or hve times, 
 and always found the length of the Image that 
 which is fet down above. With another Priim 
 of clearer Glafs and better Poliih, which feem- 
 ed free from Veins, and whofe refrading Angle 
 was 63V Degrees, the length of this Image at 
 the fame diltance of 184 Feet was alfo about 10 
 Inches, or 104. Beyond thefe Meafures for a- 
 bout 4 or 4 of an Inch at either end of the Spe- 
 ctrum the Light of the Clouds feemed to be a 
 little tinged with red and violet, but fo very 
 faintly, that I fufpedted that tinClure might ei- 
 ther wholly or in great meafure arife from fome 
 Rays of the Speflrum fcattered irregularly by 
 fome inequaUties in the Subflance and Polifh of 
 f;he Glafs, and therefore I did not include it in 
 
 l^tiefe 
 
[25] 
 
 thefe Meafures. Now the different Magnitude 
 of the hole in the Window- iliut, and different 
 thicknefs of the Prifm where the Rays pafTed 
 through it, and different inclinations of the 
 Prifm to the Hori'/on, made no fenfible chan- 
 ges in the length of the Image. Neither did 
 the different matter of the Prifms make any : 
 for in a Veffel made of poliilied Plates of Glals 
 cemented together in the ihape of a Prifm and 
 filled with Water, there is the like Succefs of 
 the Experiment according to the quantity of 
 the Refradion. It is farther to be obfcrved, 
 that the Rays WTnt 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 
 acGOfding to the L^ws of Opticks vulgarly re- 
 ceived, they could not poffibly be fo much incli- 
 ned to one another. For let KG [in F{(^. i ^] rc- 
 prefent theWindow-lliut, F the hole made there- 
 in through which a beam of the Sun's Light was 
 •tranfmitted into the darkned Chamber, and 
 2ABC a Triangular Imaginary Plane whereby the 
 •Prifm is feigned to be cut tranlVcrlly through 
 the middle of the Light. Or if you pleafe, let 
 ABC reprefent the Prifm it felf , looking di- 
 redly towards the Speftator's Eye with its near- 
 er end : And let X Y be the Sun, M N the Pa- 
 mper upon which the Solar Image or Speftrum is 
 call, and PT the Image it felf whofe Tides to- 
 wards ^'and w are Rectilinear and Parallel, and 
 ends towards P and T Semicircular, YKHP 
 
 and 
 
{26 ] 
 
 and XLJT are two Rays, the firfl of which 
 comes from the lower part of the Sun to the 
 higher part of the Image, and is refradled 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 refraded at L and J. Since 
 the Refradtions on both fides the Prifm are e- 
 qual to one another, that is the Refradion at 
 K equal to the Refraflion at J , and the Refra- 
 ction 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 Refraftions of 
 the emergent Rays at H and J taken together : 
 it follows by adding equal things to equal things, 
 that the Refradions at K and H taken together^ 
 are equal to the Refradions at J and L taken 
 together, and therefore the two Rays being e- 
 qually refraded have the fame Inclination to 
 one another after Refradion which they had 
 before, that is the Inclination of half a Degree 
 anfwering to the Sun's Diameter. For fo great 
 was the Inclination of the Rays to one another 
 before Refradion. So then, the length of the 
 Image FT 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 
 form the Image V wT v ^ ahke 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] 
 
 greatefl Refraftion, 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 leait refraded end T, and vio- 
 let at its moll refraded end P, and yellow 
 gi'een and blue in the intermediate Spaces. 
 Which agrees with the firll Proportion , that 
 Lights which differ in Colour do alio diiler in 
 Refrangibility. The length of the Image in the 
 foregoing Experiments I meafurcd from the 
 fainted and outmoit red at one end, to the 
 faintell and outmofl 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 diftance of fome Feet 
 from the hole, I held the Prifm in fuch a po- 
 flure that its Axis might be perpendicular to 
 that beam. Then I looked through the Prifm 
 Vipon 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 ftationary, I 
 ftopp'd the Prifm that the Refraftions of both 
 fides of the refracting 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- 
 fracted Image to be many times greater than 
 its breadth , and that the moft refracted part 
 thereof appeared violet, the leaft refraCted red, 
 
 the 
 
[28] 
 
 the middle parts blue green and yellow in or- 
 der. The lame thing happen'd when I remo- 
 ved the Prifm out of the Sun's Light, and look- 
 ed through it upon the hole ihining 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 refracted Image ought to have appeared 
 round. 
 
 So then, by thefe two Experiments it appears 
 that in equal Incidences there is a confiderable 
 inequality of Refraftions. But whence this in- 
 equality arifes, whether it be that fome of the 
 incident Pvays are refradcd more and others lefs, 
 conftantly, or by chance, or that one and the 
 fame Ray is by Refra61ion dillurbed, fliatter'd, 
 dilated, and as it were fplit and fpread into 
 many diverging Rays, as Grmaldo fuppofes, 
 does not yet appear by thefe Experiments, but 
 will appear by thofe that follow, 
 
 Ex^er. y. 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, or by any o- 
 ther cafual inequality of the Refradions, the 
 fame oblong Image would by a fecond Refra- 
 ction made fideways be drawn out as much in 
 breadth by the like Dilatation of the Rays, or o- 
 ther cafual inequality of the Refraftions fide- 
 ways, I tried what would be the effects of fuch 
 a fecond Refraction. For this end I ordered 
 all things as in the third Experiment, and then 
 placed a fecond Prifm immediately after the 
 
[29] 
 
 firfl in a crofs Pofition to it, that it might again 
 refrav^l: the beam of the Sun's Light which came 
 to it through the fidt Prifm. In the iirftPrilm 
 this beam was refraded upwards, and in the 
 fecond iideways. And I found that by the Re- 
 fradion of the fecond Prifm the breadth of the 
 Image was not increafed, but its fuperior part 
 which in the firll Priim fuflfered the greater 
 Refraiiiion and appeared violet and blue, did 
 again in the fecond Prifm fulfer a greater Re- 
 fraction than its inferior part, which appeared 
 red and yellow, and this without any Dilatation 
 of the Image in breadth. 
 
 llliiftration. Let S [in /Tj. 14.] reprefent 
 the Sun, F the hole in the Wmdow, ABC the 
 firit Prifm, D H the fecond Prifm, Y the round 
 Image of the Sun made by a dired beam of 
 Light when the Prifms arc taken away, PT 
 the oblong Image of the Sun made by that beam 
 palling through the tirll Prifm alone when the 
 fecond Prifm is taken away, and/^ the Image 
 made by the crofs Refractions of both Prilms 
 together. Now if the Rays which tend to- 
 wards the feveral Points of the round Image Y 
 were dilated and fpread by the RefraClion of 
 the firlt Prifm, fo that they fliould not any lon- 
 ger go in fmgle Lines to fingle Points, but that 
 every Ray being fplit, iliattered, and changed 
 from a Linear Ray to a Superficies of Rays di- 
 verging from xhe Point of Refradtion, and ly- 
 ing in the Plane of irhe Angles of Incidence and 
 Refradion, they fliould go in thofe Planes to 
 fo many Lines reaching almofl from one end of 
 the Image PT to the other, and if that Image 
 
 Hiould 
 
[3o] 
 
 fhould thence become oblong: thofcRays and 
 their feveral parts tending towards the ieveral 
 Points of the Image P T ought to be again di- 
 lated and fpread Tideways by the tranfverfe 
 Refraction of the fecond Prifm, fo as to com- 
 pofe a four fquare Image, fuch as is reprefent- 
 ed at Trj. For the better underftanding of which, 
 let the Image P T be diltinguiflied into five e- 
 qual parts PQK, KQRL, LRSM, MSVN, 
 N V T. And by the fame irregularity that the 
 orbicular Light Y is by the Refradion of the 
 firit Prifm dilated and drawn out into a long 
 Image PT, 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 tt qkp^ and the Light KQRL in- 
 to the long Image kqr l^ and the Lights LRSM, 
 MSVN, NVT, into fo many other long I- 
 mages Irsm, msv n, nvt"} \ and all thefe long 
 Images would compofe the four fquare Image 
 9r7. Thus it ought to be were every Ray dila- 
 ted byRefraftion, and fpread into a triangular 
 Superficies of Rays diverging from the Point 
 of Refraflion. For the fecond Refradtion 
 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 refraded more than others. 
 But the Event is otherwife. The Image P T 
 was not made broader by the Refradion of the 
 fecond Prifm, but only became oblique, as 'tis 
 reprefented at / r, its upper end P being by 
 
 the 
 
[31] 
 
 the Refraftion tranllatcd to a greater cliflance 
 than its lower end T. So then the Light which 
 went towards the upper end P of the Image, 
 was ( at equal Incidences) more refraded in 
 the fecond Prifm than the Light which tended 
 towards the lower end T, that is the blue and 
 violet, than the red and yellow ; and therefore 
 was more refrangible. The fame Light was by 
 the Refraftion of the firft Prifm tranllated far- 
 ther from the place Y to which it tended before 
 Refra(^Hon; and therefore fuftered as well in 
 the firft Prifm as in the fecond a greater Refra- 
 ftion than the reft of the Light, and by con- 
 fequence was more refrangible than the reft, 
 even before its incidence on the firft Prifm. 
 
 Sometimes I placed a third Prifm after the 
 fecond, and fometimes alfo a fourth after the 
 third, by all which the Image might be often 
 refraded fideways: but the Rays which were 
 more refraded than the reft in the firft Prifm 
 were alfo more refraded in all the refl, and that 
 without any Dilatation of the Image fideways : 
 and therefore thofe Rays for their conftancy of 
 a greater Refradion are defervcdly 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 perfeft 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 
 
 ^ [in 
 
[32] 
 
 [in Fig. 15-.] reprefent the Circle which all 
 the molt refrangible Rays propagated from the 
 whole Difque of the Sun, would illuminate and 
 paint upon the oppofite Wall if they were a- 
 lone ; E L the Circle which all the lead refran- 
 gible Rays would in like manner illuminate and 
 paint if they were alone; B H, CJ, DK, the 
 Circles which fo many intermediate forts of 
 Rays would fucccfTively paint upon the Wall, 
 if they were fmgly propagated from the Sun 
 in fucceffive order, the rell being always in- 
 tercepted ; and conceive that there are other 
 intermediate Circles without number, which 
 innumerable other intermediate forts of Rays 
 would fucceilively paint upon the Wall if the 
 Sun fliould fucceflively emit every fort apart. 
 And feeing the Sun emits all thefe ibrts at once, 
 they muit all together illuminate and paint in- 
 numerable equal Circles, of all which, being 
 according to their degrees of Refrangibihty 
 placed in order in a continual Series, that ob- 
 long Spedrum P T is compofed which 1 de- 
 fcribed in the third Experiment. Now if the 
 Sun's circular Image Y [in Fig. 14, 15-.] which 
 is made by an unrefraded beam of Light was 
 by any Dilatation of the iingle Rays, or by any 
 other irregularity in the Refraction of the firll 
 Prifm, converted into the oblong Speftrum, 
 FT: then ought every Circle A G, BH, CJ, 
 ^c. in that Spedrum, by the crofs Refraction 
 of the fecond Prifm again dilating or otherwife 
 fcattering the Rays as before, to be in like man- 
 ner drawn out and transformed into an oblong 
 Figure, and thereby the breadth of the Image 
 
 PT 
 
[ 33 ] 
 
 P T would be now as much augmented as the 
 length of the Image Y was before by the Refra- 
 ction of the firft Prifm ; and thus by the Refra- 
 ctions of bothPrifms togecher would be form- 
 ed a four fquare Figure / TT r7, as I defcribed a- 
 bove. Wherefore fmce the breadth of the Spe- 
 ctrum PT is not increafed by the Refraction 
 Tideways, it is certain that the Rays are not 
 fpHt or dilated, or otherways irregularly fcat- 
 ter'd by that Refraction, but that every Circle 
 is by a regular and uniform RcfraCtion tranila- 
 ted entire into another place, as the (Circle A 
 G by the greateit Refraaion into the place ag^ 
 the Circle BH by a Icfs Refradion into the 
 place b hi the Cifcle C J by a RefraCtion ftill 
 lefs into the place f /, and fo of the reft; by 
 which means a new SpeCtrum p t inclined to 
 the former P T is in like manner compofcd of 
 Circles lying in a right Line ; and thefe Circles 
 mult be of the fame bignefs with the former, 
 becaufe the breadths of all the SpeCtrums Y, 
 P T and /> /^ at equal diilances from the Prifms 
 are equal. 
 
 I confidered farther, that by the breadth of 
 the hole F through \^'hich the Light enters in- 
 to the dark Chamber, there is a Penumbra 
 made in the circuit of the SpeCtrum Y, and 
 that Penumbra remains in the reCtilinear Sides 
 of the SpeCtrums P T and pt. I placed there- 
 fore at that hole a Lens or ObjcCt-glafs of aTe- 
 lefcope which might calt the Image of the Sun 
 diftinctly on Y without any Penumbra at all, 
 and found that the Penumbra of the reCtilinear 
 Sides of the oblong SpeCtrums PT and/^ was 
 
 D alfd 
 
[34] 
 
 ^Ifo thereby taken away, . fo that thofc Sides ap- 
 peared as difdnftly defined as did the Chxum- 
 ferenee of the firlMmage Y. Thus it happens 
 if the Glais of the Prilrns be .free from. Veins, 
 and their Sides be accurately plane and well 
 pohllied without thole numberiels Waves or 
 Curies which ufually ariic from Sand-holes a 
 little fmoothed in polifliing with Putty. If the 
 Glafs be only well polillied and free from Veins 
 and the Sides not accurately plane but a Httle 
 Convex or Concave, as it frequently happens ; 
 yet may the three Speflrums V, PT and / t 
 want Penumbras, but not in e^ual diitances 
 from the Prifms. Now from this want of Pen- 
 umbras, I knew more certainly that every one 
 of the Circles was refradled according to fome 
 moft regular, uniform, and conilant law. For 
 if there were any irregularity in the Refraftion, 
 the right Lines A E and G L which all the Cir- 
 cles in the Spedrum PT do touch, could not 
 by that Refraftion be tranllated into the Lines 
 ae and ^/ as diftinft and ftraight as they were 
 before, but there would arife in thofe tranllated 
 Lines fome Penumbra or Crookednefs or Un- 
 dulation, or other fenfible Perturbation con- 
 trary tG what is found by Experience. What- 
 foever Penumbra or Perturbation Ihould be 
 made in the Circles by the crofs Refraction 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 fmce there is no fuch Penumbra or 
 Perturbation in thofe right Lines there mult be 
 none in the Circles. Since the diitance between 
 
 thofe 
 
[35] 
 
 thofe Tangents or breadth of the Spedlrum is 
 not increafed by the Refractions, the Diameters 
 of the Circles arc not increafed thereby. Since 
 thofe Tangents continue to be right Lines, e- 
 very Circle which in the firfl Priini is more or 
 lefs refraded, is exadly in the fame propor- 
 tion more or lefs refracted 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 refra- 
 ded 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^ 
 mogencal to one another, and that thofe of 
 fcveral Circles do ditier in degree of Refran- 
 gibility, and that in Ibme certain and conltant 
 proportion. W hich is the thing I was to prove. 
 
 There is yet another Circumllance or two 
 of this Experiment by which it becomes flill 
 more plaii aid convincing. Let the fecond 
 Prifm DH [in Fi^. 16.'] be placed not im- 
 mediately after the firit, but at fome diftance 
 from it 5 fuppofe in the mid- way between it 
 and the Wall on which the oblong Spectrum 
 PTis caft, lb that the Light from the firll 
 Prifm may fall upon it in the form of an oblong 
 Speftrum tt] parallel to this fecond Prifm, and 
 be refraded fideways to form the oblong 
 Speftrum p t upon the Wall. And you will 
 find as before, that this Speftmm/ ^Js. inclined 
 to that Spectrum P T, which the firit Prifm 
 forms alone without the fecond ; the blue ends 
 P and p being farther diltant from one another 
 than the red ones T and t^ and by confequence 
 
 D 2, that 
 
[ 3^ 1 
 
 that the Rays which go to the blue eftd tt of 
 the Imager? and which therefore futfer the 
 greateil Refra^ion in the firftPrifm, are again 
 in the fecond 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 lit- 
 tle round holes F and (p [in Fig. 17.] made in 
 the Window , and with two parallel Prifms 
 ABC and ctf^y placed at thofe holes (one at 
 each) refracting thole two beams of Light to 
 the oppofite Wall of the Chamber, in fuch man- 
 ner that the two colour'd Images PT 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 firft, refrafted fideways, and the Spedrums 
 thereby tranflated to fome other part of the 
 Wall of the Chamber, fuppofe the Spedrum 
 PT to/^ and the Spedrum MN to »?;?, thefe 
 tranflated Spedrums/^ and m n would not lie 
 in one ftraight Line with their ends contiguous 
 as before, but be broken off from one another 
 and become parallel, the blue end m of the L 
 mage m n being by a greater Refradion tran- 
 flated farther from its former place M T, than 
 the red end t of the other Image / 1 from the 
 fame place MT; which puts the Propoiition 
 paft difpute. And this happens whether the 
 third Prifm DH be placed immediately after 
 the two firft, or at a great diftance fro^n 
 them, fo that the Light refraded in the two 
 
 fiiit 
 
[37] 
 
 firil Prifms be either white and circular, or co- 
 loured and oblong when it falls on the third. 
 
 Expcr. 6. In the middle of two thin Boards 
 I made round holes a third part of an Inch in 
 diameter, and in the Window-lliur 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 refradt it towards the oppoiite Wall, and 
 clofe behind the Prifm I fixed one of the Boards, 
 in fuch manner that the middle of the refrafted 
 Light might pafs through the hole made in it, 
 and the relt be intercepted by the Board. Then 
 at the diftance of about twelve Feet from the 
 tirll; Board I fixed the other Board in fuch man- 
 ner that the middle of the refra6led Light which 
 came through the hole in the hrll Board and 
 fell upon the oppofiteW'all might pafs through 
 the hole in this other Board, and the rell being 
 intercepted by the Board might paint upon it 
 the coloured Spedrum of the Sun. And ciofe 
 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 ail its parts might fucceifively 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 Refraction in the fecond Prifm did pafs ; 
 aftd by the difference of the places I found that 
 the Light which being mofl refraded in the 
 
 D 3 tirft 
 
[ 38 ]i 
 
 firflPrifm didgo to the blue end of the Image, 
 was again more refracted in the fecond Prifm 
 than the Light which went to the red end of 
 that Image, which proves as well the tirlt Pro- 
 portion as the fecond. And this happened 
 whether the Axis of the two Prilms were pa- 
 rallel, or inclined to one another and to the 
 Horizon in any given Angles. 
 
 llluftratton. Let F [inF/^. i8.] be the wide 
 hole in the Window-fliut, through which the 
 Sun fhines upon the firft 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 
 de and there paint fuch an oblong coloured I- 
 mage of the Sun as was defcribed in the third 
 Experiment. By turning the Prifrn 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 w^hich is made in the mid- 
 dle of that Board. In the mean while another 
 Prifm aifcis to be fixed next after that hole g 
 to refraft the trajefted Light a fecond time. 
 And thefe things being thus ordered, I marked 
 the places M and N of the oppofite Wall upon 
 which the refradted 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- 
 tually. For when the lower part of the Light 
 
 which 
 
[39] 
 
 which fell upon the fecond Board d e was caft 
 through the hole g it went to a lower place M 
 on the Wailj and when the higher part of that 
 Light was cad through the fame hole g; it went 
 to a higher place N on the Wall, and when ^- 
 ny intermediate part of the Light was catt 
 through that hole it went to fome place' on thb 
 Wall between M andN. ■ The unchanged Po- 
 fition of the Holes in the Boards, made the In- 
 <:idence of the Rays upon-tlie fecond Prifm to 
 be the fame in all caies. And yet in that corat- 
 mon hicidence fome of the Rays were more re- 
 fraded and others lefs.. And thole were more 
 refrat^ed in this Prifm wiiich by a greater Re- 
 fradion in the firll Prifm were more turned 
 out of the way, and therefore for their con- 
 ftancy of being more retracted are- defervedly 
 called more refrangible. 
 
 Expcr. 7. At two holes made near one ano- 
 ther in my Window-flnit I placed two Prifms, 
 one at each, A^^hich might cait upon the 'opp.o- 
 fiteWall (after the manner of the thirdExpe- 
 criment) two oblong cdlour-ed Images' "oF the 
 "Sun. And at a little diitance from the Wall I 
 placed a long llender Paper with llraight and 
 parallel edges, and ordered the Prifms and Pa- 
 per fo, that the red Colour of one Image niight 
 '•fall diredly upon one half of the Paper, and "he 
 violet Colour of the other Image upon the o- 
 ther half of the fame Paper ; lo that the Pa- 
 per appeared of two Colours', red and violet, 
 much after the manner of the painted Paper 
 in the firil and fecond Experiments. Tnen 
 With a black Cloth I covered the Wall behind 
 
 D 4 the 
 
[4o] 
 
 the Paper, that no Light might be refle(fi:ed 
 from it to diflurb the Experiment , and viewr 
 ing the Paper through a third Prifm held- pa- 
 rallel to it, I faw that half of it which was il- 
 luminated by the violet Light to be divided 
 from the other half by a greater Refradiori, Cr 
 fpecially when I went a good way gff 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 Hke the painted 
 Paper in the firlt Experiment, Which alfo 
 happened when the Paper was too broad. 
 
 Sometimes inflead of the Paper I ufed a white 
 Thred, and this appeared through the Prifm 
 divided into two parallel Threds as is reprer 
 fented in the nineteenth Figure, where DG 
 denotes the Thred illuminated with violet Light 
 from D to E and with red Light from F to G, 
 and de fg are the parts of the Thred fcen by 
 Rcfradion. If one half of the Thred be con- 
 ftantly illuminated with red, and the other half 
 be illuminated with all the Colours fuccefTively, 
 ( which may be done by caufing pne of the 
 Prifms to be turned about its Axis whilll the 
 other remains unmoved) this other half in view- 
 ing the Thred through the Prifm, will appear 
 in a continued right Line with the firil 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 Hill farther when with green, 
 and farther when with blue, and go yet farther 
 pff when illuminated with indigo, and fartheft 
 
 W^hcn 
 
[4i] 
 
 when with deep violet. Which plainly iliewsV 
 that the Lights of feveral Colours are more ani 
 more refrangibkjong than (ai)pther, in this or- 
 der of theii^ Colours, red, ordfvge5,yellouVgj;pen,- 
 blue, indigo, deep violet ; ai)4;fo proves; ^^Wj^il' 
 the tirllPropolition as the;fecy>ud^ ..: ..::,,. ij^:^ 
 I G.aufed aUp tl}Q colouj-ed,. Spcclrur^s :: Pol/ 
 [in Fig. 17.'} and MN ma4^ in,a-dark Cham- 
 ber by the Rpfradions of two j^riirhiSfto lye in 
 a right Line end to end, as wasdefcril>e4-abpve 
 in- the fifth. Experiment, iind viewing: them 
 thrpugh a thir^.Prifm held parallel to theic 
 ls^>gthj they appeared no longer in a right Line, 
 })ut became broken from one another, as they 
 ^re; reprefentcjd af.//^ aijd //;.;/, the violet Qndpt 
 pf the Spe6lrum m n being by a greater Refra- 
 jftion tranllated farther from its former place 
 M T than the red end t of the otfier Spcii^trum 
 
 pi' ./rJ7^'J - 
 
 -, I farther caufcd thofe two'Spedrums PT 
 £in Ftg. 20.] and MN to become co-incident 
 in an inverted order of their Colours, the red 
 end of each falling on the violet end of the o- 
 ther, as they are reprefented in the oblong Fi- 
 gure P T M N ; and then viewing them through 
 a Prifm DH held parallel to their length, they 
 appeared not co-incident as when viewed with 
 the naked Eye, but in the form of two dillinc^l 
 Spedrums / t and m ;/ croffing one another in 
 the middle after the manner of the letter X. 
 Which iliews 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 Refi'adion of thq violet to/ and m 
 
 than 
 
f 42 ] 
 
 thai! of the red' to;;/'and^,-(ioi differ in degrees 
 of Refrangibility. •-'-- .■'>-; • - -1 
 
 i illuminated alfo a little circular piece? of 
 white Paper all over With the Lights of both 
 Prifms intermixed r^nd when it was illumina- 
 ted with the red' of one Spe(?Lrum and ddep 
 violet of the other, fo as by the mixture^of 
 thofe Colours to appear all over purple, I view-l- 
 ed the Paper, firil at a lefs diltoce,- and-theh 
 at a greater, through a third Vviihi ; ^and-^as I 
 went from the Paper, the refraijled Image t-here- 
 of became more anel-more divided by the uMi 
 qual Refraction of: the two Mxe"d> Colours, afld 
 at length parted into two diftincl'Ithages, ii tdA 
 one and a violet one, whereof the violet" Was 
 farthefl from the Paper, arid therefore,; fufFered 
 the greateflRefradion. And when that Prifm 
 at the Window wliich caft the violet on theP^- 
 per was taken away, the violet Image difap- 
 peared; but when the other Prifm was taken 
 away the red vaniflied : which lliews that thefe 
 two Images were nothing elfe than the Lights 
 df 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 viewed. 
 This alfo was obfervable , that if one of the 
 Prifms at theWindbw, 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 fucceffively on the Paper from that Prifm , 
 the violet Image changed Colour accordingly; 
 turning fucceffively 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 alibred both 
 Images became fullv co-incident. 
 
 I placed alio two Paper Circles very near 6ne 
 another, the one in the red Liglit of onePriiirtj 
 and the other in the violet Light of the othcr^. 
 The Circles were each of them an Inch in dia- 
 meter, and behind them the Wall was dark that 
 the Experiment might not be dillurbed by any 
 Light coming from thence. Thefe Circles thus 
 illuminated, I viewed through a Prifm fo heM 
 that the Refradlion might be made towards the 
 red Circle, and as I went from them they camt 
 nearer and nearer together , and' at- length be- 
 came co-incident; and afterwards when I went 
 Hill farther ofti they parted again in a cojitrary 
 order, the violet by a greater Refradion being 
 carried beyong the red. -i>i-« 
 
 Exper. 8. In Summer when the Sun's Light 
 ufes to be ftrongell, I placed a Prifm at the 
 hole of the Wind ow-lhut, as in the third Expe- 
 riment, yet lb that its Axis might be parallel to 
 the Axis of the World, and at the oppofite 
 Wall in the Sun's refracted 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 reflefted 
 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 Iheet of white Pa- 
 per much after the manner of the fecond Ex- 
 periment. The Book and Lens being made fall, 
 
 I no- 
 
[44] 
 
 I noted the place where the Paper was, when 
 thie Letters of the Book ,, illuminated by the 
 fullell red Light of the folar hnage falling up- 
 on it, did call their Species on that Paper molt 
 diftindly : And then I ftay'd til] 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 call their Species moll dillindly 
 upon it : And I found that this lalt place of the 
 i?aper was nearer to the Lens than its former 
 place by about two Inches and an half, or two 
 and three quarters. So much fooner therefore 
 did the Light in the violet end of the Image 
 by a greater Refradion converge and meet, 
 than the Light in the red end. But in trying 
 this the Chamber was as dark as I could make 
 it. For if thefe Colours, be diluted and weak- 
 tied by the mixture of any adventitious Light, 
 the diftance between the places of the Paper 
 will not be fo great. This diltance 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 imperfedion of thofe 
 Colours. Here in the Colours of the Prifm , 
 which are manifeftly more full, intenfe, and live- 
 ly than thofe of natural Bodies, the dillance is 
 two Inches and three quarters. And were the 
 Colours flill more full, I queftion not but that 
 the dillance would be confiderably greater. For 
 the coloured Light of the Prifm, by the inter- 
 fering of the Circles defcribed in the fecond 
 
 Figure 
 
45 ] 
 
 Figure of the fifth Experiment, and alfobythe 
 Light of the ^'ery bright Clouds next the Sun's 
 Body intermixing with thefe Colours, and by 
 the Light fcattered by the inequalities in the 
 Polifh of the Prifm , was fo very much com- 
 pounded, that the Species which thofe faint and 
 dark Colours, the indigo and violet, cait upon 
 the Paper were not diltinCt enough to be well 
 obferved. 
 
 Exper. 9. A Prifm, whofe two Angles at its 
 Bale were equal to one another and half, right 
 ones, and the third 2 right one, I placed in a 
 beam of the Sun's Light let into a dark Cham- 
 ber through a hole in the W'indow-ihut as in 
 the third Experiment. And turning the Prifm 
 flovvly about its Axis until all the Light which 
 went through one of its Angles and was refra- 
 fted by it began to be reflected by its Bafe, at 
 which till then it v\x>nt out of the Glafs, I ob- 
 ferved that thofe Rays which had fuffered the 
 greatell Refraction were fooner rcflecfted than 
 the reft. I conceived therefore that thofe Rays 
 of the reflecfcd Light, which were molt re- 
 frangible ^ did tirlt of all by a total Reflexion 
 become more copious in that Light than the 
 reft, and that afterwards the reft alio, by a to- 
 tal Reflexion, became as copious as thefe. To 
 try this, I made the reflected Light pais through 
 another Prifm, and being refracted by it to fall 
 afterwards upon a ilieet of white Paper placed 
 at fome diltance behind it , and there by that* 
 Refradion to paint the ufual Colours of the 
 Prifm. And then caufmg the firlt Prifm to be 
 turned about its Axis as above, I obferved that 
 
 ' wiien 
 
[40 
 
 when thofe Rays which in thisPrifm had fuf^ 
 fered the greatellRefradionand appeared of at 
 a blue and violet Colour began to be totally re-* 
 flecled, the blue and violet Light on the Papei? 
 which was moll refrafted in the fecond Prifm 
 received a fenfible increafe above that of the 
 red and yellow, which was lead refrafted ; and 
 afterwards when the rell of the Light which 
 was green, yellow and red began to be totally 
 refleded in the firfl 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 manifefl, that the beam of Light 
 refleded by the Bafe of the Prifm, being aug- 
 mented hrll bv the more refrangible Rays and 
 afterwards by the lefs refrangible ones, is com- 
 pounded of Rays diflerently refrangible. And 
 that all fuch refleded Light is of the fame na- 
 ture with the Sun's Light before its Incidence 
 on the Bale of the Prifm, no Man ever doubt- 
 ed : it being generally allowed , that Light by 
 fuch Reflexions fullers no alteration in its Mo- 
 difications and Properties. I do not here take 
 notice of any Refradions made in the fides of 
 the firll Prifm, becaufe the Light enters it per- 
 pendicularly at the firit fide, and goes out per- 
 pendicularly at the fecond fide, and therefore 
 iufFers none. So then, the Sun's incident Light 
 being of the fame Temper and Conflitution 
 with his emergent Light, and the latf being 
 compounded of Rays differently refrangible, the 
 firlt muft be in Uke manner compounded. 
 
 lllnjtrat'ion. In the twenty firll Figure, ABC 
 is the firfl Prifm, BC its Bafe, B and C its 
 
 equal 
 
[47] 
 
 equal Angles' at . the , Bafe, each . of 45- Degrees, 
 A its rettanguliir Vertex, F M a beam of the 
 Sun's Light let into a dark Room through a 
 hole F one third part of an hich broad, M its 
 Incidence on the Bale of the Prifm, M G a lefs 
 refraded Ray, M H a more rejraded Ray, MN 
 the beam of Light reflected ; from the Bafe, 
 VX Y the fecond Prifm by which this beam in 
 palling through it is refracted, N^ the lels re- 
 fraded Light of this beam, and N/ the more 
 refra(^l:ed part thereof VV hen the firll Prifm 
 ABC is turned about its Axis according to the 
 order of the Letters ABC, the Rays MH e- 
 mcrge more and more obUquely out of that 
 Prifm , and at length after their mofi: oblique 
 Emergence are reileded towards N, and going 
 on to / do increafe the number of the Rays 
 N/. Afterwards bv continuing the Morion of 
 the firfc Priim, the Rays M G are aUb refleded 
 to N and increaic the number of tiie Rays Nt. 
 And therefore the Light M N admits into its 
 Compofition , firll the more refrangible Rays, 
 and then the lefs refrangible Ravs, and yet af- 
 ter this Compoiition is of the iame nature with 
 the Sun's immediarte Light F M, the PvcHexion 
 of the fpecular Bafe B C caufmg no alteration 
 therein. 
 
 Efcper. 10. Two Prifms, which were alike 
 in fliape, I tied lo together, that then* Axes and 
 oppoiite bides being parallel, they compofed a 
 Parallelopiped. And, the Sun ihining into my 
 dark Chamber through a little hole in the Win- 
 dow-ftiut, I placed that Parallelopiped in his 
 beam at ibme dillance from the hole, in fuch a 
 - poiture 
 
[ 48 ] 
 
 poflure that the Axes of the Prifnis might Be 
 perpendicular to the incident Rays, and that 
 thole Rays being incident upon the lirlt Side 
 of one Prifm , might go oh through the two 
 contiguous Sides of both Prifms , and emerge 
 out of the laft Side of the fecond Prifm. This 
 Side being parallel to the firfl Side of the firfl 
 Prifm, caufed the emerging Light to be paral- 
 lel to the incident. Then, beyond thefe two 
 Prifms I placed a third, which might refraft 
 that emergent Light , and by that Refradlion 
 call the ulual Colours of the Prifm upon the 
 oppofite Wall, or upon a Iheet of white Papel^ 
 held at a convenient dillance behind the Prifm- 
 for that refrafted Light to fall upon it. After 
 this I turned the Parallelopiped about its Axis, 
 and found that when the contiguous Sides of 
 the two Prifms became fo oblique to the inci- 
 dent Rays that thofe Rays began all of therh to 
 be reflected, thofe Rays which in the third 
 Prifm had fuffered the greatefl Refradion and 
 painted the Paper with violet and blue, were 
 iirft of all by a total Reflexion taken out of the 
 tranfmitted Light, the rell remaining and on 
 the Paper painting their Colours of green, yel- 
 lowy orange, and red as before ; and afterwards 
 by continuing the Motion of the two Prifms, 
 the reft of the Rays alfo by a total Reflexion 
 vanifhed in order, according to their degrees 
 of Refrangibility. The Light therefore which 
 emerged out of the tw^o Prifms is compound- 
 ed of Rays diflerently refrangible, feeing the 
 more refrangible Rays may be taken out of it 
 while the lefs refrangible remain. But this 
 
 Light 
 
[49] 
 
 Light being trajefted only through the parallel 
 SuperHcies of the two Prifms, if it fuftcr'd any 
 change by the Refradion of one Superficies it 
 loll: that imprcllion by the contrary Refradion 
 of the other Superhcies, and lb being rcllored 
 to its prifline Conllitution became of the lame 
 nature and condition as at firil: before its hici- 
 dence on thofe Prifms ; and therefore, before 
 its Incidence, was as much compounded of 
 Rays differently refrangible, as afterwards. 
 
 IlliLJiration. In the twenty fecond Figure 
 ABC and BCD are the two Prifms tied toge- 
 ther in the form of a Parallelopiped, their Sides 
 B C and C B being contiguous, and their Sides 
 AB and CD parallel. And HJK is the third 
 Prifm, by which the Sun's Light propagated 
 through the hole F mto the dark Chamber, and 
 there paffing through thofe iidcs of the Prifms 
 AB, BC, CB and CD, is refraded at O tc> 
 the white P^^perPT, falling there partly upon 
 P by a greater Refradion, partly upon T by t 
 lefs Refradion, and partly upon Rand other in- 
 termediate places by intermediate Refradions. 
 By turning the Parallelopiped AC B D about its 
 Axis, according to the order of the Letters Aj 
 C, D, B, at length when the contiguous Planes 
 B C iind C B become fufficiently oblique to' the 
 RaysFM, which are incident upon them atM,- 
 there will vaniih totally out of the refraded 
 Light OPT, tirftofiill the moll refraded Rays 
 OP, (the reft OR and OT remaining as be- 
 fore) then the Rays O R and other intermedi- 
 ate ones, and laftly, theleaft refraded RaysOT- 
 For wh€Fi the Plane B C becomes futhcienrly 
 
 E oblique 
 
- [ 50 ] 
 
 oblique to the Rays incident upon it , tliole 
 Rays will begin' to be totally refiecled by it to- 
 wards N; and firll the moll refrangible Rays 
 wiTi be totally reflc(^kd (as was explained in 
 the preceding Experiment) and by confcquencc 
 mult lirfl dilappear at P, and afterwards the 
 reil as they are in order totally, rctieded to N, 
 they mull dilappear in the i'ame order at R 
 and T. So then the Rays which at O fuf- 
 fer the greateft Refrac4ion, may be taken out 
 of the Light M O whillt the reil of the Rays 
 remain in it, and therefore that Light MO 
 is. compounded of Rays diflerently refrangi- 
 ble. And becaufe the Planes A Pj and CD 
 are paiialiel, and therefore by equal and con- 
 trary Refradions dcUroy one anothers Ef- 
 fQtis, the incident Light FM mutl be of the 
 fame kind and nature with the emergent Light 
 MO, and therefore doth alfo conlid of Rays 
 differently refrangible. Thefe two Lights F M 
 and jM O, before the moil refrangible Rays arc 
 feparated out of the emergent Light MO, a- 
 gree in colour , and in all other properties fo 
 far as my oblervation reaches, and therefore 
 are defervcdly reputed of the famx nature and 
 confutution, and by confequence the one is 
 compounded as well as the other. But after 
 the moil refrangible Rays begin to be totally 
 rcileded, and thereby feparated out of the e- 
 mergent Light MO, that Light changes its co- 
 lour from white to a dilute and faint yellow, 
 a pretty good orange , a very full red iuccef- 
 iivcly and then totally vanifhes. For after the 
 moft refrangible Rays which paint the Paper at 
 
 " ■ P with 
 
[?l] 
 
 P with a purple Colour, arc by a total Refle- 
 xion taken out of the beam of Light M O, the 
 refl; of the Colours which appear on the Paper 
 at R and T being mixed in the Light MO 
 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, therelfc 
 which appear between R and T (that is the yel- 
 low, orange, red and a little green) being mix- 
 ed in the beam MO compound there an orange ; 
 and when all the Rays are by Reilexion takert 
 out of the beam MO, except the leait refran- 
 gible, which at T appear of a full red, their 
 Colour is the farrie in that beam M O as after- 
 wards at 1\ the Refradion of the Prifm H J K 
 ferving only to feparate the differently refran- 
 gible Rays, without making any alteration iri 
 their Colours, as ihall be more fully proved 
 hereafter. All which confirms as well the tiril 
 Proportion as the fecond. 
 
 Scljolinm. If this Experiment and the former 
 be conjoined and made one by applying a fourth 
 Prifm VX Y [in Fig. xx.] torefradthe refleft-^ 
 ed beam MN towards r/, the conciufion will 
 be clearer. For then the Light N/ which in 
 the fourth Prifm is more refracted, will become 
 fuller and flronger when the Light O P, which 
 in the third Prifm HJ K is more refracled, va- 
 nilhes at P ; and afterwards wiien the lefs re- 
 fracted Light OT vanifiies at T, the lefs re- 
 fracted Light N t will become ericreafed whiKl 
 the more refraded Light at p receives no far- 
 ther encreafe; And as the trajeded beam MO 
 in vanifhing is always of fuch a Colour as oiight 
 
 E 2; te^ 
 
t52l 
 
 to refult from the mixture of the Colours which 
 fall upon the Paper PT, fo is the reflc(^kd 
 beam M N always of fuch a Colour as ought to 
 refult from the mixture of the Colours which 
 fall upon the Paper p t. For when the moil 
 refrangible Rays are by a total Reflexion taken 
 out ot the beam M O, and leave that beam of 
 an orange Colour, the Excels of thole Rays in 
 the refie(^kd Light, does not only make the 
 violet, indigo and blue at / more full, but alfo 
 makes the beam MN change from the yellow- 
 ilh Colour of the Sun's Light, to a pale white 
 inclining to blue, and afterward recover its 
 yellovvifli Colour again, fo foon as all the reft 
 of the tranimitted Light MOT is refleded. 
 
 Now feeing that in all this variety of Expe- 
 riments, whether the Trial be made in Light 
 refleded, and that either from natural Bodies, 
 as in the firll and fecond Experiment, or fpe- 
 cular, as in the ninth ; or in Light refrained, 
 and that either before the unequally refradcd 
 Rays are by diverging feparated frome one an- 
 other, and lofmg their whitenefs which they 
 have altogether, appear feverally of feveral Co-^ 
 lours, as in the tifth Experiment ; or after they 
 are leparaied from one another, and appear co- 
 lour'd as in the iixth, fcventh, and eighth Ex- 
 periments ; or in Light trajeded through paral- 
 lel buperticics, deltroying each others Etfec^ls, 
 as in the tenth Experiment; there are always 
 found Ravs, which at equal Incidences on the 
 fame Alcdium luiier unequal Reflations, and 
 that without any iplitting or dilating of fingle 
 Raysj or contingence in the inequality of the 
 
 Reira- 
 
[53] 
 
 Refraflions, as is proved in the fifth and fixth 
 Experiments*. And feeing the Rays which dif- 
 fer in Refrangibility may be parted and farted 
 from one another, and that either -by Refra- 
 dion as in the third Experiment, or by Re- 
 flexion as in the tenth , and then the fevcral 
 forts apart at equal Incidences fu'der unequal 
 Refractions, and thofe forts are more refra^rted 
 than others after fcparation, which were more 
 refraded before it, as in the fixth and follow- 
 ing Experiments, and if the Sun's Light be tra- 
 jected through three or more crofs Prifms fuc- 
 cellively, thole Rays which in the tirdPrifm 
 are refrafled more than others, are in all the 
 following Prifms refracted more than others in 
 the fame rate and proportion, as appears by 
 the fifth Experiment ; it's manifcil that the 
 Sun's Light is an heterogeneous mixture of 
 Rays, fome of which are conltantly more re- 
 frangible than others, as was propoled. 
 
 TROT, in. The OR. III. 
 
 The Suns Light conjifts of Rays differing in Re- 
 flexibility^ and thofe Rays are more refiexible 
 than others which are more refrangible. 
 
 THIS is manifeft by the ninth and tentl^ 
 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 refrafled by. its Bafe, became fo 
 oblique to that Bafe, as to begin to be totally 
 
 E a refledeci 
 
[54] 
 
 reflefled thereby ; thofe Rays became -firfl of 
 all totally reflected, wnich before at equal In- 
 cidences with the reft had fuftered the greatell 
 Refradlion. And the fame thing happens in the 
 Reflexion made by the common Bafe of the 
 two Prifms in the tenth Experiment. 
 
 TROT. IV. Prob. I. 
 
 To feparate from one another the heterogeneous 
 Rays of compound Light. 
 
 Tf^H E heterogeneous Rays are in fome mea- 
 \^ fure feparated from one another by the 
 Refraftion of the Prifm in the third Experi- 
 ment, and in the fifth Expcrinient by taking a- 
 v/ay the Penumbra from the redilinear fides of 
 the coloured Image, that feparation in thofe ve- 
 ry redilinear lides- or ftraight -edges of the Ir 
 mage becomes perfec^l. But in all places be- 
 tween thofe rectilinear edges, thofe innumera- 
 ble Circles there defcribed, which are fcveral- 
 ly illuminated by homogeneal Rays, by interfe- 
 ring vvith one another, and being every where 
 comimix'd, do render the Light fufhciently 
 compound. But if thefe Circles , whilli: their 
 centers keep their diftances and pofitions, could 
 be made kfs in diameter, their interfering one 
 "with another and by confequence the mixture 
 of the heterogeneous Rays would be propor- 
 tionally diminifiied. In the tv/enty third Figure 
 let AG, BH, CJ,.DK, EL, FM be the Cir- 
 cles which iQ many forts of Rays flowing from 
 
 the 
 
[ 55 ] 
 
 the fame difqiic of the Sun, do in the third 
 Experiment illuminate ; of all which and in- 
 numerable other intermediate ones lying in a 
 continual Scries between the two rectilinear 
 and parallel edges of the Sun's oblong Image 
 P T, that Image is compofed as was explained 
 in the fifth Experiment. And let ag^ S/j, ci, 
 dk^ el, fm be fo many lefs Circles lying in a 
 like continual Series between two parallel right 
 Lines af'\wd\.gm with the fame diilances be- 
 tween their centers, and illuminated by the 
 iame forts of Rays, that is the Circle ag with 
 the fame fort by which the corrcfponding Cir- 
 cle AG was illuminated, .and the Circle bb 
 with the fame fort by which the corrcfponding 
 Circle BEI w^as illuminated, and the rell: of the 
 Circles f /*, dk, el, fni refpeCtivcly, with the 
 fame forts of Rays by which the fever al corrc- 
 fponding Circles Cj,"DK, EL, FM were il- 
 luminated. In the Figure P T compofed of the 
 greater Chxles, three of thofe Circles AG, BH, 
 C J, are fo expanded into one another, that the 
 three forts of Rays by which thofe Circles are 
 illuminated , together with other innumerable 
 forts of intermediate Rays, are mixed at QR 
 in the middle of the Circle B H. And the like 
 mixture happens throughout almod the whole 
 length of the Figure P T. But in the Figure 
 pt compofed of the lefs Circles, the three lefs 
 Circles ag, b h, c i, which anfwer to thofe three 
 greater, do not extend into one another; nor 
 are there any where mingled fo m.uch as any 
 two of the three forts of Rays by which thofe 
 
 E 4 Circles 
 
[50 
 
 Circles are illuminated , and which in the Fi- 
 gure PT are all of them intermingled at B H. 
 
 Now he that fhall thus confider it, will eafily 
 underltand that the mixture is diminiilicd in 
 the fame proportion with the Diameters of the 
 Circles. If the Diameters of the Circles whilft 
 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 PT will be to their mixture iri 
 the lefs / ^, 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 lience it caiily 
 follows, that the mixture of the Rays in the re- 
 frafted Speftrum / r is to the mixture of the 
 Rays in the direft and immediate Ligtit of the 
 Sun, as the breadth of that Speclrum is to the 
 diflerence between the length and breadth of 
 the fame Spectrum. 
 
 So then , if we would diminifh the mixture 
 of the Rays , we are to diminiih 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 diilance 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 pals through 
 
 that 
 
[ 57 ] 
 
 t\nt hole to the Prifm. For fo the Circles AG, 
 BH and the reU, would not any longer anl'wcr 
 to the whofe Dilque of the Sun, but only to 
 that part of it which could be Jeen from the 
 Prilm through that hole , that is to the appa- 
 rent magnitude of that hole viewed from the 
 Prifm. But that thefe Circles may anfwer more 
 diftindly to that hole, a Lens is to be placed by 
 the Prifm to call the Image of the hole, (that 
 is, everyone of the Circles AG, BPI, &c.) di- 
 Itindly upon the Paper at PT, after fuch a 
 manner as by a Lens placed at a W indow the 
 Species of Objeds abroad arc cail diitinCtly up- 
 on a Paper within the Room, and the redili- 
 near Sides of the oblong folar Image in the fifth 
 Experiment became dillind without any Pen- 
 umbra. If this be done it will not be nccefia- 
 ry to place that hole very far off, no not beyond 
 the \V indow. And therefore initead of that 
 hole, I ufed the hole in the Window-ihut as 
 follows. 
 
 Exper, II. In the Sun's Light let into my 
 darkned Chamber through a fmall round hole 
 in my Window- fhut, at about ten or twelve 
 Feet from the Window, I placed a Lens, by 
 which the Image of the hole might be dillinft- 
 ly call upon a Sheet of white Paper, placed at 
 the diflance of fix, eight, ten or twelve Feet 
 from the Lens. For according to the diffe- 
 rence of the Lenfes I ufed various diilances, 
 which I think not worth the v^hile to defcribe. 
 Then immediately after the Lens I placed a 
 Prifm, by which the trajec'led Light might be 
 refraded either upwards or Tideways, and there- 
 by 
 
[58] 
 
 by the round Image which the Lens alone did 
 cafl upon tlie 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 (iam.e didance from 
 the Priim as before, moving the Paper either' 
 towards the Prifm or from it, until I found the 
 juil diflance where the reciilinear Sides of the 
 image became moil diflind. For in this cafe 
 the circular Images of the hole which compofe 
 that Image after the fame manner that the Cir- 
 cles ^?^, bh^ r/', &c. do the Figure/^ \mFig. 
 a-3.] were terminated moil diitinftly without 
 any Penumbra, and therefore extended into 
 one another the lead that they could, and by 
 confcquence the mixture of the heterogeneous 
 Rays was now the Icail of all. By this means 
 I uled to form an oblong Image (luch as is/^) 
 [iniv^. 23, and 24.] of circular Images of the 
 hole (fuch as are ag^ bh^ ci^ &:c.) and by u- 
 iing a greater or lefs hole in the Window-ihut, 
 I made the circular Images ag^ bh^ c i, &c. of 
 which it was formed, to become greater or lefs 
 at pleafure, and thereby the mixture of the 
 Rays in the Iniage / ^ to be as much or as lit- 
 tle as I defired. 
 
 Illnftrat'wn. In the twenty fourth Figure, F 
 reprcicnts the circular hole in the W indow- 
 iliut, MN the Lens whereby the Image or Spe- 
 cies of that hole, is call diitindly upon a Paper 
 at J, ABC the Prifm whereby the Rays are at 
 their emerging out of the Lens refraded from 
 J towards another Paper at / ^, and the round 
 Image at J is turned into an oblong Image / 1 
 
 falling 
 
S9 ] 
 
 Ming on that other Paper. This Image/ /'con- 
 flits of Circles placed one after another in a rc- 
 ,6tilincar order, as was fuiiicienily explained in 
 the fifth Experiment; and thefe Circles are e- 
 qual to the Circle J, and conlcquently anfwer 
 in magnitude to the hole F ;. and therefore by 
 diminiihing that hole they may be at pleafure 
 diminiihed, whilil their Centers remain in their 
 places. By this means I m.ade the breadth of 
 the Image / r 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 MF the diilance of the Lens f -om 
 the hole be ii Feet? and if/B or / Mthe di- 
 ilance of the Image / t from the Prifm or Lens 
 be lo Feet, and the refra6i:ing Angle of the 
 Prifm be 61 Degrees, the breadth of the L 
 mage / / 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 Sun's diredri: Light. And 
 Light thus fir fimple and homogeneal, is fulH- 
 cicnt for trying all the Experiments in this Book 
 •about iimple Light. For the compofition of 
 -heterogeneal Rays is in this Light fo little that 
 it is fcarce to be difcovered and perceived by 
 Senfe, except perhaps in the indigo and. vio- 
 let. For thele being dark Colours, do eafily 
 .fuffer a fenfible allay by that little fcattering 
 Light which ufes to be reft-acf ed irregularly by 
 the inequalities of the Priiin. 
 
 Yet inflead of the circular hole F, 'tis better 
 to fubftitute an oblong hole ihaped like a- lontr 
 
 ParaU 
 
I^o] 
 
 Parallelogram with its length parallel to the 
 Priim 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 /i^ will beas fin^ple as before, or fimpler, 
 and the Image will become much broader, and 
 therefore more fit to have Experiments tried in 
 its Light than before. 
 
 Inilcad of this parallelogram hole may be fub- 
 llituted a triangular one of equal Sides, whofe 
 Bale for inllance is about the tenth part of an 
 Inch, and its height an Inch or more. For by 
 this means, if the Axis of the Prhm be parallel 
 to the Perpendicular of the Triangle, the Image 
 ft [in Fig. zf.] will now be formed of equi- 
 crural Triangles ag^ bh^ cl, dk^ el^ fm, ike, 
 and innumerable other intermediate ones an- 
 fwering to the triangular hole in fliape and big- 
 nefs, and lying one after another in a continual 
 Series between two parallel Lines <?/and ^/^. 
 Thefe Triangles are a little intermingled at their 
 Bafes but not at their Vertices, and therefore 
 the Light on the brighter fide afo^ thelujage 
 where the Bafes of the Triangles are, is a little 
 compounded, but on the darker fide g m is al- 
 together uncompounded, and in all places be- 
 tween the lides ttie Compolition is proportio- 
 nal to the dillances of the places from that ob- 
 fcurer fide g m. And having a Spedrum / 1 
 of inch a Compofition, we may try Experiments 
 either in its Wronger and lels fimple Light near 
 the fide af^ or in its weaker and limpler Light 
 near the other fide gm^ as it ihall ieem molt 
 convenient. 
 
 But 
 
I6i] 
 
 But in making Experiments of this kind the 
 Chamber ought to be made as dark as can be, 
 Jelt any foreign Light mingle it felf with the 
 Light of the bpedrum//', and render it com- 
 pound ; efpecially if we would try Experiments 
 in the more iimple Liht next the fide^^ m of 
 the Spedrum; which being fainter, wifl 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 Priim ought to have a large 
 Angle, fuppofe of 65- or 70 Degrees, and to be 
 well wrought, being made of Glals free from 
 bubbles and veins, with its Sides not a little 
 convex or concave, as ufually happens, but truly 
 plane, and itsPolilh elaborate, as in working 
 Optick-glafles, and not fuch as is ufually wrought 
 with Putty, whereby the edges of the Sand- 
 holes being worn av\ ay, there are left all over 
 the Glafs a numberlefs company of very little 
 convex polite Rifmgs like Waves. The edges 
 alfo of the Prilm and Lens fo far as they may 
 make any irregular Refraction, mull be covered 
 with a black Paper glewed on. And all the 
 Light of the Sun's beam let into the Chamber 
 which is uielel's and unprofitable to the Experi- 
 ment, ought to be intercepted with black Pa- 
 per or other black Obftacles. For otherwife 
 the uJelefs Light being refleded every way in 
 the Chamber, will mix with the oblong Spe- 
 d-rum and help to dillurb it. In trying thefe 
 things fo much diligence is not altogether ne- 
 €€llary, but it will promote the iuccefs of the 
 
 .^ Expe- 
 
[62-] 
 
 Experiments, and by a very fcrupiilous Exa- 
 miner of things deierves to be applied. It's 
 diiiicult to get Glafs Prifms fit for tiiis purpofe, 
 and therefore I iifed fometimes prifmatickVef- 
 fels made with pieces of broken Looking-glaf- 
 feSi and filled with Rain Water. And to in- 
 creafc the Refradion, I fometimes impregnated 
 the W ater Itrongly with Saccharttm Saturnt. 
 
 TROT, V. Theor. IV. 
 
 Homogeneal Light is refrd&ed regularly 'with^ 
 out any ^Dilatation Jplitting or Jhattering of 
 the Rays, and the confufed Vijion of ObjcBs 
 fic7i through refradting Bodies by heterogeneal 
 Light arifes from the different Refrangible 
 lity of fever al forts of Rays. 
 
 THE firil part of this Proportion has been 
 already fufiiciently proved in the fifth 
 Experiment, and will farther appear by theEx-^ 
 periments which follow. 
 
 Expcr. 12. In the middle of a black Paper I 
 made a round hole about a iifth or fixth part of 
 an Inch in diameter. Upon this Paper Icaufed 
 the Spectrum of homogeneal Light defcribed 
 in the formx.er Proportion,, fo to fall, that fome 
 part of the Light might pafs throiigh the hole: 
 of the Paper. This tranfmitted part of the 
 Light I refracted with a Prifm placed behind 
 the Paper, and letting this retraced Light fall 
 perpendicularly upon a Avhite Paper two or 
 three Feet diilant from the Prifm, I found that 
 
 the 
 
[^3] 
 
 the Spcdrum formed oa the Paper by this Light 
 was not oblong, as wlien 'tis made (in the third 
 Experiment) by refracting the Sun's compound 
 Light, but was (fo flir as I could judge by my 
 Kye) perfedly circular, the length being no 
 greater than the breadth. Which ih-ews that 
 this Light is rcfra(^ed regularly without anyDi- 
 laHation of the Rays. 
 
 Exper. 13. In the homogcneal Light I placed a 
 Paper Circle of a quarter oi:^ an Inch in diameter, 
 and in the Sun's unrefracled heterogeneal white 
 Light I placed another Paper Circle of the fame 
 bignefs. And going I'rom the Papers to the 
 diilance of fome Feet, I viewed both Circles 
 through a Priim. 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 diilinctly defined 
 as when 'tis viewed with the naked Eye. 
 Which proves the whole Proportion. 
 
 Exper. 14. In the homogeneal Light I placed 
 Flies and fuch lilce minute Objeds, and view- 
 ing them through a Prifm, I law their parts as 
 diiiintftly defined as if I had viewed them with 
 the naked Eye. The fame Objects placed in 
 the Sun's unrefraClcd heterogeneal Light which 
 was white I viewed alio through a Prifm, and 
 faw them molt confufedly derined, fo that I 
 could not diitinguilh their fmaller parts from 
 one another. I placed alio the Letters of a 
 fmall print one while in the homogeneal Light 
 aod then in the heterogeneal, and viewing them 
 
 tiirough 
 
[ ^4 ] 
 
 through a Prifm, they appeared m the latter 
 cafe lb confufed and indiltind that I could not 
 read them ; but in the former they appeared fo 
 diilinft that I could read readily, and thought 
 I faw them as diflindl as when I viewed them 
 with my naked Eye. In both cafes I viewed 
 the fame Objeds through the fame Prifm at the 
 fame dillance from me and in the fame fitfta- 
 tion. There vi^as no difterence but in the Light 
 by which the Objed:s were illuminated, and 
 which in one cafe was fimplc and in the other 
 compound, and therefore the diltinft VifiOn iit 
 the former cafe and confufed in the latter could 
 arife from nothing elfe than from that ditference 
 of the Lights. Which proves the whole Pro- 
 pofition. 
 
 And in thcfe three Experiments it is farther 
 very remarkable , that the Colour of homoge- 
 neal Light was never changed by the Refra- 
 ction. 
 
 0lh^^r^r^.^^^.^^^^^^^^ ^ * r«j ^. A #. ^ ^ ^. 
 
 T RO'P. VI. Theor. v. 
 
 The sine of Incidence of every Ray conftdered a-^ 
 farty is to its Sine of Re f ration in a givett 
 Ratio. 
 
 TH AT every Ray confidered apart is con- 
 llant to it felf in fome degree of Refran- 
 gibility, is fufficiently manifefl out of what has 
 been laid. Thofe Rays which in the firit Re- 
 fraftion are at equal Incidences moll refracted, 
 are alfoun the following Refradions at equal 
 
 Inci- 
 
[^5] 
 
 Incidences mofl refrafted ; and fo of the leaft 
 refrangible, and the reit which have any mean 
 degree of Refrangibilit}', as is manifeft by the 
 fifth, fixth, feventh, and eighth, and ninth Ex- 
 periments. And thofe which the fird time at 
 like Incidences are equally refracfed, are again 
 at like Incidences equally and uniformly refra- 
 i^ted, and that whether they be refraded 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 Refradlion there- 
 fore of every Ray apart is regular, and what 
 Rule that Refraction obierves we are now to 
 Ihew. 
 
 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 Inftruments tit- 
 ted for mealuring of Refrac^lions, ot* othervvife 
 experimentally examining this Proportion , do 
 acquaint lis that they have found it accurate. 
 But whilfl they , not underflanding the diffe- 
 rent Refrangibilitv of feveral Rays , conceived 
 them all to be refi-aftcd according to one and 
 the fame Proportion, 'tis to be preJuvned 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 
 rell appear green, are refrafted according to a 
 given Proportion of their Sines. And there- 
 fore we are now to fliew that the like given 
 
 F Pro- 
 
{66 1 
 
 Proportions obtain. in all the refl. That it 
 iliould be fo is very realbnable , Nature being 
 ever conformable to her felf : but an experi- 
 mental Proof is delired. 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 Refradion of all the Rays are in .given 
 Proportions to the Sine of Refra(ition of it Ray 
 which has a mean degree of Refrangibility, and 
 this Sine is in a given Proportion to the equal 
 Sines of hicidence, 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- 
 ction are in a given Proportion to one ano- 
 ther. 
 
 Exper. 15-. The Sun iliining into a dark 
 Chamber through a little round hole in the 
 Window-fhut, let S [in Fig. i6.] reprefent his 
 round white Image painted on the oppofite 
 Wall by his direft Light, PT his oblong co- 
 loured Image made by refrading that Light 
 with a Prifm placed at the Window; and / ty 
 or x/ z /, or 3/* 3 ^5 his oblong colour'd Image 
 made by refrading again the fame Light fide- 
 ways with a fecond Prifm placed immediately 
 after the firlf in a crofs pofition to it, as was 
 explained in the fifth Experiment : that is to 
 fay , p t when the Refradion of the fecond 
 Prifm is fmall , -Lp i.t when its Refradion is 
 greater , and 3/ 3 i^ when it is greatelt. For 
 
 i fiich 
 
[^7] 
 
 luch will be the diverfiry of the Refradions if 
 the refrading x\ngle of the fecond Prit'm be of 
 various magnitudes ; fuppoie of fifteen or twen- 
 ty Degrees to make the Image / 1, of thirty or 
 forty to make the hiiagc i.p it^ and of fixty to* 
 make the Image 3/ 3 1. But for want of folid 
 Glafs Prifms with Angles of convenient big- 
 nelies, there may be \ cilels made of poliihed 
 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 PT, /r, %p 
 ^ ^ 3 / 3 ^ did very nearly converge to the 
 place S on which the direcl: Light of the Sun 
 fell and painted his white round Image when 
 the Prifms were taken away. The Axis of the 
 SpcdrumPT, that is the Line drawn through 
 the middle of it parallel to its redilinearSidcsy 
 did when produced pafs exactly through the 
 middle of that white round Image S. And when 
 the Refradion of the fecond Prifm was equal 
 to the Refradion of the firit, the refrading An- 
 gles of them both being about 60 Degrees, the 
 Axis of the Spedrum 3 J^ i t made by that Re- 
 fradion, did when produced pafs alfo through 
 the mididle of the fame white round Image S. 
 But when the Refradion of the fecond Prifm 
 was lefs than that of the firit, the produced 
 Axes of the Spedrums r/ or x? x/ made by 
 that Refradion did cut the produced Axis of 
 the Spedrum TP 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 Httle greater than 
 
 F 2, the 
 
[«8] 
 
 the Proportion of x^T to x/P, and this Pro^ 
 portion a Httle greater than that of / T to / P. 
 Now when the Light of theSpeftrum PT falls 
 perpendicularly upon the Wall , thofe Lines 
 3 ^T, 3 / P, and x 2^ T, x/P and tT, j?F, are 
 the Tangents of the Refradions, and therefore 
 by this Experiment the Proportions of the Tan- 
 gents of the Refractions are obtained, from 
 whence the Proportions of the Sines being de- 
 rived, they come out equal, To far as by view- 
 ing the Spedrums and ufmg fome mathemati- 
 cal Reafoning I could eltimate. For I did not 
 make an accurate Computation. So then the 
 Propolition holds true in every Ray apart , fo 
 far as appears by Experiment. And that it is 
 accurately true, may be demonftrated upon this 
 Suppofition , T/^t Bodies refra6i Light by adt- 
 ing upon its Rays in Lines perpendicular to 
 their Surfaces. But in order to this Demon-^ 
 Ib'ation, .1 muil diftinguifli the Motion of every 
 Ray into two Motions , the one perpendicular 
 to the refrafting 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 byoad and 
 thin fpace terminated on both fides by two pa- 
 rallel Planes, and in its paiTage through that 
 fpace be urged perpendicularly towards the far- 
 ther Plane by any force which at given diflances 
 from the Plane is of given quantities; the per- 
 pendicular velocity of that Motion or Thing, 
 at its emerging out of that fpace, fliall be al- 
 ways equal to the fquare Root of the fum of 
 
 the 
 
[^9] 
 
 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 v\'as infinitely little. 
 
 And the fame Propofition holds true of any 
 Motion or Thing perpendicularly retarded in 
 its pafliige through that fpace, if inilead of the 
 fum of the two Squares you take their diffe- 
 rence. The demonllration ^vlathematicians will 
 eafily find out, and therefore I iliall not trouble 
 the Reader with it. 
 
 Suppofe now that a Ray cominj:; mofl oblique- 
 ly in the Line MC \\nFig. i.] be refraded at 
 C by the Plane RS into the Line CN, and if it 
 be required to find the Line C E into which 
 any other Ray A C fhall be refraded ; let MC, 
 AD, be the Sines of Incidence of the two Rays, 
 and NG, EF, their Sines of Refra6lion, and 
 let the equal Motions of the incident Rays be 
 reprefented by the equal Lines MC and AC, 
 and the Motion MC being confldered as paral- 
 lel to the refrading Plane, let the other Motion 
 A C be diflinguiihed into two Motions AD 
 and DC, one of which AD is parallel, and the 
 other DC perpendicular to the refrading Sur- 
 face. In like manner, let the Motions of the 
 emerging Rays be dilHnguifh'd into two, where- 
 of the perpendicular ones are —- CG and — CF. 
 
 And if the force of the refrading Plane begins 
 to ad upon the Rays either in that Plane or at 
 a certain diftance from it on the one fide, and 
 ends at a certain diftance from it on the other 
 
 F 3 fide, 
 
1 70 ] 
 
 fide, and in all places between thofe two limits 
 ads upon the Rays in Lines perpendicular to 
 that refrading Plane, and the Anions upon the 
 Ra^^s at equal diftances from the refrading 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- 
 fra61:ing Plane will furfer no alteration by that 
 force ,• and that Motion w^hich is perpendicular 
 to it will be altered according to the rule of the 
 foregoing Propofition. If therefore for the per- 
 pendicular velocity of the emerging Ray CN 
 
 MC 
 you write — C G as above, then the perpendi- 
 cular velocity of any other emerging Ray C E 
 which was ^,CF, will be equal to the fquare 
 
 Root of C D ^ -^ ^— ^ C G ^. And by fquaring 
 
 thefe Equals , and adding to them the Equals 
 A D ^ and M C ^ — C D ^ , and dividing the 
 Sums by the Equals G T' <^ 4- EF ^ and CGq -\- 
 
 NGq, you will have -~- equal to ■— -. Whence 
 
 AD, the Sine of Incidence, is to EF the Sine 
 pf Refraction, as MC to NG, that is, in a given 
 ratio. And this Demonltration being general, 
 without determining what Light is, or by what 
 kind of force it is refraded, or afluming any' 
 thing farther than that the refrading Body 
 ads 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. 
 
 Sq then , if the ratio of the Sines of Incir 
 
 ^ence and Refradion of any fort of Rays be 
 
 • found 
 
[71] 
 
 found in any one cafe , 'tis given in all cafes ; 
 and this may be readily found by the method 
 in the following Propoiition. / 
 
 TROT. Vn. Theor. VI. 
 
 The Terfc^ion of Telefcopes is impeded by the 
 different Rcfrangibility of the Rays of Light. 
 
 TPIE Imperfedion of Telefcopes is vul- 
 garly attributed to the ipherical Figures 
 ot the Glaffes, and therefore Mathematicians 
 have propounded to figure them by the coni- 
 cal Sedions. To fliew that they arc miilaken , 
 1 have inferted this Proportion; 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 firil Book, 
 where the refraclirig Angle of the Prifm was 
 6x4 Degrees, the half of that Angle " 31 deg. 1$ 
 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 5" 18 8, the Radius being 
 1 0000. When the Axis of this Prifm was pa- 
 rallel to the Horizon, and the Refraftion 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 al- 
 titude obferved at the fame time, I found the 
 '\ngle which the emergent Rays contained wdth 
 
 F 4 the 
 
[ 72 ] 
 
 the incident to be 44deg. 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-. 
 fradion, which is therefore 5-3 deg. 3 5- min. and 
 its Sine 8047. Thefe are the Sines of Incidence 
 and Refradion of the mean refran ible Rays, 
 and their proportion in round numbers is 20 to 
 31. This Glafs was of a colour inclining to 
 green. The lad 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 firft An- 
 gle 5x62. The Sine of half the fum of the An- 
 gles 8157. And their proportion in round num- 
 bers 20 to 31, as before. 
 
 From the length of the Image, which was a- 
 bout 94 or 10 Inches, fubduft its breadth, which 
 was 24 Inches, arid the remainder 7^ Inches 
 would be the length of the Image were the Sun 
 but a point, and therefore fubtends the Angle 
 which the mioit and leatt 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'. f. For the 
 diilance between the Image and the Prifm 
 where this Angle is made, was 184 Feet, and 
 at that diilance the Chord 7^- Inches fubtends an 
 Angle o'i 2 deg. d. y". Now half this Angle is 
 the Angle which thefe emergent Rays contain 
 with the emergent mean refrangible Rays, and 
 a quarter thereof, that is 30'. z". may be ac- 
 counted the Angle which they would contain 
 with the fame emergent mean refi'angible Rays, 
 
 were 
 
[73] 
 
 were they co-incident to them within the Gkfs 
 and fuffered no other Refra(^Hon than that at 
 their Emergence. For if two equal Refractions, 
 rhe one at the Incidence of the Rays on the 
 Prifm, the other at their Emergence, make half 
 the Angle x deg. o. f. then one of thofe Re- 
 fractions will make about a quarter oF that An- 
 gle , and this quarter added to and fubduded 
 irom the Angle of Refraction of the mean re- 
 frangible Rays, which was 5-3 deg. 35-', gives 
 the Angles of Refradion of the moll and leafl 
 refrangible Rays 5-4 deg. /x", and 53 deg. 4 58'', 
 v/hofe Sines are 8099 and 7995, the common 
 Angle of hicidence being 31 deg. 15-' and its 
 Sine 5'i88; and tiiefe Sines in the leall round 
 numbers are in proportion to one another , as 
 78 and 77 to 5-0. 
 
 Now if you fubduft the common Sine of In- 
 cidence 5-0 from the Sines of Refradion -j-j and 
 78, the remainders 27 and 28 fliew that in fmall 
 Reflations the Refradion of the leall refran- 
 gible Rays is to the Refradion of the moll re- 
 frangible ones as 27 to 28 very nearly, and that 
 the difference of the Refradion s of the leall re- 
 frangible and moll refrangible Rays is about the 
 27!th part of the whole Refradion of the mean 
 refrangible Rays. 
 
 Whence they that are skilled in Opticks will 
 safily underlland, that the breadth of the lead 
 circular fpace into which Objed-glaffes of Te- 
 'efcopes can colled all forts of parallel Rays, is 
 about the 27vth part of half the Aperture of the 
 Glafs, or ffth part of the whole Aperture ; and 
 that the Fociis of the molt refrangible Rays is 
 
 nearer 
 
[ 74 ] 
 
 nearer to the Objed-glafs than the Focus of the 
 leaft refrangible ones, by about the 274th 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 Refradion of the Lens to con- 
 verge to points not too remote from the Lens . 
 the Focus of the moil refrangible Rays fliall be 
 nearer to the Lens than the Focus of the leaf, 
 refrangible ones, by a diftance which is to the 
 a74th part of the diitance 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 diitance 
 between that lucid point and the Lens very 
 nearly. 
 
 Now to examine whether the difference be- 
 tween the Refra(^tions which the moft refrangi- 
 ble and the leafl: refrangible Rays flowing from 
 the fame point fuffer in the Object-glaffes of 
 Telefcopes and fuch like Glaffes, be fo great as 
 is here defcribed, I contrived the following Ex- 
 periment. 
 
 Exper. 16. The Lens which I ufed in the fe- 
 cond and eighth Experiments, being placed fix 
 Feet and an Inch diltant from any Objeft, col- 
 lected the Species of that Object by the mean 
 refrangible Rays at the diitance of fix Feet and 
 an Inch from the Lens on the other ilde. And 
 therefore by the foregoing Rule it ought to col- 
 lect the Species of that Objed by the leait re- 
 frangible Rays at the diitance of fix Feet and 
 37 Inches from the Lens , and by the molt re- 
 frangible 
 
[75] 
 
 frangible ones at the diitance of five Feet and 
 107 Inches from it: So that between the two 
 places where theie leall and moil refrangible 
 Rays colled the Species, there may be the di- 
 llance of about si Inches. For by that Rule, 
 as fix Feet and an hich (the diitance of the Lens 
 from the lucid Obiecft ) is to twelve Feet and 
 two Inches (the diilance of the lucid Obje6t 
 from the Focus of the mean refrangible Rays) 
 that is, as one is to two, lb is the 2<74th part 
 of iix Feet and an Inch (the diilance between 
 the Lens and the fame Focus) to the diilance 
 between the Focus of the moil refrangible Rays 
 and the Focus of the leail refrangible ones, 
 which is therefore 5"-^ Inches, that is very near- 
 ly 5| Inches. Now to know whether this mea- 
 fure was true, I repeated the fecond and eighth 
 Experiment with coloured Light , which was 
 lei's 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, ib as to 
 make a coloured Spe6lrum about twelve or fif- 
 teen times longer than broad. This Speftrum 
 I call on a printed Book, and placing the above- 
 mentioned Lens at the diilance of iix Feet and 
 an Inch from this Spedlrum to colled the Spe- 
 cies of the illuminated Letters at the fame, di- 
 ilance 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 
 
[in 
 
 fufed and indiflinft, that I could not read them : 
 Whereupon viewing the Prifm, I found it was 
 full of Veins running 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 ftroakes of the Let- 
 ters, and calling the Colours upon thefe Lines 
 in fuch manner that the Lines ran along the 
 Colours from one end of the Spedrum to the 
 other, I found that the Focus where the indigo, 
 or confine of this Colour and violet cafl the 
 Species of the black Lines molt diitindly, to 
 be about four Inches or 4-^ nearer to the Lens 
 than the Focus where the deepeit red call the 
 Species of the fame black Lines mod diflin6l- 
 ly. The violet was fo faint and dark, that I 
 could not difcern the Species of the Lines di- 
 flindlly by that Colour; and therefore confi- 
 dering that the Prifm was m,ade of a dark co- 
 loured Glafs inchning to green, I took another 
 Prifm of clear white Glais ; but the Spedrum 
 of Colours which this Prifm made had long 
 white {beams of faint Light fliooting 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 little bubbles 
 in the Glafs which refraded 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 Spedrum of Colours became 
 free from thofe irregular Strei^ms of Light, and 
 
 was 
 
[77] 
 
 was now fuch as I defired. But flill 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 deepeit part of it , which was 
 next the end of the Spedrum. I fufpeded 
 therefore that this faint and dark Colour might 
 be allayed by that fcattcring Light which was 
 refraded, and refleded irregularly, partly by 
 fomc very fmall bubbles in the Glalies, and 
 partly by the inequaUties of their PoUlh : which 
 Light, tho' it was but little, yet it being of a 
 white Colour, might fuiHce to affcd the Senfe 
 fo flrongly as to dillurb the Phsenomena of that 
 weak and dark Colour the violet , and there- 
 fore I tried, as in the nth, 13th and 14th Lx- 
 periments, whether the Light of this Colour 
 did not coniift of a fcnfible mixture of heteroge- 
 neous Rays, but found it did not. Nor did the 
 Refradio'ns 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 reafon why I 
 could- not fee the Species of the Lines diltind- 
 ly by this Colour, was only the darknefs of this 
 Colour and thinnefs of its Light, and its di- 
 Hance from the Axis of the Lens ; I divided 
 therefore thofe parallel black Lines into equal 
 parts, by which I might readily know the di- 
 Itances of the Colours in the Spedrum from 
 one another, and noted the diitances of the 
 Lens from the Foci of fuch Colours as caft the 
 Species of the Lines diliindly, and then confi- 
 
 dcred 
 
[78] 
 
 dered whether the difference of thofe diftances 
 bear fuch proportion to $-} Inches, the greateft 
 difference of the diilances which the Foci of 
 the deepefl red and violet ought to have from 
 the Lens , as the diltance of the obferved Co- 
 lours from one another in the Spectrum bear to 
 the greateft diiiance of the deepefl red and 
 violet meafured in the reftilinear fides of the 
 Spe61rum, that is, to the length of thofe Sides 
 or Excels 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 m the Confine of 
 green and blue , which at the redilincar Sides 
 of the Spectrum was diltant from it half the 
 length of thofe Sides, the Focus where the Con- 
 fine of green and blue caft the Species of the 
 Lines diitindly on the Paper, was nearer to the 
 Lens than the Focus where the red caft thofe 
 Lines diftinftly on it by about x4 or 2-| Inches. 
 For fometimes the Meafures were a little great- 
 er, fometimes a little lefs, but feldom varied 
 from one another above -f 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 reftiUnear Sides) give 24 or 24 
 difference of the diftances of their Foci from 
 the Lens , then the Colours diftant the whole 
 length oug'r.t to give 5 or 5-4 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 
 
[ 19 ] 
 
 but only to the center of the Semicircle which 
 bounded that end , or a httle farther ; and 
 therefore I compared this red not with that 
 Colour which was exadly in the middle of the 
 Spectrum, or Confine of green and blue, but 
 \\\i\\ that which verged a little more to the blue 
 than to the green: And as I reckoned the 
 whole length of the Colours not to be the whole 
 length of the Spectrum , but the length of its 
 rectilinear Sides, fo completing the lemicircu- 
 lar Ends into Circles, when either of the ob- 
 ferved Colours fell within thofc Circles, I mea- 
 furcd the dillance of that Colour from the fe- 
 micircular end of the Spedrum, and fubduci:- 
 ing half this difu\nce from the meafured di- 
 llance of the two Colours, I took the remain- 
 der for their corre(^ted dillance ; and in tliefc 
 Obfervations.fet down this corrected dillance 
 for the difference of the dillances of their Fpoi 
 from the Lens. For as the length of the recti- 
 hnear Sides of theSpedrum would be the whole 
 length of all the Colours, were the Circles of 
 which (as we ihe\^ed) that Spe61rum confills 
 contrafted and reduced to phylical Points, fo 
 in that cafe this corre(!:l:ed dillance would be the 
 real dillance of the two oblerved Colours, 
 
 When therefore 1 flirther oblerved the deep- 
 ell fenfible red, and that blue whofe corrected 
 dillance from it was tt parts of the length of 
 the rectilinear Sides of the Spe61:rum, the dif- 
 ference of the diltances of their Foci from the 
 Lens was about 3-^ inches, and as 7 to ix fo is 
 3v to 5f 
 
 When 
 
[8o] 
 
 When I obferved the deepefl fenfible red, 
 and that indigo whofe corrected diftance was 
 TT or -J of the length of the redihnear Sides of 
 the Spe6lrum, the difference of the diitances of 
 their Foci from the Lens, was about 3y Inches, 
 and as z to 3 fo is 3? to 54. 
 
 When I obferved the deepefl; fenfible red , 
 and that deep indigo whofe corrected dillance 
 from one another was -% or 4 of the length of 
 the redilinear Sides of the Spedrum , the dif- 
 ference of the dillances of their Foci from the 
 Lens was about 4 Inches ; and as 3 to 4 fo is 4 
 to si- 
 
 When I obferved the deepefl fenfible red, 
 and that part of the violet next the indigo, 
 whofe correded diflance from the red was 41 
 or -I- of the length of the rec^filinear Sides of the 
 Spedrum, the difference of the diflances of 
 their Foci from the Lens w^as about 44 Inches, 
 and as 5 to 6, fo is 44 to 54. For fometimes 
 when the Lens was advantagioufly placed, fo 
 that its Axis refpe6ted the blue, and all things 
 elfe were well ordered, and the Sun flione clear, 
 and I held my Eye very near to the Paper on 
 which the Lens cafl the Species of the Lines, I 
 could fee pretty diflindly 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 diflind 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 diflindly ; and then the red ap- 
 peared 
 
[8,] 
 
 peared much lefs diiiinft than before. Where- 
 fore I contrived to make the Spectrum of Co- 
 lours ihorter than before, fo that both its ends 
 might be nearer to the Axis of the Lens. And 
 now its length U'as about i4 Inches and breadth 
 about 4 or -^ of an Inch. Al(o inilead of the 
 black Lines on which the Spe(!:l:rum was call, I 
 made one black Line broader than thoie, that 
 I might fee its Species more eafily; and this 
 Line I divided by Ihort crofs Lines into equal 
 parts, for meafuring the dillances of the obler- 
 ved Colours. And now I could fometimes fee 
 the Species of this Line with its divilions al- 
 mofl as far as the center of the femicircular 
 violet end of the Spedrum , and made thefe 
 farther Obfervations. 
 
 When I ob'crvcd the deepclt fenfibleredjand 
 that part of the viol^et whole corrected diitance 
 from it was about 4 parts of the rectilinear Sides 
 of the Spectrum the diticrence of the dillances 
 of the Foci of thole Colours from the Lens, 
 was one time 44, another time 44? another time 
 4t Inches , and as 8 to 9, fo are 47, 44, 4-7, to 
 5*75 5't? 5*^ refpedively. 
 
 When I obl'crved the deeped fenfible red, 
 and deepelt fenlible violet , (the corrected di- 
 llance of which Colours when all things were 
 ordered to the belt advantage , and the Sun 
 fhone very clear, was about 44 or 44 parts of 
 the length of the redilinear Sides of the co^ 
 loured Spedrum) I found the dinerence of the 
 dillances of their Foci from the Lens fometimes 
 44 fometimes 5-4 , and for the moil part 5- In- 
 
 G ♦ cheg 
 
[82] 
 
 ches or thereabouts: and as ii to l^ of 15- to 
 165 fo is five Inches to 54-01' 5I Inches. 
 
 And by this progreflion of Experiments I fa- 
 tisfied my felf , that had the Light at the very 
 ends of the Spedrum been ibong enough to 
 make the Species of the black Lines appear 
 plainly on the Paper, the Focus of the deepell 
 violet would have been found nearer to the 
 Lens, than the Focus of the deepell red, by a- 
 bout Si Inches at leaft. 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 fmallell 
 Refradtions which they do in the greateit. 
 
 My progi'efs in making this nice and trouble- 
 fome Experiment I have fet down more at large, 
 that they that fliall try it after me may be aware 
 of the circumfpedtion requifite to make it fuc- 
 ceed well. And if they cannot make it fuc- 
 ceed fo well as I did , they may notwithlland- 
 ing colledl by the proportion of the diilance of 
 the Colours of the Spedlrum, to the ditierence 
 of the diflances of their Foci from the Lens, 
 what would be the fuccefs in the more diftant 
 Colours by a better trial. And yet if they ufe 
 a broader Lens than I did, and hx it to a long 
 flraight Staff by means of which it may be rea- 
 dily and truly diredted to the Colour whofe Fo- 
 cus is defired, I queflion not but the Experi- 
 ment will fucceed better with them than it did 
 with me. For I diredled the Axis as nearly as I 
 could to the middle of the Colours, and then 
 the faint ends of the Spedtrum being remote 
 from the Axis, caft their Species lefs diftindlly 
 
 on 
 
[83] 
 
 on the Pnper than they would have done had 
 the Axis been iueceflively direded to them. 
 
 Now by what has been iaid, it's certain that 
 the Rays which differ in Refrangibility do not 
 converge to the lame Focus, but if they flow 
 from a lucid point, as fl\r from the Lens on one 
 fide as their Foci are on the other, the Focus 
 of the moll refrangible Ravs fliall be nearer to 
 the Lens than that of the leall refrangible, by 
 above the fourteenth part of the whole dillance : 
 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 moli: refrangible Rays ihall be nearer to t.ie 
 Lens than the Focus of the lealt refrangible* 
 by about the 27th or xuth part of their whole 
 dillance 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 leall into which they can all be ga- 
 thered ) is about the yfth part of the diameter 
 of the Aperture of the Glafs. So that 'tis a won- 
 der that Telefcopes reprefent Objects fo diilin6t 
 as they do. But were all the Rays of Light e- 
 qually refrangible, the Error ariling only from 
 the fphericalnefs of the Figures of Gkilles would 
 be many hundred rimes lefs. For if the Objecl:- 
 glafs of a Telefcopc be Plano-convex, and the 
 Plane fide be turned towards theObjc(3:, 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 X be 
 
[ 84 ] 
 
 be to the Sine of Refradion as I to R : the Rays 
 which come parallel to the Axis of the Glals, 
 fhall in the place where the Image of the Objeft 
 is moll diftinftly made, be fcattered all over a 
 
 little Circle whofe diameter is 7-- x '■ ' ' , very 
 
 I cj O quad. •' 
 
 nearly, as I gather by computing the Errors of 
 the Rays by the method of infinite Series, and 
 rejeding the Terras whofe Quantities are in- 
 confiderable. As for inilance , if the Sine of 
 Incidence I, be to the Sine of Refraction R, as 
 20 to 31, and if D the diameter of the Sphere 
 to which the convex fide of theGlafs is ground, 
 be 100 Feet or ixoo Inches, and S the femidia- 
 meter of the Aperture be two Inches, the dia- 
 meter of the little Circle (that is ^-^—) will 
 
 , :?I XM X 8 , 961 . r T 1 
 
 be —-^ — • (or :: — • ) parts or an Inch. 
 
 2CXiO XI2OO X 1200 ^ 72000000^* 
 
 But the diameter of the little Circle through 
 which thefe Rays are fcattered by unequal Re- 
 frangibility, will be about the 5'5'th part of the 
 Aperture of the Objedt-glafs which here is four 
 Inches. And therefore the Error ariling from 
 the fpherical Figure oT the Glals, is to the Er- 
 ror arifing from the different Rcfrangibility of 
 
 the Rays, as^l^^ to ^- that is as i to ^h9 '^ 
 
 and therefore being in comparifon fo very lit- 
 tle, 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 pais that Objects appear through 
 Telefcopes fo diftind: as they do ? I anfwer, 'tis 
 
 ^ becaufe 
 
[85] 
 
 becaufe the erring Rays are not fcartered uni- 
 formly over all that circular fpace, but colleft- 
 ed intinitcly 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 llrong enough to be 
 vifibie , unlefs in the center and very near it. 
 Let ADE [in Fig. 27.] reprelent one of thofc 
 Circles defcribed with the Center C and Semi- 
 diameter AC, and let BFGbea fmallcrCircle 
 concentrick to the former, cutting wivh its cir- . 
 cumference the Diameter A C in 3, and bilecft 
 AC in N, and by my reckoning thcDenfity 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 B FG, will be to the whole 
 Light within the gi-eater AED, astheP^xcefs 
 of the Square of AC above the Square of A B, 
 is to the Square of AC. As if BC be the fifth 
 part of AC, the Light will be four times den- 
 ier 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, mult ftrike the Senfe much more ftrongly, 
 than that faint and dilated Light round about 
 between it and the circumference of the grea- 
 ter. 
 
 But it's farther to be noted, that the moft lu- 
 minous of the prifmatick Colours are the yel- 
 low and orange. Thefe affed the Senfes more 
 ilrongly than all the relt together, and next to 
 
 G 3 thefe 
 
[S6] 
 
 thefe in flrength 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 ftronger Colours are little to be regarded. 
 The Images of Objefts are therefore to be pla- 
 ced, not in the Focus of the mean refrangible 
 Rays which are in the confine of green and 
 blue, but in the Focus of thofe Rays which are 
 in the middle of the orange and yellow ; there 
 where the Colour is mod luminous and fulgent, 
 that is in "the brighteft yellow, that yellow which 
 inclines more to orange than to green. And 
 by the Refradion of thefe Rays (whofe Sines of 
 Incidence and Refradionin Glafs are as 17 and 
 11) the Refraction of Glafs and Cryilal for op- 
 tical Ufes is to be meafurcd. Let us therefore 
 place the Image of the Objed in the Focus of 
 thefe Rays, and all the yellow and orange wall 
 fall within a Circle, whofe diameter is about 
 the 25'oth 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 hfth parts 
 will fall without it round about ; and that w^hich 
 falls without will be ipread through almolt as 
 much more fpace as that which falls within, 
 and fo in the grofs be alrnofl three times rarer. 
 Of the other half of the red and green, (that is 
 oi' the deep dark red and willow green) about 
 one quarter will fall within this Circle, and 
 
 three 
 
[ 87 ] 
 
 three quarters without, and that which £\lls 
 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 25- 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 
 Spedrum of Colours made by a Priim 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 affeft the Senfe, efpecially fmce the deep 
 red and willow green of this Light, are much 
 darker Colours than the relf. And for the lame 
 reafon the blue and violet being much darker 
 Colours than thefe, and much more rarified, 
 may be negledcd. 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 almoil infenfible. The 
 fenfible Image of a lucid point is therefore 
 fcarce broader than a Circle whofe diameter is 
 the 250th part of the diameter of the Aperture 
 of the 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 Speculator will 
 fcarce regard. And therefore in a Telefcope 
 whofe aperture is four Inches, and length an 
 hundred Feet, it exceeds not 2!' 45-''', or 3". And 
 in a Telefcope whofe aperture is two Inches, 
 and length 20 or 30 Feet , it may be 5'' or 6" 
 and fcarce above. And this anfwers well to 
 
 G 4 expe^ 
 
[88] 
 
 experience : For fome Aflronomers have found 
 the Diameters of the lix'd Stars, in Telefcopes 
 of between 20 and 60 Feet in length, to be a- 
 bout s" or ^"f or at moil %" or 10" in diame- 
 ter. But if the Eye-Glafs be tincled faintly 
 with the fmoke of a Lamp or Torch, to ob- 
 fcure the Light of the Star, the fainter Light 
 in the circumference of the Star ceafes to be 
 vifible, and the Star (if the Glafs be fuliicient- 
 ly foiled with fmoke) appears fomething more 
 like a mathematical Point. And for the fame 
 reafon, the enormous part of the Light in the 
 circumference of every lucid Point ought to 
 be lefs difcernible in ihorter Telefcopes than in 
 longer, becaufe the fhorter tranfmit lefs Light 
 to the Eye. 
 
 Now that the fix'd Stars, by reafon of their 
 immenfe diftance, appear hke Points, unlefs fo 
 far as their Light is dilated by Refraction, may 
 appear from hence ; that when the Moon paf- 
 fes over them and eclipfes them, their Light 
 vaniflies, not gradually like that of the Planets, 
 but all at once ; and in the end of the Eclipfe 
 it returns into Sight all at once, or certainly in 
 lefs time than the fecond of a Minute ; the Re- 
 fradion of the Moon's Atmofphere a little pro- 
 tradiing the time in which the Light of the Star 
 firif vaniihes, and afterwards returns into Sight. 
 
 Now if we fuppofe the fenfible Image of a lu- 
 cid Point, to be even 25*0 times narrower than 
 the aperture of the Glafs : yet this Image would 
 be flill much greater than if it were only from 
 the fpherical Figure of the Glafs. For were 
 it not for the different RcfrangibiJ^ty of the 
 
 > Rays, 
 
[89] 
 
 Rays, its breadth in an loo Foot Telefcope 
 
 whofe aperture is 4 Inches would be but A^^ - 
 ■T -~ 720CC000 
 
 parts of an Inch, as is manifefl by the foregoing 
 computation. And therefore in this cafe the 
 greatell Errors ariiing from the fpherical Figure 
 of the Glafs, would be to the greatell fenlible 
 Errors arifmg from the different Refrangibility 
 
 of the Rays as -— ^ to -^ at mod, that is on- 
 
 ly as I to ixoo. And this ful^cicntlyfliews that 
 it i:, not the fpherical figures of Glallls but the 
 diucrent Refrangibility of the Rays which hin- 
 ders the perfection of Telefcopes. 
 
 There is another Argument by which it may 
 appear that the different Refrangibility of Rays, 
 is the true caufe of the imperfection of Tele- 
 fcopes. For the Errors of the Rays arifing 
 from the fpherical Figures of Objeft-glalTes, are 
 as the Cubes of the Apertures of the Objed- 
 glafies ; and thence to make Telefcopes of va- 
 rious lengths 5 magnify with equal diilinftnefs, 
 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 anfwer to experience. But the 
 Errors of the Rays arifing from the different 
 Refrangibility, are as the Apertures of the Ob- 
 jed-glaffes, and thence to make Telefcopes of 
 various lengths, magnify with equal diiHnchiefs, 
 their Apertures and Charges ought to be as the 
 fquare Roots of their lengths ; and this anfwers 
 to experience, as is well known. For inttance, 
 a Telefcope of 64 Feet in length, with an Aper- 
 ■' ture 
 
I^o] 
 
 ture of 1-} Inches, magnifies about iio times, 
 with as much diltindnefs as one of a Foot in 
 length, with -} 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 perfection than we have yet defcrib'd, 
 by compofmg the Objed-Glafs of two GlalTes 
 with Water between them. Let ADFC [in F/g. 
 28.] reprefenttheObjeft-glafscompofedoftwo 
 Glaffes ABED and BEFC, alike convex on the 
 outlidcs AGD and CHF, and aUke concave 
 on the infides BME, BNE, with Water in 
 the concavity BMEN. Let the Sine of Inci- 
 dence out of Glafs into Air be as I to R, and 
 out of Water into iVir as K to R, and by con- 
 fequence out of Glafs into Water, as I to K : 
 and let the diameter of the Sphere to which th» 
 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 K K — K I to the 
 Cube Root of RK — RI: and the Refradions^ 
 on the concave fides of the Glafles , will very 
 much corre<^t the Errors of the Refraftions 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 
 Refradions alone than that of increafing their 
 lengths, for which end the late Contrivance of 
 
[91] 
 
 Hngenius feems well accommodated. For ve- 
 ry long Tubes arc cumberlbme, and fcarcc to 
 be readily managed , and by reafon of their 
 length are very apt to bend, and ihake by bend- 
 ing lb as to caule a continual trembling in the 
 Objects, whereby it becomes difficult to fee 
 tiiem diilindly: whereas by his contrivance the 
 Glalles are readily manageable, and the Object- 
 glafs being fix'd upon a llrong upright Pole be- 
 comes more Heady. 
 
 Seeing therefore the Improvement of Tele- 
 fcopes of given lengths by Refractions is defpe- 
 rate ; I contrived heretofore a Perfpe(^tive by 
 Reflexion , ufmg inflead of an Objed-glafs a 
 concave Metal. The diameter of the Sphere 
 to which the Metal was ground concave was a- 
 bout if Engliih Inches, and by conlcquence 
 the length of the Inlhument about iix Inches 
 and a quarter. The Eye-glal's 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 limited not by an opake Circle, 
 covering the Limb of the Metal round about, 
 but by an opake Circle placed between the Eye- 
 glafs and the Eye, and perforated in the mid- 
 dle with a little round hole for the Rays to pafs 
 through to the Eye. For this Circle by being 
 placed here, Itopp'd much of the erroneous 
 Light 5 which otherwife would have dilbjrbed 
 
 the 
 
[92] 
 
 the Vifion. By comparing it with a pretty good 
 PerfpecHve of four Feet in length, made with 
 a concave Eye-glafs, I could read at a greater 
 diftance with my own Infh-ument than with the 
 Glafs. Y6t Objeds appeared much darker in 
 it than in the Glafs, and that partly becaufe 
 more Light was loil by Reflexion in the Metal, 
 than by Refraction in the Glafs, and partly be- 
 caufe my Inilrument was overcharged. Had it 
 magnified but ^o or 25- times it would have 
 made the Objeft appear more brisk and plea- 
 fant. Two of thel'e I made about 16 Years a- 
 go, and have one of them ilill by me by which 
 I can prove the truth of what I write. Yet it 
 is not fo good as at the firll. For the concave 
 has been divers times tarniihcd and cleared a- 
 gain,by rubbing it with very foft Leather. W hen 
 I made thefe, an Artift in London undertook to 
 imitate it ; but ufmg another way of polifliing 
 them than I did , he fell much fliort of what I 
 had attained to, as I afterwards underllood by 
 difcourfmg the under Workman he had em- 
 ployed. The Poliih 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 poliili'd, till it had 
 taken the Figure of the Convex and was ready 
 for a PoHlh. Then I pitched over the convex 
 very thinly, by dropping melted Pitch upon it 
 and warming it to keep the Pitch foft, whilft 
 I ground it with the concave Copper wetted 
 to make it fpread eavenly all over the convex. 
 
 Thus 
 
Thus by working it well I made it as thin as a 
 Groat, and after the convex was cold I ground 
 it again to give it as true a Figure as 1 could. 
 Then I took Putty which I had made very fine 
 by ^^"afl^ing it from all its groiler 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 Object-Metal with a brisk 
 motion , for about two or three Minutes of 
 time, leaning hard upon it. Then I put frelli 
 Putty upon tjie Pitch and ground it again till it 
 had done making a noiic,and aUerwarci;^ ground 
 the Objed-Metal upon it as before. And this 
 Work I repeated till the Metal was poliihed, 
 grinding it the lall time with all my Ibength 
 for a good while together, and frequently 
 breathing upon the Pitch to keep ic moilt with- 
 out laying on any more freih Putty. The Ob- 
 jed-?vletal v> as 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 polillied them both I tried which was 
 bell, and ground the other again to fee if I could 
 make it better than that which I kept. And 
 thus by many Trials I learn'd the way of po- 
 lifhing, till I made thofe two receding Peripe- 
 dives I {pake of above. For this Art of po- 
 Hilling will be better learn d by repeated Pra- 
 ctice than by myDefcription. Before I ground 
 the Object-McLal on the Pitch, 1 always ground 
 the Putty on it with the concave Copper till it 
 had done making a noife , becaufe ii the Parti- 
 cles of the Putty were not by this means made 
 
 to 
 
[n] 
 
 to flick faft in the Pitch, they would by rolling 
 up and down grate and fret the Objed-Metal 
 and fill it full of little holes. 
 
 But becaufe Metal is more difficult to poliili 
 than Glafs, and is afterwards very apt to be 
 fpoilcd b}' tarnilhing, 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 iide. The Glafs muft be e- 
 very where of the fame thicknefs exadly. O- 
 therwife it will make Objects look colour'd and 
 indillinft. By fuch a Glals I tried about five or 
 fix Years ago to make a receding Telcfcope of 
 four Feet in length to magnify about 15-0 times, 
 and I fatisfied my felf that there wants nothing 
 but a good Artill to bring the Defign to perfe- 
 dion. For the GMs being wrought by one of 
 our London Artills after fuch a manner as they 
 grind Glafles for Telefcopes, tho' it feemed as 
 well wrought as the Objeclil-glaires ufe to be, yet 
 when it was quick-filver'd, the Reflexion dif- 
 covered innumerable Inequalities all over the 
 Glafs. And by reafon of thefe hiequaUties, Ob- 
 jeds appeared indiilinCt in this hiilrument. For 
 the Errors of retteded Rays caufed by any In- 
 equality of the Glafs, are about fix times great- 
 er than the Errors of refrafted Rays cauicd by 
 the Hke Inequalities. Yet by this Experiment 
 I fatisfied my felf that the Reflexion on the 
 concave fide of the Glafs, which I feared would 
 difturb the Vifion, did no fenfible prejudice to 
 it, and by conlequence that nothing is wanting 
 
 to 
 
[95] 
 
 to peifecl thcfe Tclefcopes, but good Work- 
 men who can grind and polifli GlalFes truly 
 fphericaL An Object-glafs of a fourteen Foot 
 Telcfcopej made by an Artificer at London^ I 
 once mended coniiderably, by grinding it on 
 Pitch with Putty, and leaning very eafily on it 
 in the grinding, ielt the Putty ihould fcratch it. 
 Whether this way may not do well enough for 
 pohihing thefe relieving Glaires, I have not yet 
 tried. But he that fhall try either this or any 
 other way of polilhing which he may think bet- 
 ter, may do well to make his Glalles ready for 
 polilhing by grinding them without that vio- 
 lence, wherewith our London Workmen prcfs 
 their Glalles in grinding. For by I'uch violent 
 preflure, Glalles arc apt to bend a little in the 
 grinding, and inch bending will certainly fpoii 
 their Figure. To recommend therefore the 
 confidcration of thefe reiiccting Glalles, to fuch 
 Artills as are curious in figuring Glailes, I iliall 
 delcribe this optical Inltrument in the follow- 
 ing Propolition. 
 
 T ROT. vn. Prob. n. 
 
 To fl.wrten Telefto^es, 
 
 LET ABDC {inF'ig. 29.] reprefent a Glafs 
 fpherically concave on the forefide AB, 
 ana as much convex on the backfide CD, fo 
 that it be every where of an equal thicknefs. 
 Let it notjae thicker on One fide than on the 
 other, left it make Objeds appear colour'd and 
 
 ^ indi- 
 
[9^ 
 
 indiflindl, and let it be very truly wrought and 
 quick-filver'd over on the backlide ; and f^:t in 
 the Tube V X Y Z which mult be very black 
 within. Let EFG reprctent a Prifm of Glals 
 or Cryrtal placed near the other end of the 
 Tube, in the middle of it, by means of a han- 
 dle of Brafs or Iron FGK, to the end of which 
 made flat it is cemented. Let this Prifm be 
 rectangular atE, and let the other two Angles 
 at F and G be accurately equal to each otner, 
 . and by confequence equal to half right ones, 
 and let the plane fides F E and G E be fquare, 
 and by confequence the third fide F G a rectan- 
 gular Parallelogram, whofe length is to its 
 breadth m a fubdupUcate proportion of two to 
 one. Let it be fo placed in the Tube, that 
 the A^^is of the Speculum may pals through the 
 middle of the fquare fide EF perpendicularly, 
 and by confequence through the middle of the 
 fide F G at an Angle of 45- Degrees, and let the 
 fide E F be turned towards the Speculum., and 
 the diftance of this Prifm from the Speculum 
 be fuch that the Rays of the Light PQ, RS, ^c. 
 •which are incident upon the Speculum in Lines 
 parallel to the Axis thereof, may enter thePrilm 
 at the fide EF, and be reflected by the fide 
 FG, and thence go out of it through the fide 
 GE, to the point T which mutt be the com- 
 mon Focus of the Speculum ABDC, and of a 
 Plano-convex Eye-glafs H, through which thofe 
 Rays mult pafs to the Eye. And let the Rays 
 at their coming out of the Glals pafs through 
 a fmall round hole, or aperture made in a lit- 
 tle plate of Lead, Brafs, or Silver, wherewith 
 
 the 
 
[^7] 
 
 the Glafs is to be covered, which hole mud be 
 no bigger than is necellary for Light enough 
 to pals through. For ib it will render the Ob- 
 ject dillin(^i:, the Plate in which 'tis made inter- 
 cepting all the erroneous part of the Light 
 which comes from the verges of the Speculum 
 A B. Such an Inltrument well made , if it be 
 fix Foot long, (reckoning the length from the 
 Speculum to the Priim, and thence to the I'o^ 
 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 
 Inlh-ument be made longer or Ihorter, the aper- 
 ture mult be in proportion as the Cube of the 
 fquare-iquare 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 leall, and that the Glafs of 
 the bpeculum be thick, that it bend not in the 
 working. ThePrilm EFG muft be no bigger 
 than is necellary, and its back fide F G mult 
 not be quick-Tilver'd over. For without quick- 
 filver it will relied all the Light incident on it 
 from the Speculum. 
 
 In this Inlb'ument the Objed: will be invert- 
 ed , but may be ereded by making the fquare 
 fides E F and EG of the Prifm EFG not plane 
 but fpherically convex, that the Rays may crofs 
 as well before they come at it as afterwards 
 between it and the Eye-glafs. If it be defired 
 that the Inllrument bear a larger aperture, that 
 
 H may 
 
1 58 1 
 
 may be alfo done by compofingvthe" Speciilum 
 of two Glailes with Water between them. 
 
 If the Theory of making Telefcopes could at 
 length be fully brought into praftice, yet there 
 would be certain Bounds beyond which Tele- 
 fcopes could not perform. For the Air through 
 which; w„e look upon the Stars, is in a perpe- 
 tual Tremor ; as may be feen by the tremulous 
 Motion of Shadows caft from high Towers, 
 and by the twinkling of the fix'd Stars. But 
 thefe Stars do not t\\ inkle when viewed through 
 Telefcopes which have large apertures. For 
 the Rays of Light which pafs through divers 
 parts of the aperture, tremble each of them 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 conflitute one 
 broad lucid Point , compofed of thofe many 
 trembhng 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 fhort 
 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 mod ferene and quiet Air, 
 fuch as may perhaps be found on the tops of 
 the higheft Mountains above the groffer Clouds. 
 
 THE 
 
^, 
 
 Bookl.Ri-tlBatcI. 
 
kl.Paitl.BateJL 
 
-^ 
 
Book I.Rrtl.Plafe m. 
 
 J^tg 16 
 
w 
 
 BoollPaitI.Hatel\' ;e 
 
 a 
 
 o 
 
^ 
 
THE 
 
 FIRST BOOK 
 
 OPTICKS. 
 
 PART II. 
 
 TROT, I. Theor. I. 
 
 The ThanoTiiena of Colours in refraBed or re^ 
 fleBed Light are not can fed by new Modijl- 
 cations of the Light varioujly imPrefs'dy ac^ 
 cording to the -various Terminations of the 
 Light and Shadozv, 
 
 The Proof by Experiments. 
 
 Exper. iv^^^fjOR if ±e Sun fhine into a 
 very dark Chamber through 
 an oblong hole F, VmFig. i.] 
 whale breadth is the fixth or 
 eighth part of an Inch, or fomething lefs ; and 
 his beam F H do afterwards pafs Ml through a 
 
 H X very 
 
[ loo ] 
 
 vei7 large Prifm ABC, diftant about xo 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 diflance 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 w^hite Light thus trafmitted through 
 the hole H, fall afterwards upon a white Paper 
 / r, placed after that hole H, at the dilfance of 
 three. or four Feet from it, and there paint the 
 ufual Colours of the Prifm, fuppofe red at t^ 
 yellow at j, green at r, blue at ^, and violet 
 at/; you may with an Iron Wire, or any fuch 
 like flender opake Body, whofe breadth is a- 
 bout the tenth part of an Inch, by intercepting 
 the Rays at k^ /, w, 7tox o, takeaway any one 
 of the Colours at ty /, r, q or/, whilll: 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 reil remaining : So that any one 
 of the Colours as well as violet may become 
 outmpft in the Confine of the Shadow towards 
 /, and any one of them as well as red may be- 
 come outmofl 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 Obilacle 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 
 themfeives indifferently to any Confines of Sha- 
 dow, 
 
[ loi ] 
 
 dow, and therefore the differences of thefe Co- 
 lours from one another, do not arife from the 
 different Confines of Shadow, whereby Light 
 is variouily moditied , 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 diminiflied, but that the Colours 
 2Lt ptbe fufficiently vifible. To procure a Prifm 
 of folid Glafs large enough for this Experiment 
 will be difficult, and therefore a prifmatick 
 Veircl mull be made of polifli'd Glafs Plates ce- 
 mented 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.^^ 
 half an Inch wide, paifed firll through the Prifm 
 ABC placed at the hole, and then through a 
 Lens P T fomcthing more than four Inches 
 broad , and about eight Feet dillant from the 
 Prifm , and thence .converged to O the Focus 
 of the Lens diltant 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 reprefcnted in the polture DE, 
 all the Colours upon it at O appeared white. 
 But if the Paper being turned about an Axis 
 parallel to the Prifm, became very much incli- 
 ned to the Light as 'tis reprefented in the Po- 
 fitions de and h\ the fame Light in the one 
 cafe appeared yellow and red, in the other blue. 
 
 H 3 Here 
 
[ 102 ] 
 
 Here one and the fame part of the Light in 
 one and the fame place, according to the va- 
 rious Inchnations of the Paper, appeared in one 
 cafe white, in another yellow or red, in a third 
 blue, whilit 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 maybe 
 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-fliut be re- 
 fracted by a large Prifm ABC, [in Fig. 3.] 
 whofe refrading Angle C is more than 60 De- 
 grees, and io foon as it comes out of the Prifm 
 let it fall upon the white Paper DE glewed up- 
 on a ftiii' Plane ; and this Light, when the Pa- 
 per is perpendicular to it, as 'tis reprefented in 
 DE, will appear perfedly white upon the Pa- 
 per, but when the Paper is very much inclin'd 
 to it in fuch a manner as to keep always paral- 
 lel to the Axis of the Prifm, the whitenefs of 
 the whole Light upon the Paper will according 
 to the inclination of the Paper this way or that 
 way, change either into yellow and red, as in 
 the polture de^ or into blue and violet, as in 
 the poilure ^g. And if the Light before it fall 
 upon the Paper be twice refraded the fame 
 way by two parallel Prifms, thefe Colours will 
 become the more confpicuous. Here all the 
 middle parts of the broad beam of white Light 
 which fell upon the Paper, did without any 
 Confine of Shadow to modify it , become co- 
 lour'd all over with one uniform Colour , the 
 Colour being always the fame in the middle of 
 
 the 
 
[ 103 
 
 the Paper as at the edges, and this Colour chan- 
 ged according to the various ObUquity of the 
 reiicding Paper, without any change in the Re- 
 fractions or Shadow, or in the Light which fell 
 upon the Paper. And therefore theie Colours 
 are to be derived from fome other Caufe than 
 the new Modifications of Light by Refraftions 
 and Shadows. 
 
 If it be asked. What then is their Caufe ? I 
 anfwer, That the Paper in the pofture de, be- 
 ing more oblique to the more refrangible Rays 
 than to the leis refrangible ones, is more flrong- 
 ly illuminated by the latter than by the former, 
 and tliereforc the lefs refrangible Rays are pre- 
 dominant in the refleded Light. And where- 
 ever they are predominant in any Light they 
 tinge it with red or yellow, as may in fome mea- 
 fure appear by the Hrlt Propolition of the tirft 
 Book, and will more fully appear hereafter. 
 And the contrary happens in the pofture of the 
 Paper h^ the more refrangible Rays being then 
 predominant which always tinge Light with 
 blues and violets. 
 
 Ex per. 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 whilit the Eye, and the 
 Bubble, and all Bodies which emit any Light, 
 or call any Shadow, remain unmoved. And 
 therefore their Colours arife from fome regular 
 
 H 4 caufe 
 
[ I04 ] 
 
 Caufe which depends not on any Confine of 
 Shadow. What this Caufe is will be fliewed in 
 the next Book. 
 
 To thefe Experiments may be added the 
 tenth Experiment of the firit Book, where the 
 Sun's Light in a dark Room being traje61ed 
 through the parallel Superhcies 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 production of thefe Colours, the 
 Confine of Shadow can have nothing to da. 
 For the Light changes from white to yellow, 
 orange and red fucceirively, without any alte- 
 ration of the Conhne of Shadow : And at both 
 edges of the emerging Light where the con- 
 trary Confines of Shadow ought to produce 
 different Efteds, the Colour is one and the 
 fame, whether it be white, yellow, orange or 
 red: And in the middle of the emerging Light, 
 where there is no Confine of Shadow at all, the 
 Colour is the very fame as at the edges, the 
 whole Light at its very firlt 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 refraded Light after its Emergence. Nei- 
 ther can thefe Colours arife from any new Mo- 
 difications of the Light by Refractions, becaufe 
 they change fucceflively from white to yellow, 
 orange and red , while the Refradions remain 
 the fame, and alfo becaufe the Refradions are 
 made contrary ways by parallel Superficies which 
 
 deitroy 
 
[105] 
 
 deflroy one anothers Effccls. They arife not 
 therefore from any Moditications of Light made 
 by Refractions and Shadows, but have fome o- 
 ther cauic. What that Caufe is we ihewed a- 
 bove in this tenth Experiment, and need not 
 here repeat it. 
 
 There is- yet another material circumllance 
 of this Experiment. For this emerging Light 
 being by a third Prifm HIK [in Fig. 21. Tart i.] 
 refracted towards the Paper FT, and there paint- 
 ing the ufual Colours of the Prifm, red, yellow, 
 green, blue, violet: If thele Colours arofe from 
 the Refradions of that Prifm modifying the 
 Light, they would not be in the Light before 
 its Incidence on that Prifm. And yet in that 
 Experiment we found that when by turning 
 the two tiril: Prifms about their common Axis 
 all the Colours were made to vaniih 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 thii-d Prifm. 
 And in general we find by other Experiments ' 
 that when the Rays which ditl^er in Refrangibi- 
 lity are feparared from one another, and any 
 one fort of them is confidered apart, the Co- 
 lour of the Light which they compofe cannot 
 be changed by any Refraction or Reflexion 
 vv'hatever, as it ought to be were Colours no- 
 thing elfe than Modifications of Light caufed 
 by Refractions, and Reflexions, and Shadows. 
 This unchangeablenefs of Colour I am now to 
 defcribe in the following Propofition. 
 
 "PROT. 
 
[ 10^ ] 
 
 :.; TROT. II. The OR. IL 
 
 j^ll'ho'mogeneai Light has its proper Colour an- 
 fwertJig to its '\D'egrce of Refrangtbility^ and 
 
 ■ that Colour cannot be changed by Reflexions 
 and Refractions. 
 
 IN the Experiments of the fourth Propofition 
 of the hrft Book, when Ihad feparated the 
 heterogeneous Rays from one another, theSpe- 
 ^um / 1 formed by the feparated Ra^^s, did 
 in the progrefs from its end / , on which the 
 moll refrangible Rays fell, unto its other end ^, 
 on which the leall refrangible Rays fell, appear 
 tinged with this feries of Colours, violet, indi- 
 go, blue, green, yellow, orange, red, together 
 with all their intermediate degrees in a conti- 
 nual Succeilion perpetually varying. So that 
 there appeared as many degrees of Colour^,, as 
 there were forts of Rays differing in Refrangi- 
 bility. 
 
 Exper. f. Now that thefe Colours could not 
 be changed byRefracHon, I knew by refrading 
 with a Prifm fomerimes 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 Refraction the Co- 
 lour of the Light was never changed m the leali. 
 If any part of the red Light was refra(^ted, 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 
 
[ I07 ] 
 
 dways the fame red entirely as at firft. The 
 like conltancy and immutability I found alfo in 
 the blue, green, and other Colours. So alio it' 
 I looked through a Prii'm upon any Body illu^ 
 minated with any part ol' this homogeneal Light, 
 as in the fourteenth Experiment of the firil Book 
 is defcribed ; I could not perceive any new Co- 
 lour generated this way. All Bodies illumina- 
 ted with compound Light appear through Prilms 
 confuied (as was laid above) and tinged w4th 
 various new Colours, but thole illuminated with 
 homogeneal Light appeared through Prilms 
 neither lefs diilincl, nor otherwife colour'd , 
 than when viewed with the naked Eyes. Their 
 Colours were not in the lealt changed by the 
 Refraction of the intcrpofed Prii'm. I fpeak 
 here of a feniiblG change of Colour: Eor the 
 Light which I here call homogeneal, being not 
 ablolutely homogeneal , there ought to arife 
 lb me little change of Colour from its hetero- 
 geneity. But if that heterogeneity was fo lit- 
 tle as it might be ma'de by the faid Experiments 
 of the fourth Propofition, that change was not 
 fenliblc, and therefore in E.xperiments, where 
 Senle is Judge, ought to be accounted none 
 at all. 
 
 Exper. 6. And as thefe Colours were not 
 changeable byRefradions, fo neither were they 
 by Reflexions. For all white, grey, red, yel- 
 low, green, blue, violet Bodies, as Paper, Alhes, 
 red Lead, Orpiment, Indico, Bife, Gold, Sil- 
 ver, Copper, Grafs, blue Flowers, Violets, 
 Bubbles of Water tinged with various Colours^ 
 Peacock's Feathers, the Tincture of Lignum 
 
 Nepbri- 
 
[io8] 
 
 Nepkriticttm^ and fuch like, in red homogeneal 
 Light appeared totally red, in blue Light to- 
 tally blue, in green Light totally green, and lb 
 of other Colours. In the homogeneal Light 
 of any Colour they all appeared totally of that 
 fame Colour, with this only ditference, that 
 fome of them refleded that Light more Itrong- 
 ly, others more faintly. I never yet found any 
 Body which by reflefting homogeneal Light 
 could fenfibly change its Colour. 
 
 From all which it is manifeft, that if the Sun's 
 Light confifted of but one fort of Rays, there 
 would be but one Colour in the whole World, 
 nor would it be polTible to produce any new 
 Colour by Reflexions and Refraftions, and by 
 confequence that the variety of Colours de- 
 pends upon the compofition of Light. 
 
 7>EF1NITI0K 
 
 TH E homogeneal Light and Rays which 
 appear red , or rather make Objeds ap- 
 pear fo, I call Rubriiic 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 would be underftood to fpeak not philofo- 
 phically and properly, but groffly, 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 nothing elfe than a 
 
 certain 
 
[ 109 ] 
 
 certain power and dilpoiition to flir up a Sen- 
 fation of this or that Colour. For as Sound in 
 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 Objed:, 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- 
 polition to refled this or that fort of Rays more 
 copioully 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. m. Prob. I. 
 
 To define the Refrangibility of the feveral forts 
 of homogeneal Light avfjuering to the feve- 
 ral Colours. 
 
 FO R determining this Problem I made the 
 following Experiment. 
 Exper. 7. When I had caufed the rectili- 
 near fides AF, GM, [in Fig. 4.] of the Spe- 
 6lrum of Colours made by the Prifm to be di- 
 ftindly defined , as in the fifth Experiment of 
 the firil 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 
 Spedrum of fimple Light, defcribed in the 
 fourth Propofition of tliat Part. For the Cir- 
 cles of which the Spedrum of compound Light 
 
 PT 
 
[i.o] 
 
 PT is compofed, and which in the middle parts 
 of the Spedrum interfere and are intermix'd 
 with one another, are not intermix'd in their 
 outmolt parts where they touch thofe redili- 
 near fides A F and G M. And therefore in 
 thofe redilinear fides when diflindly defined, 
 there is no new Colour generated by Refra- 
 ction. I obferved alfo, that if any where be- 
 tween the two outmoft Circles T M F and 
 PGA a right Line, as y'^\ was crofs to the 
 Spe61rum, fo as at both ends to fall perpendi- 
 cularly upon its redilinear iides, 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 FA P GMT, and in trying 
 the third Experiment of the firft Book, I held 
 the Paper fo that the Speflrum might fall upon 
 this delineated Figure, and agree with it exact- 
 ly, whilflanAtFiltant whofeEyes for diftinguifh- 
 ing Colours were more critical than mine, did 
 by right Lifies *,/3, y^, e^, ^c. drawn crofs the 
 Speftrum , note the Confines of the Colours, 
 that is of the red M ^ /3 F, of the orange oLy^Bf 
 of the yellow yi(^, of the green g-/? ^ 5 of the 
 blue yjt)c&, of the indico iAi^k, and of the vio- 
 let A G A jLt. And this Operation being divers 
 tinies repeated both in the fame and in feveral 
 Papers , I found that the Obfervations agreed 
 well enough with one another, and that the 
 rectilinear fides MG and FA were by the faid 
 crofs Lines divided after the manner of a mu- 
 fical Chord. Let GM be produced to X, that 
 MX may be equal to GMj and conceive 
 
 GX 
 
[ III ] 
 
 GX, aX, iX, ^X, eX, yX, uX, MX, to be 
 
 in proportion to one another, as the numbers, 
 i» 4j h 4> h'U-^y-^y and lb to reprefent th^ 
 Chords of the Key, and of a Tone, a third Mi- 
 no]-, a fourth, a fifth, a lixth Major, a feventh 
 and an eighth above that Key : And the Inter- 
 vals Met, oLy,yey f>j, >? t, <A, and aG, wiU bc 
 the Spaces which the feveral Colours (rcdj 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 limits of thofe Colours, thas is, to 
 the Points M, <*, y, 6, ??, i. A, G, may without 
 any fenfible Error be accounted proportional 
 to the differences of the Sines of Kefradion of 
 thofe Rays having one common Sine of Inci- 
 dence, and therefore lince the common Sine of 
 Incidence of the moft and leait refrangible Rays 
 out of Glafs into Air was (by a method defcri- 
 bed above) found in. proportion to their Sines 
 ef Refraftion, as 5-0 to yy and 78, divide the 
 difference between the Sines of Refradion 77 
 and y^y as the Line G M is divided by thofe 
 Intervals, you will have 77^ 774, 77t, 77iy1'l^^ 
 77i-'> 7f7i'> 78, the Sines of Refradion of thof^ 
 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- 
 fi'adions , not greater than 5-0 to 77, nor lefs 
 than 5*0 to 7j-^y but they varied from one ano^ 
 ther according to all intermediate proportions. 
 And the Sines of the Incidences of the green- 
 
 making 
 
[H2] 
 
 making Rays were to the Sines of their Refra^ 
 dions in all proportions from that of fo to 777, 
 unto that of 50 to -j-j'^. And by the like lin:iits 
 iibovementioned were the Refradions of the 
 Rays belonging to the reft of the Colours de- 
 lined, the Sines of the red-making Rays extend- 
 ing from yy to yj^^ thofe of the orange-making 
 from yy^ to yy\,, thofe of the yellow-making 
 from yy^i to yy^^ thofe of the green-making 
 from yy~ to yy^^ thofe of the blue-making from 
 yiy^ to 777, thofe of the indigo-making from 
 .77- to yy^^ and thofe of the violet from yy-^ 
 to 78. 
 
 Thefe are the Laws of the Refradions made 
 out of Glafs into Air, and thencp by the third 
 Axiom of the firlt part of this Book, the Laws 
 of the Refractions made out of Air into Glafs 
 are eafily derived. 
 
 Exper. 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 refrading Superficies be parallel or inclin'd 
 to one another, that Light as often as by con- 
 trary Refractions 'tis lb correded, that 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 degi'ees in paffing on from the place ofE- 
 mergence, become tinged in its edges with 
 Colours. This I tryed by refrading Light with 
 Prifms of Glafs placed within a prifmatickV^f- 
 fel of Water. No W: thofe Colours argue a di- 
 verging 
 
[ "3 ] 
 
 Verging and f^aration of the heterogeneous 
 Rays from one another by m^ans of their une-^ 
 qual Refraftions, as in what follows will more 
 fully appear. And, on the contrary, the per- 
 manent whiteneis argues, that in like hiciden- 
 ces of the Rays there is no fuch feparation of 
 the emerging Kays, and by confequence no in- 
 equaUty of their whole Refradions. Whence 
 I feem to gather the two following Theorems. 
 
 I. The ExcefTes of the Sines of Refradioii 
 of feveral forts of Rays above their common 
 Sine of Incidence when the Refraftions are 
 made out of divers denfer Mediums immedi- 
 ately into one and the fame rarer Medium, fup- 
 pofe of Air, are to one another in a given Pro- 
 portion. 
 
 X. 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 
 firft 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 firlt Theorem the Refractions of the 
 Rays of every fort made out of any Medium in- 
 to Air are known by having the Refradion of 
 the Rays of any one fort. As for in (la nee, 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 ^ fub« 
 
fubdudkd from the Sines of Refradion, and 
 the Excefles will be 27 > ^74, 2,74, 274, 274, 
 27-f, 27^, 28. Suppofe now that the Sine of 
 Incidence of the leaft refrangible Rays be to 
 their Sine of Refradion out of Rain-water in- 
 to Air as 5 to 4, and fay as i the difference of 
 thofe Sines is to 3 the Sine of Incidence, fo is 
 27 the leaft of the ExcelTes above-mentioned 
 to a fourth number 81 ; and 81 will be the 
 common Sine of Incidence out of Rain-water 
 into Air, to which Sine if you add all the a- 
 bovcmentioned ExcelTes you will have the de- 
 fired Sines of the Refractions 108, io84> 1084, 
 
 1084, 1084-5 loS-i, 108:7, 109. 
 
 By the latter Theorem the Refradion out of 
 one Medium into another is gathered as often 
 as you have the RefraClions 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 Refraction, as 20 to 31, and the Sine 
 of Incidence of the fame Ray out of Air into 
 Water, be to its Sine of Rerradion as 4 to 3 ; 
 the Sine of Incidence of that Ray out of Glafs 
 into Water will be to its Sine of Refradion as 
 20 to 31 and 4 to 3 jointly, that is, as the Fa- 
 dum of 20 and 4 to the Fadlum of 3 1 and 3 > 
 or as 80 to 93. 
 
 And thefe Theorems beir^g admitted into Op- 
 ticks, there would be icope enough of hand- 
 ling that Science voluminoully after a new man- 
 ner ; not only by teaching thofe things which 
 tend to the perfeClion of Vifion , but alfo by 
 determining mathematically all kinds of Phae- 
 nomena of Colours which could be produced 
 , s by 
 
["5] 
 
 by Refia6tions. For to do this, there is nO" 
 thing elle requifite than to find out the Separa- 
 tions of heterogeneous Rays, arkd their various 
 Mixtures and Proportions in ever}^ IVlixture. 
 By this way of arguing I invented ahnoft all the 
 Phaenomena defcribed in thefe Books, befide 
 fome others lefs necelfary to the Argument; 
 and by the fuccefTes I met with in the Trials, I 
 dare promife, that to him who ihall argue tru- 
 ly, and then try all things with good Glafles 
 and fufBcient Circumfpedion, the expefted E- 
 vent will not be wanting. But he is iirft to 
 know what Colours will ariie from any others 
 mix'd in any afligned Proportion. 
 
 TROT. IV. Theor. m. 
 
 Colours may be produced by Compojitton which 
 /hall be like to the Colours of homogeneal Light 
 as to the Appearance of Colour^ but not as to 
 the Immutability of Colour and Conjiitution 
 of Light, And thofe Colours by ho'w much 
 they are ?nore compoMidedby fo much are they 
 lefs full and intenfcy and by too much Compo- 
 fition they may be diluted a7id weaken' d till 
 they ceafey and the Mixture becomes white or 
 grey. There may be alfo Colours produced by 
 Compo/itiony 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 appea- 
 rance of Colour to that orange which in the 
 
 I 2. feries 
 
[ "O 
 
 feries of unmixed prifmatick Colours lies be- 
 tween them ; but the Light of one orange is 
 homogeneal as to Refrangibility , that of the 
 oth^r 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, tlicre will be made a green the midde 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 T^quilibrio, 
 that it verge not more to the yellow on the one 
 hand, than to the blue on the other, but by 
 their mix'd Anions remain Itill 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 increafmg 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 
 vaniili or change its Species but be diluted , 
 and by adding more and more white it will be 
 diluted more and more perpetually. Laiftly, if 
 
 ', - - - ^^^ 
 
red and violet be mingled, 
 
 lere will be gene- 
 
 rated according to their various Proportions 
 various Purples, fuch 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. 
 
 TROT. V. Theor. IV. 
 
 Whitenefs and all grey Colours bet'vjecn "juhite 
 and blacky may be compounded of Colour s^ and 
 the whitenefs of the Suns Light is compound- 
 ed of all the primary Colours mix'd in a due 
 Trofortion. 
 
 The Proof by Experiments. 
 
 Exper. 9. T~^HE Sun ihining into a dark 
 1 Chamber through a little round 
 hole in the VV^indow-fhut, 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 \^ to that Image in fuch man- 
 ner that it might be illuminated by the coloured 
 Light refleded from thence, and yet not inter- 
 cept any part of that Light in its paflage from 
 the Prifm to the Spe£lrum. And I found that 
 when the Paper was held nearer to any Colour 
 thaa to the rell, it appeared of that Colour to 
 which it approached nearefi: ; but when it was 
 equally or almoil equally diflant from all the 
 Colours , fo that it might be equally illumina- 
 ted by them all it appeared white. And in this 
 kit fituation of the Paper, if fome Colours were 
 
 I 3 intcr-^ 
 
 k 
 
[n8] 
 
 intercepted, the Paper loft its white Colour, and 
 appeared of the Colour of the reft of the Light 
 which was not intercepted. So then the Pa- 
 per was illuminated with Lights of various Co- 
 lours, namely, red, yellovv, 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; 
 fo that if it had been either alone (the reft of 
 the Light being intercepted ) or if it had a- 
 boundcd moft and been predominant in the 
 Light reflected 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 Compofttion with the reft 
 produced that Colour. The fevcral parts of 
 the coloured Light reflefted from the Spectrum, 
 whilft they are propagated from thence through 
 the Air, do perpetually retain their proper Co- 
 lours, becaufe wherever they fall upon the Eyes 
 of any Spedator, they make the feveral parts of 
 the Spedrum to appear under their proper Co- 
 lours. Tliey retain therefore their proper Co- 
 lours when they fall upon the Paper V, and fo 
 by the confufion and perfedt mixture of thofe 
 Colours compound the whitenefs of the Light 
 lefleded from thence. 
 
 Exper. lo. Let that Spe(^rum or folar Image 
 PT [in F'tg. 6.] fall now upon the Lens MN 
 above four Inches broad, and about fix Feet di- 
 ftant from the Prifm ABC, and fo fi glared that 
 it may caufe the coloured Light which diverg- 
 fx\\ frOiB th^ Prifm to converge and meet again 
 
 4t 
 
at its Focus G, about fix or eight Feet diflant 
 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 de^ the whole folar Image 
 (fuppofe 2X. ft) will appear upon it intenfely 
 coloured after the manner above-expkiincd, and 
 that by receding from the Lens thole 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 pcrfed mixture they 
 will wholly vanifli and be converted into white- 
 nefs, the whole Light appearing now upon the 
 Paper like a httle white Circle. And after- 
 wards by receding futher 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 hj where the red t is now above which 
 before was below , and the violet / is below 
 which before was above. 
 
 Let us now flop the Paper at the Focus G 
 where the Light appears totally white and cir- 
 cular, and let us confidcr its \\hitcnefs. I fay, 
 that this is compofed of the converging Colours. 
 For if any of thofe Colours be intercepted at 
 the Lens, the whitencfs will ccafe and degene- 
 rate into that Colour which avifeth from the 
 compofition of the other Colours \^ich are not 
 intercepted. And then if the intercepted Co- 
 lours be let pafs and fall upon that compound 
 Colour, they mix with it, and by their mixture 
 
 I 4 reitore 
 
[ 120 ] 
 
 reflore the wKitenefs. 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 £, 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 thereb)^ as it ought to do if 
 the feveral forts of Rays aisled upon one ano- 
 ther in the Focus G, where they crofs. Nei- 
 ther wjjl the red upon the Paper be changed 
 by any alternate flopping, and letting pafs the 
 violet which crolleth 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 Refraclion 
 of thatPriftn be tranflated to the place rvy 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 diflippear 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 y 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 a^l on one 
 another. And the^e is the fame reafon of the 
 other Colours. 
 
 I confidered farther, that when the mod re- 
 frangible Rays P/, and the leaft refrangible 
 ones Tt, are by converging inclined to one a- 
 nother, the Paper, if held very oblique to thofe 
 Rays in the Focus G, might reflec^t one fort of 
 them more copioully than the other fort, and 
 by that means the reflected Light would be 
 tinged in that Focus with the Colour of the pre-^ 
 dominant Rays, provided thofe Rays feveraliy' 
 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 
 white, but became all of them feverally endued 
 there with a difpofition 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 mofl refrangible Rays might be 
 more copioufly refleded than the rell, and the 
 whitenefs at length changed fucceflively into 
 blue, indigo and violet. Then I inclined it 
 
 the 
 
[ 122 ] 
 
 the contrary way, that the leafl refrangible Rays 
 might be more copious in the retle&d Light 
 than the reil., and the whitenefs turned fuc- 
 cellively to yellow, orange and red. 
 
 Laflly, 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 fucceflivety the 
 Teeth of this Inftrument 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 D E, and 
 there ipainted a round folar Image. But the 
 Paper I had firft 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 palling 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 pais fucceffively over the Lens, and 
 when the Motion was flow , there appeared a 
 perpetual fucceftion of the Colours upon the 
 Paper : But if I fo much accelerated the Mo- 
 tion, that the Colours by reafon of their quick 
 fucceiTion could not be diitinguiflied from one 
 another , the appearance of the fmgle 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 w^as 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 Impreflions follow one another 
 flowl}', fo that they may be fev^erally perceived, 
 there is made a diilint^i: 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 arifcth 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 quickneis of the Succef- 
 iions the Imprellions of the feveral Colours are 
 confounded in the Senforium, and out of that 
 confufion arifcth 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 
 w hich 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 ImprelTion of every Co- 
 lour remains in the Senforium, until a revolu- 
 tion of all the Colours be compleated, and that 
 fir il Colour return again. The Impreflions there- 
 fore of all the fucceiRve Colours are at once in 
 
 the 
 
[ 124] 
 
 the Senforium , and jointly iHr up a Senfation. , 
 of them all ; and fo it is manifeit by this Expe- 
 riment , that the commix'd Imprellions of all 
 the Colours do llir up and beget a Senlation of 
 white, that is, that whitenefs is compounded 
 of all the Colours. 
 
 And if the Comb be now taken away, that 
 all the Colours may at once pafs from the Lens 
 to the Paper, and be there intermixed, and to- 
 gether retlecled thence to the Spedators Eyes ; 
 their Impreflions on the Senforium being now 
 more fubtilly and perfectly commixed there, 
 ought much more to ftir up a Senfation of 
 whitenefs. 
 
 You may inflead of the Lens ufe two Prifms 
 HIK and LMN, which by refrading the co- 
 loured Light the contrary way to that of the 
 iirll Refradion, may make the diverging Rays 
 converge and meet again in G, as you fee re- 
 prefcnted in the fcventh Figure. For where 
 tiiey meet and mix they will compole a white 
 Light, as when a Lens is ufed. 
 
 Exper. II. Let the Sun's coloured hnage PT 
 [in F//[. 8.] fill upon the Vv'all o. a dark Cham- 
 ber, as in the third Experiment of the firlt Book, 
 and let the fanje be vicu^ed through a Priim 
 abc^ held parallel to the Prifni A B C, by whofe 
 Refraclion that hn;^ge was made, and let it now 
 appear lower than before, fuppofe in the place 
 Sever againfl the red Colour T. And if you 
 go near to the Image P T, the Spedrum S will 
 appear oblong and coloured like thehiiagePT; 
 Ixit if you recede from it, the Colours of the 
 Spedrum S will be contradcd more and more, 
 
 and 
 
I 125 ] 
 
 and at length vanifh, that Spedrum S becoming 
 perfedly round and white ; and if you recede 
 yet farther, the Colours will emerge again, bur 
 in a contrary order. Now that Spectrum S ap- 
 pears white in that cafe when the Rays of le- 
 vcral forts which converge from the fevcrai 
 pans of the Image PT, to the Prifm al^c, are 
 lb refra(^ted 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- 
 ctrum S, and fo fall afterwards upon one and 
 the fame point in the bottom of the Eye, and 
 there be mingled. 
 
 And farther, if the Comb be here made ufe 
 of, by whofe Teeth the Colours at the Image 
 PT may be fuccellively intercepted; the Spe- 
 <!:trum S when the Comb is moved flowly will 
 be perpetually tinged w ith fucceflive Colours : 
 But when by accelerating the motion of the 
 Comb, the fucccllion of the Colours is fo quick 
 that they cannot be feverally leen, that Spe- 
 drum S, by a confufed and mix'd Senfation of 
 them all, will appear white. 
 
 Exper. 12. The Sun fliining through a large 
 Prifm ABC [in Fig. ^. ] upon a Comb X Y, 
 placed immediately behind the Prifm, his Light 
 which palled tlu'ough the Interllices of the 
 Teeth fell upon a white Paper D E. The 
 breadths of the Teeth were equal to their In- 
 terllices, and feven Teeth together with -their 
 Interllices took up an Inch in breadth. Now 
 when the Paper was about two or three Inches 
 diltant from the Comb, the Light which paf- 
 fed through its ieveral Interllices painted {q 
 
 many 
 
[126] 
 
 many ranges of Colours, kl, mn, of^ ar, &c, 
 which were parallel to one another and conti- 
 guous, and without any mixtui'e of white. And 
 thefe ranges of Colours , if the Comb was mo- 
 ved continually up and down with a reciprocal 
 motion, afcended and defcended in the Paper , 
 and when the motion of the Comb was fo quick, 
 that the Colours could not be diftinguilhed 
 from one another, the whole Paper by their 
 confufion and mixture in the Senforium appear- 
 ed white. 
 
 Let the Comb now reft, and let the Paper 
 be removed farther from the Prifm , and the 
 fevcral ranges of Colours will be dilated and 
 expanded into one another more and more, 
 and by mixing their Colours will dilute one a- 
 nother , and at length , when the diftance of 
 the Paper from the Comb is about a Foot, or a 
 little more (fuppofe in the place x D x E) they 
 will fo far dilute one another as to become 
 white. 
 
 With any obftacle let all the Light be now 
 ftopp'd which paifes 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 xD iE be now very much in- 
 cline4 to the Rays, fo that the moft refrangible 
 
 Rays 
 
[ 127 ] 
 
 Rays may be more copioufly refleded than the 
 reft, and the white Colour of the Paper through 
 the Excefs of thofe Rays will be changed into 
 blue and violet. Let the Paper be as much in- 
 clined the contrary way, that the leaft refran- 
 gible Rays may be now more copioully refle61- 
 ed than thereft, and by their Excefs the white- 
 nefs will be changed into yellow and red. The 
 feveral Rays therefore in that white Light do 
 retain their colorific quahties, 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- 
 ded 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 Phajnomenon of one Pril'm. Whence 
 mftead of thofe intei-vals ufing feveral Prifms, 
 I try'd to compound whitenefs by mixing their 
 Colours, and did it by uling only three Prifms, 
 as alfo by ufmg only two as follows. Let two 
 Prifms ABC and abc^ \mF'tg.\o.'\ whofe re- 
 frading Angles B and b are equal, be fo placed 
 parallel to one another, that the refrading An- 
 gle B of the one may touch the Angle c at the 
 Bafe of the other , and their Planes C B and 
 cby at which the Rays emerge, may lie in Di- 
 rectum, 
 
[128] 
 
 rectum. Then let the Light trajeded through 
 them fall upon the Paper MN, diitant about 8 
 or li Inches from the Prifms. And the Co- 
 lours generated by the interior limits B and ^ 
 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 PT, and when the 
 Prifm is reftored to its place again, fo that its 
 Colours may there fall upon the Colours of the 
 other, the mixture of them both will reflore 
 the whitenefs. 
 
 This Experiment fucceeds alfo, as I have tri- 
 ed, when the Angle h 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 Br, as is reprefented in 
 the Figure, and the refrading Planes B C and 
 b r, are neither in diredum, nor parallel to one 
 another. For there is nothing more requifite 
 to the fuccefs of this Experiment, 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 red 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^o- 
 the'r Prifm ought to begin at T, and take up 
 the remaining fpace TN. If one fort of the 
 Rays which have intermediate degrees of Re- 
 
 frangibility. 
 
[ 129 ] 
 
 frangibility, and come from the fupcrior.Prifm 
 be extended through the fpace MQ, and an- 
 other Ibrt of thofe Rays through the fpace MR, 
 and a third fort of them through the ipacc MS> 
 the fame forts of Rays coming from the lower 
 Prifm, ought to illuminate the remaining fpaces 
 QN, RN, SN, refpedively. And the fame 
 is to be undei'ltood of all the other forts of 
 Rays. For thus the Rays of every fort will be 
 fcattered liniformly and eavenly thro' the whole 
 fpace MN, and fo being every where mix'd in 
 the fame proportion, they mud every where 
 produce the fame Colour. And therefore fmce 
 by this mixture they produce white in the ex- 
 terior fpaces MP and TN, they mull alfo pro- 
 duce wiiite in the interior fpace PT. This is 
 the reafon of the compoiition by which white- 
 nefs was produced in this Experiment, and by 
 what other way foever I made the like compo- 
 fition the refult was whitenefs. 
 
 Laitly, If with the Teeth of a Comb of a due 
 fize, the coloured Lights of the two Prifms 
 which M upon the fpace PT be alternately 
 intercepted, that fpace PT, when the motion 
 of the Comb is How, will always appear co- 
 loured , but by accelerating the motion of the 
 Comb fo much, that the fuccellive Colours 
 cJmnot be diilinguilhed from one another, ic 
 will appear white. 
 
 Exper. 14. Hitherto I have produced Vv^hite- 
 nefs by mixing the Colours of Prii'ms. If now 
 the Colours of natural Bodies are to be min- 
 gled , let Water a little thicken'd with Soap be 
 agitated to raife a Froth, and after that Froth 
 
 K has 
 
[i3o] 
 
 has flood a little, there will appear to one that 
 fhall view it intently various Colours every where 
 in the Surfaces of the feveral Bubbles ; but to 
 one that iliall go fo far off that he cannot di- 
 llinguifli the Colours Irom one another , the 
 vvhole Froth will grow white with a perfed 
 whitenefs. 
 
 ExPer. 15-. Lailly, in attempting to com- 
 pound a white by mixing the coloured Powders 
 which Painters ufe, I confider'd that all co- 
 lour'd Powders do fupprefs and flop in them a 
 very confidcrable part of the Light by which 
 they are illuminated. For they become colour'd 
 by refleding the Light of their own Colours 
 more copioufly, and that of all other Colours 
 more fparingly, and yet they do not refleft the 
 Light of their own Colours fo copioufly as 
 white Bodies do. If red Lead , for initance , 
 and a white Paper, be placed in the red Light 
 of the colour'd Spcdrum made in a dark Cham- 
 ber by the P^efradion of a Prifm, as is defcri- 
 bed in the third Experiment of the firfl Book ; 
 the Paper will appear more lucid than the red 
 Lead , and therefore refleds the red-making 
 Rays more copioufly than red Lead doth. And 
 if they be held in the Light of any other Co- 
 lour, the Light refleded 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 flrong 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. 
 
[nl] 
 
 il&fs, or from white and black, that is, a grey^ 
 or dun, or ruiTet brown, fuch as are the Co- 
 lours of a Man's Nail, of a Moufe, of Alhes, 
 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 Viride jEris, compo- 
 fed a dun Colour Hke that of a Moufe. For 
 thefe two Colours were feverally fo compound- 
 ed of others, that in both together were a mix- 
 ture of all Colours ; and there was lefs red Lead 
 ufed than Viride ^^ris , 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 
 Viride jEris in a due proportion, the mixture 
 lolt its purple tindure , and became perfedly 
 dun. Ikit the Experiment fucceeded belt with- 
 out Minium thus. To Orpiment I added by 
 little and little a certain full bright purple ji 
 which Painters ufe until the Orpiment ceafed 
 to be yellow, and became of a pale red. Then 
 I diluted that red by adding a httle Viride M^ 
 risy and a little more blue Bife than Viride M^ 
 rus^ until it became of fuch a grey or pale vi^^hite^ 
 as verged to no one of the Colours more than 
 to another. For thus it became of a Colour e- 
 qual in whifenefs to thatof A(hes or of Wood 
 newly cut, or of a Man's Skin. The Orpiment 
 reflec^ted more Light than did any other of thd 
 Powders, and therefore conduced rnore td th^ 
 whitenefs of the compounded Colour than they. 
 
I 132 ] 
 
 To alTign 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 Icls or great- 
 er proportion. 
 
 Now confidering that thefe grey and dun Co- 
 lours may be alfo produced by mixing whites 
 and blacks, and by confequence ditier from 
 perfed whites not in fpecies of Colours but on- 
 ly in degree of Luminoufnefs , it is manifefl 
 that there is nothing more requifite to make 
 them perfedly white than to increafe their Light 
 fufficicntly; and, oh the contrary, ifbyincrea- 
 {mg their Light they can be brought to perfcft 
 vvhitenefs, it will thence alfo follow, that they 
 are of the famiC fpecies of Colour with the bell 
 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, Bifc, and Vtride ^ru) and rubbed it thick- 
 ly upon the Floor of my Chamber, where the 
 Sun llione upon it through the opened Cafe- 
 ment ; and by it, in the ihadow, I laid a piece 
 of white Paper of the fame bignels. Then going 
 from them to the diflanceof iz or 18 Feet, lo 
 that I could not difcern the uneavennefs of the 
 Surface of the Powder, nor the little Shadows 
 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 httle fliaded from the 
 Light of the Clouds, and then the Paper com- 
 pared 
 
[ '33 ] 
 
 pared with the Powder appeared of fuch a grey 
 Colour as the Powder had done before. But 
 by laying the Paper where the Sun iliines thro* 
 the Glafs of the Window, or by lliutting the 
 Window that the Sun might Ihine through the 
 Glais upon the Powder, and by fuch other fit 
 means of increafmg or decreafmg the Lights 
 wherewith the Powder and Paper were illumi- 
 nated, the Light wherewith the Powder is illu- 
 minated may be made itronger in fuch a due 
 proportion than the Light whereuith the Paper 
 is illuminated, that they fhall both appear ex- 
 adlly 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 
 beft, and wherein they differed ? And after he 
 had at that diflance 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 (Orpimcnt, 
 Purple, Bife , and Vir'tde Mr is) have in the 
 fame Sun-fliine, you muft acknowledge by this 
 Experiment, as well as by the former, that per- 
 feft 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 Avhcrewith the fe- 
 veral forts of Rays whereof that Light confifls, 
 when by their feveral Ref-ai^.gibiUtiestliey are 
 
 K 5 fepa- 
 
[i34] 
 
 feparated from one another, do tinge Paper or 
 any other white Body whereon they fall. For 
 thofe Colours by Trcp. i. 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. II. 
 
 In a mixture of primary Colours, the quantity 
 and quality of each being given, to know the 
 Colour of the Compound, 
 
 WITH the Center O [in Fig. ii.] and Ra- 
 dius OD defcribe a Circle ADF, and 
 ditlinguiili its circumference into feven parts 
 DE, EF, FG, GA, AB, BC, CD, propor- 
 tional to the feven mufical Tones or Intervals 
 of the eight Sounds, Sol, la, fa, fol, la, mi, fa^ 
 fol, contained in an eight, that is, proportional 
 to the number 7, t'^.-, t^, t> iv> tW ^. Let the 
 firit part DE reprefent a red Colour, the fe- 
 cond EF orange, the third FG yellow, the 
 fourth C A green, the fifth AB blue, thefixth 
 B C indigo, and the feventh C D violet. And 
 conceive that thefe are all the Colours of un^ 
 compounded Light gradually pafTmg into one 
 another, as they do when made by Prifms ; the 
 circumference DEFGABCD, reprefenting 
 the whofe feries of Colours from one end of 
 the Sun's colour 'd Image to the other , fo that 
 from P to E be all degrees of red, at E the 
 Xn^m CqIqi}}: between red and grange, from E 
 
 toF 
 
[ 135] 
 
 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 f be the cen- 
 ter of gravity of the Arch DE, and ^, r, j, r, 
 «, A-, the centers of gravity of the Arches E F, 
 FG, GA, AB, BC and C D refpertively, 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 / proportional to the number of the 
 red-making Rays in the Mixture , the Circle q 
 proportional to the number of the orange-ma- 
 king Rays in the Mixture, and io of the reft. 
 Find the common center of gravit)' of all rhofe 
 Circles />, ^, r, j-, /, ?/, x. Let tbat center be 
 Z; and from the center of the Circle AD F, 
 through Z to the circumference, drawing the 
 right Line O Y, the place of the Point Y in the 
 circumference fhall iliew the Colour arifing 
 from the compofition of all the Colours in the 
 given Mixture, and the Line O Z Ihall be pro- 
 portional to the fulnefs or intenfcncfs of the 
 Colour, that is, to its diilance from vvhitenefs. 
 As if Y fall in the middle between F and G, 
 the compounded Colour Ihall be the beft yel- 
 low; ^{ Y verge from the middle towards F 
 or G, the compound Colour Ihall accordingly 
 be a yellow, verging towards orange or green. 
 If Z fall upon the circumference the Colour 
 fhall be intenfe and florid in the higheii: degree ; 
 if it fall in the mid way between the circum- 
 ference and center, it fliall be but half fo 
 intenfe, that is, it fhall be fuch a Colour as 
 would be made by diluting; the intenfeft yellow 
 
 K 4 with 
 
vvith an equal quantity of whitenefs; and if it 
 fall upon the -center O, the Colour fliall have 
 lofl 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 D , 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 line 
 D 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 
 oppofitc to one another be mixed in an equal 
 proportion, the point Z fliall fall upon the cen- 
 ter O, and yet the Colour compounded of 
 thofe two fliall not be perfectly white, but fome 
 faint anonymous Colour. For I could never 
 yet by mixing only two primary Colours pro- 
 duce a perfe(^t white. Whether it may be com- 
 pounded of a mixture of three taken at equal 
 dillances in the circumference I do not know, 
 but of four or five I do not much queltion but 
 it may. But thefe are Curiofities of little 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 alf forts of 
 Rays, and by corrfequence a compofition of all 
 Colours. 
 
 To give an inflance of this Rule ; fuppofe a 
 Colour is compounded of thefe homogencal 
 Colours, of violet one part, of indigo one part, 
 of blue two parts, of green three parts, of yel- 
 low five parts, of orange fix parts, and of red 
 
 ten 
 
[i37] 
 
 ten parts. Proportional to thefe parts defcribe 
 the Circles x, v, r, j", r, c/, p, refpedivelv, that 
 is, lb that if the Circle x be one, the Circle ^' 
 may be one, the Circle t two, the Circle s three, 
 and the Circles r, ^ and /, five, fix and ten. 
 Then I tind Z the common center of gravity of 
 theie Circles, and through Z drawing the Line 
 O Y, the Point Y falls upon the circumference 
 between E and F, Ibme thing nearer to E than 
 to F, and thence I conclude , that the Colpur 
 compoundto of thefe Ingredients will be an o- 
 range, ver'};ing a little more ro red than to yel- 
 low. Alfo T tmd that O Z is a little lefs than 
 one half of O Y, and thence I conclude, that 
 this orange iiath a little lefs than half the ful- 
 ncfs or intenft nefs of an uncompounded o- 
 range ; that is to iay, that it is fuch an orange 
 as may be made by mixmg an homogeneal o- 
 range with a good while 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 reflected from them. 
 
 This Rule I conceive accurate enough for 
 pradice, though not mathematically accurate ; 
 and the truth of it may be fufficiently proved to 
 Senfe , by Hopping any of the Colours at the 
 Lens in the tenth Experiment of this Book. For 
 the relt of the Colours which are riot llopp'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 
 their Mixture, 
 
 "PROT. 
 
[i38] 
 
 TROT. Vn. Theor. V. 
 
 jill the Colours in the ^niverfe which are made 
 by Lights and depend not on the Tower of 1- 
 maginattony are either the Colours of homoge- 
 neal Light Sy or compounded of thefe^ and that 
 •either accurately or very nearly^ according to 
 the Rule of the foregoing Troblem. 
 
 FOR it has been proved (mTrop.i. Tart.z.) 
 that the changes of Colours made by Re- 
 fractions do not ariie from any new Moditica* 
 tions of the Rays imprefs'd by thofe Refractions, 
 and by the various Terminations of Light and 
 Shadow, as has been the conflant and general 
 Opinion of Philofophers. It has alfobeen pro- 
 ved that the feveral Colours of the homogeneal 
 Rays do conlbntly anfwer to their degrees of 
 Refrangibility, (Trop.i. Tart i. and Trof.i. 
 Tart 1.) and. that their degrees of Refrangibi- 
 lity cannot be changed by Refractions and Re* 
 flexions, (Trop.t. Tart, \.) and by confequence 
 that thofe their Colours are likewife immuta- 
 ble. It has alfo been proved diredtly by refra- 
 cting and reflecting homogeneal Lights apart , 
 that their Colours cannot be changed, (Trop. i, 
 Tart.-L.) 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 
 aCt on one another fo as to change each others 
 colorific qualities. (Exper. lo. Tart.i.) but by 
 mixing their ACtions in the Senforium beget a 
 Senfation differing from what either would do 
 apart, that is a Senfation of a mean Colour be- 
 tween 
 
[ 139 ] 
 
 tween their proper Colours; and particularly 
 when by the concourle and mixtures of all 
 forts of Rays, a white Colour is produced, the 
 white is a mixture of all the Colours which the 
 Rays would have apart , (Trop. $. Tart x.J 
 The Rays in that mixture do not lofe or alter 
 their feveral colorific qualities ,' but by all their 
 various kinds of Adions mix'd in the Senfori- 
 um , 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 , fo 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 tftichanged not- 
 withllanding any Refractions 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 i. or by 
 Refraction as happens in all Refraftions ) fepa- 
 rated from the reft , they then manifef t their 
 proper Colours. Thefe things have been prov'd, 
 ftnd the fum of all this amounts to the Propofi- 
 tion here to be proved, For if the Sun's Light 
 
 is 
 
[ ho] 
 
 is mix'd of feveral forts of Rays, each of which ' 
 have originally their feveral Refrangibilities and 
 colorific Qualities , and notwithlbnding their 
 Refradions 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 
 mull be fuch as conftantly ought to arife from 
 the original colorific qualities of the Rays where- . 
 of the Lights confilt 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 conlider how the Rays in the. 
 Sun's Light have by Reflexions or Refraftions, 
 or other caufes been parted from one another, 
 or mixed together ; or otherwife to find out 
 what forts of Rays are in the Light by which 
 that Colour is made , and in what proportion ; 
 and then by the lall 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 lb far as thev arife fromLio;ht. 
 For they appear fometimes by other Caufes, as 
 when by the power of Phantafy we fee Colours 
 in a dream, or a mad Man fees things before 
 him which are not there ; or when we fee Fire 
 by llriking the Eye, or fee Colours hke theE^^e 
 of a Peacock's Feather, by prefiing our Eyes in 
 either corner whillt we look the other way. 
 Where thefe and fuch like Caufes interpofe not, 
 the Colour aU'ays anfwers to the fort or forts 
 of the Rays whereof the Light confifls , as I 
 have conlfantly found in whatever Phaenomena 
 of Colours I have hitherto been able to exa- 
 
 . mine. 
 
[hi] 
 
 mine. I fhall in the following Propofitions give 
 inlhnces of this in the Phaenomena of chiefell 
 note. 
 
 TROT.VIU. Prob. m. . 
 
 By the dtfcovered Properties of Light to ex" 
 plain the Colours made by T^rtjms. 
 
 LET ABC \\riFig. IX.] reprcfcnt a Prifm 
 refra6]:ing the Light of the Sun, which 
 comes into a dark Chamber through a hole F<p 
 almolt as broad as the Prifm, and let MN re- 
 prefent a white Paper on which the refraded 
 Light is caft, and fuppofe the moil refrangible 
 or deepeil violet-making Rays fall upon the 
 Space P TT, the leaft refrangible or deepelt red- 
 making Rays upon the Space T7> the middle 
 fort between the indigo-making and blue-ma- 
 king Rays upon the Space Q;^, the middle fort 
 of the green-making Rays upon the Space R^, 
 the middle fo^t between the yellow-making and- 
 orange-makingRays upon the Space So-, ando- 
 ther intermediate forts upon intermediate Spa- 
 ces. For fo the Spaces upon which the feveral 
 forts adequately fall will by rcafon of the dif- 
 ferent Retrangibility of thole forts be one lower 
 than another. Now if the Paper M N be fo 
 near the Prifm that the Spaces P T and ;r 7 do 
 not interfere with one another, the diltance be- 
 tween them Ttt will be illuminated by all the 
 forts of Rays in that proportion to one another 
 which they have at their very firfl coming out 
 
 of 
 
[ H2 ] 
 
 of the Prifm, and confequently be white. But 
 the Spaces P T and 77-7 on either hand, will not 
 be illuminated by them all, and therefore will 
 appear coloured. And particularly at P, where 
 the outmolt violet-making Rays fall alone, phe 
 Colour mud be the deepelt violet. At Q where 
 the violet-making and indigo-making Rays are 
 mixed , it mult be a violet inclining 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 conltru6tion of the fecond Pro- 
 blem) com.pound a middle Colour between in- 
 digo and blue. At S where all the Rays are 
 mixed except the red-making and orange-ma- 
 king, their Colours ought by the fame Rule to 
 compound a faint blue, verging more to greeii 
 than indigo. And in the progrefs from S toT, 
 this blue \^'ill grow more and more faint and 
 dilute, till at T, where all the Colours begin to 
 be mixed, it ends in whitenefs. 
 
 So again, on the other fide of the white at r, 
 where the leaft refrangible or utmoft red-ma- 
 king Rays are alone, the Colour mull be the 
 deepelt red. At 0- the mixture of red and o- 
 range will compound a red inclining to orange. 
 At ^ the mixture of red, orange, yellow, and 
 one half of the green mult compound a middle 
 Colour between orange and yellow. At % the 
 mixture of all Colours but violet and indigo will 
 compound a faint yellow, verging more to green 
 than to orange. And this yellow will grow 
 more faint and dilute continually in its progrefs 
 
 from 
 
[ 143 J 
 
 from ;^ to TT, where by a mixture of all foiifs 
 of Rays it will become white. 
 
 Thefe Colours ought to appear were the Sun's 
 Light perfeftly white : But becaufe it inclines 
 to yellow, the Excefs of the yellow-making 
 Rays whereby 'tis tinged with that Colour, be- 
 ing mixed with the faint blue between S and T, 
 will draw it to a faint green. And fo the Co- 
 lours in order from P to r ought to be violet, 
 indigo, blue, very faint gfeen, white, faint yel- 
 low, orange, red. Thus it is by the computa- 
 tion : And they that pleafe to view the Colours 
 made by a Prifm will find it fo in Nature. 
 
 Thefe are the Colours on both fides the white 
 when the Paper is held between the Prifm, and 
 the Point X where the Colours meet, and the 
 interjacent white vaniihes. For if the Paper be 
 held iHll farther off from the Prifm, the moil: 
 refrangible and lead refrangible Rays will be 
 wanting in the middle of the Light, and the 
 reft of the Rays which are found there, will by 
 mixture produce a fuller green than before. Al- 
 fo the yellow and blue will now become lefs 
 compounded, and by confcquence more intenfe 
 than before. And this alfo agrees with expe- 
 rience. 
 
 And if one look through a Prifm upon a 
 white Objed encompafled with blacknefs or 
 darknefs, the reafon of the Colours arifmg^n 
 the edges is much the fame, as will appear to 
 one that Ihall a little confider it. If a black Ob- 
 u jeft be encompailed wdth a white one, the Co- 
 lours which appear through the Prifm are to be 
 derived from the Light of the white one, fpread- 
 
 ing 
 
[ 144 ] 
 
 ingiffito the Regions of the black, and there- 
 fore they appear in a contrary order to that^ 
 when a white Objed is furrounded with black. 
 And the fame is to be underllood when anOb- 
 jed is viewed , whofe parts are Ibme of them 
 lefs luminous than others. For in the borders 
 of the more and lefs luminous parts , Colours 
 ought always by the fame Principles to arife 
 from the F,xcefs of the Light of the more lu- 
 minous , and to be of the fame kind as if the 
 darker parts were black , but yet to be more 
 faint and dilute. 
 
 What is faid of Colours made byPrifms may 
 be ealily af)plied to (Colours made by theGlafles 
 of Telefcopes or Microfcopes, or by the Hu- 
 mours of the Eye. For if the Objed-glafs of 
 a Telefcope be thicker on one fide than on the 
 other, or if one half of the Glafs, or one half 
 of the Pupil of the Eye be cover'd .with any 
 opake fubltance:. the Objcd-glafs, or that part 
 of it or of the F.ye which is not cover'd , may 
 be confider'd as a Wedge with crooked Sides, 
 and every Wedge of Glafs or other pellucid 
 Subilance has the efictt of a Prifm in refrading 
 the Light which pailcs through it. 
 
 How the Colours in the ninth and tenth Ex- 
 periments of the iirlt Part arife from the diffe- 
 rent Reflexibility of Light, is evident by what 
 was there laid. But it is obfervable in the ninth 
 Experiment, that whilit the Sun's dired Light 
 is yellow, the Excefs of the blue-making Rays 
 in the retleded beam of Light MN, fuffices 
 only to bring that yellow to a pale white incli- 
 ning to blue , and not to tinge it with a mani- 
 
 - feilly 
 
[ H5 ] 
 
 feftly blue Colour. To obtain therefore a bet- 
 ter blue, I ufcd inltead of the yellow Light of 
 the Sun the white Light of the Clouds, by va- 
 rying a little the Experiment, as follows. 
 
 Ex^er.i6. LetHFG [ini^/V. 13.] repre- 
 fent a Prifm in the open Air, ancf S the Eye of 
 the Spcdator, viewing the Clouds by their 
 Light coming into the Prifm at the plane lide 
 FTGK, and reflected in it by its bale HEIG, 
 and thence going out through its plane fide 
 H E E K to the Eye. And wlien the Priim and 
 Eye are conveniently placed, lb that the Angles 
 of Incidence and Reflexion at the Bafe may be 
 about 40 Degrees, the Spedator will fee a BoW 
 M N of a blue Colour, running from one end of 
 the Bafe to the other, with the concave fide 
 towards him, and the part of the Bafe IMJ^G 
 beyond this J^ow will be brighter than the other 
 part EMNH on the other tide of it. This blue Co- 
 lour MN being made by nothing elfe than by re- 
 flexion of a fpecular Superficies, feems fo odd it 
 Phainomenon, and fo difficult to be explain- 
 ed by the vulgar Hypothecs of Philofophers^ 
 that I could not but think it deferved to be ta- 
 ken notice of. Now for undeiilanding the rea- 
 fon of it , ilippofe the Plane ABC to cut the" 
 plane Sides and Bafe of the Prifm perpendicu^ 
 larly. From the Eye to the Line B C, where-^ 
 in that Plane cuts the Bafe, draw the Lines S/ 
 and S t^ in the Angles S/ c 50 dcgr. ^, and S ^ ^ 
 49 degr. ~, and the Point/ will be the UmiC 
 beyond which none of the mod refrangible! 
 Rays can pafs through the Bafe of the Prifm^ 
 And be refracted, whofe Incidence is fuch that 
 
 L they 
 
[ H^ 
 
 they may be refle6led to the Eye; and the 
 Point t will be the like limit for the leaft re- 
 frangible Rays, that is, beyond which none of 
 them can pafs through the Bale , whofe Inci- 
 dence is fuch that by Reflexion they may come 
 to the Eye. ' And the Point r taken in the mid- 
 dle way between / and t^ will be the like limit 
 for the meanly refrangible Rays. And there- 
 fore all the leaft refrangible Rays which fall up- 
 on the Bafe beyond ^, that is, between t and B, 
 and can come from thence to the Eye will be 
 refleded thither : But on this fide t , that is, 
 between t and f , many of thefe Rays will be 
 tranfmitted through the Bafe. And all the moil 
 refrangible Rays which fall upon the Bafe be- 
 yond /, that is, between p and B , and can by 
 reflexion come from thence to the Eye, will be 
 reflefted thither, but every where between/ 
 and r, many of thefe Rays will get through the 
 Bale and be refraded; and the fame is to be 
 underitood of the meanly refrangible Rays on 
 either fide 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 ^, where all 
 the more refrangible Rays are reflcded to the 
 Eye, and many of the lefs refrangible are tranf- 
 mitted , the Excefs of the moil refrangible in 
 the refleded Light will tinge that Light with 
 their Colour, which is violet and blue. And 
 
 this 
 
[ H7 ] 
 
 this happens by taking the Line C prfE any 
 where between the ends of the Prifm H (i 
 and E I. 
 
 TROT. IX. Prob. IV. 
 
 By the difcovered Properties of Lhht to explain 
 the Colours of the Rain-bow. 
 
 THIS Bow never appears but where ic 
 rains in the Sun-fliine, and may be made 
 artificially by fpouting up Water which may 
 break aloft , and fcatter into drops , and fall 
 down like Rain. For the Sun fliining upf)nthefe 
 drops certainly caufes the Bow to appear to a 
 Spedator Handing in a due pofition to the Raiil 
 and Sun. And hence it is now agreed upon, 
 that this Bow is made by rcfradion of the Sun's 
 Light in drops of falling Rain. This was un- 
 derflood by fome of the Ancients, and of late 
 more fully difcover'd and explain'd by the fa- 
 mous Antonius de TDominis Archbilhop of Spa^ 
 lato^ in his Book T)e Radiis Visits ^ Luc is, pub- 
 lillied by his Friend Bartolm at Venice, in the 
 Year 1611, and written above 20 Years before^ 
 For he teaches there how the interior Bow is 
 made in round drops of Rain by two Refra- 
 ctions of the Sun's Light, and one Reflexion 
 between them, and the exterior by two Refra- 
 ftions 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 X with 
 
[ 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 whiUl they underllood not the true 
 origin of Colour's , it's ncceilary to purfue ic 
 here a little farther. For underilanding there- 
 fore how the Bou is made, let a drop of Rain 
 or any other Ipherical tranfparent Body be repre- 
 fented by the Sphere B N F G, [in Fi^. 14.] de- 
 fcribed with the center C, and femi-diameter 
 CN. And let AN be one of the Sun's Rays 
 incident upon it atN, and thence refra61ed to 
 F, where let it either go out of the Sphere by 
 Refraftion towards \, or be refleded to G ; 
 and at G let it either go out by Refraction to R, 
 or be refleded to H ; and at H let it go out by 
 Refra6lion towards S, cutting the incident Ray 
 in Y ; produce A N and R G, till they meet in 
 X, and upon A X and N F let fail the perpen- 
 diculars CD and CE, and produce CD till it 
 fall upon the circumference at L. Parallel to 
 the incident Ray AN draw the diameter BQ, 
 and let the Sine of Incidence out of Air into 
 Water be to the Sine of Refraftion as I to R. 
 Now if you fuppofe the Point of Incidence N 
 to move from the Point B , continually till it 
 comx to L, the Arch Q F will firll increafe and 
 then decreafe, and fo will the Angle AXR 
 which the Rays A N and G R contain ; and the 
 Arch QF and Angle AXR will be biggeft 
 when ND is to CN as v'hTIrr to v^ 3 RR, in 
 which cafe N E will be to N D as 2 R to I. Al- 
 fo the Angle AYS which the Rays AN and HS 
 
 contain 
 
H9 ] 
 
 contain will firfl decrcafe , and then increafc 
 and grow lead when ND is to C N as -/nT-'RR 
 to v/ 8 RR, in which cafe NE will be to ND 
 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/iTTrr to v/ 15- RR, in which cafe 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 fom' Reflexions, contains 
 with the incident will come to its limit, vvherf 
 ND is to CN as i/ii-rr to ^ 24 RR, in which 
 cafe NE will be to ND as fR to I; and fo on 
 infinitely, the numbers 3, 8, 15-, 24, ^c. being 
 gather'd by continual addition of the terms of 
 the arithmetical ProgrelTion 3, 5, 7, 9, &c. 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 incrcafe and 
 decreafe but a very little for a great while to- 
 gether ; fo when by increaiing the diftance CD, 
 thefe Angles come to their limits, they vary 
 their quantity but very little for fome time to- 
 gether, and therefore a far greater number of 
 the Rays which fall upon all the Points N in the 
 Quadrant BL, iliall emerge in the Hmits of 
 thefe Angles, than in any other hiclinations. 
 And farther it is to be obferved, that the Rays 
 wiiich differ in Refrangibility will have difie- 
 rent limits of their Angles of Emergence, and 
 by confequence according to their different de- 
 grees of Refrangibility emerge moft copioufly 
 
 L 3 in 
 
[ i5o] 
 
 in different Angles , and being feparated from 
 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 lead refrangible Rays the Sines I 
 and R (as was found above) are io8 and 8i, 
 and thence by computation the greatefl Angle 
 A X R will be found 41 Degrees and x Minutes, 
 and the leaft Angle AYS, 5-0 Degrees and 5*7 
 Minutes. And in the mofl refrangible Rays the 
 €ines I and R are 109 and 81 , and thence by 
 computation the greatefl Angle A X R will be 
 found 40 Degrees and 17 Minutes, and the leaft 
 Angle AYS 5-4 Degrees and 7 Minutes. 
 
 Suppofe now that O [in Fig. i^.] is the Spe- 
 ctator's Eye, and OP a Line drawn parallel to 
 the Sun's Rays, and let POE, POF, POG, 
 P O H, be Angles of 40 Degr. 1 7 Min, 41 Degr. 
 a Min. 5-0 Degr. 5-7 Min. and 5-4 Degr. 7 Min. 
 refpedlively , and thefe Angles turned about 
 their common Side O P, fliall with their other 
 Sides OE, OF; OG, OH, defcribe the Verges 
 of two Rain-bows AF B E and C H D G. For 
 if E, F, G, H , be drops placed any where in 
 the conical Superficies defcribed by OE, OF, 
 O G, OH, and be illuminated by the Sun's Rays 
 SE, SF, SG, SH; the Angle SEO being e- 
 qual to the Angle POE or 40 Degr. 17 Min, 
 fliall be the greateft Angle in which the moft 
 refrangible Rays can after one Reflexion be re- 
 fraded to the Eye, and therefore all the drops 
 in the Line O E fhall fend the mofl refrangible 
 Rays mofl popioufly to the Eye? md thereby 
 
 itrike 
 
[ 151 ] 
 
 flrike the Senfes with the deepeft violet Colour 
 in that Region. And in like manner the Angle 
 SFO being equal to the Angle POF, or 41 
 Degr. 1 Min- fhall be the greatefl in which the 
 leall refrangible Rays after one Reflexion can 
 emerge out of the drops, and therefore thofe 
 Rays fhall come mod copioufly to the Eye from 
 the drops in the Line OF, and flrike the Senfes 
 with the deeped red Colour in that Region. 
 And by the fame Argument , the Rays which 
 have intermediate degrees of Refrangibility fliall 
 come moll copioufly from drops between E and 
 F, and ilrike the Senfes with the intermediate 
 Colours in the order which their degress 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 S G O being equal to the 
 Angle POG, or 50 Gr. 5-1 Min. iliall be the lead 
 Angle in which the leall refrangible Rays can 
 after two Reflexions emerge out of the drops, 
 and therefore the lead refrangible Rays fliall 
 come mod copioufly to the Eye from the drops 
 in the Line O G, and drike the Senfc with the 
 deeped red in that Region. And the Angle 
 SHO being equal to the Angle POH or 54 Gr. 
 7 Min. fliall be the lead Angle in which the mod 
 refrangible Rays after two Reflexions can e- 
 merge out of the drops, and therefore thofe 
 Rays Ihall come mod copioufly to the Eye from 
 the drops in the Line OH, and drike the Senies 
 
 L 4 with 
 
[ 152 ] 
 
 with the deeped violet in that Region. And 
 by the fame Argument, the drops in the Re- 
 gions between G and H fhall Itrike the Senfe 
 with the intermediate Colours in the order 
 which their degrees of Refrangibility require, 
 that is, in the progrefs from G to H, or from 
 the infide of the Bow to the outlide in this or- 
 der, red, orange, yellow, green, blue, indigo, 
 violet. And fmce thefe four Lines O E, O F, 
 OG, OH, may be fituated 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 
 whepe in thofe Superficies. 
 
 Thus iliall there be made two Bows of Co^ 
 lours, an interior and flronger, by one Reflexion' 
 in the drops, and an exterior and fainter by 
 two ; for the Light becomes fainter by every 
 Reflexion. And their Colours lliall lie in a con^ 
 trary order to one another , the red of both 
 Bows bordering upon the Space GF which is 
 between the Bows. The breadth of the inte^ 
 rior Bow EOF meafured crofs the Colours 
 fhall be iDegr. 45Min. and the breadth of the 
 exterior G O H iliall be 3 Degr. loMin. and the 
 diflance between them GOF iliall be 8Gr. 15 
 Min. the greateil Semi-diameter of the inner^ 
 moft, that is, the Angle P O F being 41 Gr. x 
 Min. an'd the leaft Semi-diameter of the outer- 
 moftPOG, being foGr. 57 Min. Thefe are 
 the Meafures of the Bows , as they would be 
 were the Sun but a point ; for by the breadth 
 of his Body the breath of the Bows will be in- 
 cregfed md their diitance decreafed by half a 
 
 Degree^ 
 
[153] 
 
 Degree, and fo the breadth of the interior Iris 
 will be X Degr. ly Min. that of the exterior 3 
 Degr. 40 Min. tlieir diltance 8 Degr. z^ Min. 
 the greatefl Semi-diameter of the interior Bow 
 4x Degr. 17 Min. and the lead 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 Itronj^ and 
 perfed. For once, by fuch means as I then 
 had, I meafured the greatefl Semi-diameter of 
 the interior Iris about 42 Degrees, the breadth 
 of the red, yellow and green in that Iris 63 or 
 64 Minutes , befides the outmolt 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 fuppofing the 
 breadth of the blue and violet together to equal 
 that of the red, yellow and green together, the 
 whole breadth oF this h-is will be about z-\ De- 
 grees, as above. The lead diltance between 
 this Iris and the exterior Iris was about 8 De- 
 grees and 30 Minutes. The exterior his was 
 broader than the interior, but fo faint, efpeci- 
 ally on the blue iide, that I could not meafure 
 its breadth diilindly. At another time when 
 both Bows appeared more diiUnft , I meafured 
 the breadth of the interior Iris 2 Gr. 10', and 
 the breadth of the red, yellow and green in the 
 exterior Iris, was to the breadth of the fame 
 Colours in the interior as 3 to 2, 
 
 Tills 
 
[ 154] 
 
 , This Explication of the Rain-bow is yet far- 
 ther confirmed by the known Experiment (made 
 by Antomus de T>om'tnvs and 'T)es-Cartes ) of 
 hanging up any where in the Sun-fliine a Glafs 
 Globe tilled with Water, and viewing it in fuch 
 a poflure that the Rays which come from the 
 Globe to the Eye may contain with the Sun's 
 Rays an Angle of either 41 or 50 Degrees. For 
 if the Angle be about 4x or 43 Degrees , the 
 Spedator (fuppofe at O) fhall 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 fuccellively in the fame fide of 
 the Globe. But if the Angle be made about 
 50 Degrees (fuppofe by lifting up the Globe to 
 G) there will appear a red Colour in that fide 
 of the Globe towards the Sun, and if the An- 
 gle be made greater (luppofe by lifting up the 
 Globe to H) the red will turn fuccellively to 
 the other Colours, yellow, green and blue. 
 The fame thing I have tried by letting a Globe 
 reft, and railing or deprelfing the Eye, or o- 
 therwife moving it to make the Angle of a jull: 
 magnitude. 
 
 I have heard it reprefented, that if the Light 
 of a Candle be refracted by a Prifm to the Eye ; 
 when the blue Colour falls upon the Eye the 
 Spectator fliall fee red in the Prifm , and when 
 the red falls upon the Eye he lliall 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 tind. But the Colours 
 
 of 
 
of the Candle being very faint, the miflake 
 feems to arife from the difficulty of diicernmg 
 what Colours fall on the Eye. tor, on the con- 
 trary, I have fometimes had occafion to ob- 
 ferve in the Sun's Light refra^led by a Prifm, 
 that the Sped:ator always fees that Colour in the 
 Prifm which falls upon his Eye. And the f\me 
 I have found true alfo in Candle-light. For 
 when the Prifm is moved flowly from the Line 
 which is drawn direc^tly from the Candle to the 
 Eye, the red appears firll in the Prifm and then 
 the blue , and therefore each of them is feen 
 when it falls upon the Eye. For the red paf- 
 fes over the Eye firft, and then the blue. 
 
 The Light which comes through drops of 
 Rain by two Refradions without any Reflexion, 
 ought to appear Ibongelt at the diilance of a- 
 bout ^6 Degrees from the Sun , and to decay 
 gradually both ways as the diilance from him 
 increafes and decreafes. And the fame is to 
 be undcritood of Light tranfmitted through 
 fpherical Hail-llones. And if the Hail be a lit- 
 tle flatted, as it often is, the Light tranfmitted 
 may grow fo Ih'ong at a little lefs diilance than 
 that of 26 Degrees, as to form a Halo about 
 the Sun or Moon ; which Halo, as often as the 
 Hail-ftones are duly figured may be colour'd, 
 and then it mud be red within by the lead re- 
 frangible Rays, and blue without by the moll 
 refrangible ones , efpecially if the Hail-ftones 
 have opake Globules of Snow in their center 
 to intercept the Light within the Halo (as H/f- 
 genius has obferv'd) and make the infide there^ 
 of more diftindly defined than it would other- 
 wife 
 
wife be. For fuch Hail-ftones, though fphe- 
 rical, by terminating the Light by the Snow , 
 may make a Halo red within and colourleis 
 without, and darker in the red than without^ 
 as Halos ufe to be. For of thofe Rays which 
 pafs clofe by the Snow the Riibriform will be 
 leafl refrafted, and lb come to the Eye in the 
 direflell Lines. 
 
 The Light which pafTes through a drop of 
 Rain after two Refractions, and three or more 
 Reflexions, is fcarce llrong enough to caule a 
 fenfible Bow ; but in thofe Cylinders of Ice by 
 Vfliicli Hiigejiius explains the Tarbelia, it may 
 perhaps be fenfible. 
 
 TROT. X. Prob. V. 
 
 By the difcovered Tropertics of Light to ex- 
 flam the permanent Colours of Natural Bo- 
 dies. 
 
 THESE Colours arife from hence, that 
 fome natural Bodies reflect fome forts of 
 Rays, others other forts more copioufly than 
 the red Minium refleds the leall refrangible 
 or red-making Rays moll copioufly, and thence 
 appears red. Violets reflect the moll refrangi- 
 ble, moft copioufly, and thence have their Co- 
 lour, and fo of other Bodies. Every Body re- 
 ilefts the Rays of its own Colour more copi- 
 oufly than the rell, and from their excefs and 
 predominance in the refleded Light has its 
 Colour. 
 
 Exper, 
 
[ 157 ] 
 
 Exper. 17. For if in the homogeneal Lights 
 obtained by the Iblution of the Problem pro- 
 pofed in the fourth Propofition of the firil Part 
 you place Bodies of feveral Colours , you will 
 find, as I have done, that> every Body looks 
 moil fplendid and luminous in the Light of its 
 own Colour. Cinnaber in the homogeneal red 
 Light is molt refplendent , in the green Light 
 it is manifelUy lei's refplendent, and in the blue 
 Light Hill lefs. Indigo in the violet blue Light 
 is moll 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 Ibongly receded than the other Co- 
 lours red and violet, and fo of the reft. But to 
 make thefe Experiments the more manifcil:, fuch 
 Bodies ought to be chofen as have the fulleil: and 
 molt vivid Colours, and two of thofe Bodies 
 are to be compared together. Thus, for in- 
 ftance, if Cinnaber and ////^r^z-marine blue, or 
 fome other full blue be held together in the 
 homogeneal Light, they will both appear red, 
 but the Cinnaber will appear of a flrongly lu- 
 minous and refplendent red, and the nltra-m^- 
 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 iWq ultra- 
 marine will appear of a llrongly luminous and 
 refplendent blue , and the Cinnaber of. a faint 
 and dark blue. Which puts it out of difpute^ 
 that the Cinnaber refleds the red Light much 
 more copioufly than the ////^r^ marine doth, and 
 
 the 
 
[158] 
 
 the ultra-rmxmt refleds the blue Light much 
 more copiouily 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 ftrength or weaknefs of their Co- 
 lour and Light. 
 
 And as the rcafon of the Colours of natural 
 Bodies is evident by thefe Experiments, fo it 
 is farther confirmed and put palt difpute by the 
 two firft Experiments of the firft Part, where- 
 by 'twas proved in fuch Bodies that the refled- 
 ed Lights which differ in Colours do differ alfo 
 in degrees of RefrangibiUty. For thence it's 
 certain, that fome Bodies refled the more re- 
 frangible, others the lefs refrangible Rays more 
 copioufly. 
 
 And that this is not only a true reafon of 
 thefe Colours, but even the only reafon may ap- 
 pear farther from this confideration , that the 
 Colour of homogeneal Light cannot be chan- 
 ged by the Reflexion of natural Bodies. 
 
 For if Bodies by Reflexion cannot in the lead 
 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 mud pro- 
 duce it. 
 
 But in trying Experiments of this kind care 
 muft be had that the Light be fufliciently ho- 
 mogeneal. For if Bodies be illuminated by the 
 ordinary prifmatick Colours , they will appear 
 neither of their own Day-light Colours, nor of 
 the Colour of the Light caft on them , but of 
 
 fome 
 
[ 159 ] 
 
 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 niix'd, and in the green Light 
 all forts of Kays 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 refledled Light as to draw the Colour from 
 red towards their Colour. And becaufe the 
 red Lead refleds the red-making Rays mofl 
 copioufly in proportion to their number, and 
 next after them the orange-making and yellow- 
 making Rays ; thefe Rays in the reflected Light 
 will be more in proportion to the Light than 
 they were in the incident green Light, and there- 
 by will draw the refleded 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 inltance, a red Liquor in 
 a conical Glafs held between the Light and the 
 Eye , looks of a pale and dilute yellow at the 
 bottom where 'tis thin, and a little higher where 
 'tis thicker grows orange , and where 'tis Itill 
 thicker becomes red , and w^here 'tis thickell 
 
 the 
 
[ 1^0 ] 
 
 the red is deepeit and darkell. For it is to be 
 conceiv'd that fiich a Liquor flops the indigo- 
 making and violet-making Rays molt eafily, the 
 blue-making Rays more difficultly, the green- 
 making Rays itill more difficultly, and the red- 
 making moll difficultly : And that if the thick- 
 nefs of the Liquor be only lb much as fuffices 
 to Hop a competent number of the violet-ma- 
 king and indigo-making Rays , without dimi-^ 
 milling much the number of the relt, the reft 
 mult {by Tr op. 6. Tart z.) compound a pale 
 yellow. But if the Liquor be fo much thicker 
 as to itop alfo a great number of the blue-ma^ 
 king Rays, and Ibme of the green-making, the 
 relt mull compound an orange ; and where it 
 is fo thick as to Hop alio a great number of the 
 green-making and a conliderable number of 
 the yellow-making, the relt mult begin to com- 
 pound a red, and this red mult grow deeper 
 and darker as the yellow-making and orange- 
 making Rays are more and more Itopp'd by in- 
 creafmg the thicknefs of the Liquor, fo that 
 few Rays befides the red-making can get 
 through. 
 
 Of this kind is an Experiment lately related 
 to me by Mr. Halley^ who, in diving deep into 
 the Sea in a diving VelTel, found in a clear Sun- 
 lliineDay, that when he was funk many Fathoms 
 deep into the Water, the upper part of his Hand 
 on which the Sun Ihone directly through the 
 Water and through a fmall Glafs Window in 
 the VelTel, like that of a Damask Rofe, and the 
 Water below and the under part of his Hand 
 illuminated by Light reflefted from the Water 
 
 below 
 
below look'd green. For thence it may be ga« 
 thcr'd, that the Sea Water refledls back the 
 violet and blue-making Rays molt eafily, 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, muft ap- 
 pear red ; and the greater the depth is, the ful- 
 ler and inteni'er mull 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 relieved from be- 
 low more copioufly than the red-making ones, 
 muft compound a green. 
 
 Now if there be two Liquors of full Colours, 
 fuppofe a red and a blue, and both of them lb 
 thick as fulKces to make their Colours fuffici- 
 ently full ; though either Liquor be fufficient- 
 ly tranfparent ^part, 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 pafs through both. This Mr. Hook tried 
 cafually with Glafs Wedges filled with red and 
 blue Liquors, and was furprized at the unex- 
 peded event , the reafon of it being then un- 
 known ; which makes me trull the more to his 
 Experiment, though I have not tried it my felf 
 But he that would repeat it, mull take care the 
 Liquors be of very good and full Colours. 
 
 Now whilft Bodies become coloured by refle(^- 
 ing or tranfmitting this or that fort of Rays more 
 copioufly than the reft, it is to be conceived 
 that they flop 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 greenilh blue, 
 and therefore malTy Gold lets into its Body the 
 blue-making Rays to be reflefted to and fro 
 within it till they be itopp'd and flifled , whilft 
 it reflefts the yellow-making outwards, and 
 thereby looks yellow. And much after the 
 fame manner that Leaf Gold is yellow by re- 
 fle6ied, and blue by tranfmitted Light, and maf- 
 fy Gold is yellow in all Pofitions of the Eye ; 
 there are fome Liquors, as the Tindure of 
 L'tgnum Nephritkum^ and fome forts of Glafs 
 which tranlmit one fort of Light molt copiouf- 
 ly, and refleft another fort, and thereby look 
 bf feveral Colours, according to the pofition 
 of the Eye to the Light. But if thefe Liquors 
 or GlalFes were fo thick and maffy that no Light 
 could get through them, I quellion 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 coloured Bodies, fo far as my 
 Obfervation reaches , may be feen through if 
 made fufficiently thin, and therefore are in fome 
 meafure tranfparent, and differ only in degrees 
 of Tranfparency from tinged tranfparent Li- 
 quors ; thefe Liquors, as well as thofe Bodies, 
 by a fufficient thicknefs becoming opake. A 
 tranfparent Body which looks of any Colour by 
 tranfmitted Light , may alfo look of the fame 
 Colour by reflefted Light , the Light of that 
 Colour being refleded by the farther Surface 
 of the Body, or by the Air beyond it. And 
 
 then 
 
then the reflected Colour will be diminiflieds, 
 and perhaps ce-:\(G, by making the Body very 
 thick, and pitching it on the backfide to dimi- 
 nifli the Reflexion of its farther Surface, fo that 
 the Light refieded from the tinging Particles 
 may predominate. In fuch cafes, the Colour 
 of the retlefted Light will be apt to vary from 
 that of the Light tranfmitted. But whence it 
 is that tinged Bodies and Liquors refled fome 
 foit of Rays , and intromit or tranfmit other 
 forts, fhall be faid in the next Book. In this 
 Propofition I content my felf to have put it paft 
 dil'pute, that Bodies have fuch Properties^ and 
 thence appear coloured. 
 
 "PR OT. XL Pros. VI. 
 
 By mixhig coloured Lights to compound a beam 
 
 of Light of the fame Colour and Nature with 
 
 a beam of the Sun's dire& Lights and thereiit 
 
 to experience the Truth of the foregoing 'Fro-^ 
 
 ^ofitions. 
 
 LET. ABC ^^f {\ViFig.r6.'] reprefent a 
 Prifm by which the Sun's Light let into 
 a dark Chamber through the Hole F, may be 
 refracted towards the Lens MN, and paint up- 
 on it at/, ^, ;, J and ?, the uiual Colours vio- 
 let, blue, green, yellow and red, and let the 
 diverging Rays by theReiracfion of this Lens 
 converge again towards X^ and there, by the 
 mixture of all thoic their Colours, compound a 
 white according to what was ilievvn above. 
 
 M % Thefi 
 
Then let another Prifm D E G deg^ parallel to 
 the former, be placed at X, to refradl that 
 white Light upwards towards Y. Let the re- 
 fra^ling Angles of the Prifms, and their diltances 
 from the Lens be equal, fo that the Rays which 
 converged from the Lens towards X, and with- 
 out Refradion, would there have crofled and 
 diverged again , may by the Refraftion of the 
 fecond Prifm be reduced into Parallelifm and 
 diverge no more. For then thofe Rays will re- 
 compofe a beam of white Light X Y . If the 
 refrading Angle of either Prifm be the bigger, 
 that Prifm muil be fo much the nearer to the 
 Lens. You will know when the Prifms and the 
 Lens are well fet together, by obferving if the 
 beam of Light XY which comes out of the fe- 
 cond Prifm be perfedly white to the very edges 
 of the Light, and at all diltances from the Prifm 
 continue perfectly and totally white Hke a beam 
 of the Sun's Light. For till this happens , the 
 pofition of the Prifms and Lens to one another 
 mufl be correded, and then if by the help of a 
 long beam of Wood, as is reprefented in the 
 Figure, or by a Tube, or fome other fuch In- 
 ftrument made for that purpofe, they be made 
 fafl in that fituation , you may try all the fame 
 Experiments in this compounded beam of Light 
 X Y, which have been made in the Sun's dired 
 Light, For this compounded beam of Light 
 has the fame appearance, and is endowed with 
 all the fame Properties with a dired beam of 
 the Sun's Light, fo far as my Obfervation reaches. 
 And in trying Experiments in this beam you 
 may by flopping any of the Colours /, ^, r^ s 
 
 and 
 
[ 1^5 ] 
 
 and t^ at the Lens, fee how the Colours pro- 
 duced in the Experiments are no other than 
 thofe which the Rays had at the Lens before 
 they enter the compofition of this Beam : And 
 by confequence that they arife not from any new 
 modifications of the Light by Refradions and 
 Reflexions , but from the various Separations 
 and Mixtures of the Rays originally endow'd 
 with their colour-making qualities. 
 
 So, for inllance, having with a Lens 4-^ Inches 
 broad, and two Prifms on either hand 6^ Feet 
 diftant from the Lens, made fuch a beam of 
 compounded Light : to examin the reafon of 
 the Colours made by Prifms, I refracted this 
 compounded beam of Light X Y with another 
 Prifm HIK ^Z;, and thereby caft the ufual prif- 
 matick Colours PQRSTupon the Paper LV 
 placed behind. And then by flopping any of 
 the Colours/,^, r, j, ^, at the Lens, I found 
 that the fame Colour would vanifli at the Pa- 
 per. So if the purple / was flopp'd at the 
 Lens , the purple P upon the Paper would va- 
 nifli, and the reft 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 Refradlions. 
 And fo by intercepting the green upon the Lens, 
 the green R upon the Paper would vanifh, and 
 fo of the reft ; which plainly fhews, 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 Refraftions are no other than thofe 
 of which its whitenefs was compounded. The 
 
 M 3 Refra- 
 
I 166] 
 
 Refradiofi of thePrifm HIK >^^ generates the 
 Colours PQRST upon the Paper, not by 
 changing the colorific qualities of the Rays, but 
 by feparating the Rays which had the very fame 
 colorific qualities before they enter'd the Com- 
 pofition of the refradied beam of white Light 
 X Y. For otherwife the Rays which were of 
 one Colour at the Lens might be of another 
 upon the Paper, contrary to what we find. 
 
 So again , to examin the reafon of the Cor 
 lours of natural Bodies, I placed fuch Bodies 
 in the Beam of Light X Y, and found that they 
 all appeared there of thole their own Colours 
 which they have in Day-light , and that thofe 
 Colours depend upon the Rays which had the 
 fame Colours at the Lens before they enter'd 
 the Compofition of that beam. Thus, for in- 
 stance , Cinnaber illuminated by this beam ap- 
 pears of the fame red Colour as in Day-light 5 
 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 hke 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 L'tgnum Nephritic 
 
 cum 
 
Book! PaitirnatEl 
 
 # 
 
 X 
 
 ^8'- 5 
 
 V-W 
 
 / 
 
 • 
 
BookLPaitir.HatcI 
 
 Fio- _^. „ .^ 
 
 :- ^ ^' F 
 
 ^»*F^ 
 
 1 !. 
 
 "I iT^^^ 
 

• 
 
 o 
 
FOLDOUT BLANK 
 
Bookl Fiitl . Plate HI 
 
 o 
 
Book I Pail U/Hatc^ 
 
 L 
 
 X 
 
 ^•y^ 
 
i 
 
cum ( as I have alfo tried ) when held in this 
 beam of Light X Y, looks blue by the reflec^t- 
 ed part of the Lights ^nd. red by thie. traxifmit- 
 tjed part ^f%, as when 'tis view'd in Day-light, 
 l|ut if you inte!Pcept the blue at the Lens the 
 infufion will lofe its reflected blue Colour, whilil 
 its tranfmitted red remains perfed 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, whillt its blue will re- 
 main and become more full and perfed. Which 
 lliews, that the Infufion does not tinge the Rays 
 with blue and red, but only tranfmit thofe 
 molt copioufly which were red-making before, 
 and refleds thofe molt copioufly 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. 
 
 M4 THE 
 
li6S] 
 
 THE 
 
 SECO'ND BOOK 
 
 OPTIC KS. 
 
 PART I. 
 
 Obfervations concerning the ReJIexions, Refra- 
 Bionsy and Colours of thin transparent Bo- 
 dies. 
 
 |T has been obferved by others, that 
 trani parent Subflances, as Glafs, War 
 ter, Air, ^c. when made very thin by 
 being blown into Bubbles, or otherwile 
 formed into Plates, do exhibit various Colours 
 according to their various thinnefs, although at 
 
 a greater 
 
[ ^^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 
 neceiTary for eftabUfliing the Properties of Light 
 there difcourfed of But becaule they may con- 
 duce to farther Difcoveries for completing the 
 Theory of Light, efpecially as to the conltitu- 
 tion of the parts of natural Bodies, on which 
 their Colours or Tranfparency depend ; I have 
 here fct down an account of them. To render 
 this Difcourfe fliort and diffind, I have firlt de- 
 fcribed the principal of my Obiervations , and 
 then confider'd and made ufe of them. The 
 Obfervations are thefe. 
 
 Obf. I. Compreiling 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 Glals. 
 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 Uke a black or 
 dark fpot, by reafon that httle 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 GlaiTes. And through this hole Objeds that 
 were beyond might be feen diflinftly, which 
 could not at all be feen through other parts of 
 
 the 
 
[ I70 ] 
 
 the GlafTes where the Air was interjacent. Al- 
 though the Glalles were a little convex, yet this 
 tranlparent fpot was of a conliderable breadth, 
 which breadth fecmed principally to proceed 
 from the yielding inwards of the parts of the 
 GlaiTes, by reafon of their mutual preffure. For 
 by preihng them very hard together it would 
 become much broader than otherwife. 
 
 Obf. X. W hen the Plate of Air, by turning 
 the Prifms about their common Axis , became 
 fo little inclined to the incident Rays, that fome 
 of them l~)egan to be tranfmitted , there arofe 
 in it many llender Arcs of Colours which at firlt 
 were fhaped almoft like the Conchoid , as you 
 fee them delineated in the firft 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 contiaually grew more and 
 more contraded. 
 
 Thefe Arcs at their firlt appearance were of 
 ' a violet and blue Colour , and between them 
 were white Arcs of Circles, which prefently 
 by continuing the Motion of the Prifms became 
 a Uttle 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 
 
[I7i] 
 
 The Motion of the Prifms about their Axis 
 yoeing continued, thefe Colours contracted more 
 [and more, fhrinking towards the whitenefs on 
 either fide of it, until they totally vanillied in- 
 to it. And then the Circles in thofe parts ap- 
 peared 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. 
 
 Oiff. 3. When the Rings or fome parts of 
 them appeared only black and white, they were 
 very diftind and well defined , and the back- 
 nefs feemcd 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 diilindl, which made 
 thei3 vifible to a very great multitude. I have 
 fome times number 'd above thirty Succeflions 
 (reckoning every black and white Ring for one 
 Succeffion) and feen more of them, which by 
 reafon of their fmalnefs I could not number. 
 But in other Pofitions of the Prifms , at which 
 the Rings appeared of many Colours , I could 
 not diltinguilh 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- 
 ftind:, and without any other Colour than black 
 and white, 1 found it neceifary to hold my Eye 
 
 at 
 
[ 172 ] 
 
 at 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 blueifli Colour out of the white, 
 which by dilating it felf more and more into 
 the black, render'd the Circles lefs diltind:, and 
 left the white a little tinged with red and yel- 
 low. I found alfo by looking through a ilit or 
 oblong hole, which was narrower than the Pu- 
 pil of my Eye, and held clofe to it parallel to 
 the Prifms , I could fee the Circles much di- 
 {l:in<^t:er 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- 
 glaffes, 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 preiTed them flowly 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 fucceffive- 
 ly vanilh again in the fame place. The Colour, 
 W'hich by prelling the GlafTes together emerged 
 iaftinthe middle of the other Colours, would 
 upon its firll appearance look like a Circle of a 
 Colour almoft uniform from the circumference 
 to the center, and bycompreffingtheGlaifes ftill 
 more, grow continually broader until a new Co- 
 lour emerged in its center, and thereby it became 
 a Ring encompalling that new Colour. And by 
 
 com- 
 
I 173 ] 
 
 comprefTing the Glaflcs Hill 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 lalt: 
 And fo on until a third , a fourth , a fifth , and 
 other following new Colours fucccllivcly emer- 
 ged there, and became Rings encompaffing the 
 innermolt Colour, the lalt of which was the 
 black Spot. And, on the contrary? by hfting 
 up the upper Glafs from the lower, the diame- 
 ter of theRings would decreafe, and the breadth 
 of their Orbit increafe, until their Colours reach- 
 ed fuccefTively to the center ; and then they 
 being of a confiderable breadth, I could more 
 eafily difcern and diilinguifli their Species than 
 before. And by this means I obferv'd their Suc- 
 cefTion and Quantity to be as followeth. 
 
 Nexf to the pellucid central Spot made by 
 the contacT: of theGlafles fucceeded blue, white, 
 yello\\', and red. The blue was fo little in quan- 
 tity that I could not dilcern it in the Circles 
 made by the Prifms, nor could I well dilHnguilh 
 any violet in it, but the yellow and red were 
 pretty copious, and fcemed 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 encompafling 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 
 
Order 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 confpicuous, being as 
 brisk and copious as any of the other Colours, 
 except the yellow ; but the red began to be a 
 little faded, incHning 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 imperfed and dir- 
 ty. Alfo the fucceeding Colours became more 
 and more imperfed: and dilute, till after three 
 or four revolutions they ended in perfedl 
 whitenefs. Their form, wheri the GlafTes were 
 mofl comprefs'd fo as to make the black Spot 
 appear in the center, is deUneated in the le- 
 cond Figure ; " where a^ b^ , f, 4 ^ •* /» gt h h 
 k : /, m^ n^ o, f : q^ r : j, t : ^', x : y, 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 : greenifh blue, pale red : greenifli blue, 
 reddifti 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 firft lix Rings at the moit 
 lucid part of their Orbits, and fquaring them, I 
 found their Squares to be in the arithmetical 
 Progreffion of the odd Numbers, i, 3, $, 7, 9, 11. 
 
 And 
 
[ 175 1 
 
 And fince one of thefe Glalles was plane, and 
 the other fphcrical, their Intervals at thole Rings 
 muit be in the fame Progrefiion. I meafured 
 alfo riie Diameters of the dark or faint Rings 
 between the more lucid Colours, and found 
 their Squares to be in the arithmetical Progref- 
 fiQn of the even Numbers, 2, 4, 6, 8, 10, 12. 
 And it being very nice and difficult to take 
 theie meafures exadly ; I repeated them divers 
 times at divers parts of the Glaifes, that by their 
 Agreement I might be coniirmed in them. And 
 the fame method I ufed in determming fome 
 others of the following Obfervations. 
 
 Obf. 6. The Diameter of the fixth Ring at 
 
 the moft lucid part of its Orbit was -^ parts of 
 
 an Inch , and the Diameter of the Sphere on 
 which the double convex Objeclri: - glals was 
 ground was about lox Feet, and hence I ga- 
 thered the thicknefs of the Air or Aereal Inter- 
 val of the Glailes at that Ring. But lome time 
 after, fufpeding that in making this Obfervation 
 I had not determined the Diameter of the 
 Sphere with lufKcient accurateneib, and being 
 uncertain whether the Plano-convex Clafs was 
 truly plane, and not fomething concave or con- 
 vex on that fide which I accounted plan-j; and 
 whether I had not preiled the Glailes together, 
 as I often did , to make them touch ; (For by 
 prefling fuch Glailes together their parts eafily 
 yield inwards, and the Rings thereby become 
 fenlibly broader than they would be , did the 
 Glafles keep their Figures.) I repeated the 
 Experiment, and found the Diameter of the 
 
 fixth 
 
fixth lucid Ring about ^~ parts of an Inch. I 
 
 repeated the Experiment alfo with fuch an Ob- 
 jeft-glafs 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 dillant from it 83' Inches. And thence, 
 if the Sines of Incidence and Refradion of the 
 bright yellow Light be afllimed 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 Prelfure than that of the weight 
 of the Glafs. And now meafuring the Diame- 
 ter of the fifth dark Circle as accurately as I 
 could, I found it the fifth part of an Inch pre- 
 cifely. This Meafure was taken with the points 
 of a pair of Compafl'es on the upper Surface 
 on the upper Glafs, and my Eye was about 
 eight or nine Inches diftance from the Glafs, 
 almofl perpendicularly over it , and the' Glafs 
 was 4 of an Inch thick, and thence it is eafy to 
 colleft that the true Diameter of the Ring be- 
 tween the GlafTes was greater than its meafur'd 
 Diameter above the GlafTes in the Proportion 
 of 80 to 79, or thereabouts, and by confequence 
 equal to i4 part of an Inch, and its true Semi- 
 diameter equal to ^^- parts. Now as the Dia- 
 meter of the Sphere (i8i Inches) is to the Se- 
 mi-diameter of this fifth dark Ring (-yy parts of 
 an Inch) fo is this Semi-diameter to the thick- 
 nefs of the Air at this fifth dark Ring ; which is 
 
 there- 
 
[ 177 ] 
 
 therefore -~^ or ~— ~- parts of an Inch ; and 
 
 5-67931 17/47^4 * 
 
 the fifth part thereof, viz. the ^^ part of an 
 
 Inch, is the thicknefs of the Air at the firit 
 of thefe dark Rings. 
 
 The fame Experiment I repeated with ano- 
 ther double convex Objeft-glals ground on both 
 fides to one and the fame Sphere. Its Focus 
 was diflant from it i684 Inches, and therefore 
 the Diameter of that Sphere was 184 Inches* 
 This Glafs being laid upon the fame plain Glals, 
 the Diameter of the fitth of the dark Rings, 
 when the black Spot in their center appear 'd 
 plainly without preiling the GlalTes, was by the 
 meafure of the Compailes upon the upper Glafs 
 
 600 P^^^^ ^^ ^"^ Inch, and by confequence be- 
 
 1222 
 
 tween the GlafTes it 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 gj-:-th part of an 
 
 Inch is the thicknefs thereof at the tirft of thQ 
 Rings, as above. 
 
 I tried the fame thing by laying thefe Ob- 
 jed-glalfes 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 
 Glaffes ground to larger Spheres, though in 
 fuch GlalFes greater care mull be taken of a true 
 Plane. 
 
 Thefe Dimenfions were taken when my Eye 
 was placed almoft perpendicularly over the 
 Glalles, being about an Inch, or an Inch and. a 
 quarter , diflant from the incident Rays , and 
 eight Inches diflant from the Glafs ; fo that the 
 Rays were inclined to the Glais in an Angle of 
 about four Degrees. • Whence by the following 
 Obfervation you will underftand, that had the 
 Rays been perpendicular to the GlafTes, the 
 thicknefs of the Air at thefe Rinffs would have 
 been lefs in the proportion of the Radius to the 
 Secant of four Degrees, that is of loooo to 
 10024. Let the thicknelTes found be therefore 
 diminiih'd in this Proportion, and they will be- 
 come en — and ^r~r » or ( to ufe the ncarefl 
 88952 S9063.' ^ -^ 
 
 round number ) the 3-^th part of an Inch,! 
 
 This is the thicknefs of the Air at the darkeft " 
 part of the firlt dark Ring made by perpendi- 
 cular Rays, and half this thicknefs multiplied 
 by the Progrellion, i, 3, 5, 7, 9, 11, ^c. gives 
 the thicknefles of the Air at the moil luminous 
 
 parts of all the brightefl Rings, viz. ;zg^> 
 i"78k> f^' '-^^ ^'' ^^^'^ arithmetical 
 
 Means — h— -, ^n ■, ■■ r.' , ^c. being its 
 
 178000' 17800G' 178000' o 
 
 thicknefles iit the darkeft parts of all the dark 
 ones. 
 
 s ' Obf, 
 
[ 175 ] 
 
 Ohf 7. The Rings were leafl when my Eye 
 was placed perpendicularly over the Glalles iii 
 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 confequent- 
 ly the thicknefs of the Air at its Perimeter in 
 all thole Obliquities to be very nearly in the 
 Proportions exprefs'd in this Table. 
 
 Angle of In- 
 
 Angle of Re- 
 
 T)iameterThicknefs | 
 
 cidence on 
 
 fraction in- 
 
 of the 
 
 of the 
 
 the Air. 
 
 to the Air. 
 
 Ring. 
 
 Air. 
 
 Deg. Min. 
 
 
 
 
 00 GO 
 
 00 03 
 
 10 
 
 10 
 
 06 26 
 
 10 oo 
 
 10.V 
 
 IOtV 
 
 IX 45- 
 
 20 OQ 
 
 10-^ 
 
 IC| 
 
 18 49 
 
 30 oo 
 
 io.| 
 
 114 
 
 24 30 
 
 40 00 
 
 114 
 
 13 
 
 29 37 
 
 5*0 00 
 
 124 
 
 15-4 
 
 33 5B 
 
 60 00 
 
 H 
 
 20 
 
 35- 47 
 
 6$ 00 
 
 15-7 
 
 2'3^ 
 
 37 19 
 
 70 00 
 
 i6| 
 
 28^ 
 
 38 33 
 
 75 00 
 
 ^n 
 
 37 
 
 39 27 
 
 80 03 
 
 22^ 
 
 5-2--? 
 
 40 CO 
 
 85- 00 
 
 2-9 
 
 84.V 
 
 40 II 
 
 90 00 
 
 35" 
 
 1224 
 
 N 2/ 
 
 In 
 
[i8o] 
 
 In the two firlt 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 Refradion. In the third Column 
 the Diameter of any coloured Ring at thofe Ob- 
 liquities is expreiled 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 expreiled in parts of which alfo 
 ten conltitute its thicknefs when the Rays are 
 perpendicular. 
 
 And from thefe Mcafures 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 Refraction. And that 
 mean Proportional, fo far as by thefe Meafures 
 I can determine it, is the fird' of an hundred 
 and fix arithmetical mean Proportionals be- 
 tween thofe Sines counted from the bigger Sine, 
 that is, from the Sine of Refraction when the 
 Refradion is made out of the Glafs into the 
 Plate of Air, or from the Sine of Incidence when 
 the Refraction is made out of the Plate of Air 
 into the Glafs. 
 
 Obj: 8. The dark Spot in the middle of the 
 Rings increafed alfo by the Obliquation of the 
 Eye, although almoll infenfibly. But if inflead 
 of the Objed-glafles the Prifms were made ufe 
 of, its Increafe was more manifeit when view- 
 ed fo obliquely that no Colours appear'd about 
 it. It u as leafl when the Rays were incident 
 molt obliquely on the^ interjacent Air, and as 
 
 I the 
 
[ isi ] 
 
 the obliquity dccreafed it increafcd more and 
 more until the coloured Rings appear'd, and 
 then decreafed again, but not fo much as it in- 
 creafed before. And hence it is evident, that 
 the Tranfparency was not only at the abfolute 
 Contact of the Glaifes, but alio where they had 
 fome little Interval. I have fometimes oblcrved 
 the Diameter of that Spot to be between half 
 and two tifth parts of the Diameter of the ex- 
 terior Circumference of the red in the iiril Cir- 
 cuit or Revolution of Colours when view'd al- 
 moit perpendicularly; whereas when viev/'d 
 obliquely it hath wholly vaniili'd and become 
 opake and white like the other parts of the 
 Glafs; whence it may be colledred that the 
 Glaifes did then fcarcely, or not at all, touch 
 one another, and that their Interval at the pe- 
 rimeter of that Spot when view'd perpendicu- 
 larly was about a fifth or fixth part of their In- 
 terval at the circumference of the faid red. 
 
 Obf. 9. By looking through the two conti- 
 guous Objeft-glaHes, I found that the interja- 
 cent Air exhibited Rings of Colours, as well 
 by tranfmitting Light as by reflefting it. The 
 central Spot was now white, and from it the 
 order of the Colours were yellovvifli 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 trajecfled very obhquely through the 
 Glaifes : For by that means they became pretty 
 vivid. Only the firft yellowiili red, like the 
 blue in the fourth Obfervation, was fo little and 
 faint as fcarcely to be difcern'd. Comparing 
 
 N 3 the 
 
[l82] 
 
 the coloured 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 hke of the other Colours. The man- 
 ner you have reprefented in the third Figure, 
 where A B, CD, are the Surfaces of the Glaf- 
 fes contiguous at E, and the black Lines be- 
 tween them are their Diftances in arithmetical 
 Progreflion, and the Colours written above are 
 feen by reflefted Light, and thofe below by 
 Light tranfmitted. 
 
 Obf. lo. VVetting the Objeft-glafles a little 
 at their edges, the Water crept in flowly be- 
 tween them, and the Circles thereby became 
 lefs and the Colours more faint : hifomuch that 
 as the Water crept along one half of them at 
 which it fn*ft arrived would appear broken off 
 from the other half, and contra61cd into a lefs 
 Room. By meafuring them I found the Pro- 
 portions of their Diameters to the Diameters qf 
 the like Circles made by Air to be about fevcn 
 to eight, and confequently the hitervals of the 
 Glafles 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 Glaifes, their Inter- 
 vals ^t the Rings caufed thereby will be to their 
 
 Intervals 
 
[.1 83] 
 
 fortervals caufed by interjacent Air, as theSiue:? 
 are which meafure the Refradion made out of 
 that Medium into Air. 
 
 O^/! n. When the Water was between the 
 Glafles, if I prefTcd the upper Glafsvariou fly at 
 its edges to make the Rings move nimbly from 
 one place to another, a httle white Spot would 
 immediately follow the center of them , which 
 upon creeping in of the ambient Water into that 
 place would prcfently vanifli. Its appearance 
 was fuch as interjacent Air would have caufed, 
 and it exhibited the fame Colours. But- if was 
 not Air, for where any Bubbles cfAii* were in 
 the Water they would not vanin.. The Refle- 
 xion mufl: have rather been caufed by a fubtiler 
 Medium, which could recede through the 
 Glafles at the creeping in of the Water. 
 
 01^/^ 12. Thefe Obfervations were made in 
 the open Air. But farther co examine the Ef- 
 feds of colour'd Light Mling on the Glafl!es, I 
 darken'd the Room, and view'd them by Re- 
 flexion of the Colours of a PrifiT! cafl on a Sheet 
 of white Paper, my Eye being fo placed that I 
 could fee the colour'd Paper by Reflexion in the 
 Glafles, as in a Looking-glafs. And by this 
 means the Rings became diflincter and vifible 
 to a hi' 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. 
 
 Oi/f! 1 3. Appointing an AfTiflant to move the 
 Prifm to and fro about its Axis, that all the 
 Colours might fucceflively fall on that part of 
 the Paper which I faw by Reflexion from thai 
 
 N 4 " part 
 
I m 1 
 
 part of the Glaffes, where the Circles appear'd, 
 fo that all the Colours rrlight be fuccefiively re- 
 flefted from the Circles to my Eye whilft I held 
 it immovable, I found' the "Circles which the 
 red Li^^ht made to be manifeflly bigger than 
 thole which were made by the blue and violet. 
 And it was very pleafant to fee them gradually 
 fwell oi' conrrad 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 utmoft red Light, was to their Interval 
 at the fame Ring when made by the utmoll: 
 violet, greater than as 3 to 2, and lefs than as 
 13 to 8. By the molt of my Obfervations it was 
 as 14 to 9. And this Proportion feem'd very, 
 nearly the fame in all Obliquities of my Eye ; 
 unlefs when two Prifms were made ufe of in- 
 flead of the Objeft-glaiTes. For then at a cer- 
 tain great obliquity of my Eye, the Rings made 
 by the feveral Colours feem'd equal, and at -a 
 greater obHquity thofe made by the violet would 
 be greater than the fame Rings made by the 
 red : the Refra6lion of the Prifm in this cafe 
 cauling the moft refrangible Rays to fall more 
 obliquely on that plate of the Air than the leall 
 refrangible ones. Thus the Experiment fuc- 
 ceeded in the colour'd Light , which was fuf- 
 ficiently Ib'ong and copious to make the Rings 
 fenfible. And thence it may be gather'd, that 
 if the moft refrangible and leaft refrangible Rays 
 had been copious enough to make the Rings 
 fenfible without the mixture of other Rays, the 
 Proportion which here was 14 to 9 would have 
 been a little greater, fuppofe 144 or 144 to 9. 
 
[i85] 
 
 Ohf. 14. Whilft the Prilm was turn'd about 
 its Axis with an uniform Motion, to make all 
 the feveral Colours fi\ll luccefiivcly upon the 
 ObjcCl-glalles, and thereby to make the Rings 
 contract and dilate : The Contraction or Dila- 
 tation of each Ring thus made by the variation 
 of its Colour was fwiftelt in the red, aiKl ilow- 
 efl in the violet, and in the intermediate Colours" 
 it had intermediate degrees of Celerity. Com- 
 paring the quantity of Contraction and j)ilata- 
 tion made by all the degrees of each Colour, I 
 found that it 'was greateil in the red ; lefs in 
 the yellow, Hill lefs in the blue, and leait in the 
 violet. And to make as jull an Eltimation as I 
 could of the Proportions of their Contradions 
 or Dilatations , I obferv'd that the' whole Con- 
 traction or Dilatation of the Diameter of anv 
 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 greatelt Diame- 
 ter of the fame Ring made by the outmoll: red, 
 and the lead Diameter thereof made by the 
 outmoll violet : Contrary to what happens in 
 the Colours of the oblong Speclrum made by 
 the Refradion of a Prifm, where the red is 
 mod contraded, the violet moit expanded-, 
 aind in the midit of all the Colours is the Con- 
 fine of green and blue. And hence I feem to 
 colle(^l that the thicknelTes of the Air between 
 the Glailes there, where the Ring is fucce/Tive- 
 
[ 18^ ] 
 
 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 hmit 
 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 Hmit of blue and 
 violet in the middle of the indigo, and by the 
 extreme violet) are to one another very nearly 
 as the fix lengths of a Chord which found the 
 Notes in a /ixth Major, fol^ la^, m'l^ fa^ fol^ la. 
 But it agrees fomething better with the Obfer- 
 vation to fay , that the thicknelfes of the Air 
 between theGlafles thercj where the Rings aret 
 fucceilively made by the limits of the feven Co- 
 lours, red, orange, yellow^ ^"eep? blue, indi- 
 go , violet in order, are to one another as the 
 Cube Roots of the Squares of the eighjt lengths 
 of a Chord, which found the Notes in an eighth, 
 fol^ Idy fay foly lay ffiiy fuy fil \ that is, as the 
 Cube Roots of the Squares q{ ^he Numbers, I3 
 
 * S ? ^ J _9_ • 
 
 ObJ. 15. Thefc Rings "were not of various 
 Colours hke thofe made in the open Air, but 
 appeared all over of that prifmatick Colour on- 
 ly v/ith, which they were illuminated. And by 
 projecting the priimatick Colours immediately 
 upon the Glalles, I found that the Light which 
 fell on the dark Spaces which were between 
 the coloured Rings, was tranfmitted through the 
 GlalTes without any variation of Colour. For 
 on a white Paper placed behind, it would paint 
 Rings of the fame Colour with thofe which 
 vi^ere refleded, and of the bignefs of their im^ 
 mediate Spaces. And from thence the origin 
 
 of 
 
t ^S7] 
 
 of thefe Rings is manifeft ; namely , that the 
 Air between the Glafles, according to its vari- 
 ous thicknefs, is dilpofed in fome places to re- 
 fled, and in others to tranfmit the Light of a- 
 ny one Colour ( as you may fee reprefented in 
 the fourth Figure) ;ind in the lame place to re- 
 fleft that of one Colour where jt tranfmits that 
 of another. 
 
 Obf. id. The Squares of the Diameters of 
 thefe Rings made by any prifmatick Colour were 
 in arithmetical Progi-cllion, as in the fifth Ob- 
 fervation. And the Diameter of the fixth Cir- 
 cle, when made by the citrine yellow, and 
 
 viewed almolt 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 comprcfs'd between 
 two Glafles. In thofe that follow are fet down 
 the Appearances of a denfer Medium thin'd 
 within a rarer , fuch as are Plates of Mufcovy 
 G\'\k^ Bubbles of Water, and fome other thin 
 Subftances terminated on all fides with Air. 
 
 Obf, 17. If a Bubble be blown with Water 
 firil made tenacious by dilTolving a little Soap 
 in it, 'tis a common Obfervation, that after a 
 while it will appear tinged vi'ith 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 
 made of them,) as foon as I had blown any of 
 
 them 
 
ti88] 
 
 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 fubliding of 
 the Water, thefe Rings dilated flowly and over- 
 fpread the whole Bubble, defcending in order 
 to the bottom of it, where they vaniili'd fuc- 
 ceflively. 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, hke that in the firft Observation , which 
 continually dilated it felf till it became fome- 
 times more than 4 or i of an Inch in breadth 
 before the Bubble broke. At firlt I thought 
 there had been no Light reflefted froni the Wa- 
 ter in that place , but obferving it more curi- 
 oufly, I faw within it feveral fm-aller round 
 Spots, which appeared much blacker and dark- 
 er than the reft , 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 Vere within it. 
 
 Befides the aforefaid colour'd Rings there 
 would often appear fmall Spots of Colours, af- 
 cending and defcending up and down the fides 
 of the Bubble, by reafon of fome Inequalities 
 in the fubfiding of the Water. And fometimes 
 fmall black Spots generated at the fides would 
 
 afcend 
 
[ i89 ] 
 
 alcend up to the larger black Spot at the top 
 of the Bubble, and unite with it. 
 
 Obf. 1 8. Becaufe the Colours of thefe Bub- 
 bles were more extended and Hvely than thofe 
 of the Air thinn d between two Glalles, and fo 
 more eafy to be ditlinguiih'd , I fliall here give 
 you a farther defcription of their order, as they 
 w'ere obferv'd in viewing them by Reflexion 
 of the Skies when of a white Colour , whilil a 
 black fubltance was placed behind the Bubble. 
 And they were thefe, red, blue; red, blue.; 
 red, blue; red, green; red, yellow, green, 
 blue, purple ; red, yellow, green, blue, violet ; 
 red, yellow, white, blue, black. 
 
 The three firil Succefllons 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 w^as fcarce any other Colour 
 fenfible befides red and blue, only the blues 
 (and principally the fecond blue) inclined a Ht- 
 tle to green. 
 
 The fourth red was alfo dilute and dirty, but 
 not fo much as the foiTner three; after that 
 fucceeded little or no yellow, but a copious 
 green, w^hich at firft inclined a little to yellow, 
 and then became a pretty brisk and good wil- 
 low green, and, afterwards changed to a bluifli 
 Colour ; but there fucceeded neither blue nor 
 \dolet. 
 
 The fifth red at lirft inclined very much to 
 purple, and afterwards became more bright 
 ^nd brisk, but yet not very pure. This was 
 fucceeded with a very bright and intenfe yel- 
 low, which was but little in quantity, and foon 
 
 chang'd 
 
t ^90] 
 
 chdng'd to green : But that green was copious 
 and Ibmething more pure, deep and lively, than 
 the former green. After that follow'd an ex- 
 cellent blue of a bright Sky-colour, and then a 
 purple, which was lefs in quantity than the blue, 
 and much inclined to red. 
 
 The fixth red was at 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 bell of all the yellows , and 
 this changed firfl to a greenifli yellow, and then 
 to a greenifli blue ; but the green between the 
 yellow and the blue, was very little and dilute, 
 feeming rather a greenifli white than a green*. 
 The blue which fucceeded became very good, 
 and of a very fair bright Sky-colour , but yet 
 fomething inferior to the former blue; aud 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 tindlure of fcarlet 
 next to violet, which foon changed to a bright- 
 er Colour, inclining to an orange ; and the yel- 
 low which follow'd was at firfl pretty good 
 and lively, but afterwards it grew more dilute, 
 until by degrees it ended in perfed: whitenefs. 
 And this whitenefs, if the Water was very te- 
 nacious and well temper'd, would flovi^ly fpread 
 and dilate it felf over the greater part of the 
 Bubble ; continually growing paler at the top, 
 v/here at length it would crack in many places, 
 and thole cracks, as they dilated, would appear 
 
 of 
 
[ ^91 ] 
 
 of a pretty good, but yet obfcure and dark 
 Sky-colour ; the white between the blue Spots 
 diminifhmg, until it refembled the Threds of 
 an irregular Net-v»^orky and foon after vani(h'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 alio full of many round blue Spots, fome- 
 thing darker than the refl, there would emerge 
 one or more very black Spots, and within thofe, 
 other Spots of an intenier blacknefs , which I 
 mention'd in the former Obferv^ation ; and thefe 
 continually dilated themlelves 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 reafoa 
 that they begin to appear when the Bubble is 
 thickeft, and are mofl conveniently reckon'd 
 from the loweft and thickeft part of the Bub- 
 ble upwards. 
 
 O/ff 19. Viewing in feveral oblique Pofitions 
 of my Eye the Rings of Colours emerging on 
 
 the 
 
I ^92 ] ■ 
 
 the top of the Bubble, I found that they were 
 fenfibly dilated by increafmg 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 fo much as, when view'd molt ob- 
 liquely , to arrive at a part of the Plate more 
 than twelve times thicker than that where they 
 appear'd when viewed perpendicularly ; where- 
 as in this cafe the thicknefs of the Water, at 
 which they arrived when viewed mod oblique- 
 ly, was to that thicknefs which exhibited them 
 by perpendicular Rays , fomcthing lefs than as 
 8 to 5. By the belt of my Obfervations it was 
 between 15" and ifv to 10; an increafe about 
 24 times lefs than in the other cafe. 
 
 Sometimes the Bubble would become of an 
 uniform thicknefs all over, except at the top of 
 it near the black Spot , as I knew , becaufe it 
 would exhibit the fame appearance of Colours 
 in all Pofitions of the Eye. And then the Co- 
 lours which were fecn at its apparent circumfe- 
 rence by the obliqued Rays, would be different 
 from thofe that were feen in other places, by 
 Rays lefs oblique to it. And divers Spectators 
 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 afliftance 
 of the 4th, 14th, 1 6th and 1 8th Obfervations, 
 as they are hereafter explain'd , I colleCt the 
 thicknefs of the Water requifite to exhibit any 
 one and th'e fame Colour, at feveral Obliquities^ 
 
 to 
 
[ 193 ] 
 
 to be very nearly in the Proportion exprefTed 
 in this Table. 
 
 Incidence on 
 the JVater. 
 
 ReJra6iion in- 
 to the JVater. 
 
 Thicknefs of 
 the Water. 
 
 Deg. Min. 
 OO OO 
 
 Deg. Min. 
 00 00 
 
 10 
 
 15- 00 
 
 II II 
 
 107 
 
 30 00 
 
 22 I 
 
 IOt 
 
 45- 00 
 60 00 
 
 15 00 
 90 00 
 
 32 2 
 
 40 30 
 46 25- 
 
 48 35- 
 
 Hi 
 
 13 
 
 1^4 
 
 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 
 Refraftion. Where I fuppofe that the Sines 
 which meafure them are in round Numbers, as 
 3 to 4, though probably the dilTolution of Soap 
 in the Water, may a Uttle alter Jts refradive 
 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 conllitute its thicknefs when 
 the Rays are perpendicular. And the Rule 
 found by the feventh Obfervation agrees well 
 with thefe Meafures , if duly apply'd ; namely, 
 that the thicknefs of a Plate of Water requiiite 
 to exhibit one and the fame Colour at feveral 
 Obliquities of the Eye, is proportional to the 
 fecant of an Angle whole Sine is the firft of an 
 hundred and fix arithmetical mean Proportio- 
 
 O jials 
 
[ i?4 ] 
 
 iials between the Sines of Incidence and Refra- 
 ction counted from the lelfer Sine, 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 polifli'd Steel by heating it, or 
 on Bell-metal, and fome other metalline Sub- 
 llances, when melted and pour'd on the ground, 
 where they may cool in the open Air, have, like 
 the Colours of Water-bubbles, been a little 
 changed by viewing tliem at divers Obliquities, 
 and particularly that a deep blue,, or violet, 
 when view'd very obliquel)^ hath been changed 
 to a deep red. But the Changes of thefe Co- 
 lours are not i'o great and fenlible as of thofe 
 made by W ater. For the Scoria or vitritit d part 
 of the jVIetal, which moil Metals when heated or 
 jnelted do continually protrude, and fend out 
 to their Surface, and which by covering the 
 Metals in form of a thin glally Skin, caufes 
 thefe Colours, is much denfer than W ater ; and 
 I find that the Change made by the Obliquation 
 of tix Eye is lead in Colours of the denlcll: thin 
 Sublknces. 
 
 Oi^f xo. 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 
 ir, feemed red at its apparent circumference, 
 if the Clouds at the fame time, or immediately 
 after, were view'd through it, the Colour at its 
 circumference would be blue. And, on the 
 
 contrary, 
 
[195] 
 
 contrary, when by reflected Light it appeared 
 blue, it would appear red by trani'mitted Light. 
 
 Ob/.zi. By wetting very thin Plates of Muf- 
 covy Glafs , whofe thinnefs made the like 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 requifite to produce 
 any Colour, depends only on the denfity of the 
 Plate, and not on that or the ambient Medium. 
 And hence, by the loth and i6thObfervations, 
 may be known the thicknefs which Bubbles of 
 Water, or Plates of Mufcovy Glafs, or other 
 Subltances, have at any Colour produced by 
 them. 
 
 Ohf,%%. A thin tranfparent Body, w^hich 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 encompafled 
 with Air did exhibit Colours much more vivid 
 than thofe of Air made thin between two Glaf- 
 
 Ohf. 23. Comparing the quantity of Light 
 refleded from the feveral Rings , I found that 
 it was molt copious from the tirll or inmoil^ 
 and in the exterior Rings became gradually lefs 
 and lefs. Alfo the whitenefs of the firit King 
 was flronger than that redccfed from thofe 
 parts of the thin Medium or Plate which were 
 without the Rings ; as I could manifeilly per- 
 •ceive by viewing at a diftance the Rings made 
 
 O" X ^ bv 
 
[ ^9^ 1 
 
 b}^ the two Obje^l-glafTes ; or by comparing two 
 Bubbles of Water blown at dillant 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. 
 
 Oi^J^ 24. When the two Objeft-glafTcs were 
 lay'd upon one another, fo as to make the Rings 
 of the Colours appear, though with my naked 
 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- 
 lides many others, that were fo very fmall and 
 clofe together , that I could not keep my Eye 
 Heady 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 be- 
 lieve the Experiment may be improved to the 
 difcovery of far greater Numbers. For they 
 feem to be really unlimited, though vifible on- 
 ly fo far as they can be feparated by the Refra- 
 aion, as I Ihall hereafter explain. 
 
 But it was but one fide of thefe Rings, name- 
 ly, that towards which the Refraction was made, 
 which by that Refraction was render'd diftinft, 
 and the other fide became more confufed than 
 when view'd by the naked Eye, infomuch that 
 there I could not difcern above one or two, 
 and fometimes none of thofe Rings , of which 
 I could difcern eight or nine with, my naked 
 Eye. And their Segments or Arcs, which on 
 the other fide appear'd fo numerous, for the 
 mofl part exceeded not the third part of a Cir- 
 cle. If the Refra6lion was verv great, or the 
 
 Prifm 
 
I 197 ] 
 
 Prifm very diftant from the Objeft-glafTes , the 
 middle part of thofe Arcs became alio confu- 
 fed , fo as to difappear and conltitute an even 
 whitenefs, whilft on either fide their ends, as 
 alfo the whole Arcs fartheft from the center, 
 became diilin6ter than before, appearing in the 
 form as you fee them defign'd in the tifth Fi- 
 gure. 
 
 The Arcs, where they feem'd diftin6leil, were 
 only white and black fuccefTively, without any 
 other Colours intermix'd. But in other places 
 there appeared Colours, whofe order was in- 
 veried by the Refradion in luch manner, that 
 if I hrlt held the Prilm very near the Objedl:- 
 glafTes, and then gradually removed it farther 
 off towards myl'^ye, the Colours of the id, 3d, 
 4th , and following Rings llirunk towards the 
 white that emerged between them , until they 
 wholly vanifh'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 Objc6t-glafs 
 upon the other, that to the naked Eye they 
 have all over feem'd uniformly white, without 
 the leaft appearance of any of the colour'd 
 Rings; and yet by viewing them through a 
 Prifm, great multitudes of thofe Rings have 
 difcover'd themfelves. And in like manner 
 Plates of Mufcovy Glafs, and Bubbles of Glafs 
 blown at a Lamp Furnace, which w^ere 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 th^ 
 
 ^- 
 
1 158 ] 
 
 the form of Waves. And fo Bubbles of Wa- 
 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 
 Effeci , it was neceilary to hold the Prifm pa- 
 rallel , or very nearly parallel to the Horizon, 
 and to difpofe it fo that the Rays might be re- 
 fraded upwards. 
 
 THE 
 
[ ^99 ] 
 
 THE 
 
 SECOND BOOK 
 
 OPTIC KS. 
 
 PART II. 
 
 Remarks u^on the foregoing Obfervations. 
 
 VV I N G given my Obfervations of thefe 
 Colours, before I make ufe of them to 
 unfold the Caufes of the Colours of na- 
 tural Bodies, it is convenient that by 
 the fimpleil of them, fuch as are the id, 3d', 
 4th, 9th, nth, 1 8th, loth, and 24th, Ifirflex- 
 
 O 4 plain 
 
[ 200 ] ^ 
 
 plain the more compounded. And firfi: to fliew 
 how the Colours in the fourth and eighteenth 
 Obfervations are produced, let there be taken 
 in any right Line from the Point Y, [in Fig. 6.] 
 the lengths YA, YB, YC, YD, YE, YF, YG, 
 YH, in proportion to one another, as the Cube 
 Roots of the Squares of the Numbers, 4, t^, t> 
 T? 75 4, V, I , whereby the lengths of a mufical 
 Chord to found all the Notes in an eighth are 
 reprefented ; that is, in the proportion of the 
 Numbers 6300, 6814, 71 14, 7631, 815-5', 885-5', 
 9243, loooo. And at the Points A, B, C, D, 
 E, F, G, H, let perpendiculars A ct, B /3, &c. be 
 crcdcd , by whofe Intervals the Extent of the 
 fcveral Colours fet underneath againft them, is 
 to be reprefented. Then 'divide the Line A c* 
 in fuch proportion as the Numbers i, 2, 3, 5-, 
 6, y, ^, 10, II, ^c. fet at the Points of Divifion 
 denote. And through thofe Divifions from Y 
 draw Lines il, xK, 3 L, 5M, 6N, 7O, ^c. 
 
 Now if A 2 be fuppoled to reprefent the 
 thicknefs of any thin tranfparentBody, at which 
 the outmoft violet is molt copioufly reflected 
 in the firll Ring, or Series of Colours, then by 
 the 13th Obfcrvation, HKwill reprefent its 
 thicknefs, at which the utmoft red is molt co- 
 pioufly refledled in the fame Series. 'Alfo by 
 the 5-th and 1 6th Obfervations, A 6 and HN 
 will denote the thickneifes at which thofe ex- 
 treme Colours are moil copioufly refledcd in 
 the fecond Series, and A 10 and HQ the thick- 
 nelFes, at which they are molt copioufly reliev- 
 ed in the third Series, and fo on. And the 
 thicknefs at which any of the intermediate Co- 
 lours 
 
[ 20I ] 
 
 lours are refleded mod copioufly, will, accor- 
 ding to the 14th Obfervation, be defined by the 
 diitance of the Line AH from the intermediate 
 parts of the Lines xK, 6N, loQ, ^c, againfl 
 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 lealt thicknefs, and A3 the greatell thick- 
 nefs , at which the extreme violet in the firfl 
 Series is refleded, and let HI, and HL, de- 
 fign the like limits for the extreme red, and let 
 the intermediate Colours be limited by the in- 
 termediate parts of the Lines 1 1, and 3 L, a- 
 gainfi: which tlie Names of thofe Colours are 
 written, and fo on : But yet with this caution, 
 that the Reflexions be fuppofed firongeit at the 
 intermediate Spaces, 2K, 6 N, loQ, &c. and 
 from thence to decreafe gradually towards thefe 
 limits, 1 1, 3 L, 5- M, 7 O, ^c. on either fide ; 
 where you mufi: not conceive them to be pre- 
 cifely limited, but to decay indefinitely. And 
 whereas I have afiign d the fame Latitude to e- 
 very Series, I Aid it, becaufe although the Co- 
 lours in the firlt Scries feem to be a little broad- 
 er than the rell, by reafon of a fironger Re- 
 flexion there, yet that inequality is fo infenfi- 
 ble as fcarcely to be determin'd by Obferva- 
 tion. 
 
 Now according to this Defcription, concei- 
 ving that the Rays originally of feveral Colours 
 are by turns retleded at the Spaces il L 3, 5-1X1 
 O 7, y P R 1 1, ^c. and tranfmitted at the Spaces 
 AHIi, 3L M5, 7OP9, &c. itiscafytoknow 
 
 what 
 
[ 202 ] 
 
 what Colour muft in the open Air be exhi- 
 bited at any thicknefs of a tranfparent thin Bo- 
 dy. For if a Ruler be applied parallel to AH, 
 at that di (lance from it by which the thicknefs 
 of the Body is reprefented the alternate Spaces 
 1 1 L 3, 5-M O 7, &c. which it crdifeth will de- 
 note the refleded original Colours, of which 
 the Colour exhibited in the open Air is com- 
 pounded. Thus if the coniiitution of the green 
 in the third Series of Colours be defircd, apply 
 the Ruler as you fee at Tr^o-cp, and by its paf- 
 fmg through Ibme of the blue at tt and yellow 
 at <r, as well as through the green at ^, you may 
 conclude that the green exhibited at that thick- 
 nefs of .the Body is principally conllituted of 
 original green , but not without a mixture of 
 fome blue and yellow. 
 
 By this means you may know how the Co- 
 lours from the center of the Rings outward 
 ought to fucceed in order as they were defcri- 
 bed in the 4th and i8th Obiervations. For if 
 you move the Ruler gradually from AH through 
 all diilances, having pafs'd over the tirft Space 
 which denotes httleorno Reflexion to be made 
 by thinneitSubibnceSjit will lirli: arrive at i the 
 violet, and then very quickly at the blue and 
 green , which together with that violet com- 
 pound blue, and then at the yellow and red, by 
 whofe farther addition that blue is converted 
 into whitencfs, which whitenefs continues du- 
 ring the tranfit of the edge of the Ruler from 
 I to 3, and after that by the fucceiTive delici- 
 ence of its component Colours, turns firll to 
 compound vellow, and then to red, and lall of 
 
 ail 
 
[ 203 ] 
 
 HI the red ceafeth at L. Then begin the Co- 
 lours of the I'econd Series, which fucceed in 
 order during the tranlit of the edge of the 
 Ruler from 5 to O, and are more lively than 
 before, becaufe more expanded and fevered. 
 And for the lame reafon, inftead of the former 
 white there intercedes between the blue and 
 yellow a mixture of orange, yellow, green, 
 blue and indigo, all which together ought to 
 exhibit a dilute and imperfeft green. So the 
 Colours of the third Series all fucceed in or- 
 der; hrft, the violet, which a little interferes 
 with the red of the fccond order, and is there- 
 by inclined to a reddilh purple ; then the blue 
 and green, which are lefs mix'd with other 
 Colours, and confcquently more lively than be- 
 fore, efpccially the green: Then follows the 
 yellow, fome of which towards the green is di- 
 llindt and good, but that part of it towards the 
 fucceeding red, as alfo that red is mix'd with 
 the violet and blue of the fourth Series, where- 
 by various degrees of red very much inclining 
 to purple are compounded. This violet and 
 blue, which Ihould I'ucceed this red, being mix- 
 ed with, and hidden in it, there fuccecds a 
 green. And this at firit is much inclined to 
 blue, but foon becomes a good green, the on- 
 ly unmix'd and lively Colour in this fourth Se- 
 ries. For as it verges towards the yellow, it 
 begins to interfere with the Colours of the fifth 
 Series, by whofe mixture the fucceeding yel- 
 low and red are very much diluted and made 
 dirty, efpccially the yellow , which being the 
 weaker Colour is fcarce able to lliew it felf. 
 
 After 
 
[204] 
 
 After this the feveral Series interfere more and 
 more, and their Colours become more and more 
 intermix'd, till after three or four more revo- 
 lutions (in which the red and blue predominate 
 by turns) all forts of Colours are in all places 
 pretty equally blended, and compound an even 
 whitenels. 
 
 And fmce by the 15'thObfervation the Rays 
 endued with one Colour are tranfmitted, where 
 thofe of another Colour are refleded, the rea- 
 fon of the Colours made by the tranfmitted 
 Light in the 9th and xoth Obfervations is from 
 hence evident. 
 
 If not only the Order and Species of thefe 
 Colours , but alfo the precife thicknefs of the 
 Plate, or thin Body at which they are exhibited, 
 be defired in parts of an Inch, that may be alfo 
 obtained by allillance of the 6th or i6ih Obfer- 
 vations. For according to thofe Obfervations 
 the thicknefs of the thinned Air, which be- 
 tween two Glaffes exhibited the mod luminous 
 
 parts of the firil fix Rings were ^^, ^^ , 
 
 ^7/^0' T^' itIto, 7^0 P^^^s ^^ ^^ ^"c^- 
 Suppofe the Light reflefted mod copioufly at 
 thefe thicknefles be the bright citrine yellow, 
 or confine of yellow and orange, and thefe 
 thickneifes wiU'be F^, F v, F£, Fo, F 7. And 
 this being known, it is eafy to determine what 
 thicknefs of Air is reprefented by G(p, or by 
 any other diitance of the Ruler from AH. 
 
 But farther, fmce by the lothObfervation the 
 thicknefs of Air was to the thicknefs of Water, 
 
 which 
 
[ 205 ] 
 
 which between the fame GlaiTes exhibited the 
 fame Colour, as 4 to 3, and by the 21H: Obfer- 
 vation the Colours of thin Bodies are not varied 
 by varying the ambient Medium; the thick- 
 nefs of a Bubble of Water, exliibiting any Co- 
 lour, will be 4 of the thicknefs of Air produ- 
 cing the fame Colour. And fo according to 
 the fame loth and xiltObfervations the thick- 
 nefs of a Plate of Glafs, whofe Refraction of 
 the mean refrangible Ray , is meafured by the 
 proportion of the Sines 3 1 to 20, may be ~ of 
 the thicknefs of Air producing the fame Co- 
 lours ; and the like of other Mediums. I do 
 not affirm, that this proportion of xo to 31, 
 holds in all the Rays ; for the Sines of other 
 forts of Rays have other Proportions. But the 
 differences of thofe Proportions are fo little 
 that I do not here confider them. On thefe 
 Grounds I have compofed the following Ta- 
 ble, wherein the thicknefs of Air, Water, and 
 Glafs, at which each Colour is mod intenfe 
 and fpecifick , is exprelTed in parts of an Inch 
 divided into ten hundred thouland equal parts. 
 
 The 
 
r 20^ ] 
 
 The thicknefs of colour'' d Plates and Particles of 
 
 Their Colours of the 
 
 filft Order, 
 
 Of the third Order, 
 
 Of the fourth Order, 
 
 Of the fifth Order, 
 
 Of the fixth Order, 
 
 Of the fevcnth Or- 
 der, 
 
 Of the fecond Order, 
 
 (rVery black 
 
 Black 
 
 Beginning of 
 Black 
 
 BKie 
 
 White 
 
 Yellow 
 
 Orange 
 \.Red 
 
 Violet 
 
 Tndigo 
 jBlue 
 'Ureen 
 
 Yellow 
 
 Orange 
 
 Bright red 
 
 Scarlet 
 
 Purple 
 
 Indigo 
 jBlne 
 
 Green 
 I Yellow 
 
 Red 
 
 Bluifh red 
 
 Bluifh green 
 Green 
 
 lYellowifhgreen 
 Red 
 
 { 
 
 Green: (li blue 
 Red 
 
 f Greenifliblue 
 \Red 
 
 5"Greenifh blue 
 (_Ruddy white 
 
 r" 
 
 -^ 
 
 Air. 
 
 WAter. 
 
 G/^l^. 
 
 i_ 
 
 ? 
 
 1 
 
 "z 
 
 8 
 
 J t 
 
 I 
 
 ? 
 
 T 
 
 ■^ I 
 
 1 
 
 i4- 
 
 ly 
 
 ^Y 
 
 It 
 
 i4-T 
 
 5t 
 
 3-J 
 
 
 7-ir 
 
 sf 
 
 4-1- 
 
 8 
 
 6 
 
 5v 
 
 9 
 
 ^^ 
 
 5* 
 
 I '-r 
 
 £4 
 
 
 I^-T 
 
 9i 
 
 8-T^ 
 
 14 
 
 rc^- 
 
 9 
 
 I ST 
 
 ''T 
 
 94 
 
 i^i- 
 
 IZ| 
 
 I0| 
 
 17^- 
 
 ^3 
 
 I Iv 
 
 l^ 
 
 13-^ 
 
 I'^* 
 
 3 
 
 Mi 
 
 ^^Y 
 
 ZI 
 
 ^5i 
 
 xSrv 
 
 2-1-tV 
 
 '"t. 
 
 I4v 
 
 ^-3t 
 
 f-TT 
 
 iStV 
 
 ^5-f 
 
 I?T^ 
 
 i6i. 
 
 i7| 
 
 iC^ 
 
 -174- 
 
 Z9 
 
 ^4 
 
 i?f 
 
 3^ 
 
 14 
 
 2C^ 
 
 34 
 
 i5T 
 
 iZ 
 
 3S4 
 
 164: 
 
 xz{- 
 
 36 
 
 17 
 
 ^3'> 
 
 4cf 
 
 
 26 
 
 46 
 
 344- 
 
 29f 
 
 5^-T 
 
 3^T. 
 
 34 
 
 sH 
 
 44 
 
 38 
 
 6j 
 
 4^i 
 
 4Z 
 
 71 
 
 ^3i 
 
 4S-t 
 
 77 • 
 
 ?7^ 
 
 •4Cf 
 
 Now 
 
[ 207 ] 
 
 Now if this Table be comparcd with the 6th 
 Scheme, you will there fee the conltitution of 
 each Colour, as to its Ingredients , or the ori- 
 ginal Colours of which it is compounded , and 
 thence be enabled to judge of itslntenfenefs or. 
 Imperfedion ; which may fuiiice in explication 
 of the 4th and i8th Obfervations , unlcfs it be 
 farther dciired to delineate the manner how 
 the Colours appear, when tlie two Objeft-glaf- 
 fes are laid upon one another. To do which, 
 let there be defcribed a large Arc of a Circle, 
 and a llreight Line which may touch that Arc, 
 and parallel to that Tangent feveral occult 
 Lines, at fuch diilances from it, as the Num- 
 bers let againit the feveral Colours in the Ta- 
 ble denote. For the Arc, and its Tangent, will 
 reprefent the Superficies of the Glalles termi- 
 nating the interjacent Air ; and the places where 
 the occult Lines cut the Arc will ihow at what 
 diltances from the center, or Point of contad, 
 each Colour is refleded. 
 
 There arealfo other Ufes of this Table: For 
 by its ailiflance the thicknefs of the Bubble in 
 the 19th Obfervation was determined by theCo- 
 lours which it exhibited. And fo the bignefs 
 of the parts of natural Bodies may be conje- 
 dured by their Colours, as iliall be hereafter 
 fliewn. Alfo, if two or more very thin Plates 
 be laid one upon another, fo as to compofe one 
 Plate equalling them all in thicknefs, the refult- 
 ing Colour may be hereby determin'd. For in- 
 llance, Mr. Hook obferved, as is mentioned in 
 his Mlcrographia , that a faint yellow Plate of 
 Mufcovy Glafs laid upon a blue.one, conltituted 
 
 a verv 
 
[ 208 ] 
 
 a very deep purple. The yellow of the firft 
 Order is a faint one , and the thicknefs of the 
 Plate exhibiting it, according to the Table is 
 44, to which add 9, the thicknefs exhibiting 
 blue of the fecond Order, and the Sum will be 
 134, which is the thicknefs exhibiting the pur- 
 ple of the third Order. 
 
 To explain, in the next place, the circum- 
 fiances of the 2d and 3d Oblervations ; that is, 
 how the Rings of the Colours may (by turning 
 the Prifms about their common Axis the con- 
 trary way to that exprefTed in thofe Obferva- 
 tions) be converted into white and black Rings, 
 and afterwards into Rings of Colours again, the 
 Colours of each Ring lying now in an inverted 
 order ; it muft be remember'd, that thofe Rings 
 of Colours are dilated by the obliquation of the 
 Rays to the Air which mtercedes the GlalTes, 
 and that according to the Table in the 7th Ob- 
 fervation, their Dilatation or Increafe of their 
 Diameter is molt manifeft and fpcedy when 
 they are obliqueit. Now the Rays of yellow 
 being more refracted by the firil Superficies of 
 the laid Air than thofe of red, are thereby 
 made more oblique to the fecond Superficies, 
 at which they are reflected to produce the co- 
 lour'd Rings, and confequently the yellow Cir- 
 cle in each Ring will be more dilated than the 
 red ; and the Excefs of its Dilatation will be fo 
 much the greater, by how much the greater is 
 the obliquity of the Rays, until at lall it be- 
 come of equal extent with the red of the fame 
 Ring. And for the fame reafon the green, blue 
 and Violet, will be alfo fo much dilated by the 
 
 itill 
 
[ 209 ] 
 
 M\ greater obliquity of their Rays, as to be- 
 come all very nearly of equal extent with the 
 red, that is, equally diilant from the center of 
 the Rings. And then all the Colours of the 
 fame Ring mull be coincident, and by their 
 mixture exhibit a white Ring. And chefe white 
 Rings mull have black ai^dark Rings between 
 them, becaufe they do nftfpread and interfere 
 with one another as before. And for that rea- 
 fon alfo they muft become diitinder and vilible 
 to far greater numbers. But yet the violet be- 
 ing obHqueft will be fomething more dilated 
 in proportion to its extent than the other Co- 
 lours, and fo very apt to appear at the exterior 
 Verges of the white. 
 
 Afterwards, by a greater obliquity of the 
 Rays, the violet and blue become more fenfibly 
 dilated than the red and yellow, and fo being 
 farther removed from the center of the Rings^ 
 the Colours mult emerge out of the white in an 
 order contrary to that which they had before, 
 the violet and blue at the exterior Limbs of 
 each Ring, and the red and yellow at the in- 
 terior. And the violet, by reafon of the great- 
 ell obliquity of its Rays , being in proportion 
 molt of all expanded, will fooneft appear at 
 the exterior Limb of each white Ring, and be- 
 come more confpicuous than the reft. And the 
 feveral Series of Colours belonging to the feve- 
 ral Rings, will by their unfolding and fpread-^ 
 ing, begin again to interfere, and thereby ren- 
 der the Rings lefs diftind, and not viiible to fo 
 great numbers. 
 
 P If 
 
[ 2IO ] 
 
 If inftead of the Prifms the Objeft-glafTes be 
 made uie of, the Rings which they exhibit be- 
 come not white and diltind by the obliquity of 
 the Eye, by reafon that the Rays in their paifage 
 through that Air which intercedes the Glalies 
 are very nearly parallel to thofe Lines in which 
 they were tirll incidqj^ on the Glafles, and con- 
 fequently the Rays eii^ed with feveral Colours 
 are not inchned one more than another to that 
 Air, as it happens in the Prifms. 
 
 There is yet another circumitance. of thefe 
 Experiments to be confider'd, and that is why 
 the black and white Rings which when view'd 
 at a diflance appear diilincf, iliould not only be- 
 come confufcd by viewing them near at hand, 
 but alio yield a violet Colour at both the edges 
 of every white Ring. And the reafon is, that 
 the Rays which enter the Eye at feveral parts 
 ofthe Pupil, have feveral Obliquities to theGlaf- 
 fes, and thofe which are molt oblique, if confi- 
 der'd apart, would reprefent the Rings bigger 
 than thofe which are the leail oblique. Whence 
 the breadth of the Perimeter of every white 
 Ring is expanded outwards by the obliqued 
 Rays- ,ind inwards by the leall oblique. And 
 this Expanfion is fo much the greater by how 
 much the greater is the difference of the Obli- 
 quity ; that is, by how much the Pupil is wider, 
 or the Eye nearer to the Glalies. And the 
 breadth of the violet mull be moll expanded , 
 becaufe the Rays apt to excite a Senfation of 
 that Colour are molt obhque to a fecond, or 
 farther- Superiicies of the thinn'd Air at which 
 they are refU-'fled , and have alfo the greateft 
 
 * varia» 
 
Variation of Obliquity, which makes that Co- 
 lour foonelt emerge out of the edffes of the 
 white. And as the breadth of every Ring is 
 thus augmented, the dark Intervals muit be di- 
 minifli'd, until the neighbouring Rings become 
 continuous, and are blended, the exterior firil^ 
 and then thofe nearer the center, fo that they 
 can no longer be diitinguifli'd apart, but feem 
 to conltitute an even and unifoi'm whitenefs. 
 
 Among all the Obfervations there is none ac- 
 companied with fo odd circumftances as the 
 twenty fourth. Of thofe the principal are, that 
 in thin Plates, which to the naked Eye feem of 
 an even and uniform tranfparent whitenefs ? 
 without any terminations of Shadows, the Re- 
 fradion of a Prifm iliould make Rings of Co- 
 lours appear , whereas it mfually makes Objeds- 
 appear colour'd only there where they are ter- 
 minated with Shadows, or have parts unequal- 
 ly luminous; and that it lliould make thofe 
 Rings exceedingly diitind and white, although 
 it ufualiy renders Obje6ls confufed and colour- 
 ed. The Caufe of thefe things you will under- 
 Hand byconfidering, that all the Rings of Co- 
 lours ar6 really in the Plate, when view'd with 
 the naked Eye, although by reafon of the great 
 breadth of their Circumferences they fo much 
 interfere and are blended together, that they 
 feem to conltitute an uniform whitenefs. But 
 when the Rays pafs through the Prifm to the 
 Eye, the Orbits of the feveral Colours in every 
 Ring are refraded, fome more than others^ ac- 
 cording to their degrees of Refrangibility : By 
 which mean^ the Colours^ on ooie fide of the 
 
[212] 
 
 Ring (that is on one fide of its center) become 
 more unfolded and dilated , and thofe on the 
 other fide more complicated and contrai^led. 
 And where by a due Refradion they are lb 
 much contracted, that the leveral Rings be- 
 come narrower than to interfere with one ano- 
 ther, they mull: appear diftinCt, and alfo white, 
 if the conilituent Colours be fo much contract- 
 ed as to be wholly coincident. But, on the 
 other fide , where the Orbit of every Ring is 
 made broader by the farther unfolding of its 
 Colours, it mull interfere more with other Rings 
 than before, and fo become lels diilincL 
 
 To explain this a little farther, fuppofe the 
 concentrick Circles AV, and BX, [inF/g. 7.] 
 reprefent the red and violet of any Order, 
 which, together \^'itlf the intermediate Colours, 
 conllitute any one of theie Rings. . Now thefe 
 being view'd through a Prifm, the violet Circle 
 BX, will by a greater P.efraCtion be farther 
 tranilated from its place than the red AV, and 
 fo approach nearer to it on that fide of the Cir- 
 cles, towards which the Refractions are made. 
 For inliance , if the red be tranilated to a v, 
 the violet maybe tranilated to ^x, fo as to ap- 
 proach nearer to it at x than before, and if the 
 red be farther tranflated to a v, the violet may 
 l;e fo miuch farther tranilated to bx as to con- 
 vene with it at X, and if the red be yet farther 
 tranilated to aT, the violet may be ftiil fo much 
 farther tranilated to /S ^ as to pafs beyond it at 
 |, and convene with it at e and /. And this 
 being underilood not only of the red and vio- 
 let, but of all the other intermediate Colours, 
 
 and 
 
[ 213 ] 
 
 tnd alfo of ex^ery revolution ot thofe Colours, 
 you will cafily perceive how thofe of the fame 
 revolution Or order, by their nearnefs at xv 
 and T|, and their coincidence at x v, e and /J 
 ought to conftitute pretty dillind Arcs of Cir- 
 cles, cfpecially at xv, or at e and/, and that 
 they wdll appear feverally at xz; and at xv ex- 
 hibit whitenefs by their coincidence, and again 
 appear feveral at T^, but yet in a contrary or- 
 der to that which they had before, and itill re- 
 tain beyond e and f. But, on the other fide, 
 at a if, ab, or ccl3, thefe Colours mull: become 
 much more confufed by being dilated and fpread 
 fo, as to interfere with thofe of other Orders. 
 And the fame confufion will happen at T^ be- 
 tween ^ and /J if the Refraftion be very great, 
 or the Priim very diltant from the Objed-glaf- 
 fes : In which cafe no parts of the Rings will 
 be feen, fave only two little Arcs at e and f, 
 whofe diflance from one another, will be aug- 
 mented by removing the Prifm Itill farther from 
 the Objed-glaires : And thefe little Arcs mufl 
 be diilinclell; and whiteil at their middle, and 
 at their ends, where they begin to grow con- 
 fufed they muft be colour'd. And the Colours 
 at one end of every Arc mult be in a contrary 
 order to thofe at the other end, by reafon that 
 they crofs in the intermediate white ; namely, 
 their ends, which verge towards T|, will be 
 red and yellow^ on that fide next the center, 
 and blue and violet on the other fide. But 
 their other ends which verge from T| will on 
 the contrary be blue and violet on that fide to- 
 
 P 3 wards 
 
[214] 
 
 wards the center, and on the other fide red 
 and yellow. 
 
 Now as all thefe things follow from the pro- 
 perties of Light by a mathematical way of rea- 
 foning, fo the truth of them may be manifelled 
 by Experiments. For in a dark Room, by view- 
 ing thefe Rings through a Prifm , by reflexion 
 of the feveral prifmatick Colours, which an 
 afliftant caufes to move to and fro upon a Wall 
 or Paper from whence they are refleaed, whilfl 
 the Spectator's Eye, the Prifm and the Objeft- 
 glafTes (as in the 15th Obfervation) are placed 
 Iteady : the Pofition of the Circles made fuc- 
 ceffively by the feveral. Colours, will be found 
 fuch, in refpeft of one tmother, as I have de- 
 fcribed in the Figures abxv^ or abxv, or 
 rt/3|r. And by the fame method the truth of 
 the Explications of other Obfervations may be 
 examined. 
 
 By what hath been faid, the like Phaenomena 
 of Water, and thin Plates of Glafs may be un- 
 derftood. But in fmall fragments of thofe Plates, 
 there is this farther obfervable, that where they 
 lye flat upon a Table and are turned about their 
 centers whilil they are viewed through a Prifm, 
 they will in fome pollures exhibit Waves of va- 
 rious Colours, and fome of them exhibit thefe 
 Waves in one or two Pofitions only, but the 
 mofl of them do in all Politions exhibit them, 
 and make them for the molt part appear al- 
 moil all over the Plates. The reafon is , that 
 the Superficies of fuch Plates are not even, but 
 have many Cavities and Swelhngs, which how 
 fliallow foever do a little vary the thicknefs of 
 
 the 
 
[215] 
 
 the Plate. For at the fcveml fides of thofe Ca- 
 vities, for the Realons newly defcribed, there 
 ought to be produced Waves in feveral po- 
 llures of the Prifm. Now though it be but 
 fome very fmall, and narrower parts of the Glafs, 
 by which thefe Waves for the molt part are cau- 
 fed , yet they may feem to extend themfelves 
 over the whole Glafs, becaufefrom the narrow- 
 eft of thofe parts there are Colours of feveral 
 Orders, that is of ieveral Rings, confuledly rc- 
 flefted , which by Refradion of the Prifm are 
 unfolded, feparated, and according to their 
 degrees of Refraction, difperfed to le\Tral pla- 
 ces, fo as to conftitute fo many feveral Waves, 
 as there were divers orders of Colours promif- 
 cuoully reflefted from that part of the Glafs. 
 
 Thefe are the principal Pha^mwncna of thin 
 Plates or Bubbles, whole Explications depend 
 on the properties of I .ight, which I have here- 
 tofore deliver'd. And thefe you fee do necef- 
 farily follow from them, and agree with them, 
 even to their very leail circumilances ; and not 
 only fo, but do very much tend to their proof 
 Thus, by the i4thObfervation, it appears, that 
 the Rays of feveral Colours made as well by thin 
 Plates or Bubbles, as by Refradfions of a Prilm, 
 have feveral degrees of Refrangibility, where- 
 by thofe of each order , which at the retiexion 
 from the Plate or Bubble are intcrmix'd with 
 thofe of other Orders, are i'eparated from them 
 by Refraction, and alibciarcd together fo as to 
 become vifible bv themielves like Arcs of Cir- 
 cles. For if the Rays were all alike refrangi- 
 ble, 'tis impoilible that the whitenefs, which 
 
 P 4 to 
 
J 21^ ] 
 
 to the naked Senfe appears uniform, Ihould bjf 
 Refraclion have its parts trani'pofed and ranged 
 into thofe black and white Arcs, 
 
 It appears alio that the unequal Refradions 
 of diftorm Rays proceed not from any contin- 
 gent irregularities ; fuch as are Veins, aq uneven 
 Polifh, or fortuitous Poiirion of the Pores of 
 Glafs; unequal and cafual Motions in the Air 
 or /Ether, the fpreading, breaking, or dividing 
 the fame Pvay into many diverging parts, or the 
 like. (For, admitting any fuch irregularities, 
 it would be iiiipofTible for Refraftions to render 
 thofe Rings fo very diltinct, and well defined, 
 as they do in the 24th Obfervation. It is ne- 
 celTary therefore that every Ray have its proper 
 and conilant degree of Refrangibility connate 
 with it, accqp(ing to which its refraction is e- 
 ver juftly andregularly perform'd, and that fe- 
 veral Rays have feveral of thofe degrees. 
 
 And wliat is faid of their Refrangibility may 
 Ipe alfo underllood of their Refiexibility, that is 
 of their Difpofitions to be reflected fome at ^ 
 greater, and others at a lefs thicknefs, of thin 
 plates or Bubbles, namely, that thofe Difpofi- 
 t:ions are alio connate with the Rays , and im- 
 piutable; as may appear by the 13th, 14th, and 
 ifth Obfervations compared with the fourth 
 gnd eighteenth. 
 
 By the precedent Obfervations it appears al- 
 fo, that whitenefs is a diiiimilar mixture of all 
 Colours 9 and that Light is a mixture of Rays 
 enfiued with all thofe Colours, For conliderr 
 ing the multitude of the Rings of Colours, in 
 rhe ads 12th ar^d ^4th Obfervations, it is manir 
 
 ■ ftft. 
 
[ 217 ] 
 
 fell, that although in the 4th and iSthObfer- 
 vations there appear no more than eight or 
 nine of thofe Rings , yet there are really a far 
 gi'eatcr number, which fo much interfere and 
 mingle with one another, as after thofe eight 
 or nine revolutions to dilute one another whol- 
 ly, and conllitute an even and fenfibly uniform 
 vvhitenefs. And confequently that whitenefs 
 muil be allow'd a mixture of all Colours, and 
 the Light which conveys it to the Eye mufl 
 be a mixture of Rays endued with all thofe Co- 
 lours. 
 
 But farther, by the 24th Obfervation, it ap- 
 pears, that there is a conllant relation between 
 Colours and Refrangibility, the moll refrangi- 
 ble Rays being violet, the leail; refrangible red, 
 and thofe of intermediate Colours having pro- 
 portionably intermediate degrees of Refrangibi- 
 lity. And by the 13th, 14th and i^thObfer- 
 vations, compared with the 4th or i8th, there 
 appears to be the fame conllant relation be- 
 tween Colour and Rellexibihty, the violet be- 
 ing in like circumitances relleaed at lealt thick- 
 nelfes of any thin Plate or Bubble, the red at 
 greatefl thicknelfes, and the intermediate Co- 
 lours at intermediate thicknelfes. Whence it 
 follows, that the colorifick Diipoiitions of Rays 
 are alfo connate with them and immutable, and 
 by confequence that all the Produdions and 
 Appearances of Colours in the World are de- 
 rived not from any phyfical Change caufed in 
 Light by RefraClion or Reflexion, but only 
 f^om the various Mixtures or Separations of 
 Rays, by virtue of their different RefrangibiUty 
 
 or 
 
[2I8] 
 
 orReflexibility. And in this refpeft the Science 
 of Colours becomes a Speculation as truly ma- 
 thematical as any other part of Opticks. I mean 
 fo far as they depend on the Nature of Light , 
 and are not produced or alter'd by the Power 
 of Imagination, or by flriking or prefling the 
 Eye. 
 
 THE 
 
[ 219 ] 
 
 THE 
 
 SECOND BOOK 
 
 OP TICKS. 
 
 PART III. 
 
 Of the permanent Colours of natural Bodies^ and 
 the Analogy between them and the Colours of 
 thin tranjparent 'Plates, 
 
 j^^^l AM now come to another part of 
 ^"j'MJ this Defign, which is to confider how 
 
 pi the Phaenomena of thin tranfparent 
 "^ Plates ftand related to thofe of all o- 
 ther natural Bodies. Of thefe Bodies I have al- 
 ready told you that they appear of divers Co- 
 lours, 
 
[ 220 ] 
 
 lours, accordirigly as they are difpofed to refleft 
 moil copiouily the Rays originally endued with 
 thofe Colours. But their ConiUtutions, where- 
 by they reflect fome Rays more copioufly than 
 others, remain to be difcover'd, and thefe I 
 fhall endeavour to manifelt in the following 
 Proportions. 
 
 Prop. I. 
 
 Thofe Superficies of tranjparent Bodies refleB 
 the great efl quantity of Lights which have 
 the great eft re franking Tower ; that is, which 
 intercede Mediums that differ moft in their 
 refraBive ^enfities. u4nd in the Confines of 
 equally refra^iing Mediums there is no Re^ 
 flexion. 
 
 THE Analogy between Reflexion and Re- 
 fraftion will appear by coniidering, that 
 when Li?ht pafleth obliquely out of one Medi- 
 um into another which refrads from the per- 
 pendicular, the greater is the difference of their 
 refradive Denlity , the lefs Obliquity of Inci-^ 
 dence is requifite to caufe a total Reflexion. 
 For as the Sines are which meafure the Refra- 
 <^ion, fo is the Sine of Incidence at which the 
 total Reflexion begins, to the Radius of the 
 Circle, and confequently that Angle of Inci- 
 dence is leafl: W'here there is the greatefl: diffe- 
 rence of the Sines. Thus in the paffing of 
 Light out of Water into Air, where theRefra- 
 ftion is meafured by the Ratio of the Sines 3 to 
 4, the total Reflexion begins when the Angle 
 of Incidence is about 48 Degrees 35- Minutes. 
 
 In 
 
[ 221 ] 
 
 In pafling out of Glafs into Air, where the Re* 
 fradion is meaiured by the Ratio of the Sines 
 ao to 31, the total Retlexion begins when the 
 Angle of Incidence is 40 Degrees 10 Minutes; 
 and fo in pafling out of Cryllal, or more Itrong- 
 lyrefrading Mediums into Air, thereisliiilalefs 
 Obliquity requilite to caufe a total Retiexion. 
 Superhcies therefore which refraft moil do 
 foonelt refled all the Light which is incident 
 on tKem, and fo mult be allowed moil Itrongly 
 reflexive. 
 
 But the truth of this Proportion will farther 
 appear by obierving, that in the Superficies in- 
 terceding two traniparent Mediums, (fuch as are 
 Air, Water, Oil, common Glafs, Cryilal, me- 
 talline Glaffes, Ifland Glafles, white tranfparent 
 Arfenick, Diamonds, &c.) the Reflexion is 
 Itronger or weaker accordingly, as the Super- 
 ficies hath a greater or lefs refrading^ower 
 
 gTn 
 
 For in the Confine of Air and Sal-gem 'tis 
 fh-onger than in the Confine of Air and Water, 
 and iTill flronger in the Confine of Air and com- 
 mon Glafs or Cryllal, and llronger in the Con- 
 fine of Air and a Diamond. If any of thefe, 
 and fuch like tranfparent Solids, be immerged 
 in Water, its Reflexion becomes much weak- 
 er than before, and Hill weaker if they be im- 
 merged in the more llrongly refrading Liquors 
 of well rectified Oil of Vitriol or Spirit of Tur- 
 pentine. If Water be diltinguiih'd into tw^o 
 parts, by any imaginary Surflice, the Reflexion 
 in the Confine of thoie two parts is none at all. 
 In the Confine of Water and Ice 'tis very little, 
 in that of Water and Oil 'tis fomething greater, 
 
 in 
 
[ 2^2 ] 
 
 in that of Water and Sal-gem flill greater, and 
 in that of Water and Glafs, orCryftal, or other 
 denfer Subilances ilill greater, accordingly as 
 thofe Mediums differ more or lefs in their re- 
 fra<R:ing Powers. Hence in the Confine of com- 
 mon Glafs and Cryftal, there ought to be a 
 weak Reflexion, and a flronger Reflexion in 
 the Confine of common and metalline Glafs, 
 though I have not yet tried this. But, in the 
 Contine of two GlaiTes of equal denfity, there 
 is not any fenfible Reflexion, as was fliewn in 
 the fir ft Obfervation. And the fame may be 
 underflood of the Superficies interceding two 
 Cryftals , or two Liquors , or any other Sub- 
 ilances in which no Refradion is caufed. So 
 then the reafon why uniform pellucid Mediums, 
 (fuch as W ater, Glafs, orCryftal) have no fen- 
 fible Reflexion but in their external Superficies^i 
 wher^they are adjacent to other Mediums of 
 a difflrent denfity, is becaufe all their conti- 
 guous parts have one and the fame degree of 
 denlity. 
 
 R o p. 
 
 II. 
 
 The leap parts of almofl all natural Bodies are 
 in fome meafure tranfparent : And the Opa- 
 city of thofe Bodies arifeth from the multi- 
 tude of Reflexions caufed in their internal 
 Tarts. 
 
 TH AT this is fo has been obferved by o- 
 thers, and will eafJy be granted by theni 
 that have been converfant with Microicopes. 
 And it may be alfo tried by applying any lub- 
 
 ftancf' 
 
r 223 1 
 
 ftance to a hole through which fome Light is 
 immitted into a dark Room. For how opake 
 foever that Subltance may feem in the open 
 Air, it w^ill by that means appear very manifefl- 
 ly tranfparent , if it be of a fufficient thinnefs. 
 Only white metalline Bodies mull be excepted, 
 which by reafon of their exceflive denfity feem 
 to relied: almoll all the Light incident on their 
 firlt Superficies , unlefs by folution in Menlbu- 
 ums they be reduced into very fmall Particles, 
 and then they become tranfparent. 
 
 Prop. HI. 
 
 Between the parts of opake and colour' d Bodies 
 are many Spaces^ either empty or replcnifl? d, 
 with Mediums of other T^cnjities ; as Water 
 between the tinging Corpufcles wherewith a- 
 ny Liquor is impregnated , Air between the 
 aqueous Globules that conjiitute Clouds or 
 Miffs ; and for the moft part Spaces void of 
 both Air and JVater^ but yet perhaps not 
 wholly void of all Subjiance , between the 
 parts of hard Bodies. 
 
 ^ I ^HE truth of this is evinced by the two 
 jH^ precedent Proportions : For by the fe- 
 coud Propofition there are many Reflexions 
 maue by the internal parts of Bodies , which, 
 by the hrlt Proportion , would not happen if 
 the parts of thole Bodies were continued with- 
 out any luch Ii^terltices between them, becaule 
 Reflexions are caufed only in Superficies, which 
 intercede Mediums of a differing denfity by 
 Trop.i, 
 
 But 
 
[ 224 ] 
 
 But farther , that this difcontinuity of parts 
 is the principal Caufe of the opacity of Bodies, 
 will appear by confidering, that opake Subltan- 
 ces become tranfparent by filling their Pores 
 with any Subftance of equal or almoft equal den- 
 fity with their parts. Thus Paper dipped in 
 Water or Oil , the Oculus Mundi Stone fteep'd 
 in Water, Linen Cloth oiled or varnilh'd , and 
 and many other Subilances foaked in fuch Li- 
 quors as will intimately pervade their little 
 Pores, become by that means more tranfparent 
 than other wife ; fo, on the contrary, the moll 
 tranfparent Subilances may by evacuating their 
 Pores, or fcparating their parts > be rendh-'d 
 fufficiently opake, as Salts or wet Paper, or the 
 Oculiis Mitnd'i Stone by being dried, Horn by 
 being fcraped, Glafs by being reduced to Pow- 
 der, or othervvife flawed. Turpentine by being 
 Itirred about with Water till they mix im.per- 
 fedly,* and Water by being form'd into many 
 fmall Bubbles, either alone in the form of Froth, 
 or bylhakingit together with Oil of Turpen- 
 tine, or Oil Olive, or with Ibme other conve- 
 nient Liquor, with which it v/ill not perfectly 
 incorporate. And to the increafe of the opa- 
 city of thefe Bodies it conduces fomething, that 
 by the x3d Obfervation the Reflexions of very 
 thin tranfparent Subilances are confiderably 
 ftronger than thofe made by the fame Subilan- 
 ces of a greater thicknefs. 
 
 Prop. 
 
[ 225 ] 
 
 Prop. IV. 
 
 The farts of Bodies and their Interftices mufl 
 not be lefs than of fume definite bignefsy to 
 render them ofake and colour d. 
 
 FOR the opakeft Bodies, if 'their parts be 
 fubtily divided, (as Metals by being diirol- 
 ved in acid Menftruums, C^r.) become perfed- 
 ly tranfparent. And you may alfo remember, 
 that in the eighth Oblervation there was no 
 fenfible reflexion at the Superficies of the Ob- 
 jedt-glafTes where they were very near one an- 
 other, though they did not abfolutely touch. 
 And in the. 17th Obfervation the Reflexion of 
 the Water-bubble where it became thinneflwas 
 almofl infenfible, fo as to caufe very black Spots 
 to appear on the top of the Bubble by the want 
 of refleded Light. 
 
 On thefe grounds I perceive it is that Water, 
 Salt, Glafs, Stones, and fuch like Subflances, 
 are tranfparent. For, upon divers Confidera- 
 tions, they feem to be as full of Pores or Inter- 
 laces between their parts as other Bodies are, 
 but yet their Parts and Interftices to be too 
 fmall to caufe Reflexions in their common Sur- 
 faces. 
 
 Prop. 
 
[ i26 ] 
 
 Prop. V. 
 
 The tranjparent farts of Bodies according- to 
 their feveral Jizes refleB Rays of one Colour^ 
 and tranfmit thofe of another ^ on the fame 
 grounds that thin Tlates or Bubbles do reflet 
 or tranfmit thofe Rays. And this I take to 
 be the ground of all their Colours. 
 
 FOR if a thinri'd or plated Body, whiclif 
 being of an even thicknefs, appears all o- 
 ver of one uniform Colour, Ihould be flit into 
 Threds, or broken into Fragments, of the fame 
 thicknefs with the Plate ; I fee no reafon why 
 every Thred or Fragment fliould not keep its 
 Colour, and by confequence why a heap of 
 thofe Threds or Fragments Ihould not confli- 
 tute a Maifs or Powder of the fame Colour,' 
 which the Plate exhibited before it was broken.- 
 And the parts of all natural Bodies being like' 
 fo many Fragments of a Plate, mull on the fame 
 grounds exhibit the fame Colours. 
 
 Now that they do fo> will appear by the affi- 
 fiity of their Properties. The finely coloured' 
 Feathers of fome Birds, and particularly thofe, 
 of Peacocks Tails, d.o in the very fame part of 
 the Feather appear of feveral Colours in feveral 
 Fofitions of the Eye, after the very fame man- 
 ner that thin Plates were found to do in the 
 7th and 19th Obfervations, and therefore their 
 Colours arife from the thinnefs of the tranfpa- 
 rent parts of the Feathers ; that is, from the 
 flendernefs of the very fine Hairs, or Capilla-- 
 tnenta^ which grow out of the fides of the' 
 
 y groller 
 
grolTcr lateral Branches or Fibres of thofe Fea- 
 thers. And to the fame purpofe it is, that the 
 Webs of fome Spiders by being fpiin very fine 
 have appeared colour'd, as fome have obferv'd, 
 and that the colour'd Fibres of fome Silks by 
 varying the Pofition of the Eye do vary their 
 Colour. Alfo the Colours of Silks , Cloths , 
 and other Subftances, which Water or Oil caii 
 mtimately penetrate, become more faint and 
 obfcure by being immergcd in thofe Liquors , 
 and recover their Vigour again by being dried, 
 much after the manner declared of thin Bodies 
 in the loth and ziil Obfervations. Leaf Gold, 
 fome forts of painted Glafs, the hifufion of 
 Lignum Mephriticiim^ and fome other Subftan- 
 ces reflect one Colour, and tranfmit another,' 
 hke thill Bodies in the 9th and 20th Obferva- 
 tions. And fome of thofe colour'd Powders 
 which Painters ufe, may have their Colours a 
 little changed, by being very elaborately and 
 finely ground. \Vhere I fee not what can be 
 jullly pretended for thofe changes, befides the 
 breaking of their parts into lefs parts by that 
 contrition after the fame manner that the Co- 
 lour of a thin Plate is changed by varying its 
 thicknefs. For which reafon alfo it is that the 
 colour'd Flowers of Plants and Vegetables by 
 being bruifed ufually become more, tranfparent 
 than before, or at lealf in fome degree or o- 
 ther change their Colours. Nor is it much lefs 
 to my purpofe , that by rnixing divers Liquors 
 very odd and remarkable Productions and 
 Changes of Colours may be effeded; of which 
 no caufe can be more obvious and rational than 
 
 Q i that 
 
I 228 ] 
 
 the faline Corpufcles of one Liquor do vari- 
 oufly ad upon or unite with the tinging Cor- 
 pufcles of another, fo as to make them fwell, 
 or ilirink (whereby not only their bulk but their 
 denfity alfo may be changed) or to divide them 
 into 1 mailer Corpufcles, (whereby a colour'd 
 Liquor may become tranfparent) or to make 
 many of them aflbciate into one duller, where- 
 by two tranfparent Liquors may compofe a co- 
 lour'd one. For we fee how apt thofe faline 
 Menitruums are to penetrate and dilfolve Sub- 
 ftances to which they are applied, and fome of 
 them to precipitate what others dillblve. In 
 like manner , if we confider the various Phae- 
 nomena of the Atmofphere, we may obferve, 
 that when \^apours are tirit raifed, they hinder 
 not the tranfparency of the Air, being divided 
 into parts too fmall to caufe any Retlexion in 
 their Superficies. But when in order to com- 
 pofe Drops of Rain they begin to coalefce and 
 conilitute Globules of all intermediate fizes , ' 
 thofe Globules when they become of a conve- 
 nient iize to refled fome Colours and tranfmit 
 others, may conilitute Clouds of various Co- 
 lours according to their frzcs. And I fee not 
 what can be rationally conceived in fo tranfpa- 
 rent a Subftance as U'ater for the produdion 
 of thcfe Colours, bclidcs the various fizes of its 
 fluid and globular Parcels. 
 
 Prop. 
 
[ 229 ] 
 
 Prop. VI. 
 
 The parts of Bodies on 'vuhich their Colours de- 
 petid^ are denfer thajt the Medium, isjhich per- 
 njades their Interftices. 
 
 THIS will appear by confidering, that the 
 Colour of a Body depends not only on 
 the Rays which are incident perpendicularly 
 on its parts, but on thole alio which are inci- 
 dent at all other Angles. And that according 
 to the 7th Obfervation , a very little variation 
 of obliquity will change the reflected Colour 
 where the thin Body or fmall Particle is rarer 
 than the ambient Medium, infomuch that fuch 
 a fmall Particle will at diverily oblique Inci- 
 dences refleft all forts of Colours, in lo great a 
 variety that the Colour refulting from them all, 
 confufcdly reflected from a heap of fuch Parti- 
 cles, muft rather be a white or grey than any 
 other Colour , or at beft it muft be out a very 
 imperfeft and dirty Colour. Whereas if the 
 thin Body or fmall Particle be much denfer than 
 the ambient Medium, the Colours according to 
 the 19th Obfervation are fo little changed by 
 the variation of obliquity, that the Rays which 
 are reflected lealt obHquely may predominate 
 over the reil fo much as to caufe a heap of fuch 
 Particles to appear very intenfly of their Co- 
 lour. 
 
 It conduces alfo fomething to the confirma- 
 tion of this Propolition, that, according to the 
 2,xd Obfervation, the Colours exhibited by the 
 denfer thin Body within the rarer, are more 
 
 Q 3 brisi* 
 
[ 230 ] 
 
 brisk than tbofe exhibited by the rarer within 
 the denfer. - 
 
 Prop. VII. 
 
 The bignejs of the component farts of natural 
 Bodies may he conjeBured by their Colours. 
 
 FOR fmce the parts of thefe Bodies by 
 Trop. 5". do moil probably exhibit the 
 lame Colours with a Plate of equal thicknefs, 
 provided they have the fame refradive denfity ; 
 and fince their parts feem for the moft part to 
 h^ve much the fame denfity with Water or 
 Glafs, as by many circumftances is obvious to 
 collect; to determine the fizes of thofe parts 
 you need only have recourfe to the precedent 
 Tables, in which the thicknefs of Water or 
 Glafs exhibiting any Colour is exprefled. Thus 
 if it be defired to know the diameter of a Cor- 
 pufcle, which being of equal denfity with Glafs 
 Ihall reflcd green of the third Order ; the Num- 
 
 t)er 16-^ fhews it to be ^^^ parts of an Inch. 
 
 The greatcft difficulty is here to know of 
 what order the Colour of any Body is. And 
 for this end we mufl have recourfe to the 4th 
 and 1 8th Obfervations , from whence may be 
 collefted thefe particulars. 
 
 Scarlets^ and other reds^ oranges and j)'^/- 
 Jowsy' if they be pure and intenfe are moil pro- 
 bably of -the fee on d order. Thofe of the firll 
 ^nd thh'd order alfo may be pretty good , only 
 the yellow- of the firit order is faint, and the 
 ^>-> . ' • • • < •• ■'■ ' - - • orange 
 
orange and red of the third order have a great 
 mixture of violet and blue. 
 
 There may be good greens of the fourth or- 
 der, but the purell are of the third. And of 
 this order the green of all Vegetables feem to 
 be, partly by reafon of the intenfenefs of their 
 Colours, and partly becaufe when they wither 
 fome of them turn to a greenifli yellow, and 
 others to a more perfedl yellow or orange, or 
 perhaps to red, pafling firll through j\ll the a- 
 forefaid intermediate Colours. Which Changes 
 feem to be effeded by the exhaling oi the moi- 
 Iture which may leave the tinging Corpufcles 
 more denfe, and fomething augmented by the 
 accretion of the oily and earthy part of that 
 moiflurc. Now the green without doubt is of 
 the fame order with thofe Colours into which 
 it changeth , becaufe the Changes are gradual, 
 and thole Colours, though ufually not very full, 
 yet are often too full and lively to be of the 
 fourth order. 
 
 Blues and purples may be either of the fe- 
 cond or third order, but the befl are of the 
 third. Thus the Colour of violets feems to be 
 of that order, becaufe their Syrup by acid Li- 
 quors turns red , and by urinous and alcalizate 
 turns green. For fmce it is of the nattire of 
 Acids to diilblve or attenuate, and of Alcalies 
 to precipitate or incraflate , if the purple Co- 
 lour of the Syrup was of the fecond order, an 
 acid Liquor by attenuating its tinging Cor- 
 pufcles would change it to a red of the nrft or- 
 der, and an Alcali by incraflating them would 
 change it to a green of the lecond order; 
 
 Q 4 which 
 
[ 232 ] 
 
 which red and green , efpecially the green , 
 feem too imperfect to be the Colours produ- 
 ced by thcie Changes. But if the faid purple 
 be fuppoied of the third order, its Change to 
 red of the fecond, and green of the third, may 
 without any inconvenience be allow'd. 
 
 If there be found any Body of a deeper and 
 lefs reddiOi purple than that of the violets, its 
 Colour mod probably is of the fecond order. 
 But yet there being no Body commonly known 
 whole Colour is conltantly more deep than 
 theirs, I have made ufe oif their name to de- 
 note the deepeft and lead reddifli purples, fuch 
 as manifeflly tranfcend their Colour in purity. 
 
 The blue of the tirll order, though very faint 
 and Uttle, may poflibly be the Colour of fome 
 Subilances ; and particularl}' the azure Colour 
 of the Skies feems to be of this order. For all 
 ^^apo.urs. when they begin to condenfe and co- 
 alei'ce into fmall parcels, become firil of that 
 bignefs whereby fuch an Azure muft be refledl- 
 cd before they can contlitute Clouds of other 
 Colours. And fo this being the firfi: Colour, 
 which Vapours begin to rcfleCl, it ought to be 
 the Colour of the hned and mod tranfparent 
 Skies in which \'apours are not arrived to that 
 grofliiefs rcquifite to refled other Colours, as 
 we find, it is by experience. 
 
 Whit e fiefs ^ if mod intenfe and luminous, is 
 tjiat of the fird order., if Icfs drong and lumi- 
 nous a mixture of the Colours of fevcral or- 
 ders. Of this lad. kind is the whirencfs of 
 Froth, Paper, Linen, and mod vrhite Sub- 
 ilances; of the former I reckon that of white 
 
 ivl ctais 
 
[ 2.33 
 
 Metals to be. For whilit 
 
 le denfeft of Me- 
 
 tals, Gold, if foliated, is tranfparent, and all Me- 
 tals become tranfparent if dillblved in Men- 
 flruums or vitrified, the opacity of white Me- 
 tals arifeth not from their denfity alone. They 
 being lefs dcnfe than Gold would be more tranf- 
 parent than it, did not fome other Caufe con- 
 cur with their denfity to make them opake. 
 And this caufe I take to be fuch a bignefs of 
 their Particles as fits them to refled the white 
 of the firll order. For if they be of other thick- 
 nelTes they may refled other Colours, as is ma- 
 nifell: by the Colours which appear upon hot 
 Steel in tempering it, and fometimes upon the 
 Surface of melted Metals in the Skin or Scoria 
 which arifes upon them in their coohng. And 
 as the white of the firit order is the Itrongeit 
 which can be made by Plates of tranfparent 
 Subltances, fo it ought to be ftronger in the 
 denfer Subltances of Metals than in the rarer 
 of Air, Water and Glafs. Nor do I fee but 
 that metallic Subilances of fuch a tlijcknefs as 
 may fit them to refled the white of the firft or- 
 der, may, by reafon of their great denfity (ac- 
 cording to the tenour of the fiiil: of thefe Pro- 
 pofitions) refled; all the Light incident upon 
 them, and fo be as opake and fplendent as it's 
 pofiible for any Body to be. Gold, or Copper 
 mix'd wita lefs than half their weight of Silver, 
 or Tin, or Rcgulus of Antimony, in fufion, or 
 amalgamcd with a very little Mercury, become 
 white ; which fliews both that the Particles of 
 \yhite Metals have much more Superficies, and 
 fo are fmaller, than thofe of Gold and Copper, 
 
 and 
 
[234] 
 
 and alfo that they are fo opake as not to fufTer 
 the Particles of Gold or Copper to ftiine through 
 them. Now it is fcarce to be doubted, but 
 that the Colours of Gold and Copper are of 
 the fecond or third order, and therefore the 
 Particles of white Metals cannot be much big- 
 ger than is requiilre to make them refleft the 
 white of the firll: order. The volatility of Mer- ' 
 cury argues that they are not much bigger, 
 nor may they be much lefs, lelt they lofe their 
 opacity, and become either tranfparent as they 
 do when attenuated by vitrification, or by So- 
 lution inMenllruums, or black as they do when 
 ground fmaller, by rubbing Silver, or Tm, or 
 Lead, upon other Subilances to draw black 
 Lines. The firlt and only Colour which white 
 Metals take by grinding their Particles fmaller, 
 is black, and therefore their white ought to be 
 that which borders upon the black Spot in the 
 center of the Rings of Colours, that is, the 
 white of the f rfl order. But if you would 
 hence gather the bignefs of metallic Particles, 
 you mull allow for their denfity. For were 
 Mercury tranfparent, its denlity is fuch that 
 the Sine of Incidence upon it ( by my compu- 
 tation) would be to the Sine of its Refradion, 
 as 71 to 20, or 7 to i. And therefore the 
 thicknefs of its Particles, that they may exhibit 
 the fame Colours with thofe of Bubbles of Wa- 
 ter, ought to be lefs than the thicknefs of the 
 Skin of thofe Bubbles in the proportion of x 
 to 7. Whence it's pofTible that the Particles 
 of Mercury may be as Uttle as the Particles of 
 
 fome 
 
[235] 
 
 fome tranfparcnt and volatile Fluids, and yet 
 refleft the white of the firlt order. 
 
 Lafth', for the produdion of blacky the Cor- 
 pufcles muft be lefs than any of thofe which ex- 
 hibit' Colours. F^or at all greater iizcs there isj 
 too iiiuch Light rcfleded to conilitute this Co- 
 lour. ' But if they be fuppofed a little lefs than 
 is requifite to reflect the white and very faint 
 blue bf the firlt order, they will, according to 
 the 4th, 8th, 17th and iSthObfervations, retleft 
 fo very httle Light as to appear intcnfly black, 
 and yet may perhaps variouily refract it to and 
 frb within themfelves fo long, until it happen 
 to be Itifled and loll, by which means they will 
 appear black in all pofitions of the Eye without 
 any tranfparency. And from hence may be undcr- 
 ftood why Fire, and the more lubtile dillblver Pu- 
 trefa(5tion, by dividing the Particles of Subltan- 
 ces, turn them to black, why fmall quantities 
 of black Subilances ihipart their Colour very 
 freely and intenily to other Subilances to which 
 they are applied ; the minute Particles of thefe, 
 by reafon of their very great number, eafily o- 
 verfpreading the grofs Particles of others ; why 
 Glafs ground verv elaborately with Sand on a 
 Copper Plate, 'till it be well polifh'd, makes 
 the Sand, together w ith what is worn oft' from 
 the Glafs and Copper , become very black : 
 why black Subilances do fooncll of all others 
 become hot in the Sun's Light and burn, (which 
 Effeft may proceed partly from the multitude 
 of Refradions in a httle room, and partly from 
 ^the eafy Commotion of fo very fmall Cor- 
 pufcle^ ;) and \yhy blacks are ufually a httle in- 
 clined 
 
[236] 
 
 clined to a bluifli Colour. For that they are fo 
 may be fcen by illuminatmg white Paper by 
 Light refleded from black Subflances. For 
 the Paper will ufually appear of a bluifli white ; 
 and the reafon is, that black Borders on the ob- 
 fcure blue of the firft order defcribed in the 
 1 8th Obfervation, and therefore relieds more 
 Rays of that Colour than of" any other. 
 
 In thcfe Defcriptions I have been the more 
 particular, becaule it is not impoffible but that 
 jViicrorcopcs may at length be improved to the 
 difcovery of the Particles of Bodies on which 
 their Colours depend, if they are not already in 
 fome meaiure arrived to that degree of per- 
 fection . For if thofe Inftruments are or can be 
 ip far improved as with fufficient diltindlnefs 
 to reprefent Objeds five or fix hundred times 
 bigger than at a Foot diflance they appear to 
 our naked Eyes, I Ihould hope that we might 
 be able to dilcover fome of the greatelt of thofe 
 Corpufcles. And by one that would magnify 
 three or four thouland times perhaps they might 
 all be diicovcr'd , but thofe which produce 
 blacknefs. In the mean while I fee nothing ma- 
 terial in this Difcourie that may rationally be 
 doubted of, excepting this Pofition. That tranf- 
 parent Corpufcles of the fame thicknefs and 
 dcnfity with a Plate, do exhibit the fame Co- 
 lour. And this 1 would have underflood not 
 without fome Latitude, as well bccaufe thofe 
 Corpufcles may be of irregular Figures, and 
 many Pvavs niuil be obliquely incident on them, 
 and fo have a Ihortcr way through them than 
 the length of their Diameters, as becaufe the 
 
 Itraitnefs 
 
[ 237 ] 
 
 ftraitnefs of the Medium pent in on all fides 
 within luch Corpufcles may a little alter its Mo- 
 tions or other qualities on which the Reflexion 
 depends. But yet I cannot much fufped the 
 lall, becaufe I have obferved of fome fmall 
 Plates of Mufcovy Glafs which were of an even 
 thicknefs, that through a Microfcope they have 
 appeared of the fame Colour at their edges and 
 corners where the included Medium was ter- 
 minated, which they appeared of in other pla- 
 ces. However it will add much to our Satif- 
 fadion , if thofe Corpufcles can be difcover'd 
 with Microfcopes ; which if we Ihall at length 
 attain to, I fear it will be the utmoll improve- 
 ment of this Senfe. For it fcems impoilible 
 to fee the more fecret and noble Works of Na- 
 ture within the Corpufcles by reafon of their 
 tranfparency. 
 
 R O p. 
 
 VIII. 
 
 The Cditfe of Reflex mi is not the impinging of 
 Light on the fo lid or impervious parts of Bo^ 
 dies, as is commonly believed. 
 
 THIS will appear by the following Confi- 
 derations. Firll, That in the palfage of 
 Light out of Glafs into Air there is a Reflexion 
 as Ih'ong as in its pafliige out of Air into Glafs, 
 or rather a little flronger, and by maiiy degrees 
 ftronger than in its pallage out of Glafs into 
 Water. And it feems not probable that Air 
 fliould have more refleding parts than Water 
 or Glafs. But if that fliould poITibly be fuppo- 
 fed, yet it will avail nothing; for the Reflexion 
 
 is 
 
[ 23§ ] 
 
 is as flrong or ftronger when the Air is drawfi 
 away from the Glais^ (fuppofe in the Air-Pump 
 invented by Mr. Boyle) as when it is adjacent 
 to it. Secondly, If Light in its paflage out of 
 Glafs into Air be incident more obliquely than 
 at an Angle of 40 or 41 Degi^ees it is wholly 
 refle(5i:cd, if lefs obliquely it is in great mea- 
 fure tranfmitted. Now it is not to be imagined 
 that Light at one degree of obliquity flioiild 
 meet with Pores enough in the Air to tranfmit, 
 the greater part of it, and at another degree of 
 obliquity iliould meet with nothing but parts 
 to relied it wholly, efpeeially confidering that 
 in its paiTagc out of Air into Glafs, how ob- 
 lique foever be its hicidence, it finds Pores e- 
 nough in the Glafs to tranfmit a great part of 
 it. If any Man fuppofe that it is not reflected 
 by the Air, but by the outmoil: fuperficial parts 
 of the Glafs j there is Hill the lame difficulty : 
 Befides, that fuch a Suppofiiion is unintelligi- 
 ble, and will alfo appear to be falfe by applying 
 Water behind fome part of the Glafs initead of 
 Air. For fo in a convenient obliquity of the 
 Rays, fuppofe of 45* or 46 Degrees , at which 
 they are all refleded where the Air is adjacent 
 to the Glafs, they iliall be in great meafure tranf- 
 mitted where the Water is adjacent to it ; which 
 argues , that their Reflexion or Tranfmilliori 
 depends on the conflitution of the Air and Wa- 
 ter behind the Glafs, and not on the Ih-iking of 
 the Rays upon the parts of the Glafs. Third- 
 ly, If the Colours made by a Prifm placed at 
 the entrance of a Beam of Light into a darken'd 
 Room be fuccellively caft on a fecond Prifm 
 
 placed 
 
[ 239 ] 
 
 placed at a greater diltance from the former^ 
 in fuch manner that they are all alike incident 
 upon it, the fecond Prifm may be io inclined to 
 the incident Rays , that thofe which are of a 
 blue Colour fhall be all refleded by it, and, yet 
 thofe of a red Colour pretty copioufly tranfmit- 
 ted. Now if the Reflexion be caul'cd by the 
 parts of Air or Glafs, I would ask, why at the 
 fame Obliquity of Incidence the blue fliould 
 wholly impinge on thole parts lb as to be all 
 reflected, and yet the red find Pores enough 
 to be in a great meafure tranfmitted. Fourth- 
 ly, Where two GlafFes touch one another, there 
 is no fenfible Reflexion as was declared in the 
 firll: Obfervation; and yet I fee no reaibn why, 
 the Rays fliould not impinge on the parts of 
 Glafs as much when contiguous to other Glafs 
 as when contiguous to Air. Fifthly, When 
 the top of a Water-Bubble (in the 17th Obfer- 
 vation) by the continual fubfiding and exha-. 
 ling of the Water grew very thin, there was 
 fuch a Uttle and almoli: infeniible quantity of 
 Light refle61ed from it, that it appeared in- 
 tenlly black ; whereas round about that black 
 Spot, where the Water was thicker, the Refle- 
 xion was fo flrong as to make the Water feem 
 verf white. Nor is it only at the lead thick- 
 nefs of thin Plates or Bubbles, that there is no 
 fnanifefl: Reflexiofi , but at many other thick- 
 nelfes continually greater and greater. For in 
 the i^th' Obfervation the Rays of the fame Co- 
 four were by turns tranfmitted at one thicknefs, 
 and refleded at another thicknefs , for an in- 
 determinate number of Succeflions. And yet 
 
 ill 
 
[ 240 ] 
 
 in the Superficies of the thinned Body, where 
 it is of any one thicknefs , there are as many 
 parts for the Rays to impinge on , as where ic 
 is of any other thicknefs. Sixthly, If Reflexion 
 were cauled by the parts of refleding Bodies, 
 it would be impofTible for thin Plates or Bub- 
 bles at one and the fame place to refleft the 
 Rays of one Colour and tranfmit thofe of ano- 
 ther, as they do according to tiie 13th and 15th 
 Obfervations. For it is not to be imagined 
 that at one place the Rays which for inllance 
 exhibit a blue Colour, fhould have the fortune 
 to dafh upon the parts, and thole which exhi- 
 bit a red to hit upon the Pores of the Body ; 
 and then at another place, where the Body is 
 either a little thicker, or a httle thinner, that 
 on the contrary the blue lliould hit upon its 
 pores, and the red upon its parts. LaiUy, were 
 the Rays of Light reflected by impinging on 
 the folid parts of Bodies, their Reflexions from 
 poliih'd Bodies could not be fo regular as they 
 are. For in poUiliing Glafs with Sand, Putty or 
 Tripoly, it is not to be imagined that thofe 
 Subitances can bv grating and fretting the Glafs 
 bring all its leaft Particles to an accurate Polifh; 
 fo that all their Surfaces lliall be truly plain or 
 truly fpherical, and look all the fame way, fo 
 as together to compofe one even Surface. The 
 fmaller the Particles of thofe Subitances are, 
 thefmaller will be the Scratches by which they 
 continually fret and wear away the Glafs unti] 
 it be poliih'd , but be they never fo fmall they 
 can wear away the Glafs no otherwife than by 
 grating and icratching it, and breaking the 
 
 Protu- 
 
[2+I] 
 
 !?rotuberances , and therefore poliili it no o- 
 therwile than by bringing its roughnefs to a ve- 
 ry fine Grain, fo that the Scratches and Fret- 
 tings of the Surface become too fmali to be 
 vifible. And therefore if Light were refleded 
 by impinging upon the folid parts of the Glafs^ 
 it would be fcatter'd as much by the mofl po- 
 lifli'd Glafs as by the roughelt. So then it re- 
 mains a Problem, how^ Glafs poUlli'd by fretting 
 Subllances can reflect Light fo regularly as it 
 does. And this Problem is fcarce otherwife to 
 be folved than by faying, that the Reflexion of 
 a Ray is eftefted, not by a Tingle point of the 
 reflecling Body, but by fome power of the Bo- 
 dy which is evenly dittufed all over its Surface, 
 and by which it afts upon the Ray without im- 
 mediate ContacI:!:. For that the parts of Bodies 
 do ad upon Light at a diilance fliall be Ihewa 
 hereafter. 
 
 Now if Light be reflcded not by impinging 
 on the folid parts of Bodies, but by fome otnef 
 principle ; it's probable that as many of its Rays 
 as impinge on the folid parts of Bodies are not 
 refledled but ftifled and loll in the Bodies. For 
 otherwife we mufl: allow two forts of Refle-» 
 xions. Should all the Pvays be refleded which 
 impinge on the internal parts of clear Water or 
 Cryflal, thofe Subltances would rather have a 
 cloudy Colour than a clear Tranfparency. To 
 make Bodies look black, it's neceilary that ma- 
 ny Rays be flopp'd, retained and loii in them, 
 and it feems not probable that any Rays can be 
 flopp'd and flifled in them which do not im- 
 pinge on their parts, 
 
 R And 
 
[ 242 ] 
 
 And hence we may underfland that Bodies 
 are much more rare and porous than is com- 
 monly believed. Water is nineteen times hght- 
 er, and by confequence nineteen times rarer 
 than Gold, and Gold is fo rare as very readily 
 and without the leafl oppofition to tranlmit the 
 magnetick Effluvia, and eafily to admit Quick- 
 iilver into its Pores, and to let Water pafs 
 through it-. For a concave Sphere of Gold fil- 
 led with Water, and foder'd up, has upon pref- 
 fmg the Sphere with great force, let the Water 
 fqueeze through it , and iland all over its out- 
 fide in multitudes of fmall Drops, Uke Dew, 
 without burfling or cracking the Body of the 
 Gold as I have been inform'd by an Eye wit- 
 nefs. From all which we may conclude, that 
 Gold has more Pores than folid parts, and by 
 confequence that Water has above forty times 
 more Pores that Parts. And he that lliall find 
 out an Hypothefis, by which Water may be fo 
 rare, and yet not be capable of compreflion by 
 force, may doubtlefs by the fame Hypothefis 
 make Gold and Water, and all other Bodies as 
 much rarer as he pleafes, fo that Light may 
 find a ready pafTage through tranfparent Sub- 
 fiances. 
 
 Tile Magnet a^lsupon Iron through all denfe 
 Bodies not magnetick nor red hot, without a- 
 ny diminution of its virtue ; as for inllance , 
 through Gold, Silver, Lead, Glafs, Water. 
 The gravitating Power of the Sun is tranfmit- 
 ted through the vaft Bodies of the Planets with- 
 out any diminution, fo as to aft upon all their 
 parts to their very centers with the fame Force 
 
 and 
 
[ H3 ] 
 
 and according to the fame Laws d5 if (he part 
 Upon which it ads were not furrounded with 
 the Body of the Planet. The Rays of Light 
 whether they be very fmall Bodies projeded, 
 or only Motion or Force propagated, are mo- 
 ved in right Lines; and whenever a Ray of 
 Light is by any Obliacle turned out of its redi- 
 linear way, it will never retm'n into the fiime 
 redilinear way* unlefs perhaps by very great ac- 
 cident. And yet Light is tranfmitted through 
 pellucid folid Bodies in right Lines to very great 
 diflances. How Bodies can have a futiicient 
 quantity of Pores for producing thefe Effeds is 
 very difficult to conceive , but perhaps not al- 
 tdgether impoirible. For the Colours of Bodies 
 arife from the Magnitudes of the Particles which 
 retled them, as was explained above. Now if 
 lye conceive thefe Particles of Bodies to be fa 
 difpofed amonglt themfelves, that the Intervals 
 or empty Spaces between them may be equal in 
 magnitude to them all ; and that thefe Parti- 
 cles may be compofed of other Particles much 
 fmaller, which have as much empty Space be- 
 tween them as equals all the Magnitudes of 
 thefe fmaller Particles : And that in hke man- 
 ner thefe fmaller Particles are again compofed 
 of others much fmaller, all which together are 
 equal to all the Pores or empty Spaces betweeni 
 them ; and fo on perpetually till you come to 
 folid Particles, fuch as have no Pores or empty 
 Spaces within them : And if in any grofs Body 
 there be, for infiance, three fuch degrees of 
 Particles, the lead of which are foiid ; this Bo- 
 dy will have feven times more Pores than, folid 
 
 R X Parts, 
 
[ 244 1 
 
 Parts. But if there be four fuch degrees of 
 Particles, the lead of which are folid, the Bo- 
 dy will have fifteen times more Pores than fo- 
 lid Parts. If there be five degrees , the Body 
 will have orfe- and thirty times more Pores than 
 folid Parts. If fix degrees, the Body will have 
 fixty and three times more Pores than folid 
 Parts. And fo on perpetually. And there are 
 other ways of conceiving how Bodies may be 
 exceeding porous. But what is really their in- 
 ward Frame is not yet known to us. 
 
 Prop. IX. 
 
 Bodies rejleVt and refra6f Light by one and the 
 fame po'uuer 'varioujly exercifed in various Cir^ 
 cumfiances. 
 
 THIS appears by feveral Confiderations, 
 Firff , Becaufe when Light goes out of 
 Glafs into Air, as obliquely as it can poffibly 
 do, if its Incidence be made ftill more oblique, 
 it becomes totally reflefted. For the power of 
 the Glafs after it has refrafted the Light as ob- 
 liquely as is pofTible if the Incidence be ftill 
 made more oblique, becomes too flrong to let 
 any of its Rays go through, and by confequence 
 caufes total Reflexions. Secondly, Becaufe 
 Light is alternately reflected and and tranfmit- 
 ted by thin Plates of Glafs for many Succeflions 
 accordingly as the thicknefs of the Plate increa- 
 fes in an arithmetical Progreflion. For here 
 the thicknefs of the Glafs determines whether 
 that Power by which Glafs a6fs upon Light 
 Ihall cauie it to be retieded, or fufier it to be 
 
 tranf- 
 
[245 ] 
 
 tranfmitted. And, Thirdly, becaufe thofe Sur- 
 faces of tranfparent Bodies which have the great- 
 eft refrafting Power, refled the greateit quan- 
 tity of Light, as was iliew'd in the firil Propo- 
 fition. 
 
 Pr 
 
 o p. 
 
 X. 
 
 If Light be f-jDifter in Bodies thmi in Vacuo in 
 the proportion of the Sines iz'hich me a Jure the 
 Refraition of the Bodies ^ the Forces of the 
 Bodies to refleB and refraB Lights are very 
 nearly proportional 'to the denfities of the 
 fame Bodies^ excepting that unBuous and ful- 
 phureous Bodies refra6i more than others of 
 this fame denfity. 
 
 LE T AB reprefent the refracting plane Sur- 
 face of any Body, and IC a Ray incident 
 very obliquely upon the Body in C, fo that the 
 
 ^ 
 
 Angle AC I may be infinitely little, and letCR 
 be the refrafted Ray. From a given Point B 
 perpendicular to the refrad ing Surface ereft BR 
 meeting with the refraded Ray C R in R, and 
 if CR reprefent the Motion of the refrafted 
 Ra}^ and this Motion be diftinguifli'd into two 
 Motions CB and BR, whereof CB is paral- 
 
 R 3^ lei 
 
I 2+^ ] 
 
 iel to the refra61ing Plane, and B R perpendi- 
 cular to it : C B fliall reprefent the Motion of 
 the incident Ray, and B R the Motion genera- 
 ted by the Refraftioii, as Opticians have of late , 
 explain'd. I 
 
 Now if any Body or thing, in moving through 
 any Space of a given breadth terminated on 
 both lides by two parallel Planes, be urged for^? 
 ward in all parts of that Space by Forces tend- 
 ing direftly forwards towards the latl Plane, and 
 before its Incidence on the iirfl Plane , had no 
 Motion towards it, or but an infinitely little 
 one ; and if the Forces in all parts of that Space, 
 between the Planes be at equal diftances from 
 ithe Planes equal to one another, but at leveral 
 diitances be bigger or lefs in any given Propor- 
 tion, the Motion generated by the Forces in 
 the whole pafiage of the Body or thing through 
 that Space lliall be in a fubdupHcate Proportion 
 of the Forces, as Mathematicians will eafily 
 underftand. And therefore if the Space of acti- 
 vity of the refrading Superficies of the Body 
 be confider'd as fuch a Space, the Motion of 
 the Ray generated by the refracting Force of 
 the Body, during its pafiage through that Space, 
 that is the Motion B R, muft be in a fubdupli- 
 cate Proportion of that refrading Force. I fay 
 therefore that the Square of the Line B R, and 
 by confequence the refrafting Force of the J^o- £ 
 dy is very nearly as the denfityof the fame Bo- ^ 
 dy. For this will appear by the following Ta- 
 ble, wherein the Proportion of the Sines which 
 meafure the Refractions of feveral Bodies, the 
 Square of B R fuppofing C B an unite, the Den- 
 
 fitics 
 
[ 247 
 
 fitics of the Bodies elliPxiatec 
 gravities, and their refradive Power in re.p.d # 
 of their denfities are fet down in feveral Co- 
 lumns. 
 
 by their fpecifick 
 
 
 The Proporf.ii^ 
 
 rheS.juare 
 
 Lhi den- 
 
 l,?e rc- 
 
 
 of the Sines of 
 
 OfbRytO 
 
 ftty ami 
 
 fraciivt 
 
 
 Incidence 
 
 a77d 
 
 xuhich 
 
 fpecificK 
 
 PvWer 
 
 The refracfting Bo- 
 
 Refraclion of 
 
 the refra- 
 
 gnavitj 
 
 of the 
 
 dies. 
 
 yellozv Li 
 
 Sht. 
 
 tlingjorci. 
 
 oftheBo- 
 
 Body in 
 
 
 
 
 of the Bo- 
 
 dy. 
 
 reffect 
 
 
 
 
 dy is pro 
 
 
 of id 
 
 
 
 
 portiunaie 
 
 
 denftiy. 
 
 A Pleudo-Topazius, 
 
 
 
 
 
 
 being a natural , 
 
 
 
 
 
 
 pellucid , britt e , 
 
 12 to 
 
 14 
 
 I '6()<) 
 
 4'i7 
 
 3979 
 
 hairy Stone, of a 
 
 
 
 
 
 
 yellow Colour. 
 
 
 
 
 
 
 Air. 
 
 3ZOI to 3 
 
 20c 000062 5 
 
 0'C0I2 
 
 5208 
 
 Glafs of Antimony, 
 
 17 to 
 
 pli'S^S 
 
 5-28 
 
 4864 
 
 \ Se'enitis. 
 
 6i to 
 
 4J 
 
 r2i3 
 
 2-252 
 
 5386 
 
 GUIs vulvar. 
 
 31 to 
 
 20 
 
 l'402J 
 
 2-58 
 
 S436 
 
 Cryltal of the Rock. 
 
 IS to 
 
 16 
 
 t'44S 
 
 2-6 J 
 
 5450 
 
 Illand Cryllal. 
 
 5 to 
 
 3 
 
 i'778 
 
 2'72 
 
 6536 
 
 Sal Gemma;.' 
 
 17 to 
 
 11 
 
 ■•388 
 
 2-143' 
 
 ^477 
 
 \lurae. 
 
 3i fo 
 
 i4 
 
 t'1267 
 
 i"7i4 
 
 6570 
 
 3orax. 
 
 22, to 
 
 IS 
 
 I'lSii 
 
 i'7i4 
 
 6716 
 
 Nicer. 
 
 32, to 
 
 2ir34s 
 
 I '9 
 
 7079 
 
 Danr^,ick Vitriol. 
 
 303 to 
 
 2oO|r'295 
 
 i'7rs 
 
 7S5t 
 
 Oil of Vitriol. 
 
 ro to 
 
 7 I '04: 
 
 i'7 
 
 6124 
 
 Rain Wa.er. 
 
 S29 to 
 
 396o'7845 
 
 i' 
 
 7845 
 
 Gum Arabick. 
 
 31 to 
 
 2i>'i79 
 
 i'37J 
 
 8S74 
 
 >pirit of Win€ well 
 reftified. 
 
 100 to 
 
 73o'8765 
 
 0^66 
 
 I0I2I 
 
 "amphire. 
 
 3. fo 
 
 2 I'lj 
 
 9996 
 
 12551 
 
 Oil Olive. 
 
 21 to 
 
 15 I'isii 
 
 6'9i3 
 
 . 12607 
 
 Linfeed Oil. 
 
 40 to 
 
 27i'i948 
 
 0-932 
 
 I2819 
 
 >piric of Turpentine. 
 
 25 to 
 
 17 i':626 
 
 o'874 
 
 13222 
 
 \mbar. 
 
 14 to 
 
 9 ''42- 
 
 ro4 
 
 n^s4 
 
 \ Diamond. 
 
 100 to 
 
 41 4'049 
 
 V4 ' U^S*^ ( 
 
 The ReR-aftion of the Air in this Table is de- 
 termin'd by that of the Atmofphere obferved 
 
 R 4 by 
 
[ 248 ] 
 
 by Aftronomers. For if Light pafs through 
 many refracting Subftances or Mediums gradu- 
 ally denfer and denfer, and terminated with 
 parallel Surfaces, the fum of all the Refractions 
 will be equal to the fingle Refradion which it 
 would have fuffer'd in pafling immediately out 
 of the tirft Medium into the lall. And this holds 
 true, though the number of the refracting bub- 
 fiances be increafed to infinity, and the dilian^ 
 ces from onp another as much decreaied , fo 
 that the Light may be refracted in every point 
 of its PafTage, and by continual Pvefra'R:ions bent 
 into a curve Line. ■ And therefore the whole 
 Rcfradion of Light in palTing through the At- 
 moiphere from the highell and rareit part there- 
 of dov/n to the low ell and denfefl part, muit 
 be equal to the Refraftion which it would fuf- 
 fer in pafling at Hke obliquity out of a Vacuum 
 immediately into Air of equal denfity with that 
 in the Igwefl part of the Atmofphere. 
 
 Now, although a Pfeudo-Topaz, a Selenitis, 
 Rock Cryital, Ifland Cryflal, Vulgar Glafs 
 (that is, Sand melted together) and Glafs of 
 Antimony, which are terrcllrial flony alcalizate 
 Concretes, and Air which probably arifes from 
 fuch Subllances by FermaCntation, be Subftan- 
 ces very differing from one another in denfity, 
 yet by this Table , they have their rcfradive 
 Powers almoil in the fame proportion to one 
 another as their denfities are, excepting that 
 the Refradion of that llrange Subllance Illand 
 Cryital is a little bigger than the relt. And 
 particularly Air, which is 3500 times rarer than 
 the Pfeudo-Topaz, and 4400 times rarer than 
 
 Glafs 
 
[24-9 ] 
 
 Glafs of Antimony, and 2000 times rarer than 
 the Selenitis , Glafs vulgar , or Cryllal of the 
 Rock, has notwithitanding its rarity the fame 
 rcfradive Power in refpet^t of its denlity which 
 thoie very dcnle Suitances have in relped of 
 theirs, excepting fo far as thofe differ from one 
 another. 
 
 Again, theRefradion of Camphn-e, Oil Olive, 
 Linfeed Oil, Spirit of Turpentine andAmbar, 
 which are fat fulphureous unctuous Bodies, and 
 a Diamond, which probably is an unduousSub- 
 llance coagulated, have their refraftive Powers 
 in proportion to one another as their denfities 
 without any confiderable variation. But the 
 refradive Powers of thefe unduous Subftances 
 are two or three times greater in refped of their 
 denfities than the refractive Powers of the for- 
 mer Subilances in refpeft of theirs. 
 
 Water has a refra(!:iive Power in a middle de- 
 gree between thofe two forts of Subilances, 
 and probably is of a middle nature. For out 
 of it grow all vegetable and animal Subftances, 
 which confift as well of fulphureous fat and in- 
 flamable parts, as of earthy lean and alcalizate 
 ones. 
 
 Salts and Vitriols have rcfradive Powers in a 
 middle degree betw^een thofe of earthy Sub- 
 ftances and Water, and accordingly are com- 
 pofed of thofe two forts of Subflances. For 
 by diftillation and rcdiHcation of their Spirits a 
 great part of them goes into Water, and a great 
 part remains behind in the form of a dry fix'd 
 Earth capable of vitritication. 
 
 Spirit 
 
[25o] 
 
 Spirit of Wine has a refraclive Power in a 
 middle degree between thofe of Water and 
 oily Subtlances, and accordingly feems to be 
 compofed of both, united by Fermentation; 
 the Water, by means of ibme laline Spirits with 
 which 'tis impregnated, dilFolving the Oil, and 
 volatizing it by the adion. For Spirit of Wine 
 is intlamable by means of its oily parts, and be- 
 ing dillilled often from Salt of Tartar, grows 
 by every dillillation more and more aqueous 
 and phlegmatick. And Chymifrs obierve, that 
 Vegetables (as Lavender, Rue, Marjoram, &c.) 
 diftillcd/^ry?, before fermentation yield Oils 
 without any burning Spirits, but after fermen- 
 tation yield ardent Spirits without Oils: Which 
 ihews, that their Oil is by fermentation con- 
 verted into Spirit. They find alfo, that if Oils 
 be poured in fmall quantity upon fermentating 
 Vegetables, they diitil over after fermentation 
 in the form of Spirits. 
 
 So then, by the foregoing Table, all Bodies 
 feem to have their refractive Powers propor- 
 tional to their denfities, ( or very nearly ; ) ex- 
 cepting fo far as they partake more or lefs of 
 fulphureous oily Particles, and thereby have their 
 refradive Power made greater or lefs. Whence 
 it feems rational to attribute the refradive Pow- 
 er of all Bodies chiefly, if not wholly, to the 
 fulphureous parts with which they abound. For 
 it's probable that all Bodies abound more or lefs 
 with Sulphurs. And as Light congregated by 
 a Burning-glafs a6ts moll upon fulphureous Bo- 
 dies, to turn them into Fire and Flame ; fo, 
 lince all aftion is mutual, Sulphurs ought to aft 
 
 moll 
 
[ 251 ] 
 iiioft upon Light. For that the adion between 
 Light and Bodies is mutual, may appear from 
 this Confideration ; That the denfell Bodies 
 which refrad:!: and refleCl Light molt ftrongly 
 grow hottelt in the Summer Sun, by the adipn 
 of the refrafted or refleftcd Light. 
 
 I have' hitherto explained the Power of Bo- 
 dies to refled and refrac!:!:, and fliew'd, that thin 
 tranfparent "Plates, Fibres and Particles do, ac- 
 cording to their feveral thicknelles and denfl- 
 ties, refleft feveral forts of Rays, and thereby 
 appear of feveral Colours, and by confequence 
 that nothing more is rcquifite for producing all 
 the Colours of natural Bodies than the feveral 
 fizesand denfities of their tranfparent Particles. 
 But whence it is that thefe Plates, Fibres and 
 Particles do, according to their feveral thick- 
 neifes and deniities, retiecl: feveral forts of Rays, 
 I have not yet explain'd. To give fome infighc 
 into this matter, and make way for underlland- 
 ing the next part of this Book, I iliall conclude 
 this Part with a few more Propofitions. Thofc 
 which preceded refpc61 the nature of Bodies, 
 thefe the nature of Light: For both mull: be 
 underdood before the reafon of their actions 
 upon one another can be known. And becaufe 
 the lailPropofition depended upon the velocity 
 of Light, I will begin with a Propofition of that 
 kind. 
 
 Pro 
 
 p. 
 
[252] 
 
 Prop. XL 
 
 Light is propagated from luminom Bodies in 
 time ^ and fp ends about fev en or eight Mi- 
 nutes of an Hcnir in pafjing from the Sun to 
 
 ' the Earth. 
 
 THIS was obferved firfl by /^i^fp^^T, and 
 and then by others, by means of the E- 
 clipies of the Satellites oi Jupiter. For thefe 
 Eclipfes, wiien the Earth is between the Sun 
 and Jupiter., happen about feven or eight Mi- 
 nutes fooner than they ought to do by the Ta- 
 bles , and when the Earth is beyond the Sun 
 they happen about feven or eight Minutes later 
 than they ought to do ; the reafon being, that 
 the Light of the Satellites has farther to go in 
 the latter cafe than in the former by the Dia- 
 meter of the Earth's Orbit. Some inequalities 
 of time may arife from theExcentricities of the 
 Orbs of the Satellites ; but thofe cannot anfwer 
 in all the SateUites, and at all times to the po- 
 fition and diftance of the Earth from the Sun. 
 The mean motions of Jupiter\ Satellites is alfo 
 fwifter in his defcent from his Aphelium to his 
 Perihelium, than in his afcent in the other half 
 of his Orb : But this inequality has no refpeft 
 to the pofition of the Earth , and in the three 
 interior Satellites is infenfible, as I find by com- 
 putation from the Theory of their gravity. 
 
 Prop. 
 
[ 253 ] 
 
 Prop. XH. 
 
 Every Ray of Light in its ^ajfage through any 
 refraBing Surface is put into a certain tran-^ 
 Jient Conftitution or StatCy ijuhich in the pro- 
 grej^ of the Ray returns at equal Intervals,, 
 and difpofes the Ray at every return to be 
 eajily tranfmitted through the next refradiing 
 Surface^ and between the returns to be eajily 
 reflected by it. 
 
 THIS is manifeft by the 5-111, yth, nth, 
 and i^thObfervations. For by thole Ob- 
 fervations it appears, that one and the fame 
 fort of Rays at equal Angles of Incidence on a- 
 ny thin tranfparent Plate, is alternately reflect- 
 ed and tranfmitted for many Succellions accor- 
 dingly as the thicknefs of the Plate increafes 
 in arithmetical Progreflion of the Numbers, o, 
 
 I, 2, 3, 4, 5", 6, 7, 8, ^c. fo that if the firft Re- 
 flexion ( that which makes the firll or inner- 
 moft of the Rings of Colours there defcribed) 
 be made at the thicknefs i, the Rays fliall be 
 tranfmitted at the thickneffes o, 2, 4, 6, 8, 10, 
 12, ^c. and thereby make the central Spot and 
 Rings of Light , which appear by tranfmifhon, 
 and be reflected at the thicknefs i, 3, $, 7, 9, 
 
 II, ^c. and thereby make the Rings which 
 appear by Reflexion. And this alternate Re- 
 flexion andTranfmiffion, as I gather by the 24th 
 Obfervation , continues for above an hundred 
 viciflitudes, and by the Obfervations in the next 
 part of this Book, for many thoufands, being 
 propagated from one Surface of a Glafs Plate to 
 
 the 
 
[254] 
 
 the other, though the thicknefs of the Plate be 
 a quarter of an Inch or above : So that this al- 
 ternation feems to be propagated from every 
 refracting Surface to all dillances without end. 
 or limitation. 
 
 This alternate Reflexion and Refraction de- 
 pends on both the Surfaces of every thin Plate, 
 becaufe it depends on their dillance. By the 
 21ft Obfervation, if either Surface of a thin 
 Plate of Mufcovy Glafs be wetted, the Colours 
 caufed by the alternate Reflexion and Refra- 
 ction grow faint , and therefore it depends on 
 them both. 
 
 . It is therefore performed at the fecond Sur- 
 face; for if it were pcrform'd at the firft, be- 
 fore the Rays arrive at the fecond, it would 
 not depend on the fecond. 
 
 It is alfo influenced by fome aftioil or difpo- 
 fition, propagated from the firft to the fecond, 
 becaufe otherwife at the fecond it would not 
 depend on the firfh And this aftion or difpo- 
 fition, in its propagation, intermits and returns 
 by equal Intervals, becaufe in all its progrefs it 
 inclines the Ray at one diilance from the tirll 
 Surface to be refleCled by the fecond , at ano- 
 ther to be tranfmitted by it, and that by equal 
 Intervals for innumerable viciffitudes. And be- 
 caufe the Ray is difpofed to Reflexion at the 
 dillances i, 3, 5-, 7, 9, ^c and to TranfmilTion 
 at the difl:ances o, i, 4, 6, 8, 10, ^c. (for its 
 tranfmilFion through the firlt Surface, is at the 
 diilance o, and it is tranfmitted through both 
 together, if their diilance be infinitely little or 
 much lefs than i ) the difpofition to be tranf- 
 mitted 
 
.[255] 
 
 mitted at the diflances 2, 4, 6, 8, lo, ^r. is to 
 be accounted a return of the fame dilpofitioii 
 which the Ray firft had at the diilance c, that is 
 at its tranfniiilion through the tirll refracting 
 Surface. All which is the :hing I would prove. 
 What kind of a^Hon or dilpofuion this is; 
 Whether it confifrs in a circulating or a vibra- 
 ting motion of the Ray, or of the Medium, or 
 fomething elfe, I do not here enquire. Thofe 
 that are averfe from aOenting to any new Dif- 
 coveries, but fuch as they can explain by an 
 Hypothecs, may for the prefcnt fuppofe, that 
 as Stones by falling upon Water put the Water 
 into an undulating Motion, and all Bodies by 
 percuilion excite vibrations in the Air; fo the 
 Rays of Light, by impinging on any refrading 
 or reflec^Ung Surface , excite vibrations in the 
 refracting or refledting Medium or Subllance, 
 and by exciting them agitate the folid parts of 
 the refrading or refleding Bodv, and by agita- 
 ting them caufe the Body to grow warm or 
 hot; that the vibrations thus excited are pro- 
 pagated in the refracting or reile^ting Medium 
 or Subftance, much after the manner that vibra- 
 tions are propagated in the Air for caufmg 
 Sound, and move filter than the Rays fo as to 
 overtake them ; and that when any Ray is in 
 that part of the vibration which confpires with 
 its Motion, it eafily breaks through a refradting 
 Surface, but when it is in the contrary part of 
 the vibration which impedes its Motion, it is 
 eafily refleded ; and, by confequence, that e- 
 very Ray is fuccellively difpofed to be eafily re- 
 flected J or eafily tranfmitted , by every vibra- 
 tion 
 
[256] 
 
 tion which overtakes it. But whether this Fly^ 
 
 Fothefis be true or falfe I do not here conlider. 
 content my felf with the bare Difcovery, that 
 the Rays of Light are by fome caufe or other 
 alternately difpofed to be refleded or refrad- 
 ed for many viciflitudes. 
 
 D E F I N I T I O NT. 
 
 The returns, of the dlfpofitton of any Ray to 
 be reflected I will call its Fits of eafy Re- 
 flexion, and thofe of its difpofition to be 
 tranfmitted its Fits of eafy Tranfmiflion, 
 ajid the Jpace it pafes betijueen every re^ 
 turn and the next return^ the Interval of 
 its Fits. 
 
 R O p. 
 
 XIII. 
 
 The reafon why the Surfaces of all thick tranf 
 parent Bodies refleci part of the Light itici- 
 dent on them^ and refraEl the reft, is, that 
 fome Rays at their Incidence are in Fits of 
 eafy Reflexion, and others in Fits of eajy 
 Tranfmifflon. 
 
 THIS may be gathered from the 14th Ob- 
 fervation, where the Light refleded by 
 thin Plates of Air and Glafs, which to the naked 
 Eye appear'd evenly white all over the Plate, 
 did through a Prifm appear waved with many 
 Succeffions of Light and Darknefs made by al- 
 ternate Fits of eafy Reflexion and eafy Tranf- 
 milTion, the Prifm fevering and diitinguiihing 
 the Waves of which the white refleded Light 
 was compofed, as was explain'd above. 
 
 And 
 
[257] 
 
 And hence Light is in Fits of eafy Reflexion 
 and eafy TranfmiiEon, before its Incidence on 
 tranfparent Bodies. And probably it is put in- 
 to fuch Fits at its firll emiiiion from luminous 
 Bodies, and continues in them during all its 
 progrefs. For thefe Fits are of a lalling nature, 
 as will appear by the next part of this Book. 
 
 In this Propofition I fuppofe the tranfparent 
 Bodies to be thick, becauie if the thicknefs of 
 the Body be much lefs than the Interval of the 
 Fits of eafy Reflexion and Tranfmidion of the 
 Rays, the Body lofeth its reflecting power. For 
 if the Rays , which at their entering into the 
 Body are put into Fits of eafy Tranfmiilion, ar- 
 rive at the fartheit Surface of the Body before 
 they be out of thofe Fits they mufl be tranfmit- 
 ted. And this is the reafon why Bubbles of 
 Water lofe their refledling power when they 
 grow very thin, and why all opaivC Bodies when 
 reduced into very fmall parts become tranfpa- 
 rent. 
 
 Prop. XIV, 
 
 Thofe Surfaces of tranfparent Bodies^ which if 
 the Ray be in a Fit of Refratfion do refraif 
 it moft firongly^ if the Ray be in a Fit ofRe-y 
 flexion do reflet it moft eafily, 
 
 FOR we fhewed above mTrop. 8. that the 
 caufe of Reflexion is not the'impin ingof 
 Light on the iolid impervious parts of Bodies, 
 but fome other Power by which thofe loKd 
 parts act on Light at a diilance. We Ihewed 
 alfo in Trojf, 9. that Bodies refled ^d refraitt 
 
 S Ligat 
 
[258] 
 
 Light by one and the fame Power varioiiflyex- 
 ercifed in various circumitances, andin'Pr^/.i. 
 that the moft ftrongly refrading Surfaces refledl 
 the moft Light : All which compared together 
 evince and ratify both this and the lail Propo- 
 fition. 
 
 Prop. XV. 
 
 In any one and the fame fort of Rays emerging 
 in any Angle out of any re framing Surface in- 
 to one and the fame Medium^ the Interval of 
 the follo'wing Fits of eaf^ Reflexion andTranf 
 mifjion are either accurately or very nearly^ 
 as the Re 61 angle of the Secant of the Angle of 
 RefraBion, and of the Secant of another An- 
 gle^ 'whofe Sine is the fir ft of \o6 arithmetical 
 mean Proportionals^ between the Sines of In- 
 cidence and Ref ration counted from the Sine 
 of Refra^ion. 
 
 T 
 
 HIS is manifefl by the 7th and 19th Ob- 
 fervations. 
 
 Prop. 
 
 i 
 
[ 259 ] 
 
 Prop. XVI. 
 
 In fever al forts of Rays emerging in equal An- 
 gles out of any refrafling Surface into the 
 fame Medium^ the Intervals of the following 
 Fits of eafy Reflexion and eajy Tranfrnifflon 
 are either accurately^ or very nearly -^ as the 
 Cube-Roots of the Squares of the lengths of a, 
 Chord y which found the Notes in an Eighty 
 fol, la, fa, fol, la, mi, fa, fol, with all their 
 intermediate degrees anfwering to the Colours 
 of thofe Rays, according to the Analogy de- 
 fer ibed in the feventh Experiment of the fe^ 
 ■ cond I^art of the firfl Book. 
 
 HIS is manifeft by the 13th and i4thOb'^ 
 
 fervatioiis. 
 
 Prop. XVH. 
 
 If Rays of any fort pafs perpendicularly into 
 fever al Mediums , the Intervals of the Fits 
 of eafy Reflexion and Tranfrnifflon in any one 
 Medium^ are to thofe Intervals in any other 
 as the Sine of Incidence to the Sine of Re f ra- 
 tion, when the Rays paj^ out of the firfl of 
 thofe two Mediums into the fecond, 
 
 This is manifeil by the lothObferv^tion, 
 
 T 
 
 P R O P^ 
 
[ 2^0 1 
 
 Prop. XVffl. 
 
 If the Rays which faint the Colour in the Con- 
 fine of yellow arid orange fafs perpendicularly 
 out of any Medium into Air^ the Intervals of 
 
 their Fits of eaCy Reflexion are the th 
 
 J -^ J 89000 
 
 fart of an Inch. And of the fame length are 
 
 the Intervals of their Fits of eajy Tranfmif 
 
 Jion. 
 
 THIS is manifeft by the 6th Obfervation. 
 From thefe Propofitions it is eafy to col- 
 lect the Intervals of the Fits of eafy Reflexion 
 and eafy Tranfmiflion of any fort of Rays re- 
 framed in any Angle into any Medium , and 
 thence to know, whether the Kays ihall be re- 
 flected or tranfmitted at their fubfequent Inci- 
 dence upon any other pellucid Medium. Which 
 thing being ufeful for underftanding, the next 
 part of this Book was here to be fet down. And 
 for the fame reafon I add the two following 
 Propofitions, . 
 
 P R O P« 
 
[26l] 
 
 Prop. XIX. 
 
 If any fort of Rays falling on the -polite Surface 
 of any pellucid Medium be rejle&ed hack^ the 
 Fits of eajy Reflexion 'u;hich they have at the 
 ^oint of Reflexion y jh all ft ill continue to re* 
 turn, and the returns Jhall be at diftance^ 
 from the point of Reflexion in the arithmetic 
 cal progreflion of the Numbers 1, 4, 6, 8, 10, 
 12, d:G. and befjuecn thefe Fits the Rays fl? all 
 be in Fits of eajy Tranfmiffion. 
 
 17^ OR fmce the Fits of eafy Reflexion and 
 ^ cafy Tranfmiflioii are of a returning na- 
 ture, there is no reafon why thefe Fits, which 
 continued till the Ray arrived at the refleding 
 Medium, and there inclined the Ray to Refle- 
 xion, fliould there ceafe. And if the Ray at 
 the point of Reflexion was in a Fit of eafy Re- 
 flexionj the progreflion of the difl:ances of thefe 
 Fits from that point mult begin from o, and fo 
 be of the Numbers o, 2, 4, 6, 8, ^c. And 
 therefore the jprogreflLion of the diftances of the 
 intermediate Fits of eafy Tranfmiflion reckon'd 
 from the fame point, mufl: be in the progreflion 
 of the odd Numbers i, 3, 5-, 7, 9, iSc. contra- 
 ry to what happens when the fits are propaga- 
 ted from points of Refradion. 
 
 Pro p. 
 
[ 2^2 1 
 
 Prop. XX. 
 
 The Intervals of the Fits of eafy Reflexion and 
 eajy TranfmiJ/Ioji^ propagated from points of 
 Reflexion into any Medium^ are equal to the 
 Intervals of the like Fits which the fame 
 Rays would have^ if refracted into the fame 
 Medium in Angles ofRefradlion equal to their 
 Jingles of Reflexion. 
 
 FOR when Light is refiedcd by the fecond 
 Surface of thin Plates, it goes out after- 
 wards freely at the firft Surface to make the 
 Rings of Colours which appear by Reflexion, 
 and by the freedom of its egrefs , makes the 
 Colours of thefe Rings more vivid and ftrong 
 than thofe which appear on the other fide of 
 the Plates by the tranlmitted Light. The re- 
 flc^ied Rays arc therefore in Fits of cafy Trarif- 
 niillion at their egrefs ; which would not always 
 happen, if the Intervals of the Fits within the 
 Plate after Reflexion were not equal both in 
 length and number to their hitcrvals before it. 
 And this confirms alio the Proportions let down 
 in the former Propoiition. For if the Rays 
 both in going in and out at .the firll Surface be 
 in Fits of caly Tranfmiflion , and the hitervals 
 and Numbers of thofe Fits between the firil 
 and fecond Surface, before and after Reflexion, 
 be equal ; the diihmces of the Fits of eafy 
 TranimilTion from either Surface, mull be in 
 the fame progrefFion after Reflexion as before ; 
 that is, from the firft Surface which tranfmit- 
 ted them, in the progreilion of the even Num- 
 bers 
 
[2^3] 
 
 bers o, 2, 4, 6, 8, ^c. and from the fecond 
 which reflected them, in that of the odd Num- 
 bers I, 3, 5", 7, ^r. But thefe two Propo- 
 fitions will become much more evident by the 
 Oblervations in the following part of this 
 Book. 
 
 THE 
 
[2^4] 
 
 THE 
 
 SECOND BOOK 
 
 OPTIC KS. 
 
 PART IV. 
 
 Obfervatwns concerning the Reflexions and Co- 
 lours of thick tr an [par ent ^olijy delates. 
 
 jHERE is no Glafs or Speculum how 
 well foevcr polifh'd, buc, befides the 
 Light, which it refracts or refleds re- 
 gularly, fcatters every way irregularly 
 a faint Light , by means of which the polilh'd 
 Surface, w hen illuminated in a dark room' by a 
 
 beam 
 
beam of the Sun's Light , may be eafily feen in 
 all politions of the Eye. There are certain 
 Phasnomena of this fcatter'd Light, which when 
 I firil obferved them, feem'd veryilrange and 
 furprifmg to me. My Obfervations w^ere as fol- 
 lows. 
 
 Obf.i. T*he Sun fliining into my darkened 
 Chamber through a hole one third of an Inch 
 wide, I let the intromitted beam of Light fall 
 perpendicularly upon a Glafs Speculum ground 
 concave on one fide and convex on the other, 
 to a Sphere of five Feet and eleven Inches Ra- 
 dius, and Quick-filver'd over on the convex 
 fide. And holding a white opake Chart, or a 
 Quire of Paper at the center of the Spheres to 
 which the Speculum was ground, that is, at the 
 diltance of about five Feet and eleven Inches 
 from the Speculum, in fuch manner, that the 
 beam of Light might pafs through a little hole 
 made in the middle of the Chart to the Specu- 
 lum, and thence be reflc61ed back to the fame 
 hole : I obferved upon the Chart four or five 
 concentric Irifes or Rings of Colours, like Rain- 
 bows, encompafling the hole much after the 
 manner that thofe, which in the fourth and fol- 
 lowing Obfervations of the firfl part of this third 
 Book appear'd between the Objedt-glafTes , en- 
 compafled the black Spot, but yet larger and 
 fainter than thofe. Thefe Rings as they grew 
 larger and larger became diluter and fainter, fo 
 that the fifth was fcarce vifible. Yet fome- 
 times, when the Sun flione very clear, there 
 appear'd faint Lineaments of a fixth and fe- 
 venth. If the diflance of the Chart from the 
 
 Specu- 
 
[ 2^^ ] 
 
 Speculum was much greater or much lefs than 
 that of fix Feet , the Rings became dilute and 
 vanilli'd. And if the diitance of the Speculum 
 from the Window was much greater than that 
 of fix Feet, the refleded beam of Light would 
 be fo broad at the diffance of lix Feet from the' 
 Speculum where the Rings appear'd, as to ob- 
 fcure one or two of the innermolt Rings. And 
 therefore I ufually placed the Speculum at a- ^ 
 bout fix Feet from the Windov\^; fo that its 
 Focus might there fall in with the center of its 
 concavity at the Rings upon the Chart. And. 
 this Poilure is always to be underltood in the 
 following Obfervations where no other is . ex- 
 prefs'd. 
 
 Obf. 1/ The Colours of thefe Rain-bows 
 fuccecded one another from the center out- 
 wards, in the fame form and order with thofe 
 which were made in the ninth Obfcrvation of 
 the liril Part of this Book by Light not refled- 
 ed, but tranfmit-ted through the two Obje<ft- 
 glalFes. For, tirit, there was in their common 
 center a white round Spot of faint Light, fome- 
 thing broader than the reflccfcd beam of Light, 
 which beam fometimes fell upon the middle of 
 the Spot, and fometimes by a little incUnation 
 of the Speculum receded from the middle, and 
 left the Spot white to the center. 
 
 This white Spot was immediately encompaf- 
 fed with a dark grey or ruilet, and that dark grey 
 with the Colours of the hrlUris ; which Colour 
 on the infide next the dark grey were a little 
 violet and indigo, and next to that a blue, which' 
 on the outildc grew pale, and th:n lucceeded a 
 
 little 
 
[ 2^7 ] 
 
 little grecnifh yellow, and after that a brighter 
 yellow, and then on the outward edge of the 
 Iris a red which on the outlide inclined to pur- 
 ple. 
 
 This Iris was immediately encompafTed with 
 a fecond, whofe Colours were in order from 
 the inlide outwards, purple, blue, green, yel- 
 low, light red, a red mix'd with purple. 
 
 Then immediately foUow'd the Colours of 
 the third Iris, \^^hich were in order outwards a 
 green inclining to purple, a good green, and 
 a red more bright than that of the former Iris. 
 
 The fourth and fifth Iris feem'd of a bluiih 
 green within , and red without , but fo faintly 
 that it was difficult to difcern the Colours. 
 
 Obf. 3. Meafuring the Diameters of thefe 
 Rings upon the Chart as accurately as I could, 
 I found them alio in the fame proportion to 
 one another with the Rings made .by Light 
 tranfmitted through the two Objed-glallcs. For 
 the Diameters of the four firll of the bright 
 Rings meafured between the brightelt parts of 
 their Orbits, at the dillance of fix Feet from the 
 Speculum were it~, 24? 2,44, 34 Inches, whofe 
 Squares are in arithmetical progrellion of the 
 numbers i, 2, 3, 4. If the white circular Spot 
 in the middle be reckoned amongft the Rings, 
 and its central Light, where it feems to be rhofl 
 luminous, be put equipollent to an infinitely 
 little Ring ; the Squares of the Diameters of the 
 Rings will be in the progrellion o, i, 2, 3, 4, 
 ^c. I meafured alfo the Diameters of the dark 
 Circles between thefe luminous ones, and found 
 their Squares in the progrellion of the num- 
 bers 
 
[ 2^S ] 
 
 befs 4, I', ii, 3-', &c. the Diameters of th^' 
 lirll four at the diftance of fix Feet from the 
 Speculum, being i-V, i-r^i 2,4, 3^^ Inches. If 
 the diftance of the Chart from the Speculum 
 was increafed or diminiflied, the Diameters of 
 the Circles were increafed or diminilhed pro- 
 portionally. 
 
 OifJ^ 4. By the analogy between thefe Rings 
 and thofe defcribed in the Obfervations of the 
 liril Part of this Book, I fufpeded that there 
 WTre many more of them which fpread into 
 one another, and by interfering mix'd their Co- 
 lours, and diluted one another fo that they 
 could not be feen apart. I viewed them there- 
 fore through a Prifm, as I did thofe in the i4th 
 Obfervation of the firlt Part of this Book. And 
 when the Prifm was fo placed as by refrafting 
 the Light of their mix'd Colours to feparate 
 them, and diflinguiih the Rings from one ano- 
 ther, as it did thofe in that Obfervation, I could 
 then fee them diilinder than before, and eafily 
 number eight or nine of them , and fometimes 
 twelve or thirteen. And had not their Light 
 been fo very faint, I queftion not but that I 
 might have feen many more. 
 
 O^/? 5-. Placing a Prifm at the Window to 
 refraft the intromitted beam of Lights and cafl 
 the oblong Spedrum of Colours on the Specu- 
 lum : I covered the Speculum with a black Pa- 
 per which had in the middle of it a hole to let 
 any one of the Colours pafs through to the 
 Speculum , whilfl the rell were intercepted by 
 the Paper. And now I found Rings of that Co- 
 lour only which fell upon the Speculum. If 
 
 the' 
 
I 2^9 ] 
 
 the Speculum was illuminated with red, the 
 Rings were totally red with dark Intervals, if 
 with blue they were totally blue, and fo of the 
 other Colours. And when they were illumi- 
 nated with any one Colour, the Squares of their 
 Diameters mealured between their mofl lumi- 
 nous parts, were in the arithmetical progreiiion 
 of the numbers o, i, i, 3, 4, and the Squares 
 of the Diameters of their dark Intervals in the 
 progreflion of t e intermediate numbers 4, i4, 
 2,4, 34. But if the Colour was varied they va- 
 ried their magnitude. In the red they were lar- 
 geft, in the indigo and violet lead, and in the 
 intermediate Colours yellow, green and blue , 
 they were of feveral intermediate bignefles an- 
 fwering to the Colour, that is, greater in yel- 
 low than in green, and greater in green than in 
 blue, And hence I knew that when the Spe- 
 culum was illuminated with white Light, the 
 ^•ed and yellow on the outfide of the Rings were 
 produced by the leati refrangible Rays, and the 
 blue and violet by the molt refrangible, and that 
 the Colours of each Ring fpread into the Co- 
 lours of the neighbouring Rings on either fide, 
 after the manner explain'd in the lirll and fe- 
 cond Part of this Book, and by mixing diluted 
 one another fo that they could not be diiiin- 
 guiili'd, unlefs near the center where they were 
 lead mix d. For in this Obfervation I could 
 fee the Rings more dillindly, and to a greater 
 number than before, being able in the yellow 
 Light to number eight or nine of them, be- 
 fides a faint ihadow of a tenth. To fatisfy my 
 lelf ho\v much the Colouvs of the feveral Rings 
 
 1 fpread 
 
[ 270 ] 
 
 fprcad into one another , I meafured the Dia- 
 meters of the fecond and third Rings, and found 
 them when made by the Confine of the red and 
 orange to be to the fame Diameters when made 
 by the Confine of blue and indigo, as 9 to 8, 
 or thereabouts. For it was hard to determine 
 this Proportion accurately. Alfo the Circles 
 made fucceflively by the red, yellow and green, 
 differed more from one another than thofe made 
 fuccellivcly by the green, blue and indigo. For 
 the Circle made by the violet was too dark to 
 be feen. To carry on the computation, let us 
 therefore fuppofe that the difierences of the 
 Diameters of the Circles made by the outmofl 
 red, the Confine of red and orange, the Confine 
 of orange and yellow, the Confine of yellow 
 and green, the^ Confine of green and blue, the 
 Confine of blue and indigo, the Confine of in- 
 digo and violet, and outmoit violet, are in pro- 
 portion as the differences of the lengths of a 
 Monochord which found the Tones in an Eight ; 
 /?/, la^ fa^ Jol, la^ mi, fa, fol, that is , as the 
 numbers -;, —, tV, tt, -^tVj ^V? tV. And if the 
 Diameter of the Circle made by the Confine of 
 red and orange be 9 A, and that of the Circle 
 made by the Confine of blue and indigo be 8 A 
 as above ; their difference 9 A — 8 A will be 
 to the difference of the Diameters of the Cir- 
 cles made by the outniofl red, and by the Con- 
 fine of red and orange, as -V 4- V.- 4- -V + -^Vto 
 V, that is as 4^ to ^, or 8 to 3, and to the diffe- 
 rence of the Circles made by the out moll vio- 
 let, and by the Confine of blue and indigo, as 
 ttV -i--'r \--\ -f ^V ^o-V -1- ^o that is, as VT to -^, 
 
 or 
 
[271] 
 
 or as 1 6 to y. And therefore thefe differences 
 will be 4 A and tV A. Add the firll to 9 A and 
 fubdud the lall from 8 A, and you will have the 
 Diameters of the Circles made by the lealt and 
 
 mofi refrangible Rays ^ A and -^ A. Thefe 
 
 Diametei's are therefore to one another as 75: 
 to 6h or 5*0 to 41, and their Squares as zfoo 
 to 1 68 1,. that is, as 3 to x very nearly. Which 
 proportion differs not much from the propor- 
 tion of the Diameters of the Circles made by 
 the outmoll red and outmoit violet in the 13th 
 Obfervation of the lirlt Part of this Book. 
 
 Oi^/^ 6. Placing my Eye where thefe Rings 
 appear'd plaineil, I faw the Speculum tinged all 
 over withWaves of Colours (red, yellow, green, 
 blue ; ) hke thofe which in the Obfervations of 
 the firft Part of this Book appeared between 
 the Objed-glafles and upon Bubbles of Water, 
 but much larger. And after the manner of thofe, 
 they werp of various Magnitudes in various Po- 
 fitions of the Eye , fwelling and flirinking as I 
 moved my Eye this way and that way. They 
 were formed like Arcs of concentrick Circles as 
 thofe were, and when my Eye was over againll 
 the center of the concavity of the Speculum (that 
 IS, 5 Feet and lohiches dillant from the Specu- 
 lum) their common center was in a right Line 
 with that center of concavity , and with the 
 hole in the Window.. But in other poilures of 
 my Eye their center had other pofitions. They 
 appear'd by the Light of the Clouds propagated 
 to the Speculum through the hole in the Win- 
 dow, and when the Sun ihone through that 
 hole upon the Speculum, his Light upon it 
 
 was 
 
[272] 
 
 was of the Colour of the Ring whereon it felU 
 but by its iplendor oblcured the Rings made by 
 the Light of the Clouds, unlefs when the Spe- 
 culum was removed to a great diftance from 
 the Window, lo that his Light upon it might 
 be broad and faint. By varying the pofition of 
 my Eye, and moving it nearer to or farther 
 from the dired beam of the bun's Light, the 
 Colour of the Sun's refieded Light conltantly 
 varied upon the Speculum, as it did upon my 
 Eye, the fame Colour always appearing to a 
 By-llander upon my Eye which to me appear'4 
 upon the Speculum. And thence I knew that 
 the Rings of Colours upon the Chart were made 
 by thele retleded Colours propagated thither 
 from the Speculum in feveral Angles, and that 
 their production depended not upon the ter- 
 mination of Light and Shadow. 
 
 Obf. 7. By tiie Analogy of all thefe Phaeno- 
 mena with thole of the like Rings of Colours 
 deicribed in the firit Part of this Book, it feem- 
 ed to me that thele Colours were produced by 
 this thick Plate of Glais, much after the manner 
 that thofe were produced bv very thin Plates. 
 For, upon tryal , I found that if the Quick-lil* 
 ver were ruBb'd olf from the backfide of th^ 
 Speculum, the Glafs alone would caui'e the 
 fgme Rings of Colours, but much more faint 
 than before; and therefore the Phaenomenon 
 depends not upon the Quick-lilver, unlefs fo far 
 as the Quick-lilver by increafmg the Reflexion 
 of the backfide of the Glafs increaies the Light 
 of the Rings of Colours, I found alfo that ^ 
 Speculum of Metal without Glais made lome 
 
 Ye^rs 
 
[ 273 ] 
 
 Years fince for optical ufes, and very well 
 wrought, produced none of thofe Rings ; and 
 thence I underitood that thefe Rings arife not 
 from one fpecular Surface alone, but depend 
 upon the two Surfaces of the Plate of Glafs 
 whereof the Speculum was made, and upon the 
 thicknefs of the Glafs between them. For 
 as in the 7th and i9thObfervations of the lirll 
 Part of this Book a thin Plate of Air, Water, 
 or Glafs of an even thicknefs appeared of one 
 Colour when the Rays were perpendicular to 
 it, of another when they were a little oblique, 
 of another when more oblique, of another when 
 ftill more oblique, and fo on; fo here, in the 
 fixth Obfervation, the Lis:ht which emerged 
 out of the Glafs in feveral Obliquities, made the' 
 Glafs appear of feveral Colours, and being pro- 
 pagated in thofe Obliquities to the Chart, there 
 painted Rings of thofe Colours. And as the 
 reafon why a thin Plate appeared of feveral Co- 
 lours in feveral Obliquities of the Rays, was, 
 that the Rays of one and the fame fort are re- 
 fleded by the thin Plate at one obliquity and 
 tranfmitted at another^ and thofe of other forts 
 tranfmitted where thefe are refleded, and re- 
 flefted where thefe are tranfmitted:' So the 
 reafon why the thick Plate of Glafs whereof 
 the Speculum was made did appear of various 
 Colours in various Obliquities , and m thofe 
 Obliquities propagated thole Colours to the 
 Chart, was, that the Rays of one and the 
 fame fort did .at one Obliquity emerge out 
 of the Glafs, at another did not emerge but 
 were reflcdkd back towards the Quick-filver 
 
 1 E?y 
 
[ 274 1 
 
 by the hither Surface of the Glafs, and according- 
 ly as the Obhquity became greater and greater 
 emerged and were refleded alternately for ma- 
 ny Succeflions, and that in one and the fame 
 Obliquity the Rays of one fort were refleded, 
 and thoie of another tranfmitted. This is ma- 
 nifcd by the fifth Obfervation of this Part of this 
 Book. For in that Obfervation, when the Spe- 
 culum was illuminated by any one of the prif- 
 matick Colours, that Light made many Rings 
 of the fam^e Colour upon the Chart with dark 
 Intervals, and therefore at its emergence out of 
 the Speculum was alternately tranfmitted and 
 not tranfmitted from the Speculum to the Chart 
 for many Succeflions, according to tlie various 
 ObUquities of its Emergence. And when the 
 Colour call on the Speculum by the Prifm was 
 varied, the Rings became of the Colour caflon 
 it, and varied their bignefs with their Colour, 
 and therefore the Light was now alternately 
 tranfmitted and not tranfmitted from^the Spe- 
 culum to the Chart at other Obliquities than 
 before. It ieemcd to me therefore that thefe 
 Rings were of one and the fame original with 
 thofe.of thin Plates, but yet with this difference, 
 that thofe of thin Plates are made by the alter- 
 nate Reflexions and Tranfmifllons of the Rays 
 at the fecond Surface of the Plate after one paf- 
 fage through it, but here the Rays go twice 
 through the Plate before they are alternately re- 
 flefted and tranfmitted. Firfl, they go through 
 it from the firfl Surface to the Quick-filvcr, and 
 then return through it from the Quick-filver 
 to the firfl Surface, and there are either tranf-- 
 
 mi:tted 
 
[275 ] 
 
 mitted to the Chart or refleded back to the 
 Quick-filver , accordingly a^ they are in their 
 Fits of eafy Reflexion or Tranimiilion when 
 they arrive at that Surface. For the Intervals 
 of the Fits of the Rays which fall perpendicu- 
 larly on the Speculum, and are retlcctcd back 
 in the fame perpendicular Lines, by realon of 
 the equality of thefe Angles and Lines , are of 
 the fame length and number within the Glafs 
 after Reflexion as before by the 19th Propor- 
 tion of the third Part of this Book. And there- 
 fore fmce all the Rays that enter through the 
 firft Surface are in their Fits of eafy Tranfmif- 
 lion at their entrance, and as many of thefe as 
 are reflected by the fecond are in their Fits of 
 eafy Reflexion there, all thefe muft be again in 
 their Fits of eafy Tranfmiflion at their return 
 to the firft, and by confcquence there go out 
 of the Glafs to the Chart, and form upon it the 
 white Spot of Light in the center of the Rings. 
 For the reafon holds good in all forts of Rays, 
 and therefore all forts muft go out promilcu- 
 oufly to that Spot, and by their mixture caufe 
 it to be white. But the Intervals of the Fits of 
 thofe Rays which are reflected more obliquely 
 than they enter, muft be greater after Reflexion 
 than before by the i^th and ioth Propofitions. 
 And tnence it may happen that the Rays at their 
 return to the firft Surface, may in certain Ob- 
 liquities be in Fits of eaiy Reflexion, and return 
 back to the Quick-filver, and in other interme- 
 diate Obhquities be again in Fits of eafy Tranf- 
 miflion, and fo go out to the Chart, and paint 
 on it the Rings of Colours about the white Spot. 
 
 T 2. And 
 
[270 
 
 And becaufe the Intervals of the Pits at equal 
 Obliquities are greater and fewer in the lefs re- 
 frangible Rays, and lefs and more numerous 
 in the more refrangible , therefore the lefs re- 
 frangible at equal Obliquities fliall make fewer 
 Rings than the more refrangible, and the Rings 
 made by thofe fliall be larger than the Hke 
 number of Rings made by thefe ; that is, the 
 red Rings fliall be larger than the yellow, the 
 yellow than the green, the green than the blue, 
 and the blue than the violet, as they were real- 
 ly found to be in the fifth Obfervation. And 
 therefore the firlt Ring of all Colours encom- 
 pafling the white Spot of Light fliall be red 
 without any violet within, and yellow and 
 green and blue in the middle, as it was found 
 in the fecond Obfervation ; and thefe Colours 
 in the fecond Ring, and thofe that follow fliall 
 be more expanded till they fpread into one a- 
 nother, and blend one another by interfering. 
 
 Thefe fcem to be the Pvcafons of thefe Rings 
 in general ; and this put me upon obferving the 
 thicknefs of the Glafs, and confidering whether 
 the Dimenfions and Proportions of the Rings 
 may be truly derived from it by computation. 
 
 ObJ. 8. I meafured therefore the thicknefs of 
 this concavo-convex Plate of Glafs, and found it 
 every where ^ of an Inch precifely. Now, by 
 the fixth Obfervation of the firft Part of this 
 Book, a thin Plate of Air tranfmits the brightelt 
 Light of the firft Ring, that is the bright yel- 
 low, when its thicknefs is the g^th part of an 
 
 Inch, and by the tenth Obfervation of the fame 
 
 Part, 
 
[ 277 ] 
 
 Part, a thin Plate of Glafs tranfmits the fame 
 Light of the fame Ring when its thicknefs is 
 lefs in proportion of the Sine of Refraction to 
 the Sine of Incidence ,. that is, when its thick- 
 
 ^^^^ '' ^^^TFli^o^^ °^il7S5^^ P^'^ ""^ "^^ ^^^^' 
 fuppofing the Sines are as ii to 17. And if this 
 thicknefs be doubled it tranfmits the fame bright 
 Light of the fecond Ring, if trippled it tranf- 
 mits that of the third, and fo on, the bright 
 yellow Light in all thefe cafes being in its Fits 
 of TranfmiHion. And therefore if its thicknefs 
 be multiplied 34386 times fo as to become ^ of 
 an hich it tranfmits the fame bright Light of 
 the 34386th Ring. Suppofe this be the bright 
 yellow Light tranfmitted perpendicularly from 
 the receding convex fide of the Glafs through 
 the concave fide to the white Spot in the cen- 
 ter of the Rings of Colours on the Chart : And 
 by a Rule in the 7th and 19th Obfervations in 
 the firil Part of this Book, and by the i^th and 
 ioth Propoiitions of the third Part of this Book, 
 if the Rays be made oblique to the Glafs, the 
 thicknefs of the Glafs requifite to tranfmit the 
 fame bright Light of the fame Ring in any Ob- 
 liquity is to this thicknefs of ^ of an hich, as the 
 Secant of a certain Angle to the Radius, the 
 Sine of which Angle is the firlt of an hundred 
 and fix arithmetical Means between the Sines 
 of Incidence and Refradion, counted from the 
 Sine of Incidence when the Refraction is made 
 out of any plated Body into any Medium en- 
 compafling it, that is, in this cafe, out of Glafs 
 into Air. Now if the thicknefs of the Glafs be 
 
 T 3 increafed 
 
[278] 
 
 jincreafed by degrees , fo as to bear to its firfl 
 thickneft, (viz, that of a quarter of an Inch) 
 the Proportions which 34306 (the number of 
 Fits of the perpendicular Rays in going through 
 the Glafs towards the white Spot in the center 
 of the Rings,) hath to 34385", 343 B4, 343 B3 and 
 343 8x (the numbers of the Fits of the oblique 
 Rays in going through the Glafs towards the 
 firlt, fecond, third and fourth Rings of Co- 
 lours,) and if the firft thicknefs be divided in- 
 to 1 00000000 equal parts, the increafed thick- 
 nelTeswillbe 100001908, ioooo5'8r6, 100008725 
 and 100011633, and the Angles of which thefe 
 thickneffes are fecants will be 26' 13", 3/ $'\ 
 45"' 6" and 52' 26", the Radius being loooooooo; 
 and the Sines of thefe Angles are 762, 1079, 
 1 321 and 1525-, and the proportional vSines of 
 Refradion 11 72, 1659, 2031 and 2345-, the Ra- 
 dius being 1 00000. For fmce the Sines of In- 
 cidence out of Glafs into Air are to the Sines 
 of Refradion as 11 to 17, and to the above- 
 mentioned Secants as 11 to the firft of ic6 arith- 
 metical Means between 11 and 17, that is, as 
 
 J I to II j-^, thofe Secants will be to the Sines 
 
 of Refrai^Hon as 11 ^-^ to 17, and by this Ana- 
 logy u^ill give thefe Sines. So then if the Ob- 
 liquities of the Rays to the concave Surface of 
 the Glafs be fuch that the Sines of their Refra- 
 dion in paiTmg out of the Glafs through that 
 Surface into the Air be 1172, 165-9, ^"^Bi? 2.345-, 
 the bright Light of the 34386th Ring Ihail e- 
 merge at the tiiickneiles of the Glai's which are 
 
 to 
 
[ 279 ] 
 
 to-^ of an Inch as 34386 to 34385-, 34384, 34383, 
 34381, refpedlivcly. And therefore if thethick- 
 nefs in all thefe cafes be i of an Inch (as it is in 
 the Glafs of which the Speculum was made) 
 the bright Light of the 34385'th Ring fliall e- 
 merge where the Sine of Refraction is 1171, 
 and that of the 34384th, 384383th and 34381th 
 Ring where the Sine is 165-9, 2.031, and 1345' 
 refpedlively. And in thefe Angles of Refra- 
 dion the Light of thefe Rings fhall be propaga- 
 ted from the Speculum to the Chart, and there 
 paint Rings about the white central round Spot 
 of Light which we (aid was the Lighi of the 
 34386th Ring. And the Semidiametcrs of thefe 
 Rings Ihall fubtend the Angles of Refracftion 
 made at the concave Surface of the Speculum, 
 and by confequence their Diameters fliall be to 
 the dillance of the Chart from the Speculum as 
 thofe Sines of Refraction doubled are to the 
 Radius, that is, asiiji, 165-9, 2.031, and 1345-, 
 doubled are to 1 00000. And therefore if the 
 diitance of the Chart from the concave Surfice 
 of the Speculum be fix Feet (as it was in the 
 thir^.' of thefe Obfervations) the Diameters of 
 the Rings of this bright yellow Light upon the 
 Chmt fliall be i'688, 1*389, i'9i5', 3'375' Inches: 
 For thefe Diameters are to fix Feet, as the a- 
 bovemention'd Sines doubled are to the Ra- 
 dius. Now thefe Diameters of the bright yel- 
 low Rings, thus found by computation are the 
 very fame with thofe found in the third of thefe 
 Obfervations by meafuring them, viz. with 
 It-, ^■i, i4'-, and s-l- Inches, and therefore the 
 Theory of deriving thefe Rings from the thick- 
 
 T 4 nefs 
 
[ 28o ] 
 
 nefs of the Plate of Glafs of which the Specu- 
 lum was made , and from the Obliquity of the 
 emerging Rays agrees with the Oblervation. In 
 this computation I have equalled the Diameters 
 of the bright Rings made by Light of all Co- 
 lours, to the Diameters of the Rings made by 
 the bright yellow. For this yellow makes the 
 brighteft part of the Rings of all Colours. If you 
 defu'e the Diameters of the Rings made by the 
 Light of any other unmix d Colours you may find 
 them readily by putting them to the Diameters 
 of the bright yellow ones in a fubduplicate pro- 
 portion of the Intervals of the Fits of the Rays 
 of thofe Colours when equally inclined to the 
 refracting or refleding Surface which caufed 
 thofe Fits, that is, by putting the Diameters of 
 the Rings made by the Rays in the Exremities 
 and Limits of the feven Colours, red, orange, 
 yellovA', green, blue, indigo, viqlet, proportio- 
 nal to the Cube-roots of the Numbers, i, ^, 4, 
 4> T» T> -rv, 4, which. exprefs the lengths of a 
 Monochord founding the Notes in an Eighth : 
 For by this means the Diameters of the Rings 
 of thefe Colours will be found pretty nearly in 
 the fame proportion to one another, which 
 they ought to have by the fifth of thefe Obfer- 
 yations. 
 
 And thus I fatisfv'd my felf that thefe Rings 
 were of the fame kind and original with thofe 
 of thin Plates, and by confequence that the Fits 
 . or alternate Difpofitions of the Rays to be 
 refleded and tranfmitted are propagated to 
 great diflances from every reflecting and re- 
 frading Swfece. But yet to put the mat- 
 ter 
 
[28l] 
 
 ter out of doubt, I added the following OIv 
 fervation. 
 
 Obf. 9. If thefe Rings thus depend on the 
 ihickneis of the Plate of Glafs, their Diameters 
 at equal dilbnces from feveral Speculums made 
 of fuch concavo-convex i^lates of Glais as are 
 ground on the fame Sphere, ought to be reci- 
 procally in a fubduplicate proportion of the 
 thicknelles of the Piates of Glais. And if this 
 Proportion be found true by experience it will 
 amount to a demonlbation that thele Rings 
 (like thofe formed in thin Plates) do depend 
 on the thicknefs of the Glafs. I procured there- 
 fore another concavo-convex Plate of Glafs 
 ground on both fides to the fame Sphere with 
 the former Plate. Irs thicknefs was -V parts of 
 an Inch ; and the Diameters of the three tirll 
 bright Rings meafured between the brightelt 
 parts of their Orbits at the diitance of fix I eet 
 from the Glafs were 3. 44. s^- Inches. Now 
 the thicknefs of the other Glafs being -^ of an 
 Inch was to the thicknefs of this Glafs as ^ to A, 
 that is as 31 to 10, or 310000000 to loooooooo, 
 and the Roots of thefc Numbers are 17607 and 
 loooo, and \x\ the proportion of the firil of 
 thefe Roots to the fecond are the Diameters of 
 the bright Rings made in this Obfervation by 
 the thinner Glais, 3. 4^. 5-4, to the Diameters of 
 the fame Rings made in the third of thefe Ob- 
 fervations by the thicker Glafs i4t. i^\. 2.44, that 
 is, the Diameters of the Rings are reciprocally 
 in a fubduplicate proportion of the thicknelfes 
 of the Plates of Glafs. 
 
 So then in Plates of Glafs which are alike 
 
 con- 
 
[282] 
 
 concave on one fide, and alike convex on the 
 other fide, and alike quick-lilver'd on the con- 
 vex lides, and differ in nothing but their thick- 
 nefs, the Diameters of the Rings are recipro- 
 cally in a fubduplicate proportion of the thick- 
 nelTes of the Plates. And this flievvs fufficient- 
 ly that the Rings depend on both the Surfaces 
 of the Glafs. They depend on the convex Sur- 
 face bccaufe they are more luminous when that 
 Surface is quick-filver'd over than when it is 
 without Quick-iilver. They depend alio upon 
 the concave Surface, becaufe without that Sur- 
 face a Speculum makes them not. They de- 
 pend on both Surfaces and on the diftances be- 
 tween them, becaufe their bignefs is varied by 
 varying only that diftance. And this depen- 
 dance is of the fame kind with that which the 
 Colours of thin Plates have on the diflance of 
 the Surfaces of thofe Plates, becaufe the big- 
 nefs of the Rings and their proportion to one 
 another, and the variation of their bignefs ari- 
 fmg from the variation of the thickncfs of the 
 Glafs, and the orders of their Colours, is fuch 
 as ought to refult from the Proportions in the 
 end of the third Part of this Book, derived 
 from the Phaenomena of the Colours of thin 
 Plates fet down in the firil Part. 
 
 There are yet other Phaenomena of thcfe 
 Rings of Colours but fuch as follow from the 
 fame Propofitions, and therefore confirm both 
 the truth of thofe Propofitions, and the Analo- 
 gy between thefe Rings and the Rings of Co- 
 lours made by very tliin Plates. I fliall fubjoin 
 feme of them. 
 
[283] 
 
 Obf. lo. When the beam of the Sun's Light 
 was refkrted back from the Speculum not di- 
 redly to the hole in the Window, but to a place 
 a little diltant from it, the common center of 
 that Spot, and of all the Rings of Colours fell 
 in the middle way between the beam of the in- 
 cident Light, and the beam of the rcfledcd 
 Light, and by coniequence in the center of the 
 fpherical concavity of the Speculum, whenever 
 the Chart on which the Rings of Colours fell 
 was placed at that center. And as the beam of 
 refledted Light by inclining the Speculum re- 
 ceded more and more from the beam of inci- 
 dent Light and from the common center of the 
 colour'd Rings between them, thofe Rings grew 
 bigger and bigger, and fo alfo did the white 
 round Spot, and new Rings of Colours emer- 
 ged fucceilively out of their common center, 
 and the white Spot becam.c a white Ring en- 
 compailing them ; and the incident and reced- 
 ed beams of Light always fell iipon the oppo- 
 fite parts of this white Ring, illuminating its 
 Perimeter like two mock Suns in the oppofite 
 parts of an Iris. So then the Diameter of this 
 Ring, meafurcd from the middle of its Light 
 on one fide to the middle of its Light on the 
 other fide, was always equal to the diflance be- 
 tween the middle of the incident beam of 
 Light, and the middle of the reflefted beam 
 fneafured at the Chart on which the Rings ap- 
 peared : And the Rays which form'd this Ring 
 were refleded by the Speculum in Angles equal 
 to their Angles of Incidence, and by confe- 
 quence to their Angles of Refradion at their 
 
 entrance 
 
[ 284 ] 
 
 entrance into theGlafs,_but yet their Angles of 
 Reflexion were not in the fame Planes with 
 their Angles of Licidence. 
 
 Obf. 1 1 . The Colours of the new Rings were 
 in a contraiy order to thofe of the former, and 
 arofe after this manner. The white'round Spot 
 of Light in the middle of the Rings continued 
 white to the center till the dilknce of the in- 
 cident and rellcc^ted beams at the Chart was a- 
 bout ^ parts of an Inch, and then it began to 
 grow dark in the middle. And when that di- 
 llance was about It^ of an Inch, the white Spot 
 was become a Ring encompafling a dark round 
 Spot which in the middle inclined to violet and 
 indigo. And the luminous Rings encompafling 
 it were grown equal to thofe dark ones which 
 in the four firlt Obfervations encompailed them, 
 that is to fay, the white Spot was grown a 
 white Ring equal to the firll" of -thofe dark 
 Rings, and the tiril: of thofe luminous Rings was 
 now grown equal to the fecond-of thofe dark 
 ones, and the fecond of thofe luminous ones to 
 the third of thofe dark ones, and fo on. For 
 the Diameters of the luminous Rings were now 
 i-r^., 1-'-, 27, s-T-, ^c. Inches. 
 
 When the dilhncc between the incident and 
 refleded beams of Light became a little big- 
 ger, there emerged out of the middle of the 
 dark Spot after the indigo a blue, and then out 
 of that blue a pale green, and foon after a yel- 
 low and red. And when the. Colour at the 
 center was brightelf, being between yellow and 
 red, the bright Rings were grown equal to thofe 
 Rings which in the four firll Obfervations next 
 
 encom- 
 
[285] 
 
 encompafTed them ; that is to fliy, the white 
 Spot in the middle of thole Rings was now be- 
 come a white Ring equal to the fiiil of thofe 
 bright Rings, and the tirlt of thofe bright ones 
 was now become equal to the fecond of thofe, 
 and fo on. For the Diameters of the white 
 Ring, and of the other luminous Rings encom- 
 palling it, were now i-^-t, 2,4? 2.44, 34, &c. or 
 thereabouts. 
 
 • When the dillance of the two beams of 
 Light at the Chart was a little more increafed, 
 there emerged out of the middle in order after 
 the red, a 'purple, a blue, a green, a yellow, 
 and a red inclining much to purple, and when 
 the Colour was brightelt being between yellow 
 and red, the former indigo, blue, green, yel- 
 low and red , were become an Iris or Ring of 
 Colours equal to the firlt of thofe luminous 
 Rings which appeared in the four firft Obfer- 
 vations, and the white Rin? which was now 
 become the fecond of the luminous Rings was 
 grown equal to the iecond of thofe, and the 
 firil of thofe which was now become the third 
 Ring was become equal to the third of thofe, 
 and fo on. For their Diameters were i-f4, 2.4, 
 2-44, 34 Inches , the diltance of the two beams 
 of Light, and the Diameter of the white Ring 
 being 24 Inches. ' 
 
 When thefe two beams became more diflant 
 there emerged out of the middle of the pur- 
 plilh red, hrit a darker round Spot, and then 
 out of the middle of that Spot a brighter. And 
 now the former Colours (purple, blue, green, 
 yellow, and purplish red) were become a Ring 
 
 equal 
 
[ 2S6 ] 
 
 equal to the firft of the bright Rings mention- 
 ed in the four tirftObfervations, and the Rings 
 about this Ring were grown equal to the Rings 
 about that refpe6tively ; the diftance between 
 the two beams of Light and the Diameter of 
 the white Ring (which was now become the 
 third Ring) being about 3 Inches. 
 
 The Colours of the Rings in the middle be- 
 gan now to grow very dilute, and if the di- 
 Itance between the two Beams was increafed 
 half an Inch, or an Inch more, they van iih'd 
 whilll the white Ring, with one or two of the 
 Rings next it on either fide, contirtued itill vi- 
 fible. But if the diltance of the two beams of 
 Light was Hill more increafed, thefe alfo va- 
 niihed: For the Light which coming from fe- 
 veral parts of the hole in the \\ indow fell up- 
 on the Speculum in feveral Angles of Incidence, 
 made Rings of feveral bignefFcs, which diluted 
 and blotted out one another, as I knew byin- 
 tercepring fomc part of that Light. For if I 
 intercepted that part which was neareft to the 
 Axis of the Speculum the Rings would be lefs, 
 if the other part which was remoteil from it 
 they Vv;puld be bigger. 
 
 Oi^f iz. When the Colours of the Prifm 
 were call fuccellively on the Speculum, that 
 RinJ:^ wiiich in the two lalt Obfervations was 
 white, was of the fame bigncfs in all the Co- 
 lours, but the Rings without it were greater in 
 the green than in the blue, and Itill greater in 
 the yellow, and greateilin the red. And, on the 
 contrary, the Rings within that white Circle 
 were Icfs in the green than in the blue, and ftill 
 
 lefs 
 
[287] 
 
 lefs in the yellow, and leall in the red. For 
 the Angles of Reflexion of thofe Rays which 
 made this Ring, being equal to their Angles of 
 Incidence, the Fits of every refleded Ray within 
 the Glafs after Reflexion are equal in- length 
 and number to the Fits of the fame Ray with- 
 in the Glafs before its hicidence on the reflect- 
 ing Surface. And therefore iince all the Rays 
 r'^ '" brts at their entrance into the Glais were 
 of Franfmiflion, they were alfo in a Fit 
 o. limiilion at their returning to the fame 
 
 Su.uc after Reflexion; and by confcquence 
 were tranfmitted and went out to the white 
 Ring on the Chart. This is the»reafon why 
 thai Ring was of the fame bignefs in all the Co- 
 lours, and why in a mixture of all it appears 
 white. But in Rays which arc refledcd in o- 
 ther Angles, the Intervals of the Fits of the, 
 leait refrangible being grcatelt, make the Rings 
 of their Colour in their progreisfrom this white 
 Ring, either outwards or inwards, increafe or 
 decreafe by the greatell Iteps ; fo that the Rings 
 of this Colour without are greatefl, and within 
 leafl:. And this is the reafon why in the lal!: 
 Obfervation, when the Speculum was illumina- 
 ted with white Light, the exterior Rings made 
 by all Colours appeared red without and blue 
 within, and the interior blue without and red 
 within. 
 
 Thefe are the Phaenomena of thick convexo- 
 concave Plates of Glafs, which are every where 
 of the fame thicknefs. There are yet other 
 Phaenomena when thcfe Plates are a little thick- 
 er on one fide than on the other, and others 
 
[288] 
 
 when the Plates are more or lefs conc.ave thail^ 
 convex, or plano-convex, or double-convex. 
 For in all thele cafes the Plates make Rings of 
 Colours, but after various manners ; all which, 
 fo far aS I have yet obferved , follow from the 
 Propoiitions in the end of the third part of this 
 Book, and fo confpire to confirm the truth 6f 
 thofe Propoiitions. But the IMiaenomena arc 
 too various, and the Calculations whereby they 
 follow from thofe Proportions too intricate to 
 be here profccuted. I content my felf with ha- 
 ving profecuted this kind of Phaenomena fo far 
 as to difcover their Caufe, and by difcovering 
 it to ratify t\m Propofitions in the third Part of 
 this Book. 
 
 0/y." 13. As Light rcfleded by aLensquick- 
 filver'd on the backfide makes the Rings of Co- 
 lours above defcribed, fo it ought to make the 
 like Rings of Colours in palling through a drop 
 of Water. At the firll Rciiexion of the Rays 
 witnin the drop, fome Colours ought to be 
 tranfmittcd, as in the cafe of a Lens, and others* 
 to be resetted back to the Eye. Forinilance, 
 if the Diameter of a fmall drop or globule of 
 Water be about the focth part of an Lich, fo 
 that a red-making Ray in palling through the 
 middle of this globule has 250 Fits of eafy 
 Tranlmidion within the globule, and that all 
 the red-making Rays which are at a cert-ain di-^ 
 llance from this middle Ray round about it 
 have 249 Fits within the globule^ and all the 
 like Rays at a certain farther diilance round a- 
 bout it have 248 Fits, and all thofe at a cer- 
 tain farther diilance 247 Fits, and fo on-; thefe 
 
 conccn- 
 
[289] 
 
 concentrick Circles of Rays after their tranf- 
 miflion, tailing on a white Paper, will make 
 concentrick Rings of red upon the Paper, fup- 
 pofing the Light \^'hich pallcs through one Tin- 
 gle globule, Ih'ong enough to bcfcnliblc. And, 
 in like manner, the Rays of other Colours will 
 make Rings of other Colours. Suppofe now 
 that in a fair Day the Sun Ihines through a thin 
 Cloud of fuch globules of W ater or Hail, and 
 that the globules arc all of the fame bignefs ; 
 and the Sun fcen through this Cloud iliall ap- 
 pear cncompailed with the like concentrick 
 Rings of Colours, and the Diameter of the firil 
 Ring of red ihall be 7.;^ Degrees, that of the fe- 
 cond icv Degrees, that of the third 11 Degrees 
 33 Minutes. And accordingly as the Globules 
 of Water are bigger or Icfs, the Rings iliall be 
 lefs or bigger. This is the Theory, and Expe- 
 rience anlwers it. For in June 1692. I f\w by 
 reflexion in a Vellel of itagnating Water three 
 Halos, Crowns, or Rings of Colours about the 
 Sun, like three little Rain-bows, concentrick 
 to !iis Body. The Colours of the firll or in- 
 nermolt Crown were blue next the Sun, red 
 without, and white in the middle between the 
 blue and red. Thole of the fecond Crown 
 were purple and blue within, and pale red with- 
 out , and green in the middle. And thofe of 
 the third were pale blue within, and pale red 
 without; thefe Crowns enclofed one another 
 immediately, fo that their Colours proceeded 
 in this continual order from the Sun outward : 
 blue, white, red; purple, blue, green, pale 
 
 U yellow 
 
[ 290 ] 
 
 yellow and red ; pale blue, pale red. The Di- 
 ameter of the fecond Crown meafured from 
 the middle of the yellow and red on one fide 
 of the Sun, to the middle of the fame Colour 
 on the other fide was 9^ Degrees , or therea- 
 bouts. The Diameters of the liril and third 
 I had not time to meafure, but that of the firft 
 feemed to be about five or fix Degrees , and 
 that of the third about twelve. The like 
 Crowns appear fometimes about the Moon 5 
 for in the beginning of the Year 1664, Febr, 
 19th at Night, I faw two fuch Crowns about 
 her. The Diameter of the firft or innermofl 
 was about three Degrees, and "that of the fe- 
 cond about five Degrees and an half Next ^^. 
 bout the Moon was a Circle of white, and next 
 about that the inner Crown which was of a 
 bluifh green within next the white , and of a 
 yellow and red without, and next about thefe 
 Colours wTre blue and green on the infide of 
 the outward Crown, and red on the outfide of 
 it. At the fame time there appear'd a Halo a- 
 bout 2i Degrees 35"' dillant from the center of 
 the Moon. It was elliptical, and its long Dia- 
 nieter was perpendicular to the Horizon, verg- 
 ing below farthefl from the Moon. I am told 
 that the Moon has fometimes three or more 
 concentrick' Crowns of Colours encompafling 
 one another next about her Body. The more 
 equal the globules of Water or Ice are to one 
 another, the more Crowns of Colours will ap- 
 pear, and the Colours will be the more hvely. 
 The Halo at the diftance of z-L-i Degrees fron^ 
 
 the 
 
Kg. 2 . 
 
 L«.«"«' " rr''''''''''**'/^''/^,,,^ 
 
 tl-#" ' 'f*«'*%%j% 
 
 _bookll Flatel 
 
 cat jy^ t^ ^nrup^ r.7t-uxyz 
 
 Wl Is Rl g 
 
 -^ E 1? ^ 
 
 fell J l^liJIj 
 
is ^S^ ^ S 'S f^ 
 
 ©■■ 
 
lU.kll.Plalcn. 
 
 ■^f 3|N' 
 
 ^-. 7 
 
 7^0: s. I 
 
 "BC D E F G H 
 
[ 291 ] 
 
 the Moon is of another fort. By its being oval 
 and remoter from the Moon below than above, 
 I conclude , that it was made by Refradioh in 
 fome fort of Hail or Snow floating in the Air 
 in an horizontal pollure, the refrading Angle 
 teing about 58 or ($0 Degrees. 
 
 U % 
 
 THE 
 
t 2^2 ] 
 
 M 
 
 p 
 
 M 
 
 M 
 
 ^^ 
 
 ^m 
 
 ^^ 
 
 
 
 
 
 
 THE 
 
 THIRD BOO 
 
 OF 
 
 OPTICKS 
 
 •. 
 
 ^k r^, ^ ^ ^ ^ & ^ ^ ^ ^. ^ gk ^ & ^-. & ^''^\'l' ^ r^ p 
 
 PART I. 
 
 •g? ^ ^ # ^ # ^^^^^(^^^•^■^^•jp^'^^^^^'ii? 
 
 Qbfervations concerning the Inflexions of the, 
 Rays of Light, and the Colours made thereby. 
 
 IRIMAL'DO has inform'd us, that 
 ff^l ^ W& if a beam of the Sun's Light be let in- 
 P to a dark Room through a very fmali 
 i hole, "the Shadows of things in this 
 Light will be larger than they ought to be if 
 ^he Rays went on 'py the Bodies in f trait Lines, 
 
 and 
 
[ 253 ] 
 
 and that thefe Shadows have three parallel 
 Fringes, Bands or Ranks of colour'd Light ad- 
 jacent to them. But if the Hole be enlarged 
 the Fringes grow broad and run into one ano- 
 ther, fo that they cannot be diflinguifli'd. Thefe 
 broad Shadows and Fringes have been rcckon'd 
 by fonie to proceed from the ordinary refra- 
 ction of the Air, but without due examination 
 of the Matter. For the circumftances of tha 
 Phaenomenon , fo far as I have obferved them, 
 are as follows. 
 
 Obf. I. I made in a piece of Lead a fmall 
 Hole with a Pin, whofe breadth was the 42d 
 part of an Inch. For 21 of thofe Pins laid to- 
 gether took up the breadth of half an Inch. 
 Through this Hole I let into my darken'd 
 Chamber a beam of the Sun's Light, and found 
 that the Shadows of Hairs, Thred, Pins, Straws, 
 and fuch Uke llender Subftances placed in this 
 beam of Light, were confiderably broader than 
 they ought to be , if the Rays of Light pafTed 
 on by thefe Bodies in right Lines. And parti- 
 cularly a Hair of a Man's Head, whofe breadth 
 was but the 280th part of an Inch, being held 
 in this Light , at the diltance of about twelve 
 Feet from the Hole, did call a Shadow which 
 at the diilance of four Inches from the Hair 
 was the fixtieth part of an Inch broad, that is, 
 above four times broader than the Hair, and at 
 the diilance of two Feet from the Flair was a- 
 bout the eight and twentieth part of an Inch 
 broad, that is, ten times broader than the Hair, 
 and at the diilance of ten Feet was the eighth 
 part of an Inch broad, that is 35- times broader* . 
 
 U 3 Nor 
 
[ 294 ] 
 
 Nor is it material whether the Hair be en- 
 compaiTed with Air, or with any other pellucid 
 Subliance. For I wetted a polilh'd Plate af 
 Glais, and laid the Hair in the Water upon the 
 Glafs,, and then laying another polifli'd Plate of 
 Glais upon it, fo that the Water might fill up 
 the fpace between the Glafles , I held them in 
 the aforefaid beam of Light, (o that the Light 
 might pais through them perpendicularly, and 
 t;he Shadow of the Hair w^as at the fame di- 
 itances as big as before. The Shadows of 
 Scratches made in polilli'd Plates of Glafs were 
 alio much broader than they ought to be , and 
 the Veins in polifh'd Plates of Glafs did alfo caft 
 the like broad Shadows. And therefore the 
 great breadth of thefe Shadows proceeds from 
 fome other caufe than the Refradion of the 
 Air. 
 
 Let the Circle X [in Fig. i.1 reprefent the 
 middle of the Hair; ADG, BEH, CFl, 
 three Rays pafling by one fide of the Hair at 
 feveral diitances; KNQ, LOR, MPS, three 
 other Rays palFmg by the other fide of the Hair 
 at the like diitances ; D,E,F, and N, O, P, the 
 places where the Rays are bent in their paf- 
 fage by the Hair; G, H, I and Q, R, S, the 
 
 r laces where the Rays fall on a Paper GQ; 
 S the breadth of the Shadow of the Hair call 
 on the Paper, and TI, VS, two Rays pafTing 
 to the Points I and S without bending when 
 the Hair is taken away. And it's manifeft that 
 all the Light between thefe two Rays TI and 
 . VS is bent in pafling by the Hair, and turned 
 ofide from the Shadow I S, becaufe if any part 
 
 of 
 
[ 295 ] 
 
 df this Light were not bent it would fall on the 
 Paper within the Shadow, and there illuminate 
 the Papers .contrary to experience. And be- 
 caufe when the Paper is at a great diltance from 
 the Hair, the Shadow is broad, and therefore 
 the Rays TI and VS are at a great dif lance 
 from one another, it follows that the Hair aCls 
 upon the Rays of Light at a good -diftance iit 
 their pafling by it. But the adion is Itrongell 
 on the Rays which pafs by at leaft dillances, 
 and grows weaker and weaker accordingly as 
 the Rays pafs by at diftances greater and great- 
 er, as is reprefented in the Scheme : For thence 
 it comes to pafs, that the Shadow of the Hair 
 is much broader in proportion to the diltance 
 of the Paper from the Hair, when the Paper is 
 nearer the Hair, than when it is at a great di- 
 fiance from it. 
 
 Obf, 1. The Shadows of all Bodies (Metals^ 
 Stones, Glafs, Wood, Horn, Ice, ^c.J in this 
 Light were border'd with three parallel Fringes 
 or Bands of colour'd Light, whereof that which 
 was contiguous to the Shadow was broadeft 
 and moll luminous, and that which was remo- 
 tell from it was narrowell, and fo faint, as not 
 eafily to be vifible. It was difficult to dillinguilh 
 the Colours unlefs when the Light fell very ob- 
 liquely upon a fmooth Paper, or fome other 
 fmooth white Body, fo as to make them appear 
 much broader than they would otherwife do. 
 And then the Colours were plainly vifible in 
 this Order : The firlt or innermoft Fringe was 
 violet and deep blue next the Shadow, and then 
 light blue, green and yellow in the middle, and 
 
 U 4 red 
 
[ ^96 ] 
 
 red without. The fecond Fringe was almoft 
 contiguous to the fiiit, and the third to the fe- 
 cond , and both were blue within and yellow 
 and red without, but their Colours were very 
 faint, efpecially thole of the third. The Co- 
 lours therefore proceeded in this order from 
 the Shadow ; violet, indigo, pale blue, green, 
 yellow, red ; blue, yellow, red ; pale blue, pale 
 yellow and red. The Shadows made by Scratches 
 and Bubbles in poliih'd Plates of Glais were 
 border'd with the like Fringes of coloured Light. 
 And if Plates of Looking-glafs lloop'd off near 
 the edges with a Diamond-cut, be held in the 
 fame beam of Light, the Light which pailes 
 through the parallel Planes of the Glafs will be 
 border'd with the like Fringes of Colours where 
 thofe Planes meet with the Diamond-cut, and 
 by this means there will fometimes appear four 
 or five Fringes of Colours. Let AB, C D [in 
 Fig. 2.] reprefent the parallel Planes of a Look- 
 ing-glafs, and BD the Plane of the Diamond- 
 cut, making at B a very obtufe Angle with the 
 Plane A B. And let all the Light between the 
 Rays EN I and FBM pals directly through the 
 •parallel Planes of the Glafs, and fall upon the 
 Paper between I and M, and all the Light be- 
 tween the Rays G O and H D be refraded by 
 the oblique Plane of the Diamond-cut B D, and 
 fall upon the Paper between K and L ; and the 
 Light which pafles direftly through the parallel 
 Planes of the Glafs , and falls upon the Paper 
 between I and M, will be border'd with three 
 or more Fringes at M. 
 
 3 So 
 
[ 297 ] 
 
 So by looking on the Sun through a Feather 
 or black Riband held clofe to the Eye, leveral 
 Rain-bows will appear ; the Shadows which the 
 Fibres orThreds call on the Tunica Retina, be- 
 ing border'd with the like Fringes of Colours. 
 
 Obf 3. When the Hair was twelve Feet di- 
 Itant from this Hole, and its Shadow fell ob- 
 liquely upon a flat white Scale of Inches and 
 parts of an Inch placed half a Foot beyond it, 
 and alfo when the Shadow fell perpendicularly 
 upon the fame Scale placed nine Feet beyond 
 it ; I meafured the breadth of the Shadow and 
 Fringes as accurately as I could, and found 
 them in parts of an Inch as follows. 
 
 The 
 
[298] 
 
 At the dtfiance of 
 
 i 
 
 half a nine 
 Foot -Feet 
 
 The breadth of the Shadow 
 
 r 
 
 "* 
 
 The breadth between the Middles of 
 the brightefl: Light of the innermoft 
 Fringes on either fide the Shadow 
 
 tVoiV/ t^ 
 
 The breadth between the Middles of 
 the brightefl: Light of the raiddle- 
 mofl: Fringes on cither fide the Sha- 
 dow 
 
 I 
 
 4 
 
 The breadth between the Middles of 
 the brightefl Light of the outmofl: 
 Fringes on either fide the Shadow 
 
 I I 
 
 
 The diftance between the Middles 
 of the brightefl: Light of the firfl: 
 aiid fecond Fringes. 
 
 I 
 
 t 
 
 The diftance between the Middles 
 of the brightefl Light of the fe- 
 cond and third Fringes 
 
 t 
 
 1 
 1 
 
 7' 
 
 The breadth of the luminous part 
 (green, white, yellow and red) of 
 the firft Fringe 
 
 t 
 X 7 »' 
 
 f 
 
 The breadth of the darker Space be- 
 tween the firft and lecond Fringes 
 
 1 
 
 
 The breadth of the luminous part of 
 the fecond Fringe 
 
 I 
 
 » TT 
 
 The breadth of the darker Space be- 
 tween the lecond and third Fring;es 
 
 *7q:-r 
 
 "*T 
 
 Theie 
 
[ 299 ] 
 
 Thefe Mcafurcs I took by letting the Shadow 
 of the Hair at half a Foot diilance fall fo ob- 
 liquely on the Scale as to appear twelve times 
 broader than when it fell perpendicularly on it 
 at the fame dilbnce, and fetting down in this 
 Table the twelfth part of the Meafures I then 
 took. 
 
 Obf. 4. When the Shadow and Fringes were 
 call obliquely upon a fmooth white Body? and 
 that Body was removed farther and farther 
 from the Hair, the firft Fringe began to aippear 
 and look brighter than the reil of the Light 
 at the diftance of lefs than a quarter of an hicli 
 from the Hair, and the dark Line or Shadow 
 between that and the fecond Fringe began to 
 appear at a lefs diilance from the Hair than that 
 of the third part of an hich. The fecond Fringe 
 began to appear at a diilance from the Hair of 
 lefs than half an Inch, and the Shadow bet\^^een 
 that and the third Fringe at a diftance lefs than 
 an Inch, and the third Fringe at a diilance lefs 
 than three Inches. At greater diitances they 
 became muci» more feniible, but kept very 
 nearly the fime proportion of their breadths 
 and intervals which they had at their firil ap- 
 pearing. For the diilance between the middle 
 of the iirit and middle of the fecond Frinee, 
 was to the diilance between the middle of the 
 fecond and middle of the third Fringe, as three 
 to two, or ten to feven. And the lail of thefe 
 two diilances was equal to the bread t4i of the 
 bright Light or luminous part of the firil Fringe. 
 And this breadth was to the breadth of the 
 bright Light of the fecond Fringe as feven to 
 
 four. 
 
[ 300 ] 
 
 four, atid to the dark Interval of the firfl arid 
 fecond Fringe as three to two, and to the Hke 
 dark Interval between the fecond and third as 
 two to one. For the breadths of the Fringes 
 feem'd to be in the progrcilion of the Numbers 
 I, v" -} , y^-i , and their Intervals to be in the 
 fame progrcilion with them; that is, the Frin- 
 ges and theit' Intervals together to be in the 
 continual progrellion of the Numbers i, -v/^, V-f,- 
 '^■\-, v^Tj or thereabouts. And thefe Propor- 
 tions held the fame Very nearly at all diflances- 
 from the Hair ; the dark Intervals of the Fringes 
 being as broad in proportion to the breadth of 
 the Fringes at their. tirft appearance as after- 
 wards at great di fiances from the Hair, though 
 not fo dark and dillind. 
 
 01^/^ 5". The h'\Tn finning into my darken'd 
 Chamber through a Hole a quarter of an Inch 
 broad ; I placed at the diilance of two or three 
 Feet from the Hole a Sheet of Paftboard, which 
 was black'd all over on both fides, and in the 
 middle of it had a Hole about three quarters 
 of an Inch fquare for the Light to pafs tlu-ough. 
 And behind the Hole I falllen'd to the Pad- 
 board with Pitch the Blade of a iharp Knife, to 
 intercept fome part of the Light which pafTed 
 through the Hole. The Planes of the Paft* 
 board and Blade of the Knife were parallel to 
 one another, and perpendicular to the Rays. 
 And when they were fo placed that none of 
 the Sun's Light fell on the Paftboard, but all of 
 it palled through the Hole to the Knife, and there 
 part of it fell upon the Blade of the Knife, and 
 part of it paiTed bv its edge : I .let this part of 
 
 the 
 
[ 301 ] 
 
 the Light which pailed by, fall on a white Pa- 
 per two or three Feet beyond the Knife, and 
 there faw two ilrcams of faint Light fhoot out 
 both w^ays from the beam of Light into the flia- 
 dow like the Tails of Comets. But becaufe the 
 Sun's diredl Light by its brightnefs upon the 
 Paper obfcured thefe fliint llreams, lo that I 
 could fcarce fee them', I made a, little hole in 
 the midil of the Paper for that Light to pafs 
 through and fall on a black Cloth behind it ; 
 and then I fiw the two llreams plainly. They 
 were like one another, and pretty nearly equal 
 in length and breadth, and quantity of Light. 
 Their Light at that end next the Sun's dired: 
 Light was pretty ftrong for the fpace of about 
 a quarter of an Inch, or half an Inch, and in all 
 its progrefs from that dire(^t Light decreafed 
 gradually till it became infenfible. The whole 
 length of either of thefe llreams m^afured up- 
 on the Paper at the diltance of three Feet from 
 the Knife was about fix or eight Inches ; fo that 
 it fubtended an Angle at the edge of the Knife 
 of about lo or ii, or at molt 14 Degrees. Yet 
 fometimes I thought I law it llioot three or four 
 ]3egrees fnther, but with a Light fo very faint 
 that I could fcarce perceive it, and fufpeaed it 
 might (in fome meafure at leall) arife from 
 fome other caufe than the two ftreams did. For 
 placing my Eye in that Light beyond the end 
 of that Ib'eam which was behind the Knife, and 
 looking towards the Knife, I could fee a line of 
 Light upon its edge , and that not only when 
 my Eye was in the line of the Streams, but al- 
 fo when it was without that line either towards 
 
 the 
 
[ 302 ] 
 
 the point of the Knife, or towards the handle. 
 This hne of Light appear'd contiguous to the 
 edge of the Knife, and was narrower than the 
 Light of the innermoll Fringe, and narroweft 
 when myEye was farthefl from the dired Light, 
 and therefore feem'd to pafs between the Light 
 of that Fringe and the edge of the Knife, and 
 that which palTcd neareit the edge to be moil 
 bent, though not all of it. 
 
 Obf. 6. I placed another Knife by this, fo 
 that their edges might be parallel and look to- 
 wards one another, and that the beam of Light 
 might fall upon both the Knives, and fome part 
 of it pafs between their edges. And when the 
 diftance of their edges was about the 400th 
 part of an Inch the ih*eam parted in the mid- 
 dle, and left a Shadow between the two parts. 
 This Shadow w^as fo black and dark that all the 
 Light which palTed between the Knives feem'd 
 to be bent, and turn'd afide to the one hand 
 or to the other. And as the Knives ilill ap- 
 proached one another the Shadow grew broad- 
 er, and the Streams iliorter at their inward 
 ends which were next the Shadow, until upon 
 the contad of the Knives the whole Light va- 
 nifli'd leaving its place to the Shadow. 
 
 And hence I gather that the Light which is 
 lead: bent, and goes to the inward ends of the 
 Streams, palfes by the edges of the Knives at 
 the greatcll diilance, and this diftance when 
 the Shadow begins to appear between the 
 Streams is about the 800 part of an Inch. And 
 the Light which pafTes by the edges of the 
 Knives at diftances ftill lefs and lefs is more and 
 f more 
 
[ 303 ] 
 
 more bent, and goes to thofe parts of the 
 Streams which are farther and farther from the 
 dired Light, becaufe when the Knives approach 
 one another till they touch, thofe parts of the 
 Streams vanifli lail which are farthell from the 
 dired Light. 
 
 Oif/^ 7. In the fifth Obfervation the Fringes 
 did not appear, but by reafon of the breadth of 
 the hole in theWindow became fo broad as to run ^ 
 into one another, and by joining, to make one 
 continued Light in the beginning of the Streams. 
 But in the iixth, as the Knives approached one 
 another, a little before the Shadow appear 'd 
 between the two Streams, the Fringes began 
 to appear on the inner ends of the Streams on 
 either lide of the dired Light , three on one 
 / fide made by the edge of one Knife, and three 
 /on the other fide made by the edge of the o- 
 f ther Knife. They were diltinc^tell when the 
 Knives were placed at the greatell diftance from 
 the hole in the Window, and Itill became more 
 dillindt by making the hole lefs, infomuch that 
 I could fometimes fee a faint Lineament of a 
 fourth Fringe beyond the three above men- 
 tion'd. And as the Knives continually ap- 
 proached one another, the Fringes grew di- 
 ilinder and larger until they vaniih'd. The 
 outmoil Fringe vaniih'd firil, and the middle- 
 moll: next, and the innermoll lall. And after 
 they were all vaniili'd , and the Hne of Light 
 which was in the middle between them was 
 grown very broad, enlarging it felf on both fides 
 into the Streams of Light defcribed in the fifth 
 Obfervation, the above mentioned Shadow be- 
 gan 
 
[304] 
 
 gan to appear in the middle of this line , and 
 divide it along the middle into two lines of 
 Light, and increafed until the whole Light va- 
 niili'd. This enlargement of the Fringes was 
 fo great that the Rays which go to the inner- 
 molt Fringe feem'd to be bent above twentv 
 times more when this Frijige was ready to va- 
 niih, than when one of the Knives was taken 
 away. 
 
 And from this and the former Obfervation 
 compared, I gather, that the Light of the firit 
 Fringe palled by the edge of the Knife at a di- 
 llance greater than the ^ooth part of an Inch, 
 and the Light of the fecond Fringe palled by 
 the edge of the Knife at a greater diflance than 
 the Light of the lirll: Fringe did , and that of 
 the third at a greater diflance than that of the 
 fecond , and that of the Streams of Light de- 
 fcribed in the fifth and fixth Obfervations paf- 
 fed by the edges of the Knives at lefs diflances 
 than that of any of the Fringes. 
 
 Obf.%. I caufed the edges of two Knives 
 to be ground truly ftrait , and pricking their 
 points into a Board fo that their edges might 
 look towards one another, and meeting near 
 their points contain a redilinear Angle, I f iften'd 
 their Handles together with Pitch to make this 
 Angle invariable. The diflance of the edges of 
 the Knives from one another at the diflance of 
 four Inches from the angular Point, where the 
 edges of the Knives met , was the eighth part 
 of an Inch, and therefore the Angle contain'd 
 by the edges, was about i Degree 5-4 , The 
 Knives thus fix'd together I placed in a beam 
 
 of 
 
[ 305 ] 
 
 of the Sun's Light, let into my darkened Cham- 
 ber through a hole the 4id part of an Inch 
 wide, at the diltance of loor 15- Feet from the 
 hole, and Tet the Light which palled between 
 their edges fall very obliquely upon a imooth 
 white Ruler at the diilance of hair an Inch, or 
 an Inch from the Knives, and there law the 
 Fringes made by the two edges of the Knives 
 run along the edges of the Shadows of the 
 Knives in lines parallel to thofe edges without 
 growing fenfibly broader , till they met in An- 
 gles equal to the Angle contained by the edges 
 .of the Knives, and where they met and joined 
 they ended without eroding one another, but 
 if the Ruler was held at a much greater di- 
 ltance from the Knives, the Fringes where they 
 were farther from the place of their meetings 
 were a little narrower, and became fomcthing 
 broader and broader as they approach'd nearer 
 and nearer to one another, and after they met 
 they crofs'd one another, and then became much 
 broader than before. 
 
 Whence I gather that the diftances at which 
 the Fringes pafs by the Knives are not increa- 
 fed nor alter'd by the approach of the KniveSji 
 but the Angles in which the Rays are there bent 
 are much increafed by that approach ; and that 
 the Knife which is neareft any Ray determines 
 which way the Ray Ihall be bent, and the other 
 Knife increafes the bent. 
 
 Obf. <). When the Rays fell very obliqueiy 
 upon the Ruler at the dillance of the third part' 
 of an Inch from the Knives , the dark line be- 
 tween the tirit and fecond Fringe of the Sha- 
 
 X- dovr 
 
 k 
 
[ 3o^] 
 
 dovv of one Knife, and the dark line between 
 the fiiit and fecond Fringe of the Shadow of 
 the other Knife met with one another, at the 
 diltance of the fifth part of an Inch from the 
 end of the Light which palfed between the 
 Knives at the concourfe of their edges. And 
 therefore the dilfance of the edges of the Knives 
 at the meeting of thefe dark lines was the i6oth 
 part of an Inch. For as four Inches to the 
 eighth part of an Inch , fo is any length of the 
 edges of the Knives meafured from the point 
 of their concourfe to the diftance of the edges 
 of the Knives at the end of that length, and fO' 
 is the fifth part of an Inch to the i6oth part. 
 So then the dark lines above mention'd meet 
 in the middle of the Light which palfes be- 
 tween the Knives where they are diftant the 
 i6oth part of an Inch, and the one half of that 
 Light palFes by the edge of one Knife at a di- 
 ftance not greater than the 3ioth part of an 
 Inch, and falling upon the Paper makes the 
 Fringes of the Shadow of that Knife, and the 
 other half pafTes by the edge of the other Knife, 
 at a diltance not greater than the 310th part of 
 an Inch, and falling upon the Paper makes the 
 Fringes of the Shadow of the other Knife. But 
 if the Paper be held at a dillance from the 
 Knives greater than the third part of an Inch, 
 the dark lines above mention'd meet at a great- 
 er dillance than the fifth part of an Inch from 
 the end of the Light which pafled between the 
 knives at the concourfe of their edges ; and 
 therefore the Light which falls upon the Paper 
 where thofe dark lines meet palles between the 
 
 Knives 
 
[ 307 ] 
 
 Knives where their edges are diitant above the 
 i6oth part of an Inch. 
 
 For at another time vi^hen the two Knives 
 were diflant eight Feet and five Inches from 
 the Httle hole in the Window, made Vvith a 
 fmall Pin as above, the Light which fell upon 
 the Paper where the aforefaid dark lines' met, 
 pafled between the Knives, where the diilance 
 between their edges was as in the following 
 Table , when the diliance of the Paper from 
 the Knives was alfo as follows. 
 
 "DiJIances of theTaJ^er T>ijiances bet^^xjeen the 
 
 edges of the Knives 
 in mi lie Jim al parts of 
 an Inch. 
 
 from the Knives in 
 Inches. 
 
 O OIX 
 0'020 
 
 o'o34 
 ooSJ 
 o'o8i 
 o'o87 
 
 And hence I gather that the Light which 
 makes the Fringes upon the Paper is not the 
 fame Light at all diitances of the Paper from 
 the Knives, but when the Paper is held near 
 the Knives, the Fringes are made by Light 
 which paffes by the edges of the Knives at a 
 lefs diilance, and is more bent than when the 
 Paper is held at a greater diftance from the 
 Knives. 
 
 X X Obf 
 
[ 3o8 1 
 
 Obf. lo. When the Fringes of the Shadows 
 of the Knives fell perpendicularly upon a Paper 
 at a great diilance from the Knives, they were 
 in the form of Hyperbolas, and their Dimen- 
 fions wTre as follows. Let C A, C B [in Fig. 3.] 
 reprefent lines drawn upon the Paper parallel 
 to the edges of the Knives, and between which 
 all the Light would fall, if it palled between 
 the edges of the Knives without inflexion ; DE 
 a right hne drawn through C making the An- 
 gles A CD, BCE, equal to one another, and 
 terminating all the Light which falls upon the 
 Paper from the point where the edges of the 
 Knives meet ; e i s, f k t, and g I v., three hy- 
 perbolical lines reprefenting the Terminus of 
 the Shadow of one of the Knives, the dark line 
 between the firil and fecond Fringes of that 
 Shadow, and the dark hne between the fecond 
 and third Fringes of the fame Shadow ; x i/,jy k q 
 and%/r, three other hyperbolical lines repre- 
 fenting theTerminus of the Shadow of the other 
 Knife, the dark line between the firft and fecond 
 Fringes of that Shadow, and the dark Hne be- 
 tween the fecond and third Fringes of the fame 
 Shadow. And conceive that theie three Hyper- 
 bolas are like and equal to the former three, and 
 crofs them in the points /, k and /, and that the 
 Shadows of the Knives are terminated and diilin- 
 guifh'd from the firit luminous Fringes by the 
 lines ei s and x i/, until the meeting and crof- 
 fing of the Fringes, and then thofe lines crofs 
 the Fringes in the form of dark lines, termina- 
 ting the firft luminous Fringes within fide, and 
 diftinguifliing them from another Light which 
 
 begins 
 
[309] 
 
 begins to appear at /', and illuminates all the 
 triarlgular ipace //DE s comprehended by thcfe 
 dark lines, and the ri- ht hne D E. Of theie 
 Hyperbolas one Alymptote is the lineDE, and 
 their other Al'ymptotes are parallel to the lines 
 C A and CB. Let rv rcprefent a Hne drawn 
 any where upon the Paper parallel to the Alym- 
 ptote DE, and let this line crofs the right lines 
 AC in ?« and BC in //, and the. fix dark hy- 
 perbolical lines in />, ^, r ; s,f,v; and bv mea- 
 suring; the diilances/j-, qt, rv ^ and thence 
 collecting the lengths of the Ordinates ;//, // q, 
 nr or ms, mt^ mv, and doing this at feveral 
 diltances of the line r v from the Afymptote 
 DD, you may find as many points of thefe Hy- 
 perbolas as you plcafe, and thereby know that 
 thcfe curve lines are Hyperbolas differing little 
 from the conical Hyperbola. And by meafur- 
 ing the lines C /', Ci, C/, you may find other 
 points of thefe Curves. 
 
 For inftance, when the Knives were diftant 
 from the hole in theWindovv ten Feet, and the 
 Paper from the Knives nine Feet, and the An- 
 gle contained by the edges of the Knives to 
 which the Angle ACB is equal, was lubrend- 
 ed by a Chord which was to the Radius as i 
 to 32, and the dillance of the line r.v from the 
 Afymptote DE was half an Inch: I mcafured 
 the lines / J- , qt^ rv, and found them o'35', 
 0*65', o'9 8 Inches refpedively, and by adding 
 to their halfs the line \mn { which here wa? 
 the ixSthpart of an Inch, or o'oojS Inches) the 
 Sums ;//, nq^ nr, were o'i8x8, o'3328, 0*4978 
 Inches. I meafured alfo the diitances of the 
 
 X 3 brighteft 
 
[ 3IO ] 
 
 brightefl parts of the Fringes which run be- 
 tween / q and st^ qr and t v, and next beyond 
 r and ^', and found them oV, o'8, and I'l 7 Inches. 
 Obf. II. The Sun ihining into my darken'd 
 Room through a fraall round hole made in a 
 Plate of Lead with a flender Pin as above ; I 
 placed at the hole a Prifm to refract the Light, 
 and form on the oppofite Wall the Spedrum 
 of Colours, defcribed in the third Experiment 
 of the firfl Book. And then 1 found that the 
 Shadows of all Bodies held in the colour'd 
 Light between the Prifm and the Wall, were 
 border'd with Fringes of the Colour of that 
 Light in which they were held. In the full red 
 Light they were totally red without any fenfi- 
 ble blue or violet , and in the deep blue Light 
 they w^ere totally blue without any feniible red 
 or yellow ; and lb in the green Light they ^ere 
 totally green, excepting a little yellow and blue, 
 which were mix'd in the green Light of the 
 Prifm. And comparing the Fringes made in 
 the feveral colour'd Lights, I found that thofe 
 made in the red Light where largeit, thofe 
 made in the violet were leafl, and tho:e made 
 in the green were of a middle bignefs. lor 
 the Fringes with which the Shadow of a Man's 
 Hair were border'd, being meaiured crofs the 
 Shadow at the diflance of fix Inches from the 
 Hair ; the diflance between the middle and molt 
 luminous part of the firft or innermolf Fringe 
 on one fide of the Shadow, and that of the like 
 Fringe on the other fide of the Shadow was in 
 
 the full red Light ^. of an Inch, and in the full 
 
 violet 
 
[3ii] 
 
 violet -v^. And the like diftance between the 
 middle and moll luminous parts of the fecond 
 Fringes on either lide the Shadow was in the 
 full red Light A-, and in the violet ^r^ of an 
 Inch. And thefe diltances of the Fringes held 
 the fame proportion at all diltances from the 
 Hair without any fenfible variation. 
 
 So then the Rays which made thefe Fringes 
 in the red Light palfed by the Hair at a greater 
 diftance than thofe did which made the like 
 Fringes in the violet ; and therefore the Hair 
 in caufmg thefe Fringes aded alike upon the 
 red Light or leaft refrangible Rays at a greater 
 dilbnce, and upon the violet or moil refrangi- 
 ble Rays at a lefs. diltance, and by thofe adions 
 difpoled the red Light into larger Fringes, and 
 the violet into fmaller, and the Lights of inter- 
 mediate Colours into Fringes of intermediate 
 bignelTes without changing the Colour of any 
 fort of Light. 
 
 When therefore the Hair in the firfl and fe- 
 cond of thefe .Obfervations was held in the 
 white beam of the Sun's Light, and call a Sha- 
 dow which was border 'd with three Fringes of 
 colour'd Light , thofe Colours arofe not from 
 any new modifications imprefs'd upon the Rays 
 of Light by the Hair, but only from the vari- 
 ous intlexions whereby the feveral forts of Rays 
 were feparated from one another, which before 
 feparation by the mixture of all their Colours, 
 compofed the white beam of the Sun's Light, 
 but whenever feparated compofe Lights of the 
 feveral Colours which they are originally dilpo- 
 fed to exhibit. In this iithObfervation, where 
 
 X 4 the 
 
[312] 
 
 the Colours are feparated before the Light paf- 
 fe by the Kair, the leait refrangible Rays, which 
 when leparaied from the rclt make red, were 
 intleded at a greater diitance from the Hair, fo 
 as to make three red Fringes at a greater di- 
 ilance from the middle of the Shadow of the 
 Hair ; and the moil refrangible Rays which 
 when feparated make violet , were infie^led at 
 a lefs diilance from the Hair, fo as to make 
 three violet Fringes at a lefs diilance from the 
 middle of the Shadow of the Hair. And other 
 Rays of intermediate degrees of Refrangibility 
 were infleded at intermediate diltances from 
 the Hair, fo as to make Fringes of intermediate 
 Colours at intermediate.dillanccs from the mid- 
 dle of the Shadow of the Hair. And in the 
 fecond Obfervation, where all the Colours are 
 mi>'d in the white Light which palfes by the 
 Hair, thefe Colours are feparated by the vari- 
 ous inflexions of the Rays , and the Fringes 
 which they make appear all together, and the 
 innermoft Fringes being contiguous make one 
 broad PMnge compofed of all the Colours in 
 due order, the violet lying on the infide of the 
 Fringe next the Shadow , the red on the out- 
 fide fartheil from the Shadow, and the blue, 
 green and yellow, in the middle. And, in Hke 
 manner, the middlemoft Fringes of all the Co- 
 lours lying in order, and being contiguous, 
 make another broad Fringe compofed of all the 
 Colours; and the outmoll Fringes of all the 
 Colours lying in order, and being contiguous, 
 make a third broad Fringe compofed of all the 
 Colours, Thefe are the three Fringes of co- 
 loured 
 
[ 313 ] 
 
 lour'd Light with which the Shadows of all 
 Bodies are border'd in the fecond OHfervation. 
 
 W hen I made the foregoing Obfervations, I 
 defign'd to repeat moil of them with more care 
 and exadnefs, and to make fome new one$ for 
 determining the manner how the Rays of Light 
 are bent in their paflage by Bodies for making 
 the Fringes of Colours with the dark lines be- 
 tween them. But I was then interrupted, and 
 cannot now think of taking thefe things into 
 farther confideration. And lince I liave not li- 
 nifh'd this part of my Delign, I iliall conclude, 
 with propofing only fome Queries in order to a 
 farther fearch to be made by others. 
 
 ^fery i. Do not Bodies ad: upon Light at 
 a diitance, and by their adion bend its Rays, 
 and is not this action (cateris p/iribus) llrong- 
 ell at the Icalt diliance ? 
 
 ^i. 2. Do not the Rays which differ in Re- 
 frangibility ditFer alfo in Flexibility, and are 
 they not by their different Inflexions feparated 
 from one another, fo as after feparation to make 
 the Colours in the three Fringes above defcri- 
 bed .' And after what manner are they infle6l- 
 ed to make thofe Fringes? 
 
 ^/. 3. Are not the Rays of Light in pafling 
 by the edges and fides of Bodies , bent feveral 
 times backwards and forwards, with a motion 
 like that of an Eel ? And do not the three Frin- 
 ges of colour 'd Light above mention'd, arife 
 from three fuch bendings .^ 
 
 ^//. 4. Do not the Rays of Light which fall 
 Upori Bodies, and are refleded or refradled, be- 
 gin 
 
gin to bend before they arrive at the Bodies ; 
 and are th'ey not refleded, refraded and in- 
 fleded by one and the fame Principle, ading 
 varioufly in various Circumitances ? 
 
 ^t. $. Do not Bodies and Light aft mutu- 
 ally upon one another, that is to fay. Bodies 
 upon Light in emitting, refleding, refrading 
 arid inileding it, and Light upon Bodies for 
 heating them, and putting their parts into a vi- 
 brating motion wnerein heat coniiils ? 
 
 §lu. 6. Do not black Bodies conceive heat 
 more eafily from Light than thole of other Co- 
 lours do, by reafon that the Light falling on 
 them is not refleded outwards, but enters the 
 Bodies, and is often reflected and refracled 
 within them, until it be llifled and loit ? .j 
 
 ^/. 7. Is not the ftrength and vigour of the ' 
 aftion between Light and fulphureous Bodies 
 obferved above, one reafon why fulphureous 
 Bodies take fire more readily, and burn more 
 vehemently, than other Bodies do ? 
 
 ^. 8. Do not all tix'd i^odies when heated 
 beyond a certain degree, emit Light and fhine, 
 and is not this Emillion performed by the vi- 
 brating Motions of their parts ? And do not all 
 Bodies which abound with terreltrial parts, and 
 efpecially with fulphureous ones, emit Light 
 as often as thofe parts are fufficiently agitated ; 
 whether that agitation be made by Heat, or by 
 Fridion, or Percullion, or Putrefadion, or by 
 any vital Motion, or any other Caufe ? As for 
 inltance ; Sea Water in a raging Storm ; Quick- 
 filver agitated in vacuo ; the Back of a Cat, or 
 Neck of a Horfe obliquely Ih'uck or rubbed in 
 
 a dark 
 
[315] 
 
 a dark place ; Wood, Flefli and Fifli while they 
 putrefy; Vapours arifing from putrefy 'd Wa- 
 ters, ufually call'd J^nesFatui^ Stacks of moilt 
 Hay or Corn grovv'^ing hot by fermentation ; 
 Glow-worms and the Eyes of fome Animals by 
 vital Motions ; the vulgar Thof^horus agitated 
 by the attrition of any Body, or by the acid 
 Particles of the Air; Ambar and fome Dia- 
 monds by llriking, preffing or rubbing them ; 
 Scrapings of Steel Itruck off with a Flint ; Iron 
 hammer'd very nimbly till it become fo hot as 
 to kindle Sulphur thrown upon it ; the Axle- 
 trees of Chariots taking fire by the rapid rota- 
 tion of the W heels ; and fome Liquors mix'd 
 with one another whofe Particles come toge- 
 ther with an Impetus, as Oil of Vitriol diililled 
 from its weight of Nitre, and then mix'd with 
 twice its weight of Oil of Annifeeds. So alfo a 
 Globe of Glais about 8 or lo Inches in diameter, 
 being put into a Frame vvhere it maybe fwift- 
 ly turn'd round its Axis, will in turning fliine 
 where it rubs againll the palm of ones Hand 
 apply'd to it: And if at the fame time a piece 
 of white Paper or white Cloth, or the end of 
 ones Finger be held at the diftance of about a 
 quarter of an Inch or half an Inch from that 
 part of the Glafs where it is moil in motion, 
 the eleftrick Vapour which is excited by the 
 friction of the Glafs againft the Hand, will by 
 dafliing againit the white Paper, Cloth or Fin- 
 ger, be put into fuch an agitation as to emit 
 Light, and make the white Paper, Cloth or Fin- 
 ger, appear lucid like a Glow-worm ; and in 
 rufliing out of the Giafs will fometimes pufh 
 
 againft 
 
[31^] 
 
 againft the Finger fo as to be felt. And the 
 fame things have been found by rubbing a long 
 and large Cylinder of Glafs or Ambar with a Pa- 
 per held in ones hand, and continuing the fri- 
 dion till the Glafs grew warm. 
 
 §lu. 9. Is not Fire a Body heated fo hot as to 
 emit Light copiouily ? For what elfe is a red 
 hot Iron than Fire ? And what elfe is a burning 
 Coal than red hot Wood ? 
 
 G^t. 10. Is not Flame a Vapour, Fume or Ex- 
 halation heated red hot, that is, fo hot as to 
 ihine? For Bodies do not flame without emit- 
 ting a copious Fume, and this Fume burns in 
 the Flame. The IgnU Fatiim is a Vapour fhi- 
 ning without heat, and is there not the fame 
 difference between this Vapour and Flame , as 
 between rotten Wood lliining without heat and 
 burning Coals of Fire ? In dillilling hot Spirits , 
 if the Head of the Still be taken off, the Va- 
 pour which afcends out of the Still will take fire 
 at the Flame of a Candle, and turn into Flame, 
 and the Flame will run along the Vapour from 
 the Candle to the Still. Some Bodies heated by 
 Motion or Fermentation , if the heat grow in- 
 tenfe, fume copiouily, and if the heat be great 
 enough the Fumes will fhine and become Flame. 
 Metals in fufion do not flame for want of a co- 
 pious Fume, except Spelter, which fumes co- 
 piouily, and thereby flames. All flaming Bo- 
 dies, as Oil, Tallow, Wax, Wood, fofTil Coals, 
 Pitch, Sulphur, by flaming wafte and vanifh in- 
 to burning Smoke, which Smoke, if the Flame 
 be put out, is very thick and vifible, and fome- 
 times fmells ilrongly, but in the Flame lofes its 
 
 fmell 
 
[ 317 ] 
 
 fmell by burning, and according to the nature 
 of the Smoke the Flame is of leveral Colours, 
 as that of Sulphur blue, that of Copper open'd 
 with fublimate green, that of Tallow yellow, 
 that of Camphire white. Smoke pafling through 
 Flame cannot but grow red hot, and red hot 
 Smoke can have no other appearance than that 
 of Flame. When Gun-powder takes tire, it 
 goes away into flaming Smoke. For the Char- 
 coal and Sulphur eafily take fire, and fet fire to 
 the Nitre, and the Spirit of the Nitre being 
 thereby rarified into Vapour, rulhcs out with 
 Exploiion much after the manner that the Va- 
 pour of Water rufhes out of an a£ohpile ; the 
 Sulphur alfo beings volatile is converted into 
 Vapour, and augments the Exploiion. And 
 the acid Vapour of the Sulphur (namely that 
 which diftils under a Bell into Oil of Sulphur,) 
 entring violently into the fix't Body of the Ni- 
 tre, fets loofe the Spirit of the Nitre, and ex- 
 cites a great Ferm.entation, whereby the Heat 
 is farther augmented, and the tix'd Body of the 
 Nitre is alfo raritied into Fume, and the Explo- 
 iion is thereby made more vehement and quick. 
 For if Salt of Tartar be mix'd with Gun-povi^- 
 der , and that Mixture be warm'd till it takes 
 fire, the Exploiion will be more violent and 
 quick than that of Gun-powder alone ; which 
 cannot proceed from any other caufe than the 
 aciion of the V apour of the Gun-powder upon 
 the Salt of Tartar, whereby that Salt is rarihed. 
 TheExplofion of Gun-powder arifes therefore 
 from the violent adion whereby all the Mixture 
 being quickly and vehemently heated, is rarified 
 
 and 
 
.[318] 
 
 and converted into Fume and \ apour : which 
 ,\ apour , by the violence of that adion , be- 
 coming fo hot as to ihinc, appears in the form 
 of Flame. 
 
 ^^.11. Do not great Bodies conferve their 
 heat the longeil, their parts heating one ano- 
 ther , and may not great denfe and fix'd Bo- 
 dies, when heated beyond a certain degree, e- 
 mit Light fo copioufly, as by theEmiflion and 
 Re-adion of its Light, and the Reflexions and 
 Refractions of its Rays within its Pores to grow 
 ftill hotter , till it comes to a certain period of 
 , heat, fuch as is that of the Sun ? And are not 
 the Sun and fix'd Stars great Earths vehemently 
 hot, whofe heat is conferved by the greatnefs 
 of the Bodies, and the mutual Adion and Re- 
 adion between them, and the Light which they 
 emit, and whofe parts are kept from fuming a- 
 way, not only by their fixity, but alfo by the 
 vaft weight and denfity of the Atmofpheres in- 
 cumbent upon them , and very ftrongly com- 
 prefling them, and condenfing the Vapours and 
 Exhalations which arife from them? For if 
 Water be made warm in any pellucid VefTel 
 emptied of Air, that Water in the Vacuum will 
 bubble and boil as vehemently as it would in 
 the open Air in a Veflcl fet upon the Fire till 
 it conceives a much greater heat. For the 
 weight of the incumbent Atrnofphere keeps 
 down the Vapours, and hinders the Water from 
 boiling, until it grow much hotter than is re- 
 quifite to made in boil in vacuo, Alfo a mix- 
 ture of Tin and Lead being put upon a red hot 
 Iron in vacuo emits a Fume and Flame, but the 
 
 fame 
 
r 319 1 
 
 fame Mixture in the open Air, byreafon of the 
 incumbent Atmofphere, does not fo much as e- 
 mit any Fume which can be perceived by Sight. 
 In Hke manner the great weight of the Atmo- 
 fphere which lies upon the Globe of the Sun 
 may hinder Bodies there from rifmg up and 
 going away from the Sun in the form of W 
 pours and Fumes, unlefs by means of a far 
 greater heat than that which on the Surface of 
 our Earth would very eafily turn them into Va- 
 pours and Fumes. Aixl the fame great weight 
 maycondenfe thofe Vapours and Exhalations as 
 foon as they ihall at any time begin to afcend 
 from the Sun, and make them prefently fall 
 back again into him, and by that adion increale 
 his Heat much after the manner that in our 
 Earth the Air increafes the Heat of a cuHnary 
 Fire. And the lame weight may hinder the 
 Globe of the Sun from being diminifh'd, unlefs 
 by the Emiflion of Light, and a very fmall quan- 
 tity of Vapours and Exhalations. 
 
 ^t. 12. Do not the Rajs of Light in falling 
 upon the bottom of the Eye excite Vibrations 
 in the Tunica Retina ? Which Vibrations, be- 
 ing propagated along the folid Fibres of the op- 
 tick Nerves into the Brain , caufe the Senfe of 
 feeing. For becaufe denfe Bodies conferve their 
 Heat a long time, and the denfefl Bodies con- 
 ferve their Heat the longed, the Vibrations of 
 their parts are of a lading nature, and there- 
 fore may be propagated along folid Fibres of 
 uniform denfe Matter to a great diftance, for 
 conveying into the Brain the impreffions made 
 upon all the Organs of Senfe. For that Motion 
 
 which 
 
[ 32q] 
 
 which can continue long in one and the faiiid 
 part of a Body, can be propagated a long way 
 from one part to another, fuppoling the Body 
 homogeneal, fo that the Motion may not be re- 
 fle^led, refracted, interrupted or dilbrder'd by 
 any unevennefs of the Body. 
 
 ^. 13. Do not feveral forts of Rays make 
 Vibrations of feveral bignefles, which according 
 to their bignefTes excite Senfations of feveral 
 Colours, much after the-manner that the Vibra- 
 tions of the Air, according to their feveral big- 
 nelTes excite Senfations of feveral Sounds? And 
 particularly do not the moft refrangible Rays 
 excite the lliorteft Vibrations for making aSen- 
 fation of deep violet, the leatt refrangible the 
 largeft for making a Senfation of deep red, and 
 the feveral intermediate forts of Rays , Vibra- 
 tions of feveral intermediate bignefles to make 
 Senfations of the feveral intermediate Colours ? 
 
 ^/. 14. May not the harmony and difcord 
 of Colours arife from the proportions of the 
 Vibrations propagated through the Fibres of 
 the optick Nerves into the Brain, as the harmo- 
 ny and difcord of Sounds arife from the pro- 
 portions of the Vibrations of the Air? For 
 fome Colours, if they be view'd together, are 
 agreeable to one another, as thofe of Gold and 
 Indigo, and others difagree. 
 
 ^. 15-. Are not the Species of Objects feen 
 with both Eyes united where the optick Nerves 
 meet before they come into the Brain, the Fi- 
 bres on the right fide of both Nerves uniting 
 there, and after union going thence into the 
 Brain in the Nerve which is on the right fide of 
 
 the 
 
i 321 ] 
 
 the Head, and the Fibres on the left fide of 
 both Nerves uniting in the fame place, and af- 
 ter union going into the Brain in the Nerve 
 which is on the left fide of the Head, and thefe 
 two Nerves meeting in the Brain in fuch a man- 
 ner that their Fibres make but one entire Spe- 
 cies or Picture, half of which on the right fide 
 of the Senforium comes from the right fide of 
 both Eyes through the right fide of both op- 
 tick Nerves to the place where the Nerves meetj 
 and from thence on the right fide of the Head 
 into the Brain, and the other half on the left 
 fide of the Senforium comes in like manner 
 from the left fide of both Eyes. For the op- 
 tick Nerves of fuch Animals as look the fame 
 way with both Eyes (as of Men, Dogs, Sheep, 
 Oxen, &c.) meet before they come into the 
 Brain, but the optick Nerves of fuch Animals 
 as do not look the fime way with both Eyes 
 (as of Fiflies and of the Chameleon) do not 
 meet, if I am rightly inform'd. 
 
 ^.16. When aMan in the dark prefTes either* 
 corner of his Eye with his Finger, and turns his 
 Eye away from his Finger, he will fee a Circle 
 of Colours Hke thofe in the Feather of a Pea- 
 cock's Tail. If the Eye and the Finger remain 
 quiet thefe Colours vaniih in a fecond Minute of' 
 Time, but if the Finger be moved with a qua- 
 vering Motion they appear again. Do not thefe 
 Colours arife from fuch Motions excited in the 
 bottom of the Eye by the Preifure and Motion 
 of the Finger, as at other times are excited 
 there by Light for caufing Vifion ? And do not 
 the Motions once excited continue about a Se- 
 
 Y Gond 
 
[ 322 ] 
 
 cond of Time before they ceafe ? And when a 
 Man by a ftroke upon his Eye fees a flafli of 
 Light, are not the Hke Motions excited in the 
 Retina by the ilroke ? And when a Coal of Fire 
 moved nimbly in the circumference of a Cir- 
 cle, makes the whole circumference appear hke 
 a Circle of Fire : Is it not becaufe the Motions 
 excited in the bottom of the Eye by the Rays 
 of Light are of a lading nature, and continue 
 till the Coal of Fire in going round returns to 
 its former place? And confidering the lafting- 
 nefs of the Motions excited in the bottom of 
 the Eye by Light , are they not of a vibrating 
 nature ? 
 
 ^/. 17. If a Stone be thrown into ftagnating 
 Water, the Waves excited thereby continue 
 fome time to arife in the place where the Stone 
 fell into the Water, and are propagated from 
 thence in concentrick Circles upon the Surface 
 of the Water to great diflances. And the Vi- 
 brations or Tremors excited in the Air by per- 
 cuflion, continue a Httle time to move from the 
 place of percuflion in concentrick Spheres to 
 great diflances. And in like manner, when a 
 Ray of Light falls upon the Surface of any pel- 
 lucid Body, and is there refraded or reflec^fed : 
 may not Waves of Vibrations, or Tremors, be 
 thereby excited in the refrading or refleding 
 Medium at the point of Incidence, and continue 
 to arile there, and to be propagated from thence 
 as long as they continue to do fo, when they are 
 excited in the bottom of the Eye by the Pref- 
 fure or Motion of the Finger, or by the Li^ht 
 which comes from the Coal of Fire in the Ex- 
 periments 
 
[ 323 ] 
 
 periments above mention'd ? And are not thefe 
 Vibrations propagated from the point of Inci- 
 dence to great dilbnces? And do they not o- 
 vertake the Rays of Light, and by overtaking 
 them fucceliively, do they not put them into 
 the Fits of cafy Reflexion and ealy Tranfmiifion 
 defcribed above ? For if the Rays endeavour to 
 recede from the denfeil part of the \ ibration, 
 they may be alternately accelerated and retard- 
 ed by the Vibrations overtaking them. 
 
 ^{. 1 8. If in two large tall cyhndrical Vef^ 
 fels of Glafs inverted, two Httle Thermometers 
 be fufpendcd fo as not to touch the Veifels, and 
 the Air be drawn out of one of thefe Vellels^ 
 and thefe Velfels thus prepared be carried out 
 of a cold place into a \^'arm one ; the Thermo- 
 meter /;/ vacuo will grow warm as much, and 
 almolt as foon as the Thermometer which is 
 not /// vacuo. And when the V'eifels are carri- 
 ed back into the cold place, the Thermometer 
 i« vacuo will grow cold almolt as foon as the 
 other Thermometer. Is not the Heat of the 
 warm Room convey'd through the Vacuum by 
 the Vibrations of a much fubiiler Medium than 
 Air, which after the Air was drawn out remain* 
 ed in the Vacuum ? And is not this Medium the 
 fame with that Medium by which Light is re- 
 fraded and relle^led, and by whofe \' ibrarions 
 Light communicates Heat to Bodies , and is 
 put into Fits of ealy Rerlc^xion and eafyTranf-- 
 mifTion ? And do not the Vibrations of this Me- 
 dium in hot Bodies contribute to the intenfenefs 
 and duration of their Heat ? And do not hot 
 Bodies communicate their Heat to contiguous 
 
 Y 2, cold 
 
[ 324- ] 
 
 cold ones , by the V ibrations of this Medium 
 propagated from them into the cold ones ? And 
 is not this Medium exceedingly more rare and 
 fubtile than the Air, and exceedingly more ela- 
 llick and adive ? And doth it not readily per- 
 vade all Bodies? And is it not (by its elalUck 
 force) expanded through all the Heavens ? 
 
 §u. 19. Doth not the Refraction of Light 
 proceed from the different denlity of this ^Ethe- 
 real Medium in different places, the Light re- 
 ceding always from the denfer parts of the Me- 
 dium ? And is not the denfity thereof greater 
 in free and open Spaces void of Air and other 
 groller Bodies, than within the Pores of Wa- 
 ter, Glafs, Cryftal, Gems, and other compa6t 
 Bodies? For when Light paffes through Glafs 
 or Cryftal, and flilling very obliquely upon the 
 fln'ther Surface thereof is totally refleded, the 
 total Reliexion ought to proceed rather from 
 the denfity and vigour of the Medium without 
 and beyond the Glafs, than from the rarity and 
 weaknefs thereof. 
 
 ^/. 20. Doth not this ^Ethereal Medium in 
 palling out of Water, Glafs, Cryftal, and other 
 compact and denfe Bodies into empty Spaces, 
 grow denier and denfer by degrees, and by 
 that means refrad the Rays of Light not in a 
 point, but by bending them gradually in curve 
 Lines? And doth not the gradual condenfa- 
 tion of this Medium extend to fome^ diftance- 
 from the Bodies, and thereby caufe the Infle- 
 xions of the Rays of Light, which pafs by the 
 edges of denfe Bodies, at fome diftance from 
 the Bodies ? 
 
[325] 
 
 ^//. II. Is not this Medium much rarer with- 
 in the denfe Bodies of the Sun, Stars, Planets 
 and Comets, than in the empty celclUal Spaces 
 between them ? And in paiFmg from them to 
 great difhnces, doth it not grow denfer and 
 denfer perpetually, and thereby caufe the gra- 
 vity of thole great Bodies towards one another, 
 and of their parts towards the Bodies; every 
 Body endeavouring to go from the denier parts 
 of the Medium towards the rarer ? For if this 
 Medium be rarer within the Sun's Body than at 
 its Surface, and rarer there than at the hun- 
 dredth part of an Inch from its Body, and ra- 
 rer there than at the fiftieth part of an Inch from 
 its Body, and rarer there than at the Orb of 
 SaUirn ; I fee no rcafon wiiy the Increafe of 
 dcnlity fliould Hop any w^hcrc, and not rather 
 be continued through all dillances from the Sun 
 to Saturn^ and beyond. And though this In- 
 creafe of denilty may at great dillances be ex- 
 ceeding flow , yet if the elaflick force of this 
 Medium be exceeding great, it may fuiiice to 
 impel Bodies from the denfer parts of the Me- 
 dium' towards the rarer, with all that power 
 which we call Gravity. And that the elaftick 
 force of this Medium is exceeding great, may 
 be gather'd from the fwiftnefs of its Vibrations. 
 Sounds move about w^o Engl'ijh Feet in a fe- 
 cond Minute of Time , and in feven or eight 
 Minutes of Time they move about one hundred 
 Englifi) Miles. Light moves from the Sun to 
 us in about feven or eight Minutes of Time, 
 which diflance is about 70000000 Englijh Miles, 
 fuppoiing the horizontal Parallax oi the Sun to 
 
 V 3 be 
 
be about ix". And the Vibrations or Pulfes of 
 this Medium, that they may caufe the alternate 
 Fits of eafy Tranfmillion and eafy Reflexion , 
 mufl be fwifter than Light, and by confequence 
 above 700000 times fwifter than Sounds. And 
 therefore the elalHck force of this Medium, in 
 proportion to its denfity, mufl be above 700000 
 X 700000 (that is, above 490000000000) 
 times greater than the elallick force of the Air 
 is in proportion to its denlity. For the Veloci- 
 ties of the Pulfes of elaftick Mediums are in a 
 fubduplicate Ratio of the Elallicities and the Ra- 
 rities of the Mediums taken together. 
 
 As Attraction is llronger in fmall Magnets 
 than in great ones in proportion to their bulk, , 
 and Gravity is greater in the Surfaces of fmall 
 Planets than in thofe of great ones in propor- 
 tion to their bulk , and fmall Bodies are agita- 
 ted much more by electric attradion than great 
 ones ; fo the fmallnefs of the Rays of Light 
 may contribute very much to the the power of 
 the Agent by which they are refracted. And 
 fo if any one iliould fuppofe that Mther ( like 
 our Air) may contain Particles which endeavour 
 to recede from one another (for I do not knov/ 
 what this JEther is ) and that its Particles are 
 exceedingly fmaller than thofe of Air, or even 
 than thofe of Light: The exceeding fmallnefs 
 of its Particles may contribute to the greatnefs 
 of the force by which thofe Particles may re- 
 cede from one another, and thereby make that 
 Medium exceedingly more rare and elaftick 
 than Air, and by confequence exceedingly lefs 
 able to refift the motions of Projedtiles , and 
 
 exceed- 
 
[ 327 ] 
 
 exceedingly more able to prefs upon gi*ofs Bo- 
 dies , by endeavouring to expand it felf. 
 
 ^i. 22. May not Planets and Comets, and all 
 grols Bodies, perform their Motions more free- 
 ly, and u'ithlefs refinance in thisy^therealMe- 
 aium than in any Fluid, which fills all Space ade- 
 quately without leaving any Pores, andby confe- 
 quence is much denfer thanQuick-filver or Gold? 
 And may not its refiltancc be fo fmall, as to be 
 inconfiderable ? For inftance ; If thh JEtber (for 
 fo I will call it ) Ihould be fuppofed 700000 
 times more elaftick than our Air, and above 
 yooooo times more rare ; its refillance would 
 be above 600000000 times lefs than that of Wa- 
 ter. And fo fmall a refiltance would fcarce 
 make any fenfible alteration in the Motions of 
 the Planets in ten thoufand Years. If any one 
 would ask how a Medium can be fo rare, let 
 him tell me how the Air, in the upper parts of 
 the Atmofphere, can be above an hundred thou- 
 fand thoufand times rarer than Gold. Let him 
 alfo tell me, how an eleftrick Body can by Fri- 
 ftion emit an Exhalation fo rare ^a fubtile, and 
 yet fo potent, as by its Emiilion to caufe no 
 ienlible Diminution of the weight of the ele- 
 clrick Body, and to be expanded through a 
 Sphere, whofe Diameter is above two Feet, and 
 yet to be able to agitate and carry up Leaf Cop- 
 per, or Leaf Gold, at the diflance of above a 
 Foot from the eledrick Body? And how the 
 Effluvia of a Magnet can be fo rare and fubtile, 
 as to pafs through a Plate of Glafs without any 
 Refiftance or Diminution of their Force, and 
 yet fo potent as to turn a magnetick Needle 
 beyond the Glafs ? 
 
 Y 4 t". 
 
[ 328 1 
 
 ^.13. Is not Villon perform'd chiefly by the 
 Vibrations of this Medium, excited in the bot- 
 tom of the Eye by the Rays of Light, and pro- 
 pagated through the folid, pellucid and uniform 
 Capillamentaof the optick Nerves into the place 
 of Senlation? And is not Hearing perform'd 
 by the Vibrations either of this or fome other 
 Medium, excited in the auditory Nerves by the 
 Tremors of the Air, and propagated through 
 the folid, pellucid and uniform Capillamenta of 
 thofe Nerves into the place of Senlation? And 
 fo of the other Senfes. 
 
 ^i. 24. Is not Animal Motion perform'd by 
 the Vibrations of this Medium , excited in the 
 Brain by the power of the W ill , and propaga- 
 ted from thence tiirough the folid, pellucid and 
 uniform Capillamenta of the Nerves into the 
 Mufcles, for contrading and dilating them ? I 
 fuppofe that the Capillamenta of tie Nerves are 
 each of them folid and uniform, that the vibra- 
 ting Motion of the /P-^thereal Medium may be 
 propagated along them from one end to the o- 
 ther uniformly, and without interruption : For 
 Obftru6lions in the Nerves create Pallies. And 
 that they may be lufHciently uniform, I I'uppofe 
 them to be pellucid when view'd finely, tho* 
 the Retlcxions in their cyhndrical Surfaces may 
 make the whole Nerve (compofed of many Ca- 
 pillamenta) appear opake and white. For opaci- 
 ty arifes from refieding Surfaces, fuch as may di-- 
 Hurb and interrupt the Motions of this Medium. 
 
 ^/, 25*. Are there not other original Proper- 
 ties of the Rays of Light , befides thofe alrea- 
 dy defcribed ? An initance of another original 
 ^ ■' ' " Pro, 
 
[ 329 ] 
 
 Property we have in the Refra6lion of Ifland 
 Cryilal, defcribed firlt by Erafmus BarthoL'me^ 
 and afterwards more exadly by Hugenhts, in 
 his Book T)e la Lumiere. This Cryltal is a pel- 
 lucid fiffile Stone, clear as Water or Cryilal of 
 the Rock, and without Colour ; enduring a red 
 Heat without lofing its tranfparency, and in a 
 very llrong Heat calcining without Fulion. 
 Steep'd a Day or two in Water, it lofes its na- 
 tural Polilh. Being rubb'd on Cloth, it attrads 
 pieces of Straws and other light things, like Am- 
 bar or Glafs; and \\\xhJlqiia fortis it makes an 
 Ebullition. It feems to be a fort of Talk, and 
 is found in form of an oblique Parallelopiped, 
 with fix parallelogram Sides and eight Iblid An- 
 gles. The obtufe Angles of the Parallelograms 
 are each of them loi Degrees and ^x Minutes; 
 the acute ones 78 Degrees and 8 Minutes. Two 
 of the folid Angles oppofite to one another, as 
 C and E, are compafled each of 
 them with three of thefe obtufe %l'l'J°^l''^' 
 Angles , and each of the other "'"" 
 fix with one obtufe and two acute ones. It 
 cleaves eafily in Planes parallel to any of its 
 Sides, and not in any other Planes. It cleaves 
 with a glofTy polite Surface not perpedly plane, 
 but with fome little unevennefs. It is eafily 
 fcratch'd, and by reafon of its foftnefs it takes 
 a Pohfli very difficultly. It poHflies better up- 
 on polifli'd Ilooking-glafs than upon Metal, and 
 perhaps better upon Pitch, Leather or Parch- 
 ment. Afterwards it mult be rubb'd with a 
 little Oil or White of an Egg, to fill up its 
 Scratches ; w^hereby it will become very tranf- 
 
 parent 
 
[ 33o] 
 
 parent and polite. But for feveral Experiments, 
 it is not neceiFary to poliili it. If a piece of thiis 
 cryflalline Stone be laid upon a Book, every 
 Letter of the Book feen through it will appear 
 double, by means of a double Refraftion. And 
 if any beam of Light falls either perpendicularly, 
 or in any oblique Angle upon any Surface of this 
 Cryllal, it becomes divided into two beams by 
 means of the fame double Refraftion. Which 
 beams are of the fame Colour with the incident 
 beam of Li;:,ht, and feem equal to one another 
 in the quantity of their Light, or very nearly 
 equal. One of thefe Refradlions is perform'd 
 by the ufualRule of Opticks, the Sine of Inci- 
 dence out of Air into this Cryilal being to the 
 Sine of Refradion, as five to three. The other 
 Refraftion, which may be called the unufual 
 Refradion, is perform'd by the following Rule. 
 
 \S 
 
 Let ADBC reprefent the refrafting Surface 
 
 of 
 
[ 331 ] 
 
 of theCryllal, C the biggeft folid Angle at that 
 Surface, GEHF the oppofite Surface, andCK 
 a perpendicular on that Surface. This perpen- 
 dicular makes with the edge of the Cryilal CF, 
 an Angle of 19 Degr. 3'. Join KF, and in it 
 take K L , fo that the Angle KC L be 6 Degr. 
 40. and the Angle LCF ix Degr. zy And if 
 STreprefent any beam of Light incident atT 
 in any Angle upon the refrafting Surface ADBC, 
 let TV be the refraded beam determin'd by 
 the given Proportion of the Sines 5 to 3, accor- 
 ding to the ufual Rule of Opticks. Draw VX 
 parallel and equal to KL. Draw it the fame 
 way from V in which L lieth from K; and 
 joining TX, this line TX fliall be the other re- 
 frafted beam carried from T to X, by the un- 
 ufualRefraftion. 
 
 If therefore the incident beam ST be per- 
 pendicular to the refracting Surface, the two 
 beams TV and TX, into which it lliall be- 
 come divided, fliall be parallel to the lines C K 
 and C L ; one of thofe beams going through 
 the Cryftal perpendicularly, as it ought to do 
 by the ufual Laws of Opticks , and the other 
 TX by an unufual Refradion diverging from 
 the perpendicular, and making with it an An- 
 gle VTX of about 67 Degrees, as is found by 
 experience. And hence, the Plane VTX, 
 and fuch like Planes which are parallel to the 
 Plane CFK, may be called the Planes of per- 
 pendicular Refraftion. And the Coafl towards 
 which the lines K L and V X are drawn, may 
 be caird the Coafl of unufual Refradion. 
 
 In like maimer Cryilal of the Rock has a 
 
 double 
 
[332 ] 
 
 double Refraction : But the difference of the 
 two Refractions is not fo great and manifeil as 
 in Ifland Cryflal. 
 
 When the beam ST incident on Ifland Cry- 
 Ital, is divided into two beams TV and TX, 
 and thefe two beams arrive at the farther Sur- 
 face of the Glafs; the beam TV, which was 
 refracted at the firft Surface after the ufual man- 
 ner, fliall be again refraded entirely after the 
 ufual manner at the fecond Surface ; and the 
 beam TX, which was refrafted after the unu- 
 fual manner in the firfl: Surface, iliall be again 
 refradled entirely after the unufual manner in 
 the fecond Surface ; fo that both thefe beams 
 fhall emerge out of the fecond Surface in hnes 
 parallel to the firfl incident beam ST. 
 
 And if two pieces of Ifland Cryfl:al be pla- 
 ced one after another, in fuch manner that all 
 the Surfaces of the latter be parallel to all the 
 correfponding Surfaces of the former : The 
 Rays vv^hich are refradted after the ufual man- 
 ner in the firll: Surface of the firll Cryital fhall 
 be refraded after the ufual manner in all the 
 following Surfaces ; and the Rays which are re- 
 fraded after the unufual manner in the firil Sur- 
 face , fliall be refrafted after the unufual manner 
 in all the following Surfaces. And the fame 
 thing happens, though the Surfaces of the Cry- 
 Itals be any ways inclined to one another, provi- 
 ded that their Planes of perpendicular Refradion 
 be parallel to one another. 
 
 x\nd therefore there is an original difference 
 in the Rays of Light, by means of which fome 
 Rays are in this Experiment conftantly refrad- 
 
 ed 
 
[ 333 ] 
 
 ed after the ufual manner, and others conftant- 
 ly after the unufual manner : For if the diffe- 
 rence be not original, but arifes from new Mo- 
 difications imprefs'd on the Rays at their firil 
 Refradion,- it would be alter'd by new Modifi- 
 cations in the three following Refradions ; 
 whereas it fuff'ers no alteration, but is conftant, 
 and has the fame eifedt upon the Rays in all the 
 Refraflions. The unufual Refraction is there- 
 fore perform'd by an original property of the 
 Rays. And it remains to be enquired, whe- 
 ther the Rays have not more original Properties 
 than are yet difcover'd. 
 
 ^f. z6. Have not the Rays of Light feveral 
 fides, endued with feveral original Properties? 
 For if the Planes of perpendicular Refradion 
 of the fecond Cryftal, be at right Angles with 
 the Planes of perpendicular Refradion of the 
 firfl Cryflal, the Rays which are refraded after 
 the ufual manner in pailing through the firft 
 Cryftal, will be all of them refrafted after the 
 unufual manner in palling through the fecond 
 Cryfi;al ; and the Rays which are refraded af- 
 ter the unufual manner in paffing through the 
 firit Cryflal, will be all of them refraded after 
 the ufual manner in pafling through the fecond 
 Cryftal. And therefore there are not two forts 
 of Rays differing in their nature from one ano- 
 ther, one of which is conftantly and in all Po- 
 fitions refraded after the ufual manner, and the 
 other conftantly and in all Pofitions after the 
 unufual manner. The difference between the 
 two forts of Rays in the Experiment mention'd 
 in the ifth QuefUon, was only in the Pofitions 
 
 of 
 
[ 334] 
 
 of the Sides of the Rays to the Planes of per* 
 pendicular Refraction. For one and the fame 
 Ray is here refraded fometimes after the ufual, 
 and fometimes after the unufual manner, ac- 
 cording to the Pofition which its Sides have to 
 the Cryllals. If the fides of the Rays are pofi- 
 ted the fame way to both Cryitals, it is refract- 
 ed after the fame manner in them both : But 
 if that fide of the Ray which looks towards 
 the Coail of the unufual Refraction of the firfl 
 Cryftal, be 90 Degrees from that fide of the 
 fame Ray which loolvs towards the Coaft of the 
 unufual Refraftion of ttie fecond Cry Hal, (which 
 may be effedcd by varying the Pofition of the 
 fecond Cryllal to the firli:, and by confequence 
 to the Rays of Light) tiie Ray fliall be refraCled 
 after feveral manners in the feveral Cryflals. 
 There is nothing more required to determine 
 whether the Rays of Light which fall upon the 
 fecond Cryftal, mall be refracted after the ufual 
 or after the unufual manner , but to turn about 
 this Cryilal, fo that the Coaft of this Cryftal's 
 unufual Refradion may be on this or on that 
 fide of the Ray. And therefore every Ray may 
 be confider'd as having four Sides or Quarters, 
 two of which oppofite to one another incline 
 the Ray to be refracted after the unufual man- 
 ner , as often as either of them are turn'd to- 
 wards the Coaft of unufual Refraction ; and the 
 other two, whenever either of them are turn*d 
 towards the Coaft of unufual RefraCtion, do not 
 incline it to be otherwife BefraCted than after 
 the ufual manner. The two firft may there- 
 fore be caU'd the Sides of unufual RefraCtion. 
 
 And 
 
[ 335 ] 
 
 And fince thefe Difpofitions were in the Rays 
 before their Incidence on the fecond, third and 
 fourth Surfaces of the two Cryllals, and fuller- 
 ed no alteration (fo far as appears) by the Re- 
 fradion of the Rays in their paiTage through 
 thofe Surfaces, and the Rays were refraded by 
 the fame Laws in all the four Surfaces ; it ap- 
 pears that thofe Difpofitions were in the Rays 
 originally, and fuffer'd no alteration by the firll 
 Refradion, and that by means of thofe Difpofi- 
 tions the Rays were refrafted at their Incidence 
 on the firll Surface of the firlt Cryftal, fome of 
 them after the ufual, and fome of them after the 
 unufual manner, accordingly as their Sides of 
 unufual Refradion were then turn'd towards 
 the Coail of the unufual Refraction of that Cry- 
 Ital, or fideways from it. 
 
 Every Ray of Light has therefore two oppo- 
 fite Sides , originally endued with a Property 
 on which the unufual Refradion depends, an3 
 the other two oppofite Sides not endued with 
 that Property. And it remains to be enquired, 
 whether there are not more Properties of Light 
 by which the Sides of the Rays differ, and are 
 diflinguifli'd from one another. 
 
 In explaining the difference of the Sides of 
 the Rays above mcntion'd, I have fuppofed that 
 the Rays fall perpendicularly on the firfl Cry- 
 ftal. But if they fall obliquely on it, the Suc- 
 cefs is the fame. Thofe R?.ys which are refract- 
 ed after the ufual manner in the firfl Crytfal, 
 will be refradled after t'ie unufual manner in 
 the fecond Cryflal, fuppofmg the Planes of per- 
 pendicular Refradion to be at right Angles with 
 
 2- one 
 
f 330 
 
 one another, as above : and on the contrar}^ 
 
 If the Planes of the perpendicular RefracHon 
 of the two Cryftals be neither parallel nor per- 
 pendicular to one another, but contain an acute 
 Angle : The two beams of Light which emerge 
 out of the tirft Cryltal, will be each of them di- 
 vided into two more at their Incidence on the 
 fecond Cryftal. For in this cafe the Rays in 
 each of the two Beams will fome of them have 
 their Sides of unufual Refradtion, and fome of 
 them their other Sides turn'd towards the Coafl 
 of the unufual Refradion of the fecond Cry- 
 ftal. 
 
 ^/. ty. Are not all Hypothefes erroneous 
 which have hitherto been invented for explain- 
 ing the Phenomena of Light, by new Modifica- 
 tions of the Rays ? For thofe Phenomena de- 
 pend not upon new Modifications, as has been 
 luppofed, but upon the original and unchange- 
 able Properties of the Rays. 
 
 ^/. 28. Are not all Hypothefes erroneous, 
 in which Light is fuppofed to confifl in Pref- 
 fion or Motion, propagated through a fluid Me- 
 dium ? For in all thefe Hypothefes, the Pheno- 
 mena of Light have been hitherto explain'd by 
 fuppofing that they arife from new Modifica- 
 tions of the Rays ; which is an erroneous Sup- 
 pofition. 
 
 If Light confifted only in PrefTion propaga- 
 ted without actual Motion, it would not be a- 
 ble to agitate and heat the Bodies which refrad 
 and refled it. If it confifted in Motion propa- 
 gated to all diftances in an inflant, it would re- 
 quire an infinite force every moment, in every 
 
 fliining 
 
t 337 ] 
 
 lliining Particle, to generate that Motion. And 
 if it conliiled in Prellion or Motion, propaga- 
 ihd either in an inliant or in time, it would 
 bend into the Shadow. For Prefiion or Motion 
 cannot be propagated in a Fluid in right Lines 
 beyond an Obilacle which Hops part of the Mo- 
 tion, but will bend and Ipread every way into 
 the quiefcent Medium which hes beyond the 
 Obilacle. Gravity tends downwards, but the 
 PreHiire of Water arifmg trom Gravity tends 
 every way with equal force, and is propagated 
 as readily, and with as much force fidevv'ays as 
 downwards , and through crooked palfages as 
 through ilrait ones. The Waves on th*e Surface 
 of llagnating Water, paiEng by the fides of i 
 broad Obftacle which Hops part of them, bend 
 afterwards and dilaie themfclves gradually into 
 the quiet Water behind the Obltacle. The 
 Waves, Pulfes orVibrations of theAir, where- 
 in Sounds confilt, bend manifellly, though not 
 fo much as the Waves of Water. For a Bell 
 or a Canon may be heard beyond a Hill which 
 intercepts the fight of the founding Body, and 
 Sounds are propagated as readily through crook- 
 ed Pipes as through Ibeight ones. But Light 
 is never known to follow crooked Palfages nor 
 to bend into the Shadow. For the fix'd Stars 
 by the Interpofition of any of the Planets ceafe 
 to be feen. And fo do the Parts of the Sun 
 by the Interpofition of the Moon, Mercury or 
 Venm. The Rays which pafs very near to the 
 edges of any Body, are bent a Uttle by the adion 
 of the Body, as we fhew'd above ; but this 
 bending is not towards but from the Shadow^ 
 
 Z and 
 
[338] 
 
 and is perform'd only in the pafTage of the Ray 
 by the Body, and at a very imall dillance from 
 it. So foon as the Ray is pail the Body, it 
 goes right on. 
 
 To explain the iinufual Refradion of Ifland 
 Cryftal by Preffion or Motion propagated, has 
 not hitherto been attempted (to my knowledge) 
 except by Huygens^ who for that end fuppofed 
 two feveral vibrating Mediums within that Cry- 
 ftal. But when he tried the Refradions in two 
 fucceflive pieces of that Crj'ftal, and found 
 them fuch as is mention'd above : He confef- 
 fed himfclf at a lofs for explaining them. For 
 Preilions'or Motions, propagated from a fliining 
 Body through an uniform Medium, mult be 
 on all fides alike; whereas by thofc Experi- 
 ments it appears, that the Rays of Light have 
 different Properties in their different Sides. 
 He fufpeded that the Pulfes of Mther in paf- 
 fmg through the lirft Cryltal might receive cer- 
 tain new Modifications, which might determine 
 them to be propagated in this or that Medium 
 within the fecond Cryftal, according to the 
 
 Pofition of that Cryftal. 
 . Man pour dire ccm-.vcnt But wHat Modifications 
 
 cda [^ fait, je n,y rien ^j^^^^ ^^ ^^^ ^^ ^iQ COUld 
 trove pi au ici qui me la- _ c i • i r 
 
 uja;je. c H. de la lumi- notfay, nor thmk ot any 
 ere/c.5,p9i. thing fatisfadory in that, 
 
 Point. And if he had 
 known that the unufual Refraction depends not 
 on new Modifications, but on the original and 
 unchangeable Difpofitions of the Rays, he would 
 have found it as difficult to explain how thofe 
 Difpofitions which he fuppofed to be imprefs'd 
 
 on 
 
on the Rays by the firfl Cryllal, could be in 
 them before their Incidence on that Cryllal ; 
 and in general , how all Rays emitted by ihi- 
 ning Bodies, can have thole Difpoiitions in 
 them from the beginning. To me, at lead, 
 this feems inexplicable, if Light be nothing 
 elfe than Prellion or Motion propagated through 
 
 And it is as difficult to explain by thefe Hy- 
 pothefes, how Rays can be alternately in Fits 
 of eafy Reflexion and eafy Tranfmiffion ; unlefs 
 perhaps one might fuppofe that there are in all 
 Space two Ethereal vibrating Mediums , and 
 that the Vibrations of one of them conilitute 
 Light, and the Vibrations of the other are fwift- 
 er, and as often as they overtake the Vibrations 
 of the firll, put them into thofe Fits. But how 
 two jEthers can be diffufed through all Space, 
 one of which a61s upon the other, and by con- 
 fcquence is re-ac^ted upon, without retarding, 
 ihattering, difperfmg and confounding one an- 
 others Motions, is inconceivable. And againft 
 filling the Heavens with fluid Mediums, unlefs 
 they be exceeding rare, a great Objection arifes 
 from the regular and very lading Motions of 
 the Planets and Comets in all manner of Courfes 
 through the Heavens. For thence it is mani- 
 feft, that the Heavens are void of all feniible 
 Refiltance , and by confequence of all fenfible 
 Matter. 
 
 For the refifling Power of fluid Mediums a- 
 rifes partly from the Attrition of the Parts of 
 the Medium , and partly from the Vis inertia 
 of the Matter. That part of the Refitfance of 
 
 L z a fphe- 
 
1 340 ] 
 
 a fpherical Body which arifes from the Attri- 
 tion of the Parts of the Medium is very nearly 
 as the Diameter, or, at the moit, as the Fa6lum 
 of the Diameter, and the Velocity of the fphe- 
 rical Body together. And that part of the Re- 
 finance which arifes from the Vis inertia of 
 the Matter, is as the Square of that Fa^um. 
 And by this difference the two forts of Refi- 
 nance may be diftinguiih'd from one another 
 in any Medium ; and thefe being difiinguifli'd, 
 it will be found that almolt all the Reiilknce 
 of Bodies of a competent Magnitude moving 
 in Air, Water, Quick-filver, and luch like Flu- 
 ids with a competent Velocity, arifes from the 
 Vis inertia of the Parts of the Fluid. 
 
 Now that part of the refilling Power of any 
 Medium which arifes from the Tenacity, Fri- 
 ftion or Attrition of the Parts of the Medium, 
 may be diminiih'd by dividing the Matter into 
 fmaller Parts, and making the Parts more fmooth 
 and flippery: But. that part of the Refiliance 
 which arifes from the Vis. inertia^ is proportio- 
 nal to the Denlity of the Matter, and cannot be 
 diminifh'd by dividing the Matter into fmaller 
 Parts, nor by any other means than by decrea- 
 fing theDeniity of the Medium. And for thefe 
 Reafons the Denfity of fluid Mediums is^very 
 nearly proportional to their Reliflance. ' Li- 
 quors which differ not much in Denfity, as Wa- 
 ter, Spirit ofW^ine, Spirit of Turpentine, hot 
 Oil, differ not much in Refiftance. Water is 
 thirteen or fourteen times hghter than Quick- 
 filver, and by confequence thirteen or fourteen 
 times rarer, and its Refiftance is lefs than that 
 
 of 
 
[ 341 ] 
 
 of Quick-filver in the fame Proportion, or there- 
 abouts, as I have found by Experiments made 
 with Pendulums. The open Air in which we 
 breathe is eight or nine hundred times lighter 
 than Water, and by coniequence eight or nine 
 hundred times rarer, and accordingly its Refi- 
 ftance is lefs than that of Water in the fame 
 Proportion, or thereabouts ; as I have alfo found 
 by Experiments made with Pendulums. And in 
 thinner Air the Refiitance is Hill lefs, and at 
 length, by rarifying the Air, becomes infenfi- 
 ble. For fmall Feathers falling in the open Air 
 meet with great Refiibnce, but in a tall Glafs 
 well emptied of Air, they fall as faft as Lead or 
 Gold, as 1 have feen tried feveral times. Whence 
 the Refinance feems Itill to decreafe in propor- 
 tion to the Denfity of the Fluid. For I do not 
 find by any Experiments, that Bodies moving 
 in Quick-filver, Water or Air, meet with any 
 other fenfible Refiftance than what arifes from 
 the Denfity and Tenacity of thofe fenfible Flu- 
 ids, as they w^ould doif the Pores of thofe Flu- 
 ids, and all other Spaces, v^'ere filled with a 
 denfe and fubtile Fluid. Now if the Refiflance 
 in a VefTel well emptied of Air, was but an 
 hundred times lefs than in the open Air , it 
 would be about a million of times lefs than in 
 •Quick-filver. But it feems to be much lefs in 
 fuch a Velfel, and flill much lels in the Hea- 
 vens, at the height of three or four hundred 
 Miles from the Earth, or ^bove.' For Mr. Boy /e 
 has fhew'd that Air may be rarified above ten 
 thoufand times in Veflels of Glafs; and the 
 Heavens are much emptier of Air than any f^a- 
 
 Z 3 emm 
 
[ 34-2 ] 
 
 cuum we can make below. For fince the Air 
 is comprefs'd by the weight of the incumbent 
 Atmoiphere, and the Denfity of Air is propor- 
 tional to the Force comprelling it , it follows 
 by Computation, that at the height of about fe- 
 ven Englijh Miles from the Earth, the Air is 
 four times rarer than at the Surface of the 
 Earth ; and at the height of 14 Miles^, it is fix- 
 teen times rarer than that at the Surface of the 
 Earth ; and at the height of 21, 28, or 35 Miles, 
 it is refpc^lively 64, 256, or 1024 times rarer, 
 or thereabouts; and at the height of 70, 140, 
 2ioMiles, it is about loooooo, loooooooooooo 
 or 1 000000000000000000 times rarer; and fo 
 on. 
 
 Heat promotes Fluidity very much, by dimi- 
 nifliing the Tenacity of Bodies. It makes ma- 
 ny Bodies fluid which are not fluid in cold, and 
 increaies the Fluidity of tenacious Liquids, as 
 of Oil, Baliam and Floney, and thereby de- 
 creafes their Refillance. But it decreafes not 
 the Refiftance of Water confiderablv, as it would 
 do if any confiderable part ot the Refiltance of 
 Water arofe from the Attrition or Tenacity of 
 its Parts. And thereforcithe Refiltance of Wa- 
 ter arifes principally and almoll entirely from 
 the Vis inertia of its Matter; and by confe- 
 quence, if the Heavens were as denfe as Wa- 
 ter, they would not have much lefs Refiftance 
 than Water ; if as denfe as Quick- fiiver, they 
 would not \\vft much lefs Refiltance than Quick- 
 filver; if abiblutely denfe, or full of Matter 
 without any Vacuum^ let the Matter be never 
 fo fubtile and fluid, they would have a greater 
 
 Refiftance 
 
[ 3+3 ] 
 
 Refiflance than Quick- filvTr. A folid Globe in 
 fuch a Medium would lole above half its Mo- 
 tion in moving three times the length of its 
 Diameter, and a Globe not folid (luch as are 
 the Planets) would be retarded iboner. And 
 therefore to make way for the regular and lad- 
 ing Motions of the Planets and Comets, it's ne- 
 ceiFary to empty the Heavens of all Matter, ex- 
 cept perhaps fome very thin Vapours, Steams 
 or Effluvia, arifmg from the Atmof pheres of the 
 Earth, Planets and Comets, and from fuch an 
 exceedingly rare ^Ethereal Medium as we de- 
 fcribed above. A dcnfe Fluid can be of no ufe 
 for explaining the Phsenomena of Nature^ the 
 Motions of the Planets and Comets being better 
 explain'd without it. It ferves only to dilturb 
 and retard the Motions of thofe great ]3odies, 
 and make the Frame of Nature languiih : And 
 in the Pores of Bodies, it ferves only to flop 
 the vibrating Motions of their Parts, wherein 
 their Heat and A61ivity coniills. And as it is 
 of no ufe , and hinders the Operations of Na- 
 ture, and makes her languiih, lo there is no e- 
 vidence for its Exiilence, and therefore it ought 
 to be rejeded. And if it be rejeded, the Hy- 
 pothefes that Light confifts in Preflion or Mo- 
 tion propagated through fuch a Medium, are 
 rejefted with it. 
 
 And for rejecting fuch a Medium, we have 
 the Authority of thofe the oldefl and moll ce- 
 lebrated Philofophers of Greece and Thoenic'ta^ 
 who made a Vdcimm and Atoms, and the Gra- 
 vity of Atoms, the firlt Principles of their Phi- 
 lofophy ; tacitly attributing Gravity to fome o- 
 
 Z 4 ther 
 
[ 344 ] 
 
 ther Caufe than denfe Matter. Later Philofo- 
 phers banifli the Confidcration of iuch a Caufe 
 out of Natural Philoiophy, feigning Hypotheies 
 for explaining all things mechanically , and re- 
 ferring other Caufes to Metaphyficks : W hereas 
 the main Bufmefs of Natural Philofophy is to 
 argue from Phcenomena without fefgning Hy- 
 potheies, and to deduce Caufes from Efte6ls, 
 till we come to the very tirfl Caufe, which cer- 
 tainly is not mechanical; and not only to un- 
 fold the Mechanifm of the World, but chiefly 
 to refolve thefe and fuch like Quellions. W : at 
 is there in places almoll empty of Matter, and 
 whence is it that the Sun and Planets gravitate 
 towards one another, without denfe Matter be- 
 tween them? Whence is it that Nature doth 
 nothing in vain ; and whence arifes all that Or- 
 der and Beauty which we fee in the World? 
 To what end are Comets, and whence is it that 
 Planets move all one and the fame way in Orbs 
 concentrick, while Comets move all manner of 
 ways in Orbs very excentrick, and what hinders 
 the tix'd Stars from falling upon one another ? 
 How came the Bodies of Animals to be contri- 
 ved with lb much Art, and for what ends were 
 their feveral Parts ? Was the Eye contrived 
 without Skill in Opticks, and the Ear without 
 Knowledge of Sounds? How do the Motions 
 of the Body lollow from the Will, and whence 
 is the Inilinft in Animals ? Is not the Senfory of 
 Animals that place to which the fenfitive Sub- 
 ilance is prefent, and into which the fenfible 
 Species of Things are carried through the Nerves 
 and Brain, that there they may be perceived 
 
 • by 
 
[ 345 ] 
 
 by their immediate prefence to that Subflance ? 
 And thele things being rightly difpatch'd, does 
 it not appear from Phaenomena that there is a 
 Being incorporeal, living, intelligent, omnipre- 
 fent, who in intinite Space, as it were in his Sen- 
 lory, fees the things themfelves intimately, and 
 throughly perceives them, and comprehends 
 them wholly by their immediate prefence to 
 himfelf : Or which things the Images only car- 
 ried through the Organs of Senfe into our little 
 Senforiums, are there feen and beheld by that 
 which in us perceives and thinks. And tho* 
 every true Step made in this Philofophy brings 
 us not -immediately to the Knowledge of the 
 firll Caufe, yet it brings us nearer to it, and 
 on that account is to be highly valued. 
 
 ^i. 29. Are not the Rays of Light very 
 fmall Bodies emitted from Ihinino; Subitances? 
 For fuch Bodies will pafs through uniform Me- 
 diums in right Lines without bending into the 
 Shadow , which is the Nature of the Rays of 
 Light. They will alfo be capable of feveral 
 Properties, and be able to conlerve their Pro- 
 perties unchanged in palling through feveral 
 Mediums, which is another Condition of the 
 Rays of Light. Pellucid Subltances a<^t upon 
 the Rays of Light at a diftance in refrafting, re- 
 flecting and infleding them, and the Rays mu- 
 tually agitate the Parts of thofe Subflances at a 
 dillance for heating them ; and this Aftion and 
 Re-a(^lion at a diilance, very much refembles an 
 attractive Force between Bodies. If Refradion 
 be perform'd by Attraction of the Rays, the 
 Sines of Incidence muit be to the Sines of Re- 
 
 fradion 
 
[ 340 
 
 fra61ion in a given Proportion, as we fliew'd in 
 our Principles of Philoi'ophy : And this Rule is 
 true by Experience. The Rays of Light in 
 going out of Glafs into a Vacuum^ are bent to- 
 wards the Glafs ; and if they fall too obliquely 
 on the Vacuum they are bent backwards into 
 the Glafs, and totally receded ; and this Refle- 
 xion cannot be afcribed to the Refillance of an 
 abfolute Vacuum , but mull: be caufed by the 
 Power of the Glafs attrading the Rays at their 
 going out of it into the Vacuum^ and bringing 
 them back. For if the farther Surface of the 
 Glafs be moillen'd with Water or clear Oil, or 
 liquid and clear Honey; the Rays which would 
 otherwife be reflec^ted, will go into the Water, 
 Oil, or Honey, and therefore are not reflefted 
 before they arrive at the farther Surface of the 
 Glafs, and begin to go out of it. If they go out 
 of it into the Water, Oil or Honey, they 
 go on, becaufe the Attradion of the Glafs is 
 almoft balanced and render'd ineffedual by 
 the contrary Attradion of the Liquor. But if 
 they go out of it into a Vacuum which has no 
 Attraction to balance that of the Glafs, the At- 
 traftion of the Glafs either bends and refradls 
 them, or brings them back and refleds them. 
 And this is Hill more evident by laying together 
 two Prifms of Glafs, or two Objed-glalles of 
 of very long Telefcopes , the one plane the 6- 
 ther a little convex, and fo compreffmg them 
 that they do not fully touch, nor are too far a- 
 funder. For the Light which falls upon the 
 farther Surface of the firlt Glafs where the In- 
 terval between the GlalTes is not above the ten 
 
 hundred 
 
[ 34-7 ] 
 
 hundred thoufandth part of an Inch, will ga 
 through that Surface, and through the Air or 
 Vacuum between thcGlalTes, and enter into the 
 fecond Glafs, as was explain'd in the firft, fourth 
 and eighth Obfervations of the firtt Part of the 
 fecond Book. But if the fecond Glafs be taken 
 away, the Light which goes out of the fecond. 
 Surface of the hrlt Glafs into the Air or Va- 
 cuum^ will nor go on forwards, but turns back 
 into the tirll Glafs, and is reflected ; and there- 
 fore it is drawn back by the Power of the firfl: 
 Glafs, there being nothing elfe to turn it back. 
 Nothing more is requifite for producing all the 
 variety of Colours and degrees of Refrangibi- 
 Hty, than that the Rays of Li^iht be Bodies of 
 ditierent Sizes, the Icall: of which may make 
 violet the weakcfl and darkeft of the Colours, 
 and be more eafily diverted by rcfradiing Sur- 
 faces from the right Courfe ; and the reft as 
 they are bigger and bigger, may make the 
 Ih'onger and more lucid Colours, blue, green, 
 yellow^ and red , and be more and more difti- 
 cultly diverted. Nothing more is requifite for 
 putting the Rays of Light into Fits of eafy Re- 
 flexion and eafy TranfmilFion, than that they be 
 fmall Bodies which by their attradive Powers, 
 or fome other Force, Itir up Vibrations in what 
 they acT: upon , which Vibrations being fwifter 
 than the Rays, overtake them fucceiFively, and 
 agitate them fo as by turns to increafe ami de- 
 creafe their \^elocities, and thereby put them 
 into thofe Fits. And lailly, the unufual Refra- 
 ftion of Ifland Cryftal looks very much as if it 
 were perform'd by fome kind of attraftive vir- 
 tue 
 
[34-8] 
 
 tue lodged in certain Sides both of the Rays, 
 and of the Particles of the Cryltal. For were 
 it not for fome kind of Difpofition or Virtue 
 lodged in fome Sides of the Particles of the 
 Cryltal, and not in their other Sides, and which 
 incUnes and bends the Rays towards theCoalt 
 of unufual Refraction, the Rays which fall per- 
 pendicularly on the Cryltal, would not be re- 
 fraded towards that Coaft rather than towards 
 any other Coalt, both at their Incidence and at 
 their Emergence, fo as to to emerge perpendi- 
 cularly by a contrary Situation of the Coalt of 
 unuiual Refradion at the fecond Surface ; the 
 Cryllal acting upon the Rays after they have 
 pafs'd through it, and are emerging into the 
 Air ; or, if you pleafe, into a Vacuum. And 
 lince the Cryltal by this Difpofitjon or Virtue 
 does not act upon the Rays, unlefs when one 
 of their Sides of unufual Refradion looks to- 
 wards that Coalt, this argues a Virtue or Dif- 
 pofition in thole Sides of the Rays , which an- 
 fwers to and fympathizes with that Virtue or 
 Difpofition of the Cryftal, as the Poles of two 
 Magnets anfwer to one another. And as Mag- 
 netifm may be intended and remitted, and is 
 found only in the Magnet and in Iron : So this 
 Virtue of refrading the perpendicular Rays is 
 greater in Ifland Cryltal, lefs in Cryftal of" the 
 Rock, and is not yet found in other Bodies. I 
 do not fay that this Virtue is magnetical : It 
 feems to be of another kind. I only fay, that 
 what ever it be, it's difficult to conceive how 
 the Rays of Light, unlefs they be Bodies, can 
 have a permanent Virtue in two of their Sides 
 
 which 
 
[ 349 ] 
 
 which is not in their other Sides, and this 
 without any regard to their Polition to the 
 Space or Medium through which they pafs. 
 
 What I mean in this Queltion by a Vacuum^ 
 and by the Attradions of the Rays of Light to- 
 wards Glafs or Cryllal, may be underllood by 
 what was faid in the i8th, 19th and 2,0th Que^ 
 flions. 
 
 ^i. 30. Are not grofs Bodies and Light con- 
 vertible into one another, and may not Bodies 
 receive much of their adivity from the Parti- 
 cles of Light which enter their Compofition ? 
 For all fix'd Bodies being heated emit Light lo 
 long as they continue fufficiently hot, and Light 
 mutually Itops in Bodies as often as its Rays 
 ftrike upon their Parts, as we fliew'd above. I 
 know no Body lefs apt to fliine than Water; 
 and yet Water by frequent Dillillations c' anges 
 into fix'd Earth, as Mr. Boyle has tried ; and 
 then this Earth being enabled to endure a fuf- 
 ficientHeat, fliines by Heat like other Bodies. 
 
 The changing of Bodies into Light, and Light 
 into Bodies, is very conformable to the Courfe 
 of Nature, which feems delighted withTranf- 
 mutations. Water, which is a very fluid taft- 
 lefsSalt, flie changes byHcat into Vapour, which 
 is a fort of Air, and by Cold into Ice, which is 
 a hard, pellucid, brittle, fulible Stone : and this 
 Stone returns into Water by Heat, and Vapour 
 returns into Water by Cold. Earth by Heat be- 
 comes Fire, and by Cold returns into Earth. 
 Denie Bodies by Fermentation rarify into feve- 
 ral forts of Air, and this Air by Fermentation, 
 and fometimes without it, returns into denfe 
 
 Bodies, 
 
[ 350 ] 
 
 Bodies. Mercur}?' appears fometimes in the 
 form of a fluid Metal, fometimes in the form 
 of a hard brittle Metal, fometimes in the form 
 of a corrofive pellucid Salt call'd Sublimate , 
 fometimes in the form of a taftlefs, pellucid, 
 volatile white Earth , call'd Merctirius dulcis ; 
 jor in that of a red opake volatile Earth, call'd 
 Cinnaber ; or in that of a red or white Preci- 
 pitate, or in that of a fluid Salt ; and in Dillil- 
 lation it turns into Vapour, and being agitated 
 in I'acuOj it fliines like Fire. And after all thefe 
 Changes it returns again into its firfl form of 
 Mercury. Eggs grow from infenfible Maf^ni- 
 tudes, and change into Animals ; Tadpoles into 
 Frogs; and W'orms into Flies. All Birds, Beafts 
 and Fiflies, Infeds, Trees, and other \egeta- 
 bles, with their feveral parts, grow out of Wa- 
 ter and watry Tindures and Salts, and byPu- 
 trefadion return again into watry Subllances. 
 And Water ftanding a few Days in the open 
 Air , yields a Tindure , which ( like that of 
 Mault) by Handing longer yields a Sediment 
 and a Spirit, but before Putrefaction is lit Nou- 
 rifliment for Animals and Vegetables. And a- 
 mong fuch various and ftrange Tranfmutations, 
 why may not Nature change Bodies into Light, 
 and Light into Bodies ? 
 
 ^/. 31. Have not the fmall Particles of Bo- 
 dies certain Powers, Virtues or Forces, by 
 w^hich they aft at a diftance, not only upon the 
 Rays of Light for refleding, refrafting and in- 
 fleding them, but alio upon one another for 
 producing a great part of the Phasnomena of 
 Nature ? For it's well known that Bodies ad 
 
 one 
 
[351] 
 
 one upon another by the Attradions of Gravi- 
 ty, Magnetifm and Electricity ; and thefc In- 
 llances ihew the Tenor and Courfe of Nature, 
 and make it not improbable but that there may 
 be more attradive Powers than thefe. For Na- 
 ture is very confonant and conformable to her 
 felf. How thefe Attradions may be perform'd, 
 I do not here confider. What I call Attraction 
 may be perform'd by impulfe, or by fome other 
 means unknown to me. I ufe that Word here 
 to fignify only in general any Force by which 
 Bodies tend towards one another, whatfocver 
 be the Caufe. For we mult learn from the 
 PhcTnomena of Nature what Bodies attrad one 
 another, and what are the Laws and Properties 
 ofi>the Attradion, before we enquire the Caufe 
 by which the Attradion is perform'd, The At- 
 tradions of Gravity, Magnetifm and Eledrici- 
 ty, reach to very fenfible diltances, and fo have 
 been obferved by vulgar Eyes, and there may 
 be others which reach to fo fmall diftances as 
 hitherto efcape Obfcrvation ; and perhaps ele- 
 drical Attradion may reach to fuch fmall di- 
 ftances, even without being excited by Fridion. 
 For when Salt of Tartar runs/^r deliquiumy 
 is not this done by an Attradion between the 
 Particles of the Salt of Tartar , and the Parti- 
 cles of the Water which float in the Air in the 
 form of Vapours ? And why does not common 
 Salt, or Salt-petre, or Vitriol, run per deliqntum^ 
 but for want of fuch an Attradion ? Or w^hy 
 does not Salt of Tartar draw more W ater out 
 of the Air than in a certain Proportion to its 
 quantity, but for want of an attradive Force 
 
 after 
 
[ 352 ] 
 
 after it is fatiated with Water? And whence 
 is it but from this attractive Power that Water 
 which alone diflils with a gentle lukewarm 
 Heat, will not diitil from Salt of Tartar with- 
 out a great Heat? And is it not from the like 
 attractive Power between the Particles of Oil of 
 Vitriol and the Particles of Water, that Oil of 
 Vitriol draws to it a good quantity of Water 
 out of the Air, and after it is fatiated draws no 
 more, and in Dillillation lets go the Water ve- 
 ry difficultly ? And when Water and Oil of Vi- 
 triol poured fuccedively into the fame VelTel 
 grow very hot in the mixing, does not this 
 Heat argue a great Motion in the parts of the 
 Liquors ? And does not this Motion argue that 
 the Parts of the two Liquors in mixing coa- 
 lelce with Violence, and by confequence rufh 
 towards one another with an accelerated Mo- 
 tion ? And when Aqua fort Is or Spirit of Vi^ 
 triol poured upon Filings of Iron, difTolves the 
 Filings with a great Heat and Ebullition, is not 
 this Heat and Ebullition etfeded by a violent 
 Motion of the Parts, and does not that Motion 
 argue that the acid Parts of the Liquor rufh to- 
 wards the Parts of the Metal with violence^ 
 and run forcibly into its Pores till they get be- 
 tween its outmofl Particles and the main Mafs 
 of the Metal, and furrounding thofe Particles 
 loofen them from the main Mafs, and fet them 
 at liberty to float off into the Water? And 
 when the acid Particles which alone would 
 diitil with ancafyHeat, will not feparate from 
 the Particles of the Metal without a very vio- 
 lent 
 
[ 353 ] 
 
 lent Heat, does not this confirm the Attradion 
 between them ? 
 
 When Spirit of Vitriol poured upon com- 
 mon Salt or Salt-petre makes an Ebullition with 
 the Salt and unites with it, and in Diltillation 
 the Spirit of the common Salt or Salt-petre 
 comes over much eafier than it would do be- 
 fore, and the acid part of the Spirit of Vitriol 
 itays behind ; does not this argue that the fix'd 
 Alcaly of the Salt attrads the acid Spirit of the 
 Vitriol more Itrongly than its own Spirit, and 
 not being able to hold them both , lets go its 
 own ? And when Oil of Vitriol is drawn off 
 from its weight of Nitre, and from both the 
 Ingredients a compound Spirit of Nitre is diitil- 
 led, and two parts of this Spirit are poured on 
 one part of Oil of Cloves or Caraway Seeds, or of 
 any ponderous Oil of vegetable or animal Sub- 
 itances, or Oil of Turpentine thickcn'd with a 
 little Balfam of Sulphur, and the Liquors grow fo 
 very hot in mixing, as prelently to fend up a burn- 
 ing Flame : Does not this very great and fudden 
 Heat argue that the two Liquors mix with vio- 
 lence, and that their Parts in mixing run to- 
 wards one another with an accelerated Motion, 
 and clafli with the greateit Force? And is it 
 not for the fame reafon that well redihed Spi- 
 rit of Wine poured on the lame compound Spi- 
 rit flaflies; and xh'MX.h^Tulvis fulmifjans, com- 
 pofed of Sulphur , Nitre , and Salt of Tartar, 
 goes off with a more fudden and violent Ex- 
 plofion than Gun-powder, the acid Spirits of 
 the Sulphur and Nitre rufliing towards one an- 
 other, and towards the Salt of Tartar, with fo 
 
 A a great 
 
[ 354 ] 
 
 greilt a violence, as by the fliock to turn the 
 whole at once into Vapour and Flame? Where 
 the Diilolution is How, it makes a How Ebulli- 
 tion and a gentle Heat ; and where it is quick- 
 er, it makes a greater Ebullition with more 
 Heat ; and where it is done at once, the Ebul- 
 lition is contraded into a luddcn Blait or vio- 
 lent Explofion, with a Heat equal to that of 
 Fire and Flame. So when a Drachm of the a- 
 bove mention'd compound ^Spirit of Nitre was 
 poured upon half a Drachm of Oil of Caraway 
 Seeds /;/ vacuo ; the Mixture immediately made 
 a flafh hke Gun-pov^'der, and burll the exhau- 
 lled Receiver, which was a Glais lix Inches 
 wide, and eight Inches deep. And even the 
 grofs Body of Sulphur powder 'd , and with an 
 equal weight of Iron Filings, and a little Water 
 made into Palle, afts upon the Iron, and in five 
 OS iix Hours grows too hot to be touch'd, and 
 emits a Flame. And by thele Experiments com- 
 pared with the great quantity of Sulphur with 
 which the Earth abounds, and the warmth of 
 the interior Parts of the Earth, and hot Springs, 
 and burning Mountains, and with Damps, mi- 
 neral Corufcations, Earthquakes, hot fuffoca- 
 ting Exhalations, Hurricanes and Spouts; we 
 may learn that fulphurcous Steams abound in 
 the Bowels of the Earth and ferment with Mi- 
 nerals, and fometimes take Fire with a fudden 
 Corufcation and Explofion ; and if pent up in 
 fubterraneous Caverns, burlt the Caverns with a 
 great fhaking of the Earth, as in fpringing of a 
 Mine. And then the Vapour generated \y^ the 
 F^xplofion, expiring through- the Pores of the 
 -• - Earth, 
 
I 355 ] 
 
 Earth, feels hot and fulTocates, and makes Teni- 
 pells and Hurricanes, and iometiines caufes the 
 Land to Aide , or the Sea to boil, and carries 
 up the Water thereof in Drops, which by their 
 weight fall down again in Spouts. Alfo icme 
 fulphureous Steams, at all times when the Earth 
 is dry, afcending into the Air, ferment there 
 with nitrous Acids, and fornetimes taking fire: 
 caufe Lightening and Thunder , and tiery .Me- 
 teors. For the Air abounds with acid Vapours 
 fit to promote Fermentations, as appears by the 
 ruffing of Iron and Copper in it, the kindling 
 of Fire by blowing, and the beating of the 
 Heart by means of Relpiration. Now the a- 
 bove mention'd Motions are fo ^reat and vio- 
 lent as to fliew that in Fermentations, the Par- 
 ticles of Bodies which almoif relt, arc put into 
 new Motions by a very potent Principle, which 
 adls upon them only when they approach ond 
 another, and caules them to meet and clafli 
 with great violence, and grow hot with the 
 Motion, and dalli one another into pieces, and 
 vanifli into Air, and Vapour, and Flame. 
 
 When Salt of Tartar J>er dellqu'nimy being 
 poured into the Solution of any iMetal, preci- 
 pitates the Metal, and makes it fall down to the 
 bottom of the Liquor in the form of Mud : 
 Does not this argue that the acid Particles are 
 attraded more Itrongly by the Salt of Tartar 
 than by the Metal, and by the ftronger Attra- 
 dion go from the Metal to the Salt of Tartar ? 
 And lo when a Solution of Iron in Aqua fort is 
 diifolves the Lapis Calarmnaris and lets go the 
 Iron, or a Solution of Copper dilTolves Iron im-^ 
 
 A a i merfed 
 
t 356 ] 
 
 inerfcd in it and lets go the Copper, or a So- 
 lution of Silver difiblves Copper and lets go the 
 Silver, or a Solution of Mercury in Aqua fort is 
 being poured upon Iron, Copper, Tin or Lead, 
 diilblves the Metal and lets go the Mercury, 
 docs not this argue that the acid Particles of 
 the Aqua fort'is are attraded more ih'ongly by 
 the Laps Calam'maris than by Iron, and more 
 flrongly by Iron than by Copper, and more 
 ftrongly by Copper than by Silver, and more 
 flrongly by Iron, Copper, Tin ahdXead, than 
 by Mercury? And is it not for the fame reafon 
 that Iron requires moxc Aqua fort is to dillblve 
 it than Copper, and Copper more than the o- 
 ther Metals ; and that ot all Metals, Iron is dif- 
 folved moft eafily, and is moll apt to rult ; and 
 next after Iron, Copper ? 
 
 When Oil of Vitriol is mix'd with a little 
 Water, or is run per dcl'tquuim^ and in Dillil- 
 lation the Water afcends difficultly, and brings 
 over with it fome part of the Oil of Vitriol in 
 the form of Spirit of \ itriol, and this Spirit be- 
 ing poured upon Iron, Copper, or Salt of Tar- 
 tar, unites with the Bod}' and lets go the Wa- 
 ter, doth not this flievv that the acid Spirit is at- 
 traded by the Water, and more attracted by 
 the tix'd Body than by the Water, and there- 
 fore lets go the Water to clofe with the fix'd 
 Body ? And is it not for the fame reafon that 
 the Water and acid Spirits which are mix'd to- 
 gether in Vinegar, Aqua forth , and Spirit of 
 Salt, cohere and rile together in Diflillation ; 
 but if the Menfiruum be poured on Salt of Tar- 
 tar, or on Lead or Iron, or any fix'd Body 
 
 which 
 
. ; . [357] 
 
 which it can difTolvc, the Acid b}^ a {Irongcr At- 
 tradion adheres to the Body, and lets go the 
 Water ? And is it not aUb from a mutual At- 
 traction that the Spirits of Soot and Sea-Salt 
 unite and compofe the Particles of Sal-armo- 
 niac , which are Icfs volatile than before , be- 
 caufe grofler and freer from Water; and that 
 the Particles of Sal-armoniac in Sublimation car- 
 ry up the Particles of Antimony, which will not 
 fublime alone ; and that the Particles of Mer- 
 cury uniting with the acid Particles of Spirit 
 of Salt compofe Mercury fublimate, and with 
 the Particles of Sulphur, compofe Cinnaber ; 
 and that the Particles of Spirit of Wine and 
 Spirit of Urine well reclified unite, and letting 
 go the Water which dillblved them, compofe a 
 confillent Body; and that in fubliming Cinna- 
 ber from Salt of Tartar, or from quick Lime, 
 the Sulphur by a f Ironger Attraction of the Salt 
 or Lime lets go the Mercury, and llays with 
 the fix'd Body ; and that when Mercury fubli- 
 mate is fublimed from Antimony, or from Re- 
 gulus of Antimony, the Spirit of Salt lets go the 
 Mercury, and unites with the antimonial Me- 
 tal which attrads it more llrongly, and Hays 
 with it till the Heat be great enough to make 
 them both afcend toget.ier, and then carries 
 up the Metal Avith it in the form of a very fu- 
 lible Salt, called Butter of Antimony, although 
 the Spirit of Salt alone be almoll as volatile as 
 Water, and the Antimony alone as fix'd as 
 Lead ? 
 
 V>J\\tr\.^^Ha fort is dilTolves Silver and not 
 Gold, afid jfqza regia dilfolves Gold and not 
 
 Aa 3 Silver, 
 
[ 358 ] 
 
 Silver , may it not be faid that Aqua forth is 
 fubtile enough to penetrate Gold as well as Sil- 
 ver, but wants the attractive Force to give it 
 Entrance ; and that Aqua reg'ia is fubtile enough 
 to penetrate Silver as well as Gold, but wants 
 the attractive Force to give it Entrance? For 
 Aqua reg'ta is nothing elfe than Aqua fort is 
 mix'd with fome Spirit of Salt, or with Sal ar- 
 moniac ; and even common Salt diflblved in A- 
 quafortis, enables xhQ Menffruum to diflblve 
 Gold, though the Salt be a grofs Body. When 
 therefore Spirit of Salt precipitates Silver out 
 oi Aqua fort is:, is it not done by attrading and 
 mixing with the Aqua fortis^ and not attraft- 
 ing, or perhaps repeUing Silver? And when 
 Water precipitates Antimony out of the Subli- 
 mate of Antimony and Sal-armoniac, or out of 
 Butter of Antimony, is it not done by its dif- 
 folving, mixing with, and weakening the Sal^ 
 armoniac or Spirit of Salt, and its not attract- 
 ing, or perhaps repelling the Antimony? And 
 is it not for want of an attra(!:tive Virtue be- 
 tween the Parts of Water and Oil, of Quick- 
 filver and Antimony , of Lead and Iron, that 
 thefe Subilances do not mix ; and by a weak 
 Attraction, that Quick-filver and Copper mix 
 difficultly ; and from a ftrong one, that Quick- 
 filver and Tin, A^ntimony and Iron, Water and 
 Salts, mix readily ? And in general, is it not 
 from the fame Principle that Heat congregates 
 homogeneal Bodies, and feparates heterogeneal 
 ones? 
 
 When Arfnick with Soap gives ^^Regulus, 
 and with Mercury fublimate a- volatile fufible 
 
 Salt, 
 
[ 359 ] 
 
 Salt, like Butter of Antimony, doth not this 
 ilievv that Arfnick, which is a Subltance totally 
 volatile, is compounded of fix'd and volatile 
 Parts, llrongly cohering by a mutual Attraftion, 
 fo that the volatile will not afcend without car- 
 rying up the fixed? And fo, when an equal 
 weight of Spirit of Wine and Oil of Vitriol 
 are digefled together , and in Diilillation yield 
 two fragrant and volatile Spirits which will not 
 mix with one another, and a tix'd black Earth 
 remains behind; doth not this fliew^ that Oil of 
 Vitriol is compoCed of volatile and fix'd Parts 
 ftrongly united by Attraction, fo as to afcend 
 togetiier in form of a volatile, acid, fluid bait, 
 until the Spirit of VV^ine attrai^fs and feparatcs 
 the volatile Parts from the fixed ? And tlicre- 
 fore, iince Oil of Sulphur per cmnpanam is of 
 the iame Nature with Oil of Mtriol, mav it not 
 be inferred, that Sulphur is alfo a mixture of 
 volatile and fix'd Parts fo flrongly cohering by 
 Attradion, as to afcend together in Sublima- 
 tion. By dilfolving Flowers of Sulphur in Oil 
 of Turpentine, and diflilhng the Solution, it is 
 found that Sulphur is compofed of an inflama- 
 ble thick Oil or fat Bitumen, an acid Salt, a ve- 
 ry fix'd Earth, and a little Metal. The three 
 firft were found not much unequal to one 
 another, the fourth in fo fmall a quantity as 
 fcarce to be worth confidering. The acid Salt 
 dilTolved in Water, is the fame with Oil of Sul- 
 phur per campanant^ and abounding much in 
 the Bowels of the Earth, and particularly in 
 Markafites, unites it 'felf to the other Ingredi- 
 ents of the Markafite, which are. Bitumen, I- 
 
 A a 4 ron. 
 
i*on, Copper and Earth, and with them com- 
 pounds Alume, Vitriol and Sulphur. With the 
 Earth alone it compounds Alume ; with the 
 Metal alone, or Metal and Earth together, it 
 compounds Vitriol ; and v^ith the Bitumen and 
 Earth it compounds Sulphur. Whence it comes 
 to pafs that Markafites abound with thofe three 
 Minerals. And is it not from the mutual At- 
 traction of the Ingredients that they flick toge- 
 ther for compounding thefe Minerals, and that 
 the Bitumen carries up the other Ingredients of 
 the Sulphur, which without it would not i'ub- 
 lime? And the fame Queflion may be put con- 
 cerning all, or almoft all the grofs Bodies in 
 Nature. For all the Parts of Animals and Ve- 
 getables are compofed of Subllances volatile 
 and fix'd, fluid and folid, as appears by their 
 Analyfis : and fo are Salts and Minerals, fo tar 
 as Chymifts have been hitherto able to examine 
 their Compoiition. 
 
 When Mercury fublimate is refublimed with 
 frefli Mercury, and becomes Mercurms dulcis^ 
 which is a white taftlefs Earth fcarce dillblva- 
 ble in Water, and Mercurim dulc'ts refublimed 
 with Spirit of Salt returns into Mercury fubli- 
 mate ; and when Metals corroded with a little 
 acid turn into Ruft, which is an Earth taltlefs 
 and indifTolvable in Water, and this Earth im- 
 bibed with more Acid becomes a metallick 
 Salt; and when fome Stones, as Spar of Lead, 
 diifolved in proper MenJIrmims become Salts; 
 do not thefe things fliew that Salts are dry Earth 
 ^nd watryAcid united byAttradion, and that 
 the Earth will not become a Salt without fo 
 
 much 
 
[3^1 ] 
 
 much Acid as makes it difToivnble in Water? 
 Do not the (harp and pungent Taites of Acids 
 arife from the llrong Attradion whereby the 
 acid Particles rufli upon and agitate the Parti- 
 cles of the Tongue? And when iMetals are dif- 
 folved in acid Menftriinms^ and the Acids in 
 conjunction with the Metal ad: after a ditlerent 
 manner, fo that the Compound has a different 
 talle much milder than before, and fomctimes 
 a fwcet one ; is it not becaufc the Acids ad- 
 here to the metallickParticles, and thereby lofe 
 much of their Adivity ? And if the Acid be in 
 too fmall a Proportion to make the Compound 
 diffolvable in Water, will it not by adhering 
 Ih'ongly to the Metal become unadive and lofe 
 its taite, and the Compound be a taillefs Earth ? 
 For fuch things as are not diffolvable by the 
 Moiilure of the Tongue, ad not upon the 
 Tafte. 
 
 As Gravity makes the Sea flow round the 
 denier and weightier Parts of the Globe of the 
 Earth , fo the Attradion may make the u^atry 
 Acid flow round, the denfer and compader 
 Particles of Earth for compofmg the Particles 
 of Salt. For othcrwife the Acid would not do 
 the office of a Medium between the Earth and 
 common Water, for making Salts diffolvable in 
 the Water; nor would Salt of Tartar readily 
 draw off the Acid from diffolved Metals, nor 
 Metals the Acid from Mercury. Now as in the 
 great Globe of the Earth and Sea, the denfell 
 J^odies by their Gravity fmk down in Water, 
 and always endeavour to go towards the Cen- 
 ter of the Globe ; fo in Particles of Salt , the 
 
 denfefl 
 
denfell Matter may always endeavour to ap- 
 proach the Center of the Particle : So that a 
 Particle of Salt may be compared to a Chaos ; 
 being denfe, hard, dry, and earthy in the Cen- 
 ter ; and rare, foft, moilt, and watry in the 
 Circumference. And hence it leems to be that 
 Salts are of a lading nature , being fcarce de- 
 ftroy'd, unlefs by drawing away their watry 
 Parts by violence, or by letting them foak into 
 the Pores of the central Earth by a gentle Heat 
 in Putrefaction, until the Earth be diifolved by 
 the Water, and feparated into fmaller Particles, 
 which by reafon of their fmallncfs make the 
 rotten Compound appear of a black Colour. 
 Hence alfo it may be that the Parts of Animals 
 and Vegetables preferve their feveral Forms, 
 and aflimilate their Nourifliment ; the foft and 
 moiit Nourilhment cafily changing its Texture 
 by a gentle Heat and Motion , till it becomes 
 like the denfe, hard, dry, and durable Earth 
 in the Center of each Particle. But when the 
 Nourifliment grows unfit to be ailimilated, or 
 the central Earth grows too feeble to aflimilate 
 it, the Motion ends in Confulion, Putrefaction 
 and Death. 
 
 If a very fmall quantity of any Salt or Vitriol 
 be diiiblved in a great quantity of Water, the 
 Particles of the Salt or V itriol will not fink to 
 the bottom, though they be heavier^ in Specie 
 than the W^'ater, but will evenly diffufe them- 
 felves into all the Water, fo as to make it as fa- 
 line at the top as at the bottom. And does not 
 this imply that the Parts of the Salt or Vitriol 
 recede from one another, and endeavour to ex- 
 pand 
 
[ 3^3 ] 
 
 pand themfelves, and get as far afunder as the 
 quantity of Water in vviiich they float, will al- 
 low? And does not this Endeavour imply that 
 they have a repulfive Force by which they fly 
 from one another, or at leafl, that they attrac^t 
 the Water more llrongly than they do one ano- 
 ther? For as all things afcend in VV^ater which 
 are lefs attra^led than Water, by the gravitating 
 Power of the Earth ; fo all the Particles of Salt 
 which float in Water, and are lefs attracted 
 than Water by any one Particle of Salt, mult 
 recede from that Particle, and give way to the 
 more attracted Water. 
 
 When any faline Liquor is evaporated to a 
 Cuticle and let cool, the Salt concretes in re- 
 gular Figures ; which argues, that the Particles 
 of the Salt before they concreted, floated in 
 the Liquor at equal diilances in rank and file, 
 and by confequence that they ac^led upon one 
 another by lome Power which at equal diflances 
 is equal, at unequal diltances unequal. For by 
 fuch a Power they will range themfelves uni- 
 formly, and without it they will float irregular- 
 ly, and come together as irregularly. And 
 fince the Particles of Ifland Cryltal acl all the 
 fame way upon the Rays of Light for caufmg 
 the unulual Refraftion, may it not be fuppofed 
 that in the Formation of this Cryflal, the Par- 
 ticles not only ranged themfelves in rank and 
 file for concreting in regular Figures, but alfo 
 by fome kind of polar Virtue turned their ho- 
 mogeneal Sides the fame way. 
 
 The Parts of all homogeneal hard Bodies 
 which fully touch one another, flick together 
 
 very 
 
[ 3^4 ] 
 
 very ftrongly. And for explaining how this 
 may be, lome have invented hooked Atoms, 
 which is begging the Queflion; and others tell 
 us that Bodies are glued together by reft, that 
 is,^ by an occult Quality, or rather by nothing; 
 and others, that they flick together by confpi- 
 ring N4otions, that is, by relacive rell ainongfl 
 themfelvcs. I had rather inter from their Co- 
 hefion, that their Particles attrad one another 
 by fome Force, which in immediate Conta6i: is 
 exceed' ng ftrong, at fmall diflances performs 
 the chymical Operations above mentioned, and 
 reaches not far from the Particles with any fen- 
 fible Eircd. 
 
 All Bodies feem to be compofed of hard Par- 
 ticles : For otherwife Fluids would not congeal ; 
 as Water, Oils, Vinegar, and Spirit or Oil of 
 Vitriol do by freezing ; Mercury by Fumes of 
 Lead; Spirit of Nitre and Mercury, bydiflbl- 
 ving the Mercury and evaporating the Flegm ; 
 Spirit of Wine and Spirit of Urine, bydeiiegm- 
 ing and mixing them ; and Spirit of Urine and 
 Spirit of Salt, by fubliming them together to 
 make Sal-armoniac. Even the Kays of Light 
 feem to be hard Bodies; for otherwife they 
 would not retain different Propenics in their 
 different Sides. And therefore Hardnefs may 
 be reckon'd the Property of all uncompounded 
 Matter. At leall, this leems to be as evident 
 as the univerfal Impenetrability of Matter. For 
 all Bodies, fo far as Experience reaches, are ei- 
 ther hard , or may be harden'd ; and we have 
 no other Evidence of univerfal Impenetrability, 
 befides a large Experience without an experi- 
 mental 
 
[ 3^5 ] 
 
 mental Exception. Now if compound Bodies 
 are fo very hard as we find fome of them to 
 be, and yet are very porous, and confill of Parts 
 which are only laid together ; the fimple Par- 
 ticles which are void of Pores, and were never 
 ]fet divided, muft be much harder. For fuch 
 hard Particles being heaped up together, can 
 fcarce touch one another in more than a few 
 Points, and therefore muft be feparable by 
 much lefs Force than is rcquifite to break a Ib- 
 lid Particle, whofe Parts touch in all the Space 
 between them, wituout any Pores or Interfaces 
 to weaken their Cohefion. And how fuch ve- 
 ry hard Particles which are only laid together 
 and touch only in a few Points, can Hick toge- 
 ther, and that fo firmly as they do, without the 
 afliilance of fomething which caufes them to 
 be attracted or prefs'd towards one another, is 
 very difficult to conceive. 
 
 The fame thing I infer alfo from the cohe- 
 ring of two polilli'd Marbles m vacuo, and from 
 the {landing of Quick-filver in the Barometer at 
 the height of 50, 60 or 70 Inches, or above, 
 when ever it is well purged of Air and careful- 
 ly poured in, fo that its Parts be every where 
 contiguous both to one another and to the 
 Glafs. The xltmolphere by its weight prelfes 
 the Quick-lilver into the Glafs, to the height of 
 29 or 30 Inches. And fome other Agent raifes 
 it higher, not bv preliing it into the Glafs, but 
 by making its Parts Hick to the Glafs , and to 
 one another. For upon any dilcontinuation of 
 Parts, made either by Bubbles or by iliaking the 
 
 Glafs, 
 
[ 366 ] 
 
 Glafs, the whole Mercury falls down to the 
 height of ^<) or 30 Inches. 
 
 And of the fame kind with thefe Experi- 
 ments are thofe that follow. If two plane po- 
 li(h'd Plates of Glais (fuppofe two pieces of a 
 pohfli'd Looking-glafs) be laid together^ fo that 
 their fides be parallel and at a very Imall di- 
 ftance from one another, and then their lower 
 edges be dipped into Water, the Water will 
 rife up between them. And the lefs the di- 
 flance of the Glalles is, the greater will be the 
 height to which the Water will rife. If the 
 dif lance be about the hundredth part of an Inch, 
 the Water will rife to the height of about an 
 Inch; and if the diflance be greater or lefs«in 
 any Proportion, the height will be reciprocally 
 proportional to the diftance very nearly. For 
 the attractive Force of the Glafies is the fame, 
 whether the dillance between them be greater 
 or lefs ; and the weight of the Water drawn 
 up is the fame, if the Height of it be recipro- 
 cally proportional to the height of the Glalles. 
 And in like manner. Water afcends between 
 two Marbles poHfli'd plane, when their polifh- 
 ed fides are parallel, and at a very httle diflance 
 from one another. And if ilender Pipes of 
 Glafs be dipped at one end into flagnating Wa- 
 ter, the Water will rife up within the Pipe, and 
 the height to which it riies will be reciprocally 
 proportional to the Diameter of the Cavity of 
 the Pipe, and will equal the height to which it 
 rifes between two Planes of Glafs, if the Semi- 
 diameter of the Cavity of the Pipe be equal to 
 the diflance between the Planes, or thereabouts. 
 
 And 
 
And thefe Experiments fucceed after the fame 
 manner iu vacuo as in the open Air, (as hath- 
 been tried before the Royal Society,) and there-;, 
 fore are not influenced by the Weight or Pref- 
 fure of the Atmofphere. 
 
 Ajid if a large Pipe of Glafs be filled with 
 fifted Aflies well prcHed together in the Glafs, 
 and one end of the Pipe be dipped into flag- 
 nating Water, the Water will rife up llowly in 
 the Aflies, fo as in the fpace of a \Veek or. Fort- 
 night to reach up within the Glafs, to the height 
 of 30 or 40 hiches above the Itagnating Water. 
 And the Water rifes up to this height by the 
 A(;:iion only of thofe Particles of the Aflies which 
 are upon the Surface of the elevated Water;- 
 the Particles which are within the Water, at-* 
 trading or repelling it as much downwards 
 as upwards. And therefore the^(!:l:ion of the 
 Particles is very Itrong. But the Particles of 
 the Aflics being not fo denfe and clofe toge- 
 ther as thofe of Glafs, their Action is not fo 
 ib'ong as that of Glafs, which keeps Quick-fil- 
 ver fulpended to the height of 60 or 70 Inches, 
 and therefore ads with a Force which would 
 keep Water fufpended to the height of above 
 60 Feet. 
 
 By the fame Principle, a Sponge fucks in 
 Water, and the Glands in the Bodies of Ani- 
 mals, according to their feveral Natures and 
 Dilpofitions, luck in various Juices from the 
 Blood. 
 
 If two plane polifli'd Plates of Glafs three or 
 four Inches broad, and twenty or twenty five 
 long, be laid, one of them parallel to the Ho- 
 rizon, 
 
[ 3^8 ] 
 
 rizon, the other upon the fiiil, fo as at one of 
 their ends to touch one another , and contain 
 an Angle of about lo or 15" Minutes, and the 
 fame be firlt moillen'd on their inward fides 
 with a clean Cloth dipp'd into Oil of Oranges 
 or Spirit of Turpentime, and a Drop or two of 
 the Oil or Spirit be let fall upon the loWer 
 Glafs at the other end ; fo foon as the upper 
 Glafs is laid down upon the lower fo as to 
 touch it at one end as above, and to touch the 
 Drop at the other end, making with the lower 
 Glafs an Angle of about 10 or 15" Minutes ; the 
 Drop will begin to move towards the Concourfe 
 of the Glalfes, and will continue to move with 
 an accelerated Motion, till it arrives at that 
 Concourfe of the Glafles. For the two GlalTes 
 attradl the Drop, and make it run that way to- 
 wards which the Attradions incline. And if 
 when the Drop is in motion you lift up that end 
 of the Glalfes where they meet , and towards 
 which the Drop moves , the Drop will afcend 
 between the Glalfes, and therefore is attraded. 
 And as you lift up the Glalfes more and more, 
 the Drop will afcend flower and flower, and at 
 length reft, being then carried downward by 
 its Weight, as much as upwards by the Attra- 
 dion. And by this means you may know the 
 Force by which the Drop is attraded at all di- 
 fiances from the Concourfe of the Glalfes. 
 
 Now by fomc Experiments of this kind, 
 (made by Mr. HawksbyJ it has been found that 
 the Attradion is almolt reciprocally in a dupli- 
 cate Proportion of the diftance of the middle 
 of the Drop from the Concourfe of the Glalfes, 
 » viz. 
 
[3^9] 
 
 viz. reciprocally in a fimple Proportion, by 
 reafon of the fpreading of the Drop, and its 
 touching each Glafs in a larger Surface; and 
 again reciprocally in a fimple Proportion , by 
 real on of the Attractions growing Itronger 
 within the fame quantity of attracting Sur- 
 face. The Attradioa therefore within the 
 fame quantity of attraCtiAg Surface , is reci- 
 procally as the dillancc betu^een the GlalTes. 
 And therefore where the diilance is exceed- 
 ing fm.all, the Attraction mult be exceeding 
 great. By the Table in the fecond Part of 
 the fecond Book, wherein the thicknelles of 
 colour 'd Plates of Water between two Glalfes 
 are fet down , the thicknefs of the Plate where 
 it appears very black, is three eighths of the 
 ten hundred thoufandth part of an Inch. And 
 where the Oil of Oranges between the GlaiFes 
 is of this thicknefsj theAttradion colleded by 
 the foregoing Rule, feems to be fo Itrong, as 
 within a Circle of an Inch in diameter, to fuf- 
 fice to iiold up a Weight equal to that of a Cy- 
 linder of Water of an Inch in diameter j and 
 two or three Furlongs in length. And where 
 it is of a lefs thicknefs the Attradion may be 
 proportionally greater, and continue to increafe, 
 until the thicknefs do not exceed that of a fm- 
 gle Particle of the Oil. There are therefore 
 Agents in Nature able to make the Particles of 
 Bodies ilick together by very ilrong Attra6tions. 
 And it is the Bufmefs of experimental Philofo- 
 phy to find them out. 
 
 B b Now 
 
[ ?70 ] 
 
 Now the fmalleft Particles of Matter may co- 
 here by the ftrongelt Attradions, and compofe 
 bigger Particles of weaker Virtue; and many 
 of thefe may cohere and compofe bigger Par- 
 ticles whofe Virtue is itill weaker, and loon for 
 divers Succeflions, until the Progreflion end in 
 the biggeft Particles on which the Operations 
 in Chymiilry, and the Colours of natural Bodies 
 depend , and which by coliering compofe Bo- 
 dies of a fenfible Magnitude. If the Body is 
 compa^l, and bends or yields inward to Pref- 
 fion without any Hiding of its Parts, it is hard 
 and elaltick, returning to its Figure with a Force 
 arifmg from the mutual Attraction of its Parts. 
 If the Parts Aide upon one another, the Body- 
 is malleable or foft. If they flip eafily, and are 
 of a fit fize to be agitated byHeaty and the Heat 
 is big enough to keep them in Agitation, the 
 Body is fluid'; and if it be apt to Hick to things,- 
 it is humid ; and the Drops of every Fluid af- 
 feft a round Figure by the mutual Attraftion of 
 their Parts, as the Globe of the Earth and Sea^ 
 affedls a round Figure by the mutual Attractions 
 of its Parts by Gravity. 
 
 Since Metals dilTolved in Acids attradl but ^' 
 frnall quantity of the Acid, their attradtive Force' 
 can reach but to a fmall diftance from them. 
 And as in Algebra, where affirmative Quanti- 
 ties vaniih and ceafe, there negative ones be- 
 gin ; fo in Mechanicks, where Attraction cea- 
 fes, there a repulfive Virtue ought to fucceed*.. 
 And that there is fuch a Virtue , feems to fol* 
 low from the Reflexions and Inflexions of the 
 
 Rayt 
 
[371 ] 
 
 Rays of Light. For the Rays are repelled by 
 Bodies in both thefe Cafes, without the imme- 
 diate Contad of the retlefting or intletting Bo- 
 dy. It feems alfo to follow from the Emiffion 
 of Light ; the Ray fo foon as it is fhaken oif 
 from a fliining Body by the vibrating Motion of 
 the Parts of the Body, and gets beyond the 
 reach of Attradlion, being driven away with ex- 
 ceeding great Velocity. For that Force which 
 is fufficient to turn it back in Reflexion, may 
 be futficient to emit it. It feems alfo to fol- 
 low from the Production of Air and Vapour. 
 The Particles when they are Ihaken oti from 
 Bodies by Heat or Fermentation > fo ioon as 
 they are beyond the reach of the Attradion of 
 the Body, receding from it, and alfo from one 
 another with great Strength , and keeping at a 
 dilfance, fo as fometimes to take up above a 
 million of times more fpace than they did be- 
 fore in the form of a denfe Body. Which vafl 
 Contradion andExpanfion feems unintelligible^ 
 by feigning the Panicles of Air to be fpringy 
 and ramous, or rolled up like Hoops, or by a- 
 ny other means than a repulfive Power. The 
 Particles of Fluids which do not cohere too 
 flrongly, and are of fuch a fmallnefs as renders 
 them molt fufceptible of thofe Agitations which 
 keep Liquors in a Fluor, are moil eafily fepa- 
 rated and rarified into Vapour, and in the Lan- 
 guage of the Chymilts, they are volatile, rati- 
 fying with an eafy Heat, and condenfmg with 
 Cold. But thofe which are grolTer, and fo lefs 
 fufceptible of Agitation, or cohere by a flrong- 
 
 Bb i er 
 
t 372 ] 
 
 er Attraction, are not feparatcd without a 
 itronger Heat, or perhaps not without Fermen- 
 tation. And thcie ]ait are the Bodies which 
 Chymiits call fix'd, and being rarihed by Fer- 
 mentation,, become true permanent Air : thofe 
 Particles receding from one another with the 
 greatell Force, and being mofl difficultly brought 
 together, which upon Contad: cohere moll 
 Ih'ongly. And becaufe the Particles of perma- 
 nent iVir are groflcr, and arife from denier Sub- 
 llanccs than thofe of \ apours, thence it is:that 
 true Air is more ponderous than Vapour, and 
 that a moift Atmofphere is lighter than a dry 
 one, quantity for quantity. From the fame re- 
 pelling Power it feems to- be that Flies walk 
 upon the Water without wetting their Feet; 
 and that the Objedl-glafTes of long Telefcopes 
 Jie upon one another without touching; and 
 that dry Powders are difficultly made to touch 
 one another fo as to Hick together, unlefs by 
 melting them , or wetting them with Water, 
 which by exhaling may bring them together; 
 and that two polifli'd Marbles, which by im- 
 mediate Contad Hick together, are difficultly? 
 brought fo clofe together as to lUck. 
 
 And thus Nature will be very conformable 
 to her felf and very fimple, performing all the 
 great Motions of the heavenly Bodies by the 
 Attradion of Gravity which intercedes thofe 
 Bodies, and almoft all the fmall ones of their 
 Particles by fome other attradive and repelling 
 Powers which intercede the Particles. The 
 yis inertia is a paflive Principle by which Bo- 
 dies 
 
[373 ] 
 
 ^ics perfifl in their Motion or RelTT receive 
 Motion in proportion to the Force imprelling 
 it, and refill as much as they are refilted. By 
 this Principle alone there never could have been 
 any Motion in the World. Some other Prin- 
 ciple was necelTary for putting Bodies into Mo- 
 tion; and now they are in Motion, fome other 
 Principle is necelfary for conferving the Mo- 
 tion. For from the various Compofition of two 
 Motions, 'tis very certain that there is not al- 
 ways the lame quantity of Motion in the World. 
 For if two Glooes joined by a DenderRod, re- 
 volve about their common Center of Gravity 
 with an uniform Motion, while that Center 
 moves <^n uniformly in a right Line drawn in 
 the Plane of their circular Motion ; the Sum of 
 the Motions of the two Globes, as often as the 
 Globes are in the right Line •dcfcribcd by their 
 common Center of Gravity, will be bigger than 
 the Sum of their Motions, when they are in a 
 Line perpendicular to that right Line. By this 
 Inlbnce it appears that Motion may be got or 
 loll. But by reafon of the Tenacity of Fluids, 
 and Attrition of their Parts, and uhe Weaknefs 
 of Elallicity in Solids, Motion is much more 
 apt to be loll than got, and is always upon the 
 Decay. For Bodies which are either abfolute- 
 ly hard, or fo foft as to be void of Elallicity, 
 will not rebound from one another. Impene- 
 trability makes them only flop. If two equal 
 Bodies meet directly in vacuo^ they will by the 
 Laws of Motion Hop where they meet, and 
 lofe ail their Motion, and remain in. refl, unleis 
 
 B b 3; they 
 
[ 374 ] 
 
 they be ekftick, and receive new Motion froni 
 their Spring. If they have fo much Elafticity 
 as fufhces to make them rebound with a quar- 
 ter, or half, or three quarters of the Force with 
 which they come together, they will loie three 
 quarters, or half, or a quarter of their Motion. 
 And this may be tried, by letting two equal 
 Pendulums fall againft one another from equal 
 heights. If the Pendulums be of Lead or loft 
 Clay , they will lofe all or almolt all their Mo- 
 tions : If of elaflick Bodies they will lofe all but 
 what they recover from their Elailicity. If it 
 be faid, that they can lofe no Motion but what 
 they communicate to other Bodies, the confe- 
 quence is, that in vacuo they can lofe no Mo- 
 tion, but when they meet they mud go on and 
 penetrate one anothers Dimenfions. If three 
 equal round Velfels be filled, the one with Wa- 
 ter, the other with Oil, the third with molten 
 Pitch, and the Liquors be llirred about alike 
 to give them a vortical Motiou ; the Pitch by 
 its Tenacity will lofe its Motion quickly , the 
 Oil being lefs tenacious will keep it longer, and 
 the Water being leis tenacious will keep it Ibng- 
 eit, but yet will lofe it in a fliort time. Whence 
 it is eafy to underltand, that if many contiguous 
 Vortices of molten Pitch were each of them as 
 large as thofe which fome fuppofe to revolve 
 about the Sun and fix'd Stars, yet thefe and all 
 their Parts would, by their tenacity and lliffiicfs, 
 communicate their Motion to one another till 
 they ai! reiled among themfelves. Vortices of 
 Oil or Water, or fome fluidev Matter, might 
 
 con- 
 
[ 375 I 
 
 .continue longer in Motion ; but unlefs the Mat- 
 ter were void of all Tenacity and Attrition of 
 Parts, and Communication of Motion, (which 
 is not to be fuppofed) the Motion would con- 
 itantly decay. Seeing therefore the variety of 
 Motion which we find in the World is always 
 decreafing, there is a neceflity of conferving 
 .and recruiting it by ^dive Principles, luch as 
 ,are the caufe of Gravity, by which Planets and 
 -Comets keep their Motions in their Orbs, and 
 Bodies acquire great Motion in falling; and the 
 caufe of Fermentation, by which the Heart and 
 Blood of Animals are kept in perpetual Motion 
 .and Heat ; rhe inward Parts of the Earth are 
 confiantly warm'd, and in fome places grow 
 very hot ; Bodies burn and fliine. Mountains 
 take Fire, the Caverns of the Earth are blown 
 up, and the Sun continues violently hot and 
 lucid, and warms all things by his Light. For 
 we meet with very Httle Motion in the World, 
 befides what is owing to thefe aftive Principles. 
 And if it were not for thefe Principles the Bo- 
 dies of the Earth, Planets, Comets, Sun, and 
 all things in them would grow cold and freeze, 
 and become inadive Malles ; and all Putrefa- 
 ftion. Generation, Vegetation and Life would 
 ceafe, 'and the Planets and Comets would not 
 remain in their Orbs. 
 
 AH thefe things being confider'd, it feems pro- 
 bable to me, that God in the Beginning form'd 
 Matter in folid, malTy, hard, impenetrable, move- 
 able Particles, of fuch Sizes and Figures, and with 
 fuch other Properties, and in fuch Proportion 
 
 Bb 4 to 
 
[316] 
 
 to Space , as moft conduced to the End for 
 which he form'd them ; and that thefe primi- 
 tive Particles being Solids, are incomparably 
 iiarder th^n any porous Bodies compounded of 
 them ; even lo very hard, as never to wear or 
 break in pieces: No ordinary Power being able 
 to divide what God himlelf made one in the firll 
 Creation. While the Particles continue entire, 
 they may compote Bodies of one and the lame 
 Nature and Texture in all Ages : But ihould 
 they wear away, or break in pieces, the Nature 
 of Things depending on them, would be chan^- 
 ged. Water and Earth compofed of old worn 
 Particles and Fragments of Particles, would not 
 be of the fame Nature and Texture now, with 
 Water and Earth compofed of entire Particles, 
 in the Beginning. And therefore that Nature 
 may be lailing, the Changes of corporeal Things 
 are to be placed only in the various Separations 
 and new AiTociations and Motions of thefe per- 
 manent Particles ; compound Bodies being apt 
 to break, not in themidlloflblid Particles, but 
 wJiere thofe Particles are laid together, and 
 only touch in a few Points. 
 
 It feems to me farther, that thefe Particles 
 have not only a Vu inertia, accompanied with 
 fuch pailive Laws of Motion as naturally rcfult 
 from that Force, but alfo that they are moved 
 by certain active Principles, fuch as is that of 
 Gravity, and that which caufcs Fermentation, 
 and thcCohefion of Bodies. Thefe Principles 
 I conlidcr not as occult Qualities, fuppofcd to 
 refult from the fpecihck Forms of Tilings, but 
 
[ 377 ] 
 
 as general Laws of Nature, by which the Things 
 themfelves are form'd : their Truth appearing 
 to us by Phaenomena ,' though their Caufes be 
 not yet difcover'd. For thele are manifeii: Qua- 
 lities, and their Caufes only are occult. And 
 the Ariftotelians' gave the Name of occult Qua- 
 lities not to manifeil: Qualities, but to fuch 
 Qualities only as they fuppofed to lie hid in 
 Bodies, and to be the unknown Caufes of ma- 
 nifeil Effeds : Such as would be the Caufes of 
 Gravity , and of magnetick and eledrick At- 
 tractions, and of Fermentations, if we fhould 
 fuppofe that thefe Forces or Anions arofe from 
 Qualities unknown to us, and uncapable of be- 
 ing difcovered and made manifeit. Such oc- 
 cult Qualities put a flop to the Improvement 
 of natural Philolbphy , and therefore of late 
 Years have been rejeCled. To tell us that 
 every Species of Things is endow'd withan oc- 
 cult fpecitick Quality by which it ads and pro- 
 duces manifeft Kifeds, is to tell us nothing: 
 But to derive two or three general Principles 
 of Motion from Phaenomena, and afterwards 
 to tell us how the Properties and Adions of all 
 corporeal Things follow from thofe manifeit 
 Principles, would be a very great Itep in Phi- 
 lolbphy, though the Caufes of thofe Principles 
 were not yet difcover'd : And therefore I fcru- 
 ple not to propofe the Principles of Motion a- 
 bove mentioned, they being of very general Ex- 
 tent, and leave their Caufes to be found out. 
 
 Now by the help of thcfe Principles, all ma- 
 terial Things feem to have been compofed of 
 
 the 
 
[ 378 ] 
 
 jlie hard and folid Particles above mention'dar 
 varioufly affociated in the firft Creation by the 
 Counfel of an intelligent Agents For it became 
 him who created them to fet them in order. 
 And if he did fo, it's unpliilofophical to feek 
 for any dther Origin of the World, or to pre- 
 tend that it might arife out of a Chaos by the 
 mere Laws of Nature; though being once 
 form'd, it may continue by thofe Laws for ma- 
 ny Ages. For while Comets move in very ex- 
 centrick Orbs in all manner of Pofitions, blind 
 Fate could never make all the Planets move 
 one and the fame way in Orbs concentrick, 
 fome inconfiderable Irregularities excepted 
 which may have rifen from the mutual Acftions 
 of Comets and Planets upon one another, ancj 
 which will be apt to increafe, till this Syilem 
 wants a Reformation. Such a wonderful Uni- 
 formity in the Planetary Syilem mult be allow- 
 ed the EfFed of Choice. And fo mult the 
 Uniformity in the Bodies of Animals, they ha- 
 ving generally a right and a left fide Ihaped a- 
 like, and on either fide of their Bodies two 
 Legs behind, and either two Arms, or two 
 Legs, or two Wings before upon their Shoul- 
 ders, and between their Shoulders a Neck run- 
 ning down into a Back-bone, and a Head up- 
 on it ; and in the Head two Ears, two Eyes, a 
 Nofe, a Mouth and a Tongue, alike lituated. 
 Alfo the firll Contrivance of thofe very artifi- 
 cial Parts of Animals, the Eyes, Ep.rs, Brain, 
 Muxcles, Hc?rt, Lungs, Midrift Glands La- 
 rynx, Hands, Wings, Swimming Bladders, na- 
 tural 
 
r 379 ] 
 
 tural Spedlacles, and other Organs of Senfe and 
 Motion ; and the Inftind of Brutes and Infers, 
 can be the effed of nothing elfe than the Wif- 
 dom and Skill of a powerful ever-living Agent, 
 who being in all Places, is more able by 
 his Will to move the Bodies within his bound- 
 lefs uniform Senforium, and thereby to form 
 and reform the Parts of the Univerfe, than we 
 are by our Will to move the Parts of our own 
 Bodies. And yet we are not to confider the 
 World as the Body of God, or the feveral Parts 
 thereof, as the Parts of God. He is an uni- 
 form Being, void of Organs, Members or Parts, 
 and they are his Creatures fubordinate to him, 
 and fubfervient to his Will; and he is no more 
 the Soul of them, than the Soul of a Man is the 
 Soul of the Species of Things carried through 
 the Organs of Senfe into the place of its Sen- 
 fation, where it perceives them by means of its 
 immediate Prefence, without the Intervention 
 of any third thing. The Organs of Senfe are 
 not for enabling the Soul to perceive the Spe- 
 cies of Things in its Senforium , but only for 
 conveying them thither ; and God has no need 
 of fuch Organs, he being every where prefent 
 to the Things themfelves. And fmce Space is 
 divifible in iftfinuum^ and Matter is not necef- 
 farily in all places, it may be alfo allow'd that 
 God is able to create Particles of Matter of fe- 
 veral Sizes and Figures, and in feveral Propor- 
 tions to Space, and perhaps of different Denfi- 
 ties and Forces, and thereby to vary the Laws 
 of Nature, and make Worlds of feveral forts in 
 
 feveral 
 
[ 3So ] 
 
 feveral Parts of the Univerfc. At leafl, I fee 
 nothing of Contradidion in all this. 
 
 As in Mathematicks, fo in Natural Philofo- 
 phy, the Invefligation of difficult Things by the 
 Method of Analyfis, ought ever to precede the 
 Method of Compofition. This Analyfis con- 
 iifts in making Experiments and Obfervations, 
 and in drawing general Conclufions from them 
 by Indudion, and admitting of no Objedions 
 jigainll the Conclufions , but fuch as are taken 
 from Experiments, or other certain Truths. 
 For Hypothefes are not to be regarded in ex- 
 perimental Philofophy. And although the ar- 
 guing from Experiments and Obfervations by 
 Indudion be no Demonflration of general Con- 
 clufions ; yet it is the beft way of arguing which 
 the Nature of Things admits of, and may be 
 looked upon as fo much the itronger, by how 
 much the Induction is more general. And if 
 no Exception occur from Phaenomena, theCon- 
 clufion may be pronounced generally. But if 
 at any time afterwards any Exception fliall oc- 
 cur from Experiments, it may then begin to be 
 pronounced with luch Exceptions as occur. By 
 this way of Analyiis we may proceed from Com- 
 pounds to Ingredients, and from Motions to 
 the Forces producing them; and in general, 
 from Effects to their Caufes, and from particu- 
 lar Caufes to more general ones, till the Argu- 
 ment end in the moil general. This is the Me- 
 thod of Analyfis: And theSynthefis confiils in 
 alFuming the Caufes difcovcr'd, and ellablilh'd 
 as Principles, and by them explaining the Phae^ 
 
 nomena 
 
[38i] 
 
 nomena proceeding from theniy and proving 
 the Explanations. 
 
 In the two tirfl Books of thefe Opticks, I 
 proceeded by this Analyfis to difcover and prove 
 the original Ditlerences of the Rays of Light in 
 refpedof Refrangibility, Refiexibility, and Co- 
 lour, and their alternate Pits of ealy Retlexion 
 and eafy Tranfmiflion , and the Properties of 
 Bodies, both opake and pellucid, on which 
 their Reflexions and Colours depend. And 
 thefe Diiboveries being proved, may be alTumed 
 in the Method of-,Compoiition for explaining 
 the Phsenomena arifmg from them : An In- 
 llance of which Method I gave in the End of 
 the tirfl Book. In this third Book I have only- 
 begun the Analyfis of v\hat remains to be dif- 
 cover'd about Light and its Effeds upon the 
 Frame of Nature, hinting fevcral things about 
 it, and leaving the Hints to be examin'd and 
 improved by the farther Experiments and Ob- 
 fervacions of fuch as are inquilitive. And if 
 natural Philofophy in all its Parts, by purfuing 
 this Method, ihall nt length be perfc<^i:ed, the 
 Bounds of moral Philofophy will be alfo enlar- 
 ged. For fo far as we can know by natural 
 Philofophy what is the firllCaule, what Power 
 he has over us, and what Benehts we receive 
 from him, fo far our Duty towards him, as well 
 as that towards one another, will appear to us 
 by the Light of Nature. And no doubt, if the 
 Woriliip of falle Gods had not blinded the Hea- 
 then, their moral Philofophy would have gone 
 farther than to the four Cardinal Virtues ; and 
 
 inftead 
 
1 382 ] 
 
 inftead of teaching the Tranfmigration of Souls, 
 and to worlhip the Sun and Moon , and dead 
 Heroes, rhey would have taught us to worlhip 
 our true Author and Benefador. 
 
 F I N I S. 
 
Book III Hafe I 
 
1 
 
A Catalogue of Books printed for and fold hy 
 Will. Innys, at the Prince's- Arms in St. PaulV 
 Church-yard. 
 
 THE Pofthumous Works of Dr. Robert Hoeke; in which, 
 I. rhs prefent Deficiency of natural Philofophy is dif- 
 courfed of, with the Methods of rendring it more cer- 
 tain and beneficial, II. Of the Nature, Motion and Effefts of 
 Light, particularly that of the Sun and Comets. III. An hypo- 
 thetical Explication of M.emory ; how the Organs made ufe of 
 hy the Mind in its Operation may be mechanically underftood. 
 IV. An Hypothefis and Explication of the Caufe of Gravity, or 
 Gravitation, Magnetifm , c^c. V. Difcourfes of Earthquakes^ 
 their Caufes and Effeds, and Hiftories of feveral : To which are 
 annex'd, Phyfical Explications of feveral of the Fables in Ovid' 
 Metamorphofes, very different from other Mythologick Interpr 
 ters. VI. Ledlures for improving Navigation and Aftronon. 
 with the Uefcriptions of feveral new and ufeful Inftruments an 
 Contrivances ; the whole full of curious Difquifitions and Experi- 
 ments, illuftrated with Sculptures. To thefe Difcourfes is pre- 
 fix'd the Author's Life. By Richard Waller, R. S. Sec. Folio. 
 
 A Treatife of Algebra v both Hiftorical and Pradical ; with 
 fome additional Treatifes. I. Of the Cono-Cuneus. II. Of an- 
 gular SeAions and Trigonometry. III. Of the Angle of Conta<3v 
 with other things appertaining to theCompofition of Magnitudes, 
 the Inceptives of Magnitudes, and the Compofition of Motions, 
 with the Refults thereof. IV. Of Combinations, Alternations, 
 and aliquot Parts, hy John JVallis, D. D. Folio. 
 
 New Experiments Phyfico-Mechanical, touching the Air and 
 its Effedls, made, for the moft part, in a new Pneumatical En- 
 gine. The third Edition. Whereunio is added, A Defence of 
 the Author's Explication of the Experiments againft the Obje- 
 €iions oi Francij'cus Linus, znd Tho. Hob hs ; with Cats. By the 
 Honourable Robert Boyle, Efq; 4/0. 
 
 Jo. Alph. Borellus de Motu Animalium. Editio Nova, 4/5. 
 
 Lugd. Bat. 1710^ 
 
 Phil. Ckverii Introdudio in univerfam Geographiam tarn 
 ▼eterem quam novara. Editio Nova, a Johan. Bunone, ^to. 
 
 Lond. 17H. 
 
 Afta Eruditorum publicata Lipfis ab Initio, A. D. i68z ad 
 1717. incl. cum Supplementis & Indicibus, in 43 Tom. vel fepa- 
 ratlm. 
 
 Jo. Craig Methodus Figurarum, 4/0. Lond. i68j. 
 
 [ Euclides demonftratus per Coetfium, Svo. Lugd. Bat. 1692. 
 
 Geographic Pradique, par. N. Chemerau, ^to. Amft. 17 15, 
 
 Hermanni (Jac.) Phoronomia feude motu Corp 4rp. Amft.iiiC. 
 
 Mela 
 
Mela (Pomp.) de fitii Orbis cuin*Notis Groyovii, e^c. 2vo. 
 
 Lugd. Bat. 1(^96 
 
 Newtoni (Ifaaci, Eq. Aur.) Analyfis, per Quantitatum Series 
 Fludtiones ac DitFerentias cum Enumerauone Linearum Tertii 
 Ordinis, ^to. Land. 1711 
 
 Taylor (Brook) Methodus Incrementorum Diredla & Inver- 
 fa, ^to. ibid, i-jj-] 
 
 Tabulae Chronologicae continentes turn Sacra, turn Profana 
 maxime notatu digna a Creatione Mundi, ufque ad Chrifti Nati- 
 vitatem, per Ben. Marfliall, A. M. lolh. . Oxon. 1713 
 
 The Ancient and Modern Hiftdry of the Balearick Iflands, or 
 of the Kingdom oi Majorca ; which comprehends the Iflands of 
 Majorca, Minorca, Yvyfa, Fermentera, and others ; with their 
 Natural and Geographical Defcription By Collin Camphell, 2vo; 
 
 Analyfis j^quationum Univerfalis feu ad i^squationes Algebrai- 
 cas relblvendas methodus generalis, per Jof. Raphfon, ^to. i-joz 
 
 Barrow Lecliones Mathematics, Svo. Lend. 1683 
 
 Dionyfii Orbis Defcriptio, cnm Comment. Euflathii, Grjec.Lat. 
 
 ivo. Oxon. 1710 
 
 Horroccii opera Poflhuma Aftronomica, accedunt Guil. Crab- 
 traei Obfervationes Coeleftes, quibus acceflerunt Jo. Flamfledii de 
 Temporisi^quatione Diatriba, numeri ad Lunoe Theoriam Hor- 
 
 roccianam, &c. 4:0. Lond. 1678 
 
 Keill Introdudio ad veraip Phyficamii Svd. ibid. 1715; 
 
 ' Philofophical Tranfadions, giving fome Account of the pre- 
 fent Undertakings, Studies and Labours of the Ingenious, in ma- 
 ny confiderable Parts of the World. Vol. zp. for the Years 1714,- 
 1 7 15, 1 7 16. Gontinoed and publiflied by Dr. Edmund' Halley^ 
 Reg. Soc. Seer. 
 
 In the Prefs, the Seventh Edition of 
 
 The Wifdom of God manifefted in the Works of the Creation ; 
 in two Parts, viz. The Heavenly Bodies, Elements, Meteors^ 
 Foffils, Vegetables, Animals (Beafts, Birds, FiQies and Infeds) 
 more particularly in the Body of the Earth, its Figure, Motion 
 and Coniiflency, and in the admirable Strudure of the Bodies of 
 Man, and other Animals; as alfo in their Generation, crc. With 
 Anfwers to fome Objedions. By JohnRajf late Fellow of the 
 Royal Society. 
 
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