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src/testdata/Isaac.Newton-Opticks.txt
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10 OPTICKS:
11
12 OR, A
13
14 TREATISE
15
16 OF THE
17
18 _Reflections_, _Refractions_,
19 _Inflections_ and _Colours_
20
21 OF
22
23 LIGHT.
24
25 _The_ FOURTH EDITION, _corrected_.
26
27 By Sir _ISAAC NEWTON_, Knt.
28
29 LONDON:
30
31 Printed for WILLIAM INNYS at the West-End of St. _Paul's_. MDCCXXX.
32
33 TITLE PAGE OF THE 1730 EDITION
34
35
36
37
38 SIR ISAAC NEWTON'S ADVERTISEMENTS
39
40
41
42
43 Advertisement I
44
45
46 _Part of the ensuing Discourse about Light was written at the Desire of
47 some Gentlemen of the_ Royal-Society, _in the Year 1675, and then sent
48 to their Secretary, and read at their Meetings, and the rest was added
49 about twelve Years after to complete the Theory; except the third Book,
50 and the last Proposition of the Second, which were since put together
51 out of scatter'd Papers. To avoid being engaged in Disputes about these
52 Matters, I have hitherto delayed the printing, and should still have
53 delayed it, had not the Importunity of Friends prevailed upon me. If any
54 other Papers writ on this Subject are got out of my Hands they are
55 imperfect, and were perhaps written before I had tried all the
56 Experiments here set down, and fully satisfied my self about the Laws of
57 Refractions and Composition of Colours. I have here publish'd what I
58 think proper to come abroad, wishing that it may not be translated into
59 another Language without my Consent._
60
61 _The Crowns of Colours, which sometimes appear about the Sun and Moon, I
62 have endeavoured to give an Account of; but for want of sufficient
63 Observations leave that Matter to be farther examined. The Subject of
64 the Third Book I have also left imperfect, not having tried all the
65 Experiments which I intended when I was about these Matters, nor
66 repeated some of those which I did try, until I had satisfied my self
67 about all their Circumstances. To communicate what I have tried, and
68 leave the rest to others for farther Enquiry, is all my Design in
69 publishing these Papers._
70
71 _In a Letter written to Mr._ Leibnitz _in the year 1679, and published
72 by Dr._ Wallis, _I mention'd a Method by which I had found some general
73 Theorems about squaring Curvilinear Figures, or comparing them with the
74 Conic Sections, or other the simplest Figures with which they may be
75 compared. And some Years ago I lent out a Manuscript containing such
76 Theorems, and having since met with some Things copied out of it, I have
77 on this Occasion made it publick, prefixing to it an_ Introduction, _and
78 subjoining a_ Scholium _concerning that Method. And I have joined with
79 it another small Tract concerning the Curvilinear Figures of the Second
80 Kind, which was also written many Years ago, and made known to some
81 Friends, who have solicited the making it publick._
82
83 _I. N._
84
85 April 1, 1704.
86
87
88 Advertisement II
89
90 _In this Second Edition of these Opticks I have omitted the Mathematical
91 Tracts publish'd at the End of the former Edition, as not belonging to
92 the Subject. And at the End of the Third Book I have added some
93 Questions. And to shew that I do not take Gravity for an essential
94 Property of Bodies, I have added one Question concerning its Cause,
95 chusing to propose it by way of a Question, because I am not yet
96 satisfied about it for want of Experiments._
97
98 _I. N._
99
100 July 16, 1717.
101
102
103 Advertisement to this Fourth Edition
104
105 _This new Edition of Sir_ Isaac Newton's Opticks _is carefully printed
106 from the Third Edition, as it was corrected by the Author's own Hand,
107 and left before his Death with the Bookseller. Since Sir_ Isaac's
108 Lectiones Opticæ, _which he publickly read in the University of_
109 Cambridge _in the Years 1669, 1670, and 1671, are lately printed, it has
110 been thought proper to make at the bottom of the Pages several Citations
111 from thence, where may be found the Demonstrations, which the Author
112 omitted in these_ Opticks.
113
114 * * * * *
115
116 Transcriber's Note: There are several greek letters used in the
117 descriptions of the illustrations. They are signified by [Greek:
118 letter]. Square roots are noted by the letters sqrt before the equation.
119
120 * * * * *
121
122 THE FIRST BOOK OF OPTICKS
123
124
125
126
127 _PART I._
128
129
130 My Design in this Book is not to explain the Properties of Light by
131 Hypotheses, but to propose and prove them by Reason and Experiments: In
132 order to which I shall premise the following Definitions and Axioms.
133
134
135
136
137 _DEFINITIONS_
138
139
140 DEFIN. I.
141
142 _By the Rays of Light I understand its least Parts, and those as well
143 Successive in the same Lines, as Contemporary in several Lines._ For it
144 is manifest that Light consists of Parts, both Successive and
145 Contemporary; because in the same place you may stop that which comes
146 one moment, and let pass that which comes presently after; and in the
147 same time you may stop it in any one place, and let it pass in any
148 other. For that part of Light which is stopp'd cannot be the same with
149 that which is let pass. The least Light or part of Light, which may be
150 stopp'd alone without the rest of the Light, or propagated alone, or do
151 or suffer any thing alone, which the rest of the Light doth not or
152 suffers not, I call a Ray of Light.
153
154
155 DEFIN. II.
156
157 _Refrangibility of the Rays of Light, is their Disposition to be
158 refracted or turned out of their Way in passing out of one transparent
159 Body or Medium into another. And a greater or less Refrangibility of
160 Rays, is their Disposition to be turned more or less out of their Way in
161 like Incidences on the same Medium._ Mathematicians usually consider the
162 Rays of Light to be Lines reaching from the luminous Body to the Body
163 illuminated, and the refraction of those Rays to be the bending or
164 breaking of those lines in their passing out of one Medium into another.
165 And thus may Rays and Refractions be considered, if Light be propagated
166 in an instant. But by an Argument taken from the Æquations of the times
167 of the Eclipses of _Jupiter's Satellites_, it seems that Light is
168 propagated in time, spending in its passage from the Sun to us about
169 seven Minutes of time: And therefore I have chosen to define Rays and
170 Refractions in such general terms as may agree to Light in both cases.
171
172
173 DEFIN. III.
174
175 _Reflexibility of Rays, is their Disposition to be reflected or turned
176 back into the same Medium from any other Medium upon whose Surface they
177 fall. And Rays are more or less reflexible, which are turned back more
178 or less easily._ As if Light pass out of a Glass into Air, and by being
179 inclined more and more to the common Surface of the Glass and Air,
180 begins at length to be totally reflected by that Surface; those sorts of
181 Rays which at like Incidences are reflected most copiously, or by
182 inclining the Rays begin soonest to be totally reflected, are most
183 reflexible.
184
185
186 DEFIN. IV.
187
188 _The Angle of Incidence is that Angle, which the Line described by the
189 incident Ray contains with the Perpendicular to the reflecting or
190 refracting Surface at the Point of Incidence._
191
192
193 DEFIN. V.
194
195 _The Angle of Reflexion or Refraction, is the Angle which the line
196 described by the reflected or refracted Ray containeth with the
197 Perpendicular to the reflecting or refracting Surface at the Point of
198 Incidence._
199
200
201 DEFIN. VI.
202
203 _The Sines of Incidence, Reflexion, and Refraction, are the Sines of the
204 Angles of Incidence, Reflexion, and Refraction._
205
206
207 DEFIN. VII
208
209 _The Light whose Rays are all alike Refrangible, I call Simple,
210 Homogeneal and Similar; and that whose Rays are some more Refrangible
211 than others, I call Compound, Heterogeneal and Dissimilar._ The former
212 Light I call Homogeneal, not because I would affirm it so in all
213 respects, but because the Rays which agree in Refrangibility, agree at
214 least in all those their other Properties which I consider in the
215 following Discourse.
216
217
218 DEFIN. VIII.
219
220 _The Colours of Homogeneal Lights, I call Primary, Homogeneal and
221 Simple; and those of Heterogeneal Lights, Heterogeneal and Compound._
222 For these are always compounded of the colours of Homogeneal Lights; as
223 will appear in the following Discourse.
224
225
226
227
228 _AXIOMS._
229
230
231 AX. I.
232
233 _The Angles of Reflexion and Refraction, lie in one and the same Plane
234 with the Angle of Incidence._
235
236
237 AX. II.
238
239 _The Angle of Reflexion is equal to the Angle of Incidence._
240
241
242 AX. III.
243
244 _If the refracted Ray be returned directly back to the Point of
245 Incidence, it shall be refracted into the Line before described by the
246 incident Ray._
247
248
249 AX. IV.
250
251 _Refraction out of the rarer Medium into the denser, is made towards the
252 Perpendicular; that is, so that the Angle of Refraction be less than the
253 Angle of Incidence._
254
255
256 AX. V.
257
258 _The Sine of Incidence is either accurately or very nearly in a given
259 Ratio to the Sine of Refraction._
260
261 Whence if that Proportion be known in any one Inclination of the
262 incident Ray, 'tis known in all the Inclinations, and thereby the
263 Refraction in all cases of Incidence on the same refracting Body may be
264 determined. Thus if the Refraction be made out of Air into Water, the
265 Sine of Incidence of the red Light is to the Sine of its Refraction as 4
266 to 3. If out of Air into Glass, the Sines are as 17 to 11. In Light of
267 other Colours the Sines have other Proportions: but the difference is so
268 little that it need seldom be considered.
269
270 [Illustration: FIG. 1]
271
272 Suppose therefore, that RS [in _Fig._ 1.] represents the Surface of
273 stagnating Water, and that C is the point of Incidence in which any Ray
274 coming in the Air from A in the Line AC is reflected or refracted, and I
275 would know whither this Ray shall go after Reflexion or Refraction: I
276 erect upon the Surface of the Water from the point of Incidence the
277 Perpendicular CP and produce it downwards to Q, and conclude by the
278 first Axiom, that the Ray after Reflexion and Refraction, shall be
279 found somewhere in the Plane of the Angle of Incidence ACP produced. I
280 let fall therefore upon the Perpendicular CP the Sine of Incidence AD;
281 and if the reflected Ray be desired, I produce AD to B so that DB be
282 equal to AD, and draw CB. For this Line CB shall be the reflected Ray;
283 the Angle of Reflexion BCP and its Sine BD being equal to the Angle and
284 Sine of Incidence, as they ought to be by the second Axiom, But if the
285 refracted Ray be desired, I produce AD to H, so that DH may be to AD as
286 the Sine of Refraction to the Sine of Incidence, that is, (if the Light
287 be red) as 3 to 4; and about the Center C and in the Plane ACP with the
288 Radius CA describing a Circle ABE, I draw a parallel to the
289 Perpendicular CPQ, the Line HE cutting the Circumference in E, and
290 joining CE, this Line CE shall be the Line of the refracted Ray. For if
291 EF be let fall perpendicularly on the Line PQ, this Line EF shall be the
292 Sine of Refraction of the Ray CE, the Angle of Refraction being ECQ; and
293 this Sine EF is equal to DH, and consequently in Proportion to the Sine
294 of Incidence AD as 3 to 4.
295
296 In like manner, if there be a Prism of Glass (that is, a Glass bounded
297 with two Equal and Parallel Triangular ends, and three plain and well
298 polished Sides, which meet in three Parallel Lines running from the
299 three Angles of one end to the three Angles of the other end) and if the
300 Refraction of the Light in passing cross this Prism be desired: Let ACB
301 [in _Fig._ 2.] represent a Plane cutting this Prism transversly to its
302 three Parallel lines or edges there where the Light passeth through it,
303 and let DE be the Ray incident upon the first side of the Prism AC where
304 the Light goes into the Glass; and by putting the Proportion of the Sine
305 of Incidence to the Sine of Refraction as 17 to 11 find EF the first
306 refracted Ray. Then taking this Ray for the Incident Ray upon the second
307 side of the Glass BC where the Light goes out, find the next refracted
308 Ray FG by putting the Proportion of the Sine of Incidence to the Sine of
309 Refraction as 11 to 17. For if the Sine of Incidence out of Air into
310 Glass be to the Sine of Refraction as 17 to 11, the Sine of Incidence
311 out of Glass into Air must on the contrary be to the Sine of Refraction
312 as 11 to 17, by the third Axiom.
313
314 [Illustration: FIG. 2.]
315
316 Much after the same manner, if ACBD [in _Fig._ 3.] represent a Glass
317 spherically convex on both sides (usually called a _Lens_, such as is a
318 Burning-glass, or Spectacle-glass, or an Object-glass of a Telescope)
319 and it be required to know how Light falling upon it from any lucid
320 point Q shall be refracted, let QM represent a Ray falling upon any
321 point M of its first spherical Surface ACB, and by erecting a
322 Perpendicular to the Glass at the point M, find the first refracted Ray
323 MN by the Proportion of the Sines 17 to 11. Let that Ray in going out of
324 the Glass be incident upon N, and then find the second refracted Ray
325 N_q_ by the Proportion of the Sines 11 to 17. And after the same manner
326 may the Refraction be found when the Lens is convex on one side and
327 plane or concave on the other, or concave on both sides.
328
329 [Illustration: FIG. 3.]
330
331
332 AX. VI.
333
334 _Homogeneal Rays which flow from several Points of any Object, and fall
335 perpendicularly or almost perpendicularly on any reflecting or
336 refracting Plane or spherical Surface, shall afterwards diverge from so
337 many other Points, or be parallel to so many other Lines, or converge to
338 so many other Points, either accurately or without any sensible Error.
339 And the same thing will happen, if the Rays be reflected or refracted
340 successively by two or three or more Plane or Spherical Surfaces._
341
342 The Point from which Rays diverge or to which they converge may be
343 called their _Focus_. And the Focus of the incident Rays being given,
344 that of the reflected or refracted ones may be found by finding the
345 Refraction of any two Rays, as above; or more readily thus.
346
347 _Cas._ 1. Let ACB [in _Fig._ 4.] be a reflecting or refracting Plane,
348 and Q the Focus of the incident Rays, and Q_q_C a Perpendicular to that
349 Plane. And if this Perpendicular be produced to _q_, so that _q_C be
350 equal to QC, the Point _q_ shall be the Focus of the reflected Rays: Or
351 if _q_C be taken on the same side of the Plane with QC, and in
352 proportion to QC as the Sine of Incidence to the Sine of Refraction, the
353 Point _q_ shall be the Focus of the refracted Rays.
354
355 [Illustration: FIG. 4.]
356
357 _Cas._ 2. Let ACB [in _Fig._ 5.] be the reflecting Surface of any Sphere
358 whose Centre is E. Bisect any Radius thereof, (suppose EC) in T, and if
359 in that Radius on the same side the Point T you take the Points Q and
360 _q_, so that TQ, TE, and T_q_, be continual Proportionals, and the Point
361 Q be the Focus of the incident Rays, the Point _q_ shall be the Focus of
362 the reflected ones.
363
364 [Illustration: FIG. 5.]
365
366 _Cas._ 3. Let ACB [in _Fig._ 6.] be the refracting Surface of any Sphere
367 whose Centre is E. In any Radius thereof EC produced both ways take ET
368 and C_t_ equal to one another and severally in such Proportion to that
369 Radius as the lesser of the Sines of Incidence and Refraction hath to
370 the difference of those Sines. And then if in the same Line you find any
371 two Points Q and _q_, so that TQ be to ET as E_t_ to _tq_, taking _tq_
372 the contrary way from _t_ which TQ lieth from T, and if the Point Q be
373 the Focus of any incident Rays, the Point _q_ shall be the Focus of the
374 refracted ones.
375
376 [Illustration: FIG. 6.]
377
378 And by the same means the Focus of the Rays after two or more Reflexions
379 or Refractions may be found.
380
381 [Illustration: FIG. 7.]
382
383 _Cas._ 4. Let ACBD [in _Fig._ 7.] be any refracting Lens, spherically
384 Convex or Concave or Plane on either side, and let CD be its Axis (that
385 is, the Line which cuts both its Surfaces perpendicularly, and passes
386 through the Centres of the Spheres,) and in this Axis produced let F and
387 _f_ be the Foci of the refracted Rays found as above, when the incident
388 Rays on both sides the Lens are parallel to the same Axis; and upon the
389 Diameter F_f_ bisected in E, describe a Circle. Suppose now that any
390 Point Q be the Focus of any incident Rays. Draw QE cutting the said
391 Circle in T and _t_, and therein take _tq_ in such proportion to _t_E as
392 _t_E or TE hath to TQ. Let _tq_ lie the contrary way from _t_ which TQ
393 doth from T, and _q_ shall be the Focus of the refracted Rays without
394 any sensible Error, provided the Point Q be not so remote from the Axis,
395 nor the Lens so broad as to make any of the Rays fall too obliquely on
396 the refracting Surfaces.[A]
397
398 And by the like Operations may the reflecting or refracting Surfaces be
399 found when the two Foci are given, and thereby a Lens be formed, which
400 shall make the Rays flow towards or from what Place you please.[B]
401
402 So then the Meaning of this Axiom is, that if Rays fall upon any Plane
403 or Spherical Surface or Lens, and before their Incidence flow from or
404 towards any Point Q, they shall after Reflexion or Refraction flow from
405 or towards the Point _q_ found by the foregoing Rules. And if the
406 incident Rays flow from or towards several points Q, the reflected or
407 refracted Rays shall flow from or towards so many other Points _q_
408 found by the same Rules. Whether the reflected and refracted Rays flow
409 from or towards the Point _q_ is easily known by the situation of that
410 Point. For if that Point be on the same side of the reflecting or
411 refracting Surface or Lens with the Point Q, and the incident Rays flow
412 from the Point Q, the reflected flow towards the Point _q_ and the
413 refracted from it; and if the incident Rays flow towards Q, the
414 reflected flow from _q_, and the refracted towards it. And the contrary
415 happens when _q_ is on the other side of the Surface.
416
417
418 AX. VII.
419
420 _Wherever the Rays which come from all the Points of any Object meet
421 again in so many Points after they have been made to converge by
422 Reflection or Refraction, there they will make a Picture of the Object
423 upon any white Body on which they fall._
424
425 So if PR [in _Fig._ 3.] represent any Object without Doors, and AB be a
426 Lens placed at a hole in the Window-shut of a dark Chamber, whereby the
427 Rays that come from any Point Q of that Object are made to converge and
428 meet again in the Point _q_; and if a Sheet of white Paper be held at
429 _q_ for the Light there to fall upon it, the Picture of that Object PR
430 will appear upon the Paper in its proper shape and Colours. For as the
431 Light which comes from the Point Q goes to the Point _q_, so the Light
432 which comes from other Points P and R of the Object, will go to so many
433 other correspondent Points _p_ and _r_ (as is manifest by the sixth
434 Axiom;) so that every Point of the Object shall illuminate a
435 correspondent Point of the Picture, and thereby make a Picture like the
436 Object in Shape and Colour, this only excepted, that the Picture shall
437 be inverted. And this is the Reason of that vulgar Experiment of casting
438 the Species of Objects from abroad upon a Wall or Sheet of white Paper
439 in a dark Room.
440
441 In like manner, when a Man views any Object PQR, [in _Fig._ 8.] the
442 Light which comes from the several Points of the Object is so refracted
443 by the transparent skins and humours of the Eye, (that is, by the
444 outward coat EFG, called the _Tunica Cornea_, and by the crystalline
445 humour AB which is beyond the Pupil _mk_) as to converge and meet again
446 in so many Points in the bottom of the Eye, and there to paint the
447 Picture of the Object upon that skin (called the _Tunica Retina_) with
448 which the bottom of the Eye is covered. For Anatomists, when they have
449 taken off from the bottom of the Eye that outward and most thick Coat
450 called the _Dura Mater_, can then see through the thinner Coats, the
451 Pictures of Objects lively painted thereon. And these Pictures,
452 propagated by Motion along the Fibres of the Optick Nerves into the
453 Brain, are the cause of Vision. For accordingly as these Pictures are
454 perfect or imperfect, the Object is seen perfectly or imperfectly. If
455 the Eye be tinged with any colour (as in the Disease of the _Jaundice_)
456 so as to tinge the Pictures in the bottom of the Eye with that Colour,
457 then all Objects appear tinged with the same Colour. If the Humours of
458 the Eye by old Age decay, so as by shrinking to make the _Cornea_ and
459 Coat of the _Crystalline Humour_ grow flatter than before, the Light
460 will not be refracted enough, and for want of a sufficient Refraction
461 will not converge to the bottom of the Eye but to some place beyond it,
462 and by consequence paint in the bottom of the Eye a confused Picture,
463 and according to the Indistinctness of this Picture the Object will
464 appear confused. This is the reason of the decay of sight in old Men,
465 and shews why their Sight is mended by Spectacles. For those Convex
466 glasses supply the defect of plumpness in the Eye, and by increasing the
467 Refraction make the Rays converge sooner, so as to convene distinctly at
468 the bottom of the Eye if the Glass have a due degree of convexity. And
469 the contrary happens in short-sighted Men whose Eyes are too plump. For
470 the Refraction being now too great, the Rays converge and convene in the
471 Eyes before they come at the bottom; and therefore the Picture made in
472 the bottom and the Vision caused thereby will not be distinct, unless
473 the Object be brought so near the Eye as that the place where the
474 converging Rays convene may be removed to the bottom, or that the
475 plumpness of the Eye be taken off and the Refractions diminished by a
476 Concave-glass of a due degree of Concavity, or lastly that by Age the
477 Eye grow flatter till it come to a due Figure: For short-sighted Men see
478 remote Objects best in Old Age, and therefore they are accounted to have
479 the most lasting Eyes.
480
481 [Illustration: FIG. 8.]
482
483
484 AX. VIII.
485
486 _An Object seen by Reflexion or Refraction, appears in that place from
487 whence the Rays after their last Reflexion or Refraction diverge in
488 falling on the Spectator's Eye._
489
490 [Illustration: FIG. 9.]
491
492 If the Object A [in FIG. 9.] be seen by Reflexion of a Looking-glass
493 _mn_, it shall appear, not in its proper place A, but behind the Glass
494 at _a_, from whence any Rays AB, AC, AD, which flow from one and the
495 same Point of the Object, do after their Reflexion made in the Points B,
496 C, D, diverge in going from the Glass to E, F, G, where they are
497 incident on the Spectator's Eyes. For these Rays do make the same
498 Picture in the bottom of the Eyes as if they had come from the Object
499 really placed at _a_ without the Interposition of the Looking-glass; and
500 all Vision is made according to the place and shape of that Picture.
501
502 In like manner the Object D [in FIG. 2.] seen through a Prism, appears
503 not in its proper place D, but is thence translated to some other place
504 _d_ situated in the last refracted Ray FG drawn backward from F to _d_.
505
506 [Illustration: FIG. 10.]
507
508 And so the Object Q [in FIG. 10.] seen through the Lens AB, appears at
509 the place _q_ from whence the Rays diverge in passing from the Lens to
510 the Eye. Now it is to be noted, that the Image of the Object at _q_ is
511 so much bigger or lesser than the Object it self at Q, as the distance
512 of the Image at _q_ from the Lens AB is bigger or less than the distance
513 of the Object at Q from the same Lens. And if the Object be seen through
514 two or more such Convex or Concave-glasses, every Glass shall make a new
515 Image, and the Object shall appear in the place of the bigness of the
516 last Image. Which consideration unfolds the Theory of Microscopes and
517 Telescopes. For that Theory consists in almost nothing else than the
518 describing such Glasses as shall make the last Image of any Object as
519 distinct and large and luminous as it can conveniently be made.
520
521 I have now given in Axioms and their Explications the sum of what hath
522 hitherto been treated of in Opticks. For what hath been generally
523 agreed on I content my self to assume under the notion of Principles, in
524 order to what I have farther to write. And this may suffice for an
525 Introduction to Readers of quick Wit and good Understanding not yet
526 versed in Opticks: Although those who are already acquainted with this
527 Science, and have handled Glasses, will more readily apprehend what
528 followeth.
529
530 FOOTNOTES:
531
532 [A] In our Author's _Lectiones Opticæ_, Part I. Sect. IV. Prop 29, 30,
533 there is an elegant Method of determining these _Foci_; not only in
534 spherical Surfaces, but likewise in any other curved Figure whatever:
535 And in Prop. 32, 33, the same thing is done for any Ray lying out of the
536 Axis.
537
538 [B] _Ibid._ Prop. 34.
539
540
541
542
543 _PROPOSITIONS._
544
545
546
547 _PROP._ I. THEOR. I.
548
549 _Lights which differ in Colour, differ also in Degrees of
550 Refrangibility._
551
552 The PROOF by Experiments.
553
554 _Exper._ 1.
555
556 I took a black oblong stiff Paper terminated by Parallel Sides, and with
557 a Perpendicular right Line drawn cross from one Side to the other,
558 distinguished it into two equal Parts. One of these parts I painted with
559 a red colour and the other with a blue. The Paper was very black, and
560 the Colours intense and thickly laid on, that the Phænomenon might be
561 more conspicuous. This Paper I view'd through a Prism of solid Glass,
562 whose two Sides through which the Light passed to the Eye were plane and
563 well polished, and contained an Angle of about sixty degrees; which
564 Angle I call the refracting Angle of the Prism. And whilst I view'd it,
565 I held it and the Prism before a Window in such manner that the Sides of
566 the Paper were parallel to the Prism, and both those Sides and the Prism
567 were parallel to the Horizon, and the cross Line was also parallel to
568 it: and that the Light which fell from the Window upon the Paper made an
569 Angle with the Paper, equal to that Angle which was made with the same
570 Paper by the Light reflected from it to the Eye. Beyond the Prism was
571 the Wall of the Chamber under the Window covered over with black Cloth,
572 and the Cloth was involved in Darkness that no Light might be reflected
573 from thence, which in passing by the Edges of the Paper to the Eye,
574 might mingle itself with the Light of the Paper, and obscure the
575 Phænomenon thereof. These things being thus ordered, I found that if the
576 refracting Angle of the Prism be turned upwards, so that the Paper may
577 seem to be lifted upwards by the Refraction, its blue half will be
578 lifted higher by the Refraction than its red half. But if the refracting
579 Angle of the Prism be turned downward, so that the Paper may seem to be
580 carried lower by the Refraction, its blue half will be carried something
581 lower thereby than its red half. Wherefore in both Cases the Light which
582 comes from the blue half of the Paper through the Prism to the Eye, does
583 in like Circumstances suffer a greater Refraction than the Light which
584 comes from the red half, and by consequence is more refrangible.
585
586 _Illustration._ In the eleventh Figure, MN represents the Window, and DE
587 the Paper terminated with parallel Sides DJ and HE, and by the
588 transverse Line FG distinguished into two halfs, the one DG of an
589 intensely blue Colour, the other FE of an intensely red. And BAC_cab_
590 represents the Prism whose refracting Planes AB_ba_ and AC_ca_ meet in
591 the Edge of the refracting Angle A_a_. This Edge A_a_ being upward, is
592 parallel both to the Horizon, and to the Parallel-Edges of the Paper DJ
593 and HE, and the transverse Line FG is perpendicular to the Plane of the
594 Window. And _de_ represents the Image of the Paper seen by Refraction
595 upwards in such manner, that the blue half DG is carried higher to _dg_
596 than the red half FE is to _fe_, and therefore suffers a greater
597 Refraction. If the Edge of the refracting Angle be turned downward, the
598 Image of the Paper will be refracted downward; suppose to [Greek: de],
599 and the blue half will be refracted lower to [Greek: dg] than the red
600 half is to [Greek: pe].
601
602 [Illustration: FIG. 11.]
603
604 _Exper._ 2. About the aforesaid Paper, whose two halfs were painted over
605 with red and blue, and which was stiff like thin Pasteboard, I lapped
606 several times a slender Thred of very black Silk, in such manner that
607 the several parts of the Thred might appear upon the Colours like so
608 many black Lines drawn over them, or like long and slender dark Shadows
609 cast upon them. I might have drawn black Lines with a Pen, but the
610 Threds were smaller and better defined. This Paper thus coloured and
611 lined I set against a Wall perpendicularly to the Horizon, so that one
612 of the Colours might stand to the Right Hand, and the other to the Left.
613 Close before the Paper, at the Confine of the Colours below, I placed a
614 Candle to illuminate the Paper strongly: For the Experiment was tried in
615 the Night. The Flame of the Candle reached up to the lower edge of the
616 Paper, or a very little higher. Then at the distance of six Feet, and
617 one or two Inches from the Paper upon the Floor I erected a Glass Lens
618 four Inches and a quarter broad, which might collect the Rays coming
619 from the several Points of the Paper, and make them converge towards so
620 many other Points at the same distance of six Feet, and one or two
621 Inches on the other side of the Lens, and so form the Image of the
622 coloured Paper upon a white Paper placed there, after the same manner
623 that a Lens at a Hole in a Window casts the Images of Objects abroad
624 upon a Sheet of white Paper in a dark Room. The aforesaid white Paper,
625 erected perpendicular to the Horizon, and to the Rays which fell upon it
626 from the Lens, I moved sometimes towards the Lens, sometimes from it, to
627 find the Places where the Images of the blue and red Parts of the
628 coloured Paper appeared most distinct. Those Places I easily knew by the
629 Images of the black Lines which I had made by winding the Silk about the
630 Paper. For the Images of those fine and slender Lines (which by reason
631 of their Blackness were like Shadows on the Colours) were confused and
632 scarce visible, unless when the Colours on either side of each Line were
633 terminated most distinctly, Noting therefore, as diligently as I could,
634 the Places where the Images of the red and blue halfs of the coloured
635 Paper appeared most distinct, I found that where the red half of the
636 Paper appeared distinct, the blue half appeared confused, so that the
637 black Lines drawn upon it could scarce be seen; and on the contrary,
638 where the blue half appeared most distinct, the red half appeared
639 confused, so that the black Lines upon it were scarce visible. And
640 between the two Places where these Images appeared distinct there was
641 the distance of an Inch and a half; the distance of the white Paper from
642 the Lens, when the Image of the red half of the coloured Paper appeared
643 most distinct, being greater by an Inch and an half than the distance of
644 the same white Paper from the Lens, when the Image of the blue half
645 appeared most distinct. In like Incidences therefore of the blue and red
646 upon the Lens, the blue was refracted more by the Lens than the red, so
647 as to converge sooner by an Inch and a half, and therefore is more
648 refrangible.
649
650 _Illustration._ In the twelfth Figure (p. 27), DE signifies the coloured
651 Paper, DG the blue half, FE the red half, MN the Lens, HJ the white
652 Paper in that Place where the red half with its black Lines appeared
653 distinct, and _hi_ the same Paper in that Place where the blue half
654 appeared distinct. The Place _hi_ was nearer to the Lens MN than the
655 Place HJ by an Inch and an half.
656
657 _Scholium._ The same Things succeed, notwithstanding that some of the
658 Circumstances be varied; as in the first Experiment when the Prism and
659 Paper are any ways inclined to the Horizon, and in both when coloured
660 Lines are drawn upon very black Paper. But in the Description of these
661 Experiments, I have set down such Circumstances, by which either the
662 Phænomenon might be render'd more conspicuous, or a Novice might more
663 easily try them, or by which I did try them only. The same Thing, I have
664 often done in the following Experiments: Concerning all which, this one
665 Admonition may suffice. Now from these Experiments it follows not, that
666 all the Light of the blue is more refrangible than all the Light of the
667 red: For both Lights are mixed of Rays differently refrangible, so that
668 in the red there are some Rays not less refrangible than those of the
669 blue, and in the blue there are some Rays not more refrangible than
670 those of the red: But these Rays, in proportion to the whole Light, are
671 but few, and serve to diminish the Event of the Experiment, but are not
672 able to destroy it. For, if the red and blue Colours were more dilute
673 and weak, the distance of the Images would be less than an Inch and a
674 half; and if they were more intense and full, that distance would be
675 greater, as will appear hereafter. These Experiments may suffice for the
676 Colours of Natural Bodies. For in the Colours made by the Refraction of
677 Prisms, this Proposition will appear by the Experiments which are now to
678 follow in the next Proposition.
679
680
681 _PROP._ II. THEOR. II.
682
683 _The Light of the Sun consists of Rays differently Refrangible._
684
685 The PROOF by Experiments.
686
687 [Illustration: FIG. 12.]
688
689 [Illustration: FIG. 13.]
690
691 _Exper._ 3.
692
693 In a very dark Chamber, at a round Hole, about one third Part of an Inch
694 broad, made in the Shut of a Window, I placed a Glass Prism, whereby the
695 Beam of the Sun's Light, which came in at that Hole, might be refracted
696 upwards toward the opposite Wall of the Chamber, and there form a
697 colour'd Image of the Sun. The Axis of the Prism (that is, the Line
698 passing through the middle of the Prism from one end of it to the other
699 end parallel to the edge of the Refracting Angle) was in this and the
700 following Experiments perpendicular to the incident Rays. About this
701 Axis I turned the Prism slowly, and saw the refracted Light on the Wall,
702 or coloured Image of the Sun, first to descend, and then to ascend.
703 Between the Descent and Ascent, when the Image seemed Stationary, I
704 stopp'd the Prism, and fix'd it in that Posture, that it should be moved
705 no more. For in that Posture the Refractions of the Light at the two
706 Sides of the refracting Angle, that is, at the Entrance of the Rays into
707 the Prism, and at their going out of it, were equal to one another.[C]
708 So also in other Experiments, as often as I would have the Refractions
709 on both sides the Prism to be equal to one another, I noted the Place
710 where the Image of the Sun formed by the refracted Light stood still
711 between its two contrary Motions, in the common Period of its Progress
712 and Regress; and when the Image fell upon that Place, I made fast the
713 Prism. And in this Posture, as the most convenient, it is to be
714 understood that all the Prisms are placed in the following Experiments,
715 unless where some other Posture is described. The Prism therefore being
716 placed in this Posture, I let the refracted Light fall perpendicularly
717 upon a Sheet of white Paper at the opposite Wall of the Chamber, and
718 observed the Figure and Dimensions of the Solar Image formed on the
719 Paper by that Light. This Image was Oblong and not Oval, but terminated
720 with two Rectilinear and Parallel Sides, and two Semicircular Ends. On
721 its Sides it was bounded pretty distinctly, but on its Ends very
722 confusedly and indistinctly, the Light there decaying and vanishing by
723 degrees. The Breadth of this Image answered to the Sun's Diameter, and
724 was about two Inches and the eighth Part of an Inch, including the
725 Penumbra. For the Image was eighteen Feet and an half distant from the
726 Prism, and at this distance that Breadth, if diminished by the Diameter
727 of the Hole in the Window-shut, that is by a quarter of an Inch,
728 subtended an Angle at the Prism of about half a Degree, which is the
729 Sun's apparent Diameter. But the Length of the Image was about ten
730 Inches and a quarter, and the Length of the Rectilinear Sides about
731 eight Inches; and the refracting Angle of the Prism, whereby so great a
732 Length was made, was 64 degrees. With a less Angle the Length of the
733 Image was less, the Breadth remaining the same. If the Prism was turned
734 about its Axis that way which made the Rays emerge more obliquely out of
735 the second refracting Surface of the Prism, the Image soon became an
736 Inch or two longer, or more; and if the Prism was turned about the
737 contrary way, so as to make the Rays fall more obliquely on the first
738 refracting Surface, the Image soon became an Inch or two shorter. And
739 therefore in trying this Experiment, I was as curious as I could be in
740 placing the Prism by the above-mention'd Rule exactly in such a Posture,
741 that the Refractions of the Rays at their Emergence out of the Prism
742 might be equal to that at their Incidence on it. This Prism had some
743 Veins running along within the Glass from one end to the other, which
744 scattered some of the Sun's Light irregularly, but had no sensible
745 Effect in increasing the Length of the coloured Spectrum. For I tried
746 the same Experiment with other Prisms with the same Success. And
747 particularly with a Prism which seemed free from such Veins, and whose
748 refracting Angle was 62-1/2 Degrees, I found the Length of the Image
749 9-3/4 or 10 Inches at the distance of 18-1/2 Feet from the Prism, the
750 Breadth of the Hole in the Window-shut being 1/4 of an Inch, as before.
751 And because it is easy to commit a Mistake in placing the Prism in its
752 due Posture, I repeated the Experiment four or five Times, and always
753 found the Length of the Image that which is set down above. With another
754 Prism of clearer Glass and better Polish, which seemed free from Veins,
755 and whose refracting Angle was 63-1/2 Degrees, the Length of this Image
756 at the same distance of 18-1/2 Feet was also about 10 Inches, or 10-1/8.
757 Beyond these Measures for about a 1/4 or 1/3 of an Inch at either end of
758 the Spectrum the Light of the Clouds seemed to be a little tinged with
759 red and violet, but so very faintly, that I suspected that Tincture
760 might either wholly, or in great Measure arise from some Rays of the
761 Spectrum scattered irregularly by some Inequalities in the Substance and
762 Polish of the Glass, and therefore I did not include it in these
763 Measures. Now the different Magnitude of the hole in the Window-shut,
764 and different thickness of the Prism where the Rays passed through it,
765 and different inclinations of the Prism to the Horizon, made no sensible
766 changes in the length of the Image. Neither did the different matter of
767 the Prisms make any: for in a Vessel made of polished Plates of Glass
768 cemented together in the shape of a Prism and filled with Water, there
769 is the like Success of the Experiment according to the quantity of the
770 Refraction. It is farther to be observed, that the Rays went on in right
771 Lines from the Prism to the Image, and therefore at their very going out
772 of the Prism had all that Inclination to one another from which the
773 length of the Image proceeded, that is, the Inclination of more than two
774 degrees and an half. And yet according to the Laws of Opticks vulgarly
775 received, they could not possibly be so much inclined to one another.[D]
776 For let EG [_Fig._ 13. (p. 27)] represent the Window-shut, F the hole
777 made therein through which a beam of the Sun's Light was transmitted
778 into the darkened Chamber, and ABC a Triangular Imaginary Plane whereby
779 the Prism is feigned to be cut transversely through the middle of the
780 Light. Or if you please, let ABC represent the Prism it self, looking
781 directly towards the Spectator's Eye with its nearer end: And let XY be
782 the Sun, MN the Paper upon which the Solar Image or Spectrum is cast,
783 and PT the Image it self whose sides towards _v_ and _w_ are Rectilinear
784 and Parallel, and ends towards P and T Semicircular. YKHP and XLJT are
785 two Rays, the first of which comes from the lower part of the Sun to the
786 higher part of the Image, and is refracted in the Prism at K and H, and
787 the latter comes from the higher part of the Sun to the lower part of
788 the Image, and is refracted at L and J. Since the Refractions on both
789 sides the Prism are equal to one another, that is, the Refraction at K
790 equal to the Refraction at J, and the Refraction at L equal to the
791 Refraction at H, so that the Refractions of the incident Rays at K and L
792 taken together, are equal to the Refractions of the emergent Rays at H
793 and J taken together: it follows by adding equal things to equal things,
794 that the Refractions at K and H taken together, are equal to the
795 Refractions at J and L taken together, and therefore the two Rays being
796 equally refracted, have the same Inclination to one another after
797 Refraction which they had before; that is, the Inclination of half a
798 Degree answering to the Sun's Diameter. For so great was the inclination
799 of the Rays to one another before Refraction. So then, the length of the
800 Image PT would by the Rules of Vulgar Opticks subtend an Angle of half a
801 Degree at the Prism, and by Consequence be equal to the breadth _vw_;
802 and therefore the Image would be round. Thus it would be were the two
803 Rays XLJT and YKHP, and all the rest which form the Image P_w_T_v_,
804 alike refrangible. And therefore seeing by Experience it is found that
805 the Image is not round, but about five times longer than broad, the Rays
806 which going to the upper end P of the Image suffer the greatest
807 Refraction, must be more refrangible than those which go to the lower
808 end T, unless the Inequality of Refraction be casual.
809
810 This Image or Spectrum PT was coloured, being red at its least refracted
811 end T, and violet at its most refracted end P, and yellow green and
812 blue in the intermediate Spaces. Which agrees with the first
813 Proposition, that Lights which differ in Colour, do also differ in
814 Refrangibility. The length of the Image in the foregoing Experiments, I
815 measured from the faintest and outmost red at one end, to the faintest
816 and outmost blue at the other end, excepting only a little Penumbra,
817 whose breadth scarce exceeded a quarter of an Inch, as was said above.
818
819 _Exper._ 4. In the Sun's Beam which was propagated into the Room through
820 the hole in the Window-shut, at the distance of some Feet from the hole,
821 I held the Prism in such a Posture, that its Axis might be perpendicular
822 to that Beam. Then I looked through the Prism upon the hole, and turning
823 the Prism to and fro about its Axis, to make the Image of the Hole
824 ascend and descend, when between its two contrary Motions it seemed
825 Stationary, I stopp'd the Prism, that the Refractions of both sides of
826 the refracting Angle might be equal to each other, as in the former
827 Experiment. In this situation of the Prism viewing through it the said
828 Hole, I observed the length of its refracted Image to be many times
829 greater than its breadth, and that the most refracted part thereof
830 appeared violet, the least refracted red, the middle parts blue, green
831 and yellow in order. The same thing happen'd when I removed the Prism
832 out of the Sun's Light, and looked through it upon the hole shining by
833 the Light of the Clouds beyond it. And yet if the Refraction were done
834 regularly according to one certain Proportion of the Sines of Incidence
835 and Refraction as is vulgarly supposed, the refracted Image ought to
836 have appeared round.
837
838 So then, by these two Experiments it appears, that in Equal Incidences
839 there is a considerable inequality of Refractions. But whence this
840 inequality arises, whether it be that some of the incident Rays are
841 refracted more, and others less, constantly, or by chance, or that one
842 and the same Ray is by Refraction disturbed, shatter'd, dilated, and as
843 it were split and spread into many diverging Rays, as _Grimaldo_
844 supposes, does not yet appear by these Experiments, but will appear by
845 those that follow.
846
847 _Exper._ 5. Considering therefore, that if in the third Experiment the
848 Image of the Sun should be drawn out into an oblong Form, either by a
849 Dilatation of every Ray, or by any other casual inequality of the
850 Refractions, the same oblong Image would by a second Refraction made
851 sideways be drawn out as much in breadth by the like Dilatation of the
852 Rays, or other casual inequality of the Refractions sideways, I tried
853 what would be the Effects of such a second Refraction. For this end I
854 ordered all things as in the third Experiment, and then placed a second
855 Prism immediately after the first in a cross Position to it, that it
856 might again refract the beam of the Sun's Light which came to it through
857 the first Prism. In the first Prism this beam was refracted upwards, and
858 in the second sideways. And I found that by the Refraction of the second
859 Prism, the breadth of the Image was not increased, but its superior
860 part, which in the first Prism suffered the greater Refraction, and
861 appeared violet and blue, did again in the second Prism suffer a greater
862 Refraction than its inferior part, which appeared red and yellow, and
863 this without any Dilatation of the Image in breadth.
864
865 [Illustration: FIG. 14]
866
867 _Illustration._ Let S [_Fig._ 14, 15.] represent the Sun, F the hole in
868 the Window, ABC the first Prism, DH the second Prism, Y the round Image
869 of the Sun made by a direct beam of Light when the Prisms are taken
870 away, PT the oblong Image of the Sun made by that beam passing through
871 the first Prism alone, when the second Prism is taken away, and _pt_ the
872 Image made by the cross Refractions of both Prisms together. Now if the
873 Rays which tend towards the several Points of the round Image Y were
874 dilated and spread by the Refraction of the first Prism, so that they
875 should not any longer go in single Lines to single Points, but that
876 every Ray being split, shattered, and changed from a Linear Ray to a
877 Superficies of Rays diverging from the Point of Refraction, and lying in
878 the Plane of the Angles of Incidence and Refraction, they should go in
879 those Planes to so many Lines reaching almost from one end of the Image
880 PT to the other, and if that Image should thence become oblong: those
881 Rays and their several parts tending towards the several Points of the
882 Image PT ought to be again dilated and spread sideways by the transverse
883 Refraction of the second Prism, so as to compose a four square Image,
884 such as is represented at [Greek: pt]. For the better understanding of
885 which, let the Image PT be distinguished into five equal parts PQK,
886 KQRL, LRSM, MSVN, NVT. And by the same irregularity that the orbicular
887 Light Y is by the Refraction of the first Prism dilated and drawn out
888 into a long Image PT, the Light PQK which takes up a space of the same
889 length and breadth with the Light Y ought to be by the Refraction of the
890 second Prism dilated and drawn out into the long Image _[Greek: p]qkp_,
891 and the Light KQRL into the long Image _kqrl_, and the Lights LRSM,
892 MSVN, NVT, into so many other long Images _lrsm_, _msvn_, _nvt[Greek:
893 t]_; and all these long Images would compose the four square Images
894 _[Greek: pt]_. Thus it ought to be were every Ray dilated by Refraction,
895 and spread into a triangular Superficies of Rays diverging from the
896 Point of Refraction. For the second Refraction would spread the Rays one
897 way as much as the first doth another, and so dilate the Image in
898 breadth as much as the first doth in length. And the same thing ought to
899 happen, were some rays casually refracted more than others. But the
900 Event is otherwise. The Image PT was not made broader by the Refraction
901 of the second Prism, but only became oblique, as 'tis represented at
902 _pt_, its upper end P being by the Refraction translated to a greater
903 distance than its lower end T. So then the Light which went towards the
904 upper end P of the Image, was (at equal Incidences) more refracted in
905 the second Prism, than the Light which tended towards the lower end T,
906 that is the blue and violet, than the red and yellow; and therefore was
907 more refrangible. The same Light was by the Refraction of the first
908 Prism translated farther from the place Y to which it tended before
909 Refraction; and therefore suffered as well in the first Prism as in the
910 second a greater Refraction than the rest of the Light, and by
911 consequence was more refrangible than the rest, even before its
912 incidence on the first Prism.
913
914 Sometimes I placed a third Prism after the second, and sometimes also a
915 fourth after the third, by all which the Image might be often refracted
916 sideways: but the Rays which were more refracted than the rest in the
917 first Prism were also more refracted in all the rest, and that without
918 any Dilatation of the Image sideways: and therefore those Rays for their
919 constancy of a greater Refraction are deservedly reputed more
920 refrangible.
921
922 [Illustration: FIG. 15]
923
924 But that the meaning of this Experiment may more clearly appear, it is
925 to be considered that the Rays which are equally refrangible do fall
926 upon a Circle answering to the Sun's Disque. For this was proved in the
927 third Experiment. By a Circle I understand not here a perfect
928 geometrical Circle, but any orbicular Figure whose length is equal to
929 its breadth, and which, as to Sense, may seem circular. Let therefore AG
930 [in _Fig._ 15.] represent the Circle which all the most refrangible Rays
931 propagated from the whole Disque of the Sun, would illuminate and paint
932 upon the opposite Wall if they were alone; EL the Circle which all the
933 least refrangible Rays would in like manner illuminate and paint if they
934 were alone; BH, CJ, DK, the Circles which so many intermediate sorts of
935 Rays would successively paint upon the Wall, if they were singly
936 propagated from the Sun in successive order, the rest being always
937 intercepted; and conceive that there are other intermediate Circles
938 without Number, which innumerable other intermediate sorts of Rays would
939 successively paint upon the Wall if the Sun should successively emit
940 every sort apart. And seeing the Sun emits all these sorts at once, they
941 must all together illuminate and paint innumerable equal Circles, of all
942 which, being according to their degrees of Refrangibility placed in
943 order in a continual Series, that oblong Spectrum PT is composed which I
944 described in the third Experiment. Now if the Sun's circular Image Y [in
945 _Fig._ 15.] which is made by an unrefracted beam of Light was by any
946 Dilation of the single Rays, or by any other irregularity in the
947 Refraction of the first Prism, converted into the oblong Spectrum, PT:
948 then ought every Circle AG, BH, CJ, &c. in that Spectrum, by the cross
949 Refraction of the second Prism again dilating or otherwise scattering
950 the Rays as before, to be in like manner drawn out and transformed into
951 an oblong Figure, and thereby the breadth of the Image PT would be now
952 as much augmented as the length of the Image Y was before by the
953 Refraction of the first Prism; and thus by the Refractions of both
954 Prisms together would be formed a four square Figure _p[Greek:
955 p]t[Greek: t]_, as I described above. Wherefore since the breadth of the
956 Spectrum PT is not increased by the Refraction sideways, it is certain
957 that the Rays are not split or dilated, or otherways irregularly
958 scatter'd by that Refraction, but that every Circle is by a regular and
959 uniform Refraction translated entire into another Place, as the Circle
960 AG by the greatest Refraction into the place _ag_, the Circle BH by a
961 less Refraction into the place _bh_, the Circle CJ by a Refraction still
962 less into the place _ci_, and so of the rest; by which means a new
963 Spectrum _pt_ inclined to the former PT is in like manner composed of
964 Circles lying in a right Line; and these Circles must be of the same
965 bigness with the former, because the breadths of all the Spectrums Y, PT
966 and _pt_ at equal distances from the Prisms are equal.
967
968 I considered farther, that by the breadth of the hole F through which
969 the Light enters into the dark Chamber, there is a Penumbra made in the
970 Circuit of the Spectrum Y, and that Penumbra remains in the rectilinear
971 Sides of the Spectrums PT and _pt_. I placed therefore at that hole a
972 Lens or Object-glass of a Telescope which might cast the Image of the
973 Sun distinctly on Y without any Penumbra at all, and found that the
974 Penumbra of the rectilinear Sides of the oblong Spectrums PT and _pt_
975 was also thereby taken away, so that those Sides appeared as distinctly
976 defined as did the Circumference of the first Image Y. Thus it happens
977 if the Glass of the Prisms be free from Veins, and their sides be
978 accurately plane and well polished without those numberless Waves or
979 Curles which usually arise from Sand-holes a little smoothed in
980 polishing with Putty. If the Glass be only well polished and free from
981 Veins, and the Sides not accurately plane, but a little Convex or
982 Concave, as it frequently happens; yet may the three Spectrums Y, PT and
983 _pt_ want Penumbras, but not in equal distances from the Prisms. Now
984 from this want of Penumbras, I knew more certainly that every one of the
985 Circles was refracted according to some most regular, uniform and
986 constant Law. For if there were any irregularity in the Refraction, the
987 right Lines AE and GL, which all the Circles in the Spectrum PT do
988 touch, could not by that Refraction be translated into the Lines _ae_
989 and _gl_ as distinct and straight as they were before, but there would
990 arise in those translated Lines some Penumbra or Crookedness or
991 Undulation, or other sensible Perturbation contrary to what is found by
992 Experience. Whatsoever Penumbra or Perturbation should be made in the
993 Circles by the cross Refraction of the second Prism, all that Penumbra
994 or Perturbation would be conspicuous in the right Lines _ae_ and _gl_
995 which touch those Circles. And therefore since there is no such Penumbra
996 or Perturbation in those right Lines, there must be none in the
997 Circles. Since the distance between those Tangents or breadth of the
998 Spectrum is not increased by the Refractions, the Diameters of the
999 Circles are not increased thereby. Since those Tangents continue to be
1000 right Lines, every Circle which in the first Prism is more or less
1001 refracted, is exactly in the same proportion more or less refracted in
1002 the second. And seeing all these things continue to succeed after the
1003 same manner when the Rays are again in a third Prism, and again in a
1004 fourth refracted sideways, it is evident that the Rays of one and the
1005 same Circle, as to their degree of Refrangibility, continue always
1006 uniform and homogeneal to one another, and that those of several Circles
1007 do differ in degree of Refrangibility, and that in some certain and
1008 constant Proportion. Which is the thing I was to prove.
1009
1010 There is yet another Circumstance or two of this Experiment by which it
1011 becomes still more plain and convincing. Let the second Prism DH [in
1012 _Fig._ 16.] be placed not immediately after the first, but at some
1013 distance from it; suppose in the mid-way between it and the Wall on
1014 which the oblong Spectrum PT is cast, so that the Light from the first
1015 Prism may fall upon it in the form of an oblong Spectrum [Greek: pt]
1016 parallel to this second Prism, and be refracted sideways to form the
1017 oblong Spectrum _pt_ upon the Wall. And you will find as before, that
1018 this Spectrum _pt_ is inclined to that Spectrum PT, which the first
1019 Prism forms alone without the second; the blue ends P and _p_ being
1020 farther distant from one another than the red ones T and _t_, and by
1021 consequence that the Rays which go to the blue end [Greek: p] of the
1022 Image [Greek: pt], and which therefore suffer the greatest Refraction in
1023 the first Prism, are again in the second Prism more refracted than the
1024 rest.
1025
1026 [Illustration: FIG. 16.]
1027
1028 [Illustration: FIG. 17.]
1029
1030 The same thing I try'd also by letting the Sun's Light into a dark Room
1031 through two little round holes F and [Greek: ph] [in _Fig._ 17.] made in
1032 the Window, and with two parallel Prisms ABC and [Greek: abg] placed at
1033 those holes (one at each) refracting those two beams of Light to the
1034 opposite Wall of the Chamber, in such manner that the two colour'd
1035 Images PT and MN which they there painted were joined end to end and lay
1036 in one straight Line, the red end T of the one touching the blue end M
1037 of the other. For if these two refracted Beams were again by a third
1038 Prism DH placed cross to the two first, refracted sideways, and the
1039 Spectrums thereby translated to some other part of the Wall of the
1040 Chamber, suppose the Spectrum PT to _pt_ and the Spectrum MN to _mn_,
1041 these translated Spectrums _pt_ and _mn_ would not lie in one straight
1042 Line with their ends contiguous as before, but be broken off from one
1043 another and become parallel, the blue end _m_ of the Image _mn_ being by
1044 a greater Refraction translated farther from its former place MT, than
1045 the red end _t_ of the other Image _pt_ from the same place MT; which
1046 puts the Proposition past Dispute. And this happens whether the third
1047 Prism DH be placed immediately after the two first, or at a great
1048 distance from them, so that the Light refracted in the two first Prisms
1049 be either white and circular, or coloured and oblong when it falls on
1050 the third.
1051
1052 _Exper._ 6. In the middle of two thin Boards I made round holes a third
1053 part of an Inch in diameter, and in the Window-shut a much broader hole
1054 being made to let into my darkned Chamber a large Beam of the Sun's
1055 Light; I placed a Prism behind the Shut in that beam to refract it
1056 towards the opposite Wall, and close behind the Prism I fixed one of the
1057 Boards, in such manner that the middle of the refracted Light might pass
1058 through the hole made in it, and the rest be intercepted by the Board.
1059 Then at the distance of about twelve Feet from the first Board I fixed
1060 the other Board in such manner that the middle of the refracted Light
1061 which came through the hole in the first Board, and fell upon the
1062 opposite Wall, might pass through the hole in this other Board, and the
1063 rest being intercepted by the Board might paint upon it the coloured
1064 Spectrum of the Sun. And close behind this Board I fixed another Prism
1065 to refract the Light which came through the hole. Then I returned
1066 speedily to the first Prism, and by turning it slowly to and fro about
1067 its Axis, I caused the Image which fell upon the second Board to move up
1068 and down upon that Board, that all its parts might successively pass
1069 through the hole in that Board and fall upon the Prism behind it. And in
1070 the mean time, I noted the places on the opposite Wall to which that
1071 Light after its Refraction in the second Prism did pass; and by the
1072 difference of the places I found that the Light which being most
1073 refracted in the first Prism did go to the blue end of the Image, was
1074 again more refracted in the second Prism than the Light which went to
1075 the red end of that Image, which proves as well the first Proposition as
1076 the second. And this happened whether the Axis of the two Prisms were
1077 parallel, or inclined to one another, and to the Horizon in any given
1078 Angles.
1079
1080 _Illustration._ Let F [in _Fig._ 18.] be the wide hole in the
1081 Window-shut, through which the Sun shines upon the first Prism ABC, and
1082 let the refracted Light fall upon the middle of the Board DE, and the
1083 middle part of that Light upon the hole G made in the middle part of
1084 that Board. Let this trajected part of that Light fall again upon the
1085 middle of the second Board _de_, and there paint such an oblong coloured
1086 Image of the Sun as was described in the third Experiment. By turning
1087 the Prism ABC slowly to and fro about its Axis, this Image will be made
1088 to move up and down the Board _de_, and by this means all its parts from
1089 one end to the other may be made to pass successively through the hole
1090 _g_ which is made in the middle of that Board. In the mean while another
1091 Prism _abc_ is to be fixed next after that hole _g_, to refract the
1092 trajected Light a second time. And these things being thus ordered, I
1093 marked the places M and N of the opposite Wall upon which the refracted
1094 Light fell, and found that whilst the two Boards and second Prism
1095 remained unmoved, those places by turning the first Prism about its Axis
1096 were changed perpetually. For when the lower part of the Light which
1097 fell upon the second Board _de_ was cast through the hole _g_, it went
1098 to a lower place M on the Wall and when the higher part of that Light
1099 was cast through the same hole _g_, it went to a higher place N on the
1100 Wall, and when any intermediate part of the Light was cast through that
1101 hole, it went to some place on the Wall between M and N. The unchanged
1102 Position of the holes in the Boards, made the Incidence of the Rays upon
1103 the second Prism to be the same in all cases. And yet in that common
1104 Incidence some of the Rays were more refracted, and others less. And
1105 those were more refracted in this Prism, which by a greater Refraction
1106 in the first Prism were more turned out of the way, and therefore for
1107 their Constancy of being more refracted are deservedly called more
1108 refrangible.
1109
1110 [Illustration: FIG. 18.]
1111
1112 [Illustration: FIG. 20.]
1113
1114 _Exper._ 7. At two holes made near one another in my Window-shut I
1115 placed two Prisms, one at each, which might cast upon the opposite Wall
1116 (after the manner of the third Experiment) two oblong coloured Images of
1117 the Sun. And at a little distance from the Wall I placed a long slender
1118 Paper with straight and parallel edges, and ordered the Prisms and Paper
1119 so, that the red Colour of one Image might fall directly upon one half
1120 of the Paper, and the violet Colour of the other Image upon the other
1121 half of the same Paper; so that the Paper appeared of two Colours, red
1122 and violet, much after the manner of the painted Paper in the first and
1123 second Experiments. Then with a black Cloth I covered the Wall behind
1124 the Paper, that no Light might be reflected from it to disturb the
1125 Experiment, and viewing the Paper through a third Prism held parallel
1126 to it, I saw that half of it which was illuminated by the violet Light
1127 to be divided from the other half by a greater Refraction, especially
1128 when I went a good way off from the Paper. For when I viewed it too near
1129 at hand, the two halfs of the Paper did not appear fully divided from
1130 one another, but seemed contiguous at one of their Angles like the
1131 painted Paper in the first Experiment. Which also happened when the
1132 Paper was too broad.
1133
1134 [Illustration: FIG. 19.]
1135
1136 Sometimes instead of the Paper I used a white Thred, and this appeared
1137 through the Prism divided into two parallel Threds as is represented in
1138 the nineteenth Figure, where DG denotes the Thred illuminated with
1139 violet Light from D to E and with red Light from F to G, and _defg_ are
1140 the parts of the Thred seen by Refraction. If one half of the Thred be
1141 constantly illuminated with red, and the other half be illuminated with
1142 all the Colours successively, (which may be done by causing one of the
1143 Prisms to be turned about its Axis whilst the other remains unmoved)
1144 this other half in viewing the Thred through the Prism, will appear in
1145 a continual right Line with the first half when illuminated with red,
1146 and begin to be a little divided from it when illuminated with Orange,
1147 and remove farther from it when illuminated with yellow, and still
1148 farther when with green, and farther when with blue, and go yet farther
1149 off when illuminated with Indigo, and farthest when with deep violet.
1150 Which plainly shews, that the Lights of several Colours are more and
1151 more refrangible one than another, in this Order of their Colours, red,
1152 orange, yellow, green, blue, indigo, deep violet; and so proves as well
1153 the first Proposition as the second.
1154
1155 I caused also the coloured Spectrums PT [in _Fig._ 17.] and MN made in a
1156 dark Chamber by the Refractions of two Prisms to lie in a Right Line end
1157 to end, as was described above in the fifth Experiment, and viewing them
1158 through a third Prism held parallel to their Length, they appeared no
1159 longer in a Right Line, but became broken from one another, as they are
1160 represented at _pt_ and _mn_, the violet end _m_ of the Spectrum _mn_
1161 being by a greater Refraction translated farther from its former Place
1162 MT than the red end _t_ of the other Spectrum _pt_.
1163
1164 I farther caused those two Spectrums PT [in _Fig._ 20.] and MN to become
1165 co-incident in an inverted Order of their Colours, the red end of each
1166 falling on the violet end of the other, as they are represented in the
1167 oblong Figure PTMN; and then viewing them through a Prism DH held
1168 parallel to their Length, they appeared not co-incident, as when view'd
1169 with the naked Eye, but in the form of two distinct Spectrums _pt_ and
1170 _mn_ crossing one another in the middle after the manner of the Letter
1171 X. Which shews that the red of the one Spectrum and violet of the other,
1172 which were co-incident at PN and MT, being parted from one another by a
1173 greater Refraction of the violet to _p_ and _m_ than of the red to _n_
1174 and _t_, do differ in degrees of Refrangibility.
1175
1176 I illuminated also a little Circular Piece of white Paper all over with
1177 the Lights of both Prisms intermixed, and when it was illuminated with
1178 the red of one Spectrum, and deep violet of the other, so as by the
1179 Mixture of those Colours to appear all over purple, I viewed the Paper,
1180 first at a less distance, and then at a greater, through a third Prism;
1181 and as I went from the Paper, the refracted Image thereof became more
1182 and more divided by the unequal Refraction of the two mixed Colours, and
1183 at length parted into two distinct Images, a red one and a violet one,
1184 whereof the violet was farthest from the Paper, and therefore suffered
1185 the greatest Refraction. And when that Prism at the Window, which cast
1186 the violet on the Paper was taken away, the violet Image disappeared;
1187 but when the other Prism was taken away the red vanished; which shews,
1188 that these two Images were nothing else than the Lights of the two
1189 Prisms, which had been intermixed on the purple Paper, but were parted
1190 again by their unequal Refractions made in the third Prism, through
1191 which the Paper was view'd. This also was observable, that if one of the
1192 Prisms at the Window, suppose that which cast the violet on the Paper,
1193 was turned about its Axis to make all the Colours in this order,
1194 violet, indigo, blue, green, yellow, orange, red, fall successively on
1195 the Paper from that Prism, the violet Image changed Colour accordingly,
1196 turning successively to indigo, blue, green, yellow and red, and in
1197 changing Colour came nearer and nearer to the red Image made by the
1198 other Prism, until when it was also red both Images became fully
1199 co-incident.
1200
1201 I placed also two Paper Circles very near one another, the one in the
1202 red Light of one Prism, and the other in the violet Light of the other.
1203 The Circles were each of them an Inch in diameter, and behind them the
1204 Wall was dark, that the Experiment might not be disturbed by any Light
1205 coming from thence. These Circles thus illuminated, I viewed through a
1206 Prism, so held, that the Refraction might be made towards the red
1207 Circle, and as I went from them they came nearer and nearer together,
1208 and at length became co-incident; and afterwards when I went still
1209 farther off, they parted again in a contrary Order, the violet by a
1210 greater Refraction being carried beyond the red.
1211
1212 _Exper._ 8. In Summer, when the Sun's Light uses to be strongest, I
1213 placed a Prism at the Hole of the Window-shut, as in the third
1214 Experiment, yet so that its Axis might be parallel to the Axis of the
1215 World, and at the opposite Wall in the Sun's refracted Light, I placed
1216 an open Book. Then going six Feet and two Inches from the Book, I placed
1217 there the above-mentioned Lens, by which the Light reflected from the
1218 Book might be made to converge and meet again at the distance of six
1219 Feet and two Inches behind the Lens, and there paint the Species of the
1220 Book upon a Sheet of white Paper much after the manner of the second
1221 Experiment. The Book and Lens being made fast, I noted the Place where
1222 the Paper was, when the Letters of the Book, illuminated by the fullest
1223 red Light of the Solar Image falling upon it, did cast their Species on
1224 that Paper most distinctly: And then I stay'd till by the Motion of the
1225 Sun, and consequent Motion of his Image on the Book, all the Colours
1226 from that red to the middle of the blue pass'd over those Letters; and
1227 when those Letters were illuminated by that blue, I noted again the
1228 Place of the Paper when they cast their Species most distinctly upon it:
1229 And I found that this last Place of the Paper was nearer to the Lens
1230 than its former Place by about two Inches and an half, or two and three
1231 quarters. So much sooner therefore did the Light in the violet end of
1232 the Image by a greater Refraction converge and meet, than the Light in
1233 the red end. But in trying this, the Chamber was as dark as I could make
1234 it. For, if these Colours be diluted and weakned by the Mixture of any
1235 adventitious Light, the distance between the Places of the Paper will
1236 not be so great. This distance in the second Experiment, where the
1237 Colours of natural Bodies were made use of, was but an Inch and an half,
1238 by reason of the Imperfection of those Colours. Here in the Colours of
1239 the Prism, which are manifestly more full, intense, and lively than
1240 those of natural Bodies, the distance is two Inches and three quarters.
1241 And were the Colours still more full, I question not but that the
1242 distance would be considerably greater. For the coloured Light of the
1243 Prism, by the interfering of the Circles described in the second Figure
1244 of the fifth Experiment, and also by the Light of the very bright Clouds
1245 next the Sun's Body intermixing with these Colours, and by the Light
1246 scattered by the Inequalities in the Polish of the Prism, was so very
1247 much compounded, that the Species which those faint and dark Colours,
1248 the indigo and violet, cast upon the Paper were not distinct enough to
1249 be well observed.
1250
1251 _Exper._ 9. A Prism, whose two Angles at its Base were equal to one
1252 another, and half right ones, and the third a right one, I placed in a
1253 Beam of the Sun's Light let into a dark Chamber through a Hole in the
1254 Window-shut, as in the third Experiment. And turning the Prism slowly
1255 about its Axis, until all the Light which went through one of its
1256 Angles, and was refracted by it began to be reflected by its Base, at
1257 which till then it went out of the Glass, I observed that those Rays
1258 which had suffered the greatest Refraction were sooner reflected than
1259 the rest. I conceived therefore, that those Rays of the reflected Light,
1260 which were most refrangible, did first of all by a total Reflexion
1261 become more copious in that Light than the rest, and that afterwards the
1262 rest also, by a total Reflexion, became as copious as these. To try
1263 this, I made the reflected Light pass through another Prism, and being
1264 refracted by it to fall afterwards upon a Sheet of white Paper placed
1265 at some distance behind it, and there by that Refraction to paint the
1266 usual Colours of the Prism. And then causing the first Prism to be
1267 turned about its Axis as above, I observed that when those Rays, which
1268 in this Prism had suffered the greatest Refraction, and appeared of a
1269 blue and violet Colour began to be totally reflected, the blue and
1270 violet Light on the Paper, which was most refracted in the second Prism,
1271 received a sensible Increase above that of the red and yellow, which was
1272 least refracted; and afterwards, when the rest of the Light which was
1273 green, yellow, and red, began to be totally reflected in the first
1274 Prism, the Light of those Colours on the Paper received as great an
1275 Increase as the violet and blue had done before. Whence 'tis manifest,
1276 that the Beam of Light reflected by the Base of the Prism, being
1277 augmented first by the more refrangible Rays, and afterwards by the less
1278 refrangible ones, is compounded of Rays differently refrangible. And
1279 that all such reflected Light is of the same Nature with the Sun's Light
1280 before its Incidence on the Base of the Prism, no Man ever doubted; it
1281 being generally allowed, that Light by such Reflexions suffers no
1282 Alteration in its Modifications and Properties. I do not here take
1283 Notice of any Refractions made in the sides of the first Prism, because
1284 the Light enters it perpendicularly at the first side, and goes out
1285 perpendicularly at the second side, and therefore suffers none. So then,
1286 the Sun's incident Light being of the same Temper and Constitution with
1287 his emergent Light, and the last being compounded of Rays differently
1288 refrangible, the first must be in like manner compounded.
1289
1290 [Illustration: FIG. 21.]
1291
1292 _Illustration._ In the twenty-first Figure, ABC is the first Prism, BC
1293 its Base, B and C its equal Angles at the Base, each of 45 Degrees, A
1294 its rectangular Vertex, FM a beam of the Sun's Light let into a dark
1295 Room through a hole F one third part of an Inch broad, M its Incidence
1296 on the Base of the Prism, MG a less refracted Ray, MH a more refracted
1297 Ray, MN the beam of Light reflected from the Base, VXY the second Prism
1298 by which this beam in passing through it is refracted, N_t_ the less
1299 refracted Light of this beam, and N_p_ the more refracted part thereof.
1300 When the first Prism ABC is turned about its Axis according to the order
1301 of the Letters ABC, the Rays MH emerge more and more obliquely out of
1302 that Prism, and at length after their most oblique Emergence are
1303 reflected towards N, and going on to _p_ do increase the Number of the
1304 Rays N_p_. Afterwards by continuing the Motion of the first Prism, the
1305 Rays MG are also reflected to N and increase the number of the Rays
1306 N_t_. And therefore the Light MN admits into its Composition, first the
1307 more refrangible Rays, and then the less refrangible Rays, and yet after
1308 this Composition is of the same Nature with the Sun's immediate Light
1309 FM, the Reflexion of the specular Base BC causing no Alteration therein.
1310
1311 _Exper._ 10. Two Prisms, which were alike in Shape, I tied so together,
1312 that their Axis and opposite Sides being parallel, they composed a
1313 Parallelopiped. And, the Sun shining into my dark Chamber through a
1314 little hole in the Window-shut, I placed that Parallelopiped in his beam
1315 at some distance from the hole, in such a Posture, that the Axes of the
1316 Prisms might be perpendicular to the incident Rays, and that those Rays
1317 being incident upon the first Side of one Prism, might go on through the
1318 two contiguous Sides of both Prisms, and emerge out of the last Side of
1319 the second Prism. This Side being parallel to the first Side of the
1320 first Prism, caused the emerging Light to be parallel to the incident.
1321 Then, beyond these two Prisms I placed a third, which might refract that
1322 emergent Light, and by that Refraction cast the usual Colours of the
1323 Prism upon the opposite Wall, or upon a sheet of white Paper held at a
1324 convenient Distance behind the Prism for that refracted Light to fall
1325 upon it. After this I turned the Parallelopiped about its Axis, and
1326 found that when the contiguous Sides of the two Prisms became so oblique
1327 to the incident Rays, that those Rays began all of them to be
1328 reflected, those Rays which in the third Prism had suffered the greatest
1329 Refraction, and painted the Paper with violet and blue, were first of
1330 all by a total Reflexion taken out of the transmitted Light, the rest
1331 remaining and on the Paper painting their Colours of green, yellow,
1332 orange and red, as before; and afterwards by continuing the Motion of
1333 the two Prisms, the rest of the Rays also by a total Reflexion vanished
1334 in order, according to their degrees of Refrangibility. The Light
1335 therefore which emerged out of the two Prisms is compounded of Rays
1336 differently refrangible, seeing the more refrangible Rays may be taken
1337 out of it, while the less refrangible remain. But this Light being
1338 trajected only through the parallel Superficies of the two Prisms, if it
1339 suffer'd any change by the Refraction of one Superficies it lost that
1340 Impression by the contrary Refraction of the other Superficies, and so
1341 being restor'd to its pristine Constitution, became of the same Nature
1342 and Condition as at first before its Incidence on those Prisms; and
1343 therefore, before its Incidence, was as much compounded of Rays
1344 differently refrangible, as afterwards.
1345
1346 [Illustration: FIG. 22.]
1347
1348 _Illustration._ In the twenty second Figure ABC and BCD are the two
1349 Prisms tied together in the form of a Parallelopiped, their Sides BC and
1350 CB being contiguous, and their Sides AB and CD parallel. And HJK is the
1351 third Prism, by which the Sun's Light propagated through the hole F into
1352 the dark Chamber, and there passing through those sides of the Prisms
1353 AB, BC, CB and CD, is refracted at O to the white Paper PT, falling
1354 there partly upon P by a greater Refraction, partly upon T by a less
1355 Refraction, and partly upon R and other intermediate places by
1356 intermediate Refractions. By turning the Parallelopiped ACBD about its
1357 Axis, according to the order of the Letters A, C, D, B, at length when
1358 the contiguous Planes BC and CB become sufficiently oblique to the Rays
1359 FM, which are incident upon them at M, there will vanish totally out of
1360 the refracted Light OPT, first of all the most refracted Rays OP, (the
1361 rest OR and OT remaining as before) then the Rays OR and other
1362 intermediate ones, and lastly, the least refracted Rays OT. For when
1363 the Plane BC becomes sufficiently oblique to the Rays incident upon it,
1364 those Rays will begin to be totally reflected by it towards N; and first
1365 the most refrangible Rays will be totally reflected (as was explained in
1366 the preceding Experiment) and by Consequence must first disappear at P,
1367 and afterwards the rest as they are in order totally reflected to N,
1368 they must disappear in the same order at R and T. So then the Rays which
1369 at O suffer the greatest Refraction, may be taken out of the Light MO
1370 whilst the rest of the Rays remain in it, and therefore that Light MO is
1371 compounded of Rays differently refrangible. And because the Planes AB
1372 and CD are parallel, and therefore by equal and contrary Refractions
1373 destroy one anothers Effects, the incident Light FM must be of the same
1374 Kind and Nature with the emergent Light MO, and therefore doth also
1375 consist of Rays differently refrangible. These two Lights FM and MO,
1376 before the most refrangible Rays are separated out of the emergent Light
1377 MO, agree in Colour, and in all other Properties so far as my
1378 Observation reaches, and therefore are deservedly reputed of the same
1379 Nature and Constitution, and by Consequence the one is compounded as
1380 well as the other. But after the most refrangible Rays begin to be
1381 totally reflected, and thereby separated out of the emergent Light MO,
1382 that Light changes its Colour from white to a dilute and faint yellow, a
1383 pretty good orange, a very full red successively, and then totally
1384 vanishes. For after the most refrangible Rays which paint the Paper at
1385 P with a purple Colour, are by a total Reflexion taken out of the beam
1386 of Light MO, the rest of the Colours which appear on the Paper at R and
1387 T being mix'd in the Light MO compound there a faint yellow, and after
1388 the blue and part of the green which appear on the Paper between P and R
1389 are taken away, the rest which appear between R and T (that is the
1390 yellow, orange, red and a little green) being mixed in the beam MO
1391 compound there an orange; and when all the Rays are by Reflexion taken
1392 out of the beam MO, except the least refrangible, which at T appear of a
1393 full red, their Colour is the same in that beam MO as afterwards at T,
1394 the Refraction of the Prism HJK serving only to separate the differently
1395 refrangible Rays, without making any Alteration in their Colours, as
1396 shall be more fully proved hereafter. All which confirms as well the
1397 first Proposition as the second.
1398
1399 _Scholium._ If this Experiment and the former be conjoined and made one
1400 by applying a fourth Prism VXY [in _Fig._ 22.] to refract the reflected
1401 beam MN towards _tp_, the Conclusion will be clearer. For then the Light
1402 N_p_ which in the fourth Prism is more refracted, will become fuller and
1403 stronger when the Light OP, which in the third Prism HJK is more
1404 refracted, vanishes at P; and afterwards when the less refracted Light
1405 OT vanishes at T, the less refracted Light N_t_ will become increased
1406 whilst the more refracted Light at _p_ receives no farther increase. And
1407 as the trajected beam MO in vanishing is always of such a Colour as
1408 ought to result from the mixture of the Colours which fall upon the
1409 Paper PT, so is the reflected beam MN always of such a Colour as ought
1410 to result from the mixture of the Colours which fall upon the Paper
1411 _pt_. For when the most refrangible Rays are by a total Reflexion taken
1412 out of the beam MO, and leave that beam of an orange Colour, the Excess
1413 of those Rays in the reflected Light, does not only make the violet,
1414 indigo and blue at _p_ more full, but also makes the beam MN change from
1415 the yellowish Colour of the Sun's Light, to a pale white inclining to
1416 blue, and afterward recover its yellowish Colour again, so soon as all
1417 the rest of the transmitted Light MOT is reflected.
1418
1419 Now seeing that in all this variety of Experiments, whether the Trial be
1420 made in Light reflected, and that either from natural Bodies, as in the
1421 first and second Experiment, or specular, as in the ninth; or in Light
1422 refracted, and that either before the unequally refracted Rays are by
1423 diverging separated from one another, and losing their whiteness which
1424 they have altogether, appear severally of several Colours, as in the
1425 fifth Experiment; or after they are separated from one another, and
1426 appear colour'd as in the sixth, seventh, and eighth Experiments; or in
1427 Light trajected through parallel Superficies, destroying each others
1428 Effects, as in the tenth Experiment; there are always found Rays, which
1429 at equal Incidences on the same Medium suffer unequal Refractions, and
1430 that without any splitting or dilating of single Rays, or contingence in
1431 the inequality of the Refractions, as is proved in the fifth and sixth
1432 Experiments. And seeing the Rays which differ in Refrangibility may be
1433 parted and sorted from one another, and that either by Refraction as in
1434 the third Experiment, or by Reflexion as in the tenth, and then the
1435 several sorts apart at equal Incidences suffer unequal Refractions, and
1436 those sorts are more refracted than others after Separation, which were
1437 more refracted before it, as in the sixth and following Experiments, and
1438 if the Sun's Light be trajected through three or more cross Prisms
1439 successively, those Rays which in the first Prism are refracted more
1440 than others, are in all the following Prisms refracted more than others
1441 in the same Rate and Proportion, as appears by the fifth Experiment;
1442 it's manifest that the Sun's Light is an heterogeneous Mixture of Rays,
1443 some of which are constantly more refrangible than others, as was
1444 proposed.
1445
1446
1447 _PROP._ III. THEOR. III.
1448
1449 _The Sun's Light consists of Rays differing in Reflexibility, and those
1450 Rays are more reflexible than others which are more refrangible._
1451
1452 This is manifest by the ninth and tenth Experiments: For in the ninth
1453 Experiment, by turning the Prism about its Axis, until the Rays within
1454 it which in going out into the Air were refracted by its Base, became so
1455 oblique to that Base, as to begin to be totally reflected thereby; those
1456 Rays became first of all totally reflected, which before at equal
1457 Incidences with the rest had suffered the greatest Refraction. And the
1458 same thing happens in the Reflexion made by the common Base of the two
1459 Prisms in the tenth Experiment.
1460
1461
1462 _PROP._ IV. PROB. I.
1463
1464 _To separate from one another the heterogeneous Rays of compound Light._
1465
1466 [Illustration: FIG. 23.]
1467
1468 The heterogeneous Rays are in some measure separated from one another by
1469 the Refraction of the Prism in the third Experiment, and in the fifth
1470 Experiment, by taking away the Penumbra from the rectilinear sides of
1471 the coloured Image, that Separation in those very rectilinear sides or
1472 straight edges of the Image becomes perfect. But in all places between
1473 those rectilinear edges, those innumerable Circles there described,
1474 which are severally illuminated by homogeneal Rays, by interfering with
1475 one another, and being every where commix'd, do render the Light
1476 sufficiently compound. But if these Circles, whilst their Centers keep
1477 their Distances and Positions, could be made less in Diameter, their
1478 interfering one with another, and by Consequence the Mixture of the
1479 heterogeneous Rays would be proportionally diminish'd. In the twenty
1480 third Figure let AG, BH, CJ, DK, EL, FM be the Circles which so many
1481 sorts of Rays flowing from the same disque of the Sun, do in the third
1482 Experiment illuminate; of all which and innumerable other intermediate
1483 ones lying in a continual Series between the two rectilinear and
1484 parallel edges of the Sun's oblong Image PT, that Image is compos'd, as
1485 was explained in the fifth Experiment. And let _ag_, _bh_, _ci_, _dk_,
1486 _el_, _fm_ be so many less Circles lying in a like continual Series
1487 between two parallel right Lines _af_ and _gm_ with the same distances
1488 between their Centers, and illuminated by the same sorts of Rays, that
1489 is the Circle _ag_ with the same sort by which the corresponding Circle
1490 AG was illuminated, and the Circle _bh_ with the same sort by which the
1491 corresponding Circle BH was illuminated, and the rest of the Circles
1492 _ci_, _dk_, _el_, _fm_ respectively, with the same sorts of Rays by
1493 which the several corresponding Circles CJ, DK, EL, FM were illuminated.
1494 In the Figure PT composed of the greater Circles, three of those Circles
1495 AG, BH, CJ, are so expanded into one another, that the three sorts of
1496 Rays by which those Circles are illuminated, together with other
1497 innumerable sorts of intermediate Rays, are mixed at QR in the middle
1498 of the Circle BH. And the like Mixture happens throughout almost the
1499 whole length of the Figure PT. But in the Figure _pt_ composed of the
1500 less Circles, the three less Circles _ag_, _bh_, _ci_, which answer to
1501 those three greater, do not extend into one another; nor are there any
1502 where mingled so much as any two of the three sorts of Rays by which
1503 those Circles are illuminated, and which in the Figure PT are all of
1504 them intermingled at BH.
1505
1506 Now he that shall thus consider it, will easily understand that the
1507 Mixture is diminished in the same Proportion with the Diameters of the
1508 Circles. If the Diameters of the Circles whilst their Centers remain the
1509 same, be made three times less than before, the Mixture will be also
1510 three times less; if ten times less, the Mixture will be ten times less,
1511 and so of other Proportions. That is, the Mixture of the Rays in the
1512 greater Figure PT will be to their Mixture in the less _pt_, as the
1513 Latitude of the greater Figure is to the Latitude of the less. For the
1514 Latitudes of these Figures are equal to the Diameters of their Circles.
1515 And hence it easily follows, that the Mixture of the Rays in the
1516 refracted Spectrum _pt_ is to the Mixture of the Rays in the direct and
1517 immediate Light of the Sun, as the breadth of that Spectrum is to the
1518 difference between the length and breadth of the same Spectrum.
1519
1520 So then, if we would diminish the Mixture of the Rays, we are to
1521 diminish the Diameters of the Circles. Now these would be diminished if
1522 the Sun's Diameter to which they answer could be made less than it is,
1523 or (which comes to the same Purpose) if without Doors, at a great
1524 distance from the Prism towards the Sun, some opake Body were placed,
1525 with a round hole in the middle of it, to intercept all the Sun's Light,
1526 excepting so much as coming from the middle of his Body could pass
1527 through that Hole to the Prism. For so the Circles AG, BH, and the rest,
1528 would not any longer answer to the whole Disque of the Sun, but only to
1529 that Part of it which could be seen from the Prism through that Hole,
1530 that it is to the apparent Magnitude of that Hole view'd from the Prism.
1531 But that these Circles may answer more distinctly to that Hole, a Lens
1532 is to be placed by the Prism to cast the Image of the Hole, (that is,
1533 every one of the Circles AG, BH, &c.) distinctly upon the Paper at PT,
1534 after such a manner, as by a Lens placed at a Window, the Species of
1535 Objects abroad are cast distinctly upon a Paper within the Room, and the
1536 rectilinear Sides of the oblong Solar Image in the fifth Experiment
1537 became distinct without any Penumbra. If this be done, it will not be
1538 necessary to place that Hole very far off, no not beyond the Window. And
1539 therefore instead of that Hole, I used the Hole in the Window-shut, as
1540 follows.
1541
1542 _Exper._ 11. In the Sun's Light let into my darken'd Chamber through a
1543 small round Hole in my Window-shut, at about ten or twelve Feet from the
1544 Window, I placed a Lens, by which the Image of the Hole might be
1545 distinctly cast upon a Sheet of white Paper, placed at the distance of
1546 six, eight, ten, or twelve Feet from the Lens. For, according to the
1547 difference of the Lenses I used various distances, which I think not
1548 worth the while to describe. Then immediately after the Lens I placed a
1549 Prism, by which the trajected Light might be refracted either upwards or
1550 sideways, and thereby the round Image, which the Lens alone did cast
1551 upon the Paper might be drawn out into a long one with Parallel Sides,
1552 as in the third Experiment. This oblong Image I let fall upon another
1553 Paper at about the same distance from the Prism as before, moving the
1554 Paper either towards the Prism or from it, until I found the just
1555 distance where the Rectilinear Sides of the Image became most distinct.
1556 For in this Case, the Circular Images of the Hole, which compose that
1557 Image after the same manner that the Circles _ag_, _bh_, _ci_, &c. do
1558 the Figure _pt_ [in _Fig._ 23.] were terminated most distinctly without
1559 any Penumbra, and therefore extended into one another the least that
1560 they could, and by consequence the Mixture of the heterogeneous Rays was
1561 now the least of all. By this means I used to form an oblong Image (such
1562 as is _pt_) [in _Fig._ 23, and 24.] of Circular Images of the Hole,
1563 (such as are _ag_, _bh_, _ci_, &c.) and by using a greater or less Hole
1564 in the Window-shut, I made the Circular Images _ag_, _bh_, _ci_, &c. of
1565 which it was formed, to become greater or less at pleasure, and thereby
1566 the Mixture of the Rays in the Image _pt_ to be as much, or as little as
1567 I desired.
1568
1569 [Illustration: FIG. 24.]
1570
1571 _Illustration._ In the twenty-fourth Figure, F represents the Circular
1572 Hole in the Window-shut, MN the Lens, whereby the Image or Species of
1573 that Hole is cast distinctly upon a Paper at J, ABC the Prism, whereby
1574 the Rays are at their emerging out of the Lens refracted from J towards
1575 another Paper at _pt_, and the round Image at J is turned into an oblong
1576 Image _pt_ falling on that other Paper. This Image _pt_ consists of
1577 Circles placed one after another in a Rectilinear Order, as was
1578 sufficiently explained in the fifth Experiment; and these Circles are
1579 equal to the Circle J, and consequently answer in magnitude to the Hole
1580 F; and therefore by diminishing that Hole they may be at pleasure
1581 diminished, whilst their Centers remain in their Places. By this means I
1582 made the Breadth of the Image _pt_ to be forty times, and sometimes
1583 sixty or seventy times less than its Length. As for instance, if the
1584 Breadth of the Hole F be one tenth of an Inch, and MF the distance of
1585 the Lens from the Hole be 12 Feet; and if _p_B or _p_M the distance of
1586 the Image _pt_ from the Prism or Lens be 10 Feet, and the refracting
1587 Angle of the Prism be 62 Degrees, the Breadth of the Image _pt_ will be
1588 one twelfth of an Inch, and the Length about six Inches, and therefore
1589 the Length to the Breadth as 72 to 1, and by consequence the Light of
1590 this Image 71 times less compound than the Sun's direct Light. And Light
1591 thus far simple and homogeneal, is sufficient for trying all the
1592 Experiments in this Book about simple Light. For the Composition of
1593 heterogeneal Rays is in this Light so little, that it is scarce to be
1594 discovered and perceiv'd by Sense, except perhaps in the indigo and
1595 violet. For these being dark Colours do easily suffer a sensible Allay
1596 by that little scattering Light which uses to be refracted irregularly
1597 by the Inequalities of the Prism.
1598
1599 Yet instead of the Circular Hole F, 'tis better to substitute an oblong
1600 Hole shaped like a long Parallelogram with its Length parallel to the
1601 Prism ABC. For if this Hole be an Inch or two long, and but a tenth or
1602 twentieth Part of an Inch broad, or narrower; the Light of the Image
1603 _pt_ will be as simple as before, or simpler, and the Image will become
1604 much broader, and therefore more fit to have Experiments try'd in its
1605 Light than before.
1606
1607 Instead of this Parallelogram Hole may be substituted a triangular one
1608 of equal Sides, whose Base, for instance, is about the tenth Part of an
1609 Inch, and its Height an Inch or more. For by this means, if the Axis of
1610 the Prism be parallel to the Perpendicular of the Triangle, the Image
1611 _pt_ [in _Fig._ 25.] will now be form'd of equicrural Triangles _ag_,
1612 _bh_, _ci_, _dk_, _el_, _fm_, &c. and innumerable other intermediate
1613 ones answering to the triangular Hole in Shape and Bigness, and lying
1614 one after another in a continual Series between two Parallel Lines _af_
1615 and _gm_. These Triangles are a little intermingled at their Bases, but
1616 not at their Vertices; and therefore the Light on the brighter Side _af_
1617 of the Image, where the Bases of the Triangles are, is a little
1618 compounded, but on the darker Side _gm_ is altogether uncompounded, and
1619 in all Places between the Sides the Composition is proportional to the
1620 distances of the Places from that obscurer Side _gm_. And having a
1621 Spectrum _pt_ of such a Composition, we may try Experiments either in
1622 its stronger and less simple Light near the Side _af_, or in its weaker
1623 and simpler Light near the other Side _gm_, as it shall seem most
1624 convenient.
1625
1626 [Illustration: FIG. 25.]
1627
1628 But in making Experiments of this kind, the Chamber ought to be made as
1629 dark as can be, lest any Foreign Light mingle it self with the Light of
1630 the Spectrum _pt_, and render it compound; especially if we would try
1631 Experiments in the more simple Light next the Side _gm_ of the Spectrum;
1632 which being fainter, will have a less proportion to the Foreign Light;
1633 and so by the mixture of that Light be more troubled, and made more
1634 compound. The Lens also ought to be good, such as may serve for optical
1635 Uses, and the Prism ought to have a large Angle, suppose of 65 or 70
1636 Degrees, and to be well wrought, being made of Glass free from Bubbles
1637 and Veins, with its Sides not a little convex or concave, as usually
1638 happens, but truly plane, and its Polish elaborate, as in working
1639 Optick-glasses, and not such as is usually wrought with Putty, whereby
1640 the edges of the Sand-holes being worn away, there are left all over the
1641 Glass a numberless Company of very little convex polite Risings like
1642 Waves. The edges also of the Prism and Lens, so far as they may make any
1643 irregular Refraction, must be covered with a black Paper glewed on. And
1644 all the Light of the Sun's Beam let into the Chamber, which is useless
1645 and unprofitable to the Experiment, ought to be intercepted with black
1646 Paper, or other black Obstacles. For otherwise the useless Light being
1647 reflected every way in the Chamber, will mix with the oblong Spectrum,
1648 and help to disturb it. In trying these Things, so much diligence is not
1649 altogether necessary, but it will promote the Success of the
1650 Experiments, and by a very scrupulous Examiner of Things deserves to be
1651 apply'd. It's difficult to get Glass Prisms fit for this Purpose, and
1652 therefore I used sometimes prismatick Vessels made with pieces of broken
1653 Looking-glasses, and filled with Rain Water. And to increase the
1654 Refraction, I sometimes impregnated the Water strongly with _Saccharum
1655 Saturni_.
1656
1657
1658 _PROP._ V. THEOR. IV.
1659
1660 _Homogeneal Light is refracted regularly without any Dilatation
1661 splitting or shattering of the Rays, and the confused Vision of Objects
1662 seen through refracting Bodies by heterogeneal Light arises from the
1663 different Refrangibility of several sorts of Rays._
1664
1665 The first Part of this Proposition has been already sufficiently proved
1666 in the fifth Experiment, and will farther appear by the Experiments
1667 which follow.
1668
1669 _Exper._ 12. In the middle of a black Paper I made a round Hole about a
1670 fifth or sixth Part of an Inch in diameter. Upon this Paper I caused the
1671 Spectrum of homogeneal Light described in the former Proposition, so to
1672 fall, that some part of the Light might pass through the Hole of the
1673 Paper. This transmitted part of the Light I refracted with a Prism
1674 placed behind the Paper, and letting this refracted Light fall
1675 perpendicularly upon a white Paper two or three Feet distant from the
1676 Prism, I found that the Spectrum formed on the Paper by this Light was
1677 not oblong, as when 'tis made (in the third Experiment) by refracting
1678 the Sun's compound Light, but was (so far as I could judge by my Eye)
1679 perfectly circular, the Length being no greater than the Breadth. Which
1680 shews, that this Light is refracted regularly without any Dilatation of
1681 the Rays.
1682
1683 _Exper._ 13. In the homogeneal Light I placed a Paper Circle of a
1684 quarter of an Inch in diameter, and in the Sun's unrefracted
1685 heterogeneal white Light I placed another Paper Circle of the same
1686 Bigness. And going from the Papers to the distance of some Feet, I
1687 viewed both Circles through a Prism. The Circle illuminated by the Sun's
1688 heterogeneal Light appeared very oblong, as in the fourth Experiment,
1689 the Length being many times greater than the Breadth; but the other
1690 Circle, illuminated with homogeneal Light, appeared circular and
1691 distinctly defined, as when 'tis view'd with the naked Eye. Which proves
1692 the whole Proposition.
1693
1694 _Exper._ 14. In the homogeneal Light I placed Flies, and such-like
1695 minute Objects, and viewing them through a Prism, I saw their Parts as
1696 distinctly defined, as if I had viewed them with the naked Eye. The same
1697 Objects placed in the Sun's unrefracted heterogeneal Light, which was
1698 white, I viewed also through a Prism, and saw them most confusedly
1699 defined, so that I could not distinguish their smaller Parts from one
1700 another. I placed also the Letters of a small print, one while in the
1701 homogeneal Light, and then in the heterogeneal, and viewing them through
1702 a Prism, they appeared in the latter Case so confused and indistinct,
1703 that I could not read them; but in the former they appeared so distinct,
1704 that I could read readily, and thought I saw them as distinct, as when I
1705 view'd them with my naked Eye. In both Cases I view'd the same Objects,
1706 through the same Prism at the same distance from me, and in the same
1707 Situation. There was no difference, but in the Light by which the
1708 Objects were illuminated, and which in one Case was simple, and in the
1709 other compound; and therefore, the distinct Vision in the former Case,
1710 and confused in the latter, could arise from nothing else than from that
1711 difference of the Lights. Which proves the whole Proposition.
1712
1713 And in these three Experiments it is farther very remarkable, that the
1714 Colour of homogeneal Light was never changed by the Refraction.
1715
1716
1717 _PROP._ VI. THEOR. V.
1718
1719 _The Sine of Incidence of every Ray considered apart, is to its Sine of
1720 Refraction in a given Ratio._
1721
1722 That every Ray consider'd apart, is constant to it self in some degree
1723 of Refrangibility, is sufficiently manifest out of what has been said.
1724 Those Rays, which in the first Refraction, are at equal Incidences most
1725 refracted, are also in the following Refractions at equal Incidences
1726 most refracted; and so of the least refrangible, and the rest which have
1727 any mean Degree of Refrangibility, as is manifest by the fifth, sixth,
1728 seventh, eighth, and ninth Experiments. And those which the first Time
1729 at like Incidences are equally refracted, are again at like Incidences
1730 equally and uniformly refracted, and that whether they be refracted
1731 before they be separated from one another, as in the fifth Experiment,
1732 or whether they be refracted apart, as in the twelfth, thirteenth and
1733 fourteenth Experiments. The Refraction therefore of every Ray apart is
1734 regular, and what Rule that Refraction observes we are now to shew.[E]
1735
1736 The late Writers in Opticks teach, that the Sines of Incidence are in a
1737 given Proportion to the Sines of Refraction, as was explained in the
1738 fifth Axiom, and some by Instruments fitted for measuring of
1739 Refractions, or otherwise experimentally examining this Proportion, do
1740 acquaint us that they have found it accurate. But whilst they, not
1741 understanding the different Refrangibility of several Rays, conceived
1742 them all to be refracted according to one and the same Proportion, 'tis
1743 to be presumed that they adapted their Measures only to the middle of
1744 the refracted Light; so that from their Measures we may conclude only
1745 that the Rays which have a mean Degree of Refrangibility, that is, those
1746 which when separated from the rest appear green, are refracted according
1747 to a given Proportion of their Sines. And therefore we are now to shew,
1748 that the like given Proportions obtain in all the rest. That it should
1749 be so is very reasonable, Nature being ever conformable to her self; but
1750 an experimental Proof is desired. And such a Proof will be had, if we
1751 can shew that the Sines of Refraction of Rays differently refrangible
1752 are one to another in a given Proportion when their Sines of Incidence
1753 are equal. For, if the Sines of Refraction of all the Rays are in given
1754 Proportions to the Sine of Refractions of a Ray which has a mean Degree
1755 of Refrangibility, and this Sine is in a given Proportion to the equal
1756 Sines of Incidence, those other Sines of Refraction will also be in
1757 given Proportions to the equal Sines of Incidence. Now, when the Sines
1758 of Incidence are equal, it will appear by the following Experiment, that
1759 the Sines of Refraction are in a given Proportion to one another.
1760
1761 [Illustration: FIG. 26.]
1762
1763 _Exper._ 15. The Sun shining into a dark Chamber through a little round
1764 Hole in the Window-shut, let S [in _Fig._ 26.] represent his round white
1765 Image painted on the opposite Wall by his direct Light, PT his oblong
1766 coloured Image made by refracting that Light with a Prism placed at the
1767 Window; and _pt_, or _2p 2t_, _3p 3t_, his oblong colour'd Image made by
1768 refracting again the same Light sideways with a second Prism placed
1769 immediately after the first in a cross Position to it, as was explained
1770 in the fifth Experiment; that is to say, _pt_ when the Refraction of the
1771 second Prism is small, _2p 2t_ when its Refraction is greater, and _3p
1772 3t_ when it is greatest. For such will be the diversity of the
1773 Refractions, if the refracting Angle of the second Prism be of various
1774 Magnitudes; suppose of fifteen or twenty Degrees to make the Image _pt_,
1775 of thirty or forty to make the Image _2p 2t_, and of sixty to make the
1776 Image _3p 3t_. But for want of solid Glass Prisms with Angles of
1777 convenient Bignesses, there may be Vessels made of polished Plates of
1778 Glass cemented together in the form of Prisms and filled with Water.
1779 These things being thus ordered, I observed that all the solar Images or
1780 coloured Spectrums PT, _pt_, _2p 2t_, _3p 3t_ did very nearly converge
1781 to the place S on which the direct Light of the Sun fell and painted his
1782 white round Image when the Prisms were taken away. The Axis of the
1783 Spectrum PT, that is the Line drawn through the middle of it parallel to
1784 its rectilinear Sides, did when produced pass exactly through the middle
1785 of that white round Image S. And when the Refraction of the second Prism
1786 was equal to the Refraction of the first, the refracting Angles of them
1787 both being about 60 Degrees, the Axis of the Spectrum _3p 3t_ made by
1788 that Refraction, did when produced pass also through the middle of the
1789 same white round Image S. But when the Refraction of the second Prism
1790 was less than that of the first, the produced Axes of the Spectrums _tp_
1791 or _2t 2p_ made by that Refraction did cut the produced Axis of the
1792 Spectrum TP in the points _m_ and _n_, a little beyond the Center of
1793 that white round Image S. Whence the proportion of the Line 3_t_T to the
1794 Line 3_p_P was a little greater than the Proportion of 2_t_T or 2_p_P,
1795 and this Proportion a little greater than that of _t_T to _p_P. Now when
1796 the Light of the Spectrum PT falls perpendicularly upon the Wall, those
1797 Lines 3_t_T, 3_p_P, and 2_t_T, and 2_p_P, and _t_T, _p_P, are the
1798 Tangents of the Refractions, and therefore by this Experiment the
1799 Proportions of the Tangents of the Refractions are obtained, from whence
1800 the Proportions of the Sines being derived, they come out equal, so far
1801 as by viewing the Spectrums, and using some mathematical Reasoning I
1802 could estimate. For I did not make an accurate Computation. So then the
1803 Proposition holds true in every Ray apart, so far as appears by
1804 Experiment. And that it is accurately true, may be demonstrated upon
1805 this Supposition. _That Bodies refract Light by acting upon its Rays in
1806 Lines perpendicular to their Surfaces._ But in order to this
1807 Demonstration, I must distinguish the Motion of every Ray into two
1808 Motions, the one perpendicular to the refracting Surface, the other
1809 parallel to it, and concerning the perpendicular Motion lay down the
1810 following Proposition.
1811
1812 If any Motion or moving thing whatsoever be incident with any Velocity
1813 on any broad and thin space terminated on both sides by two parallel
1814 Planes, and in its Passage through that space be urged perpendicularly
1815 towards the farther Plane by any force which at given distances from the
1816 Plane is of given Quantities; the perpendicular velocity of that Motion
1817 or Thing, at its emerging out of that space, shall be always equal to
1818 the square Root of the sum of the square of the perpendicular velocity
1819 of that Motion or Thing at its Incidence on that space; and of the
1820 square of the perpendicular velocity which that Motion or Thing would
1821 have at its Emergence, if at its Incidence its perpendicular velocity
1822 was infinitely little.
1823
1824 And the same Proposition holds true of any Motion or Thing
1825 perpendicularly retarded in its passage through that space, if instead
1826 of the sum of the two Squares you take their difference. The
1827 Demonstration Mathematicians will easily find out, and therefore I shall
1828 not trouble the Reader with it.
1829
1830 Suppose now that a Ray coming most obliquely in the Line MC [in _Fig._
1831 1.] be refracted at C by the Plane RS into the Line CN, and if it be
1832 required to find the Line CE, into which any other Ray AC shall be
1833 refracted; let MC, AD, be the Sines of Incidence of the two Rays, and
1834 NG, EF, their Sines of Refraction, and let the equal Motions of the
1835 incident Rays be represented by the equal Lines MC and AC, and the
1836 Motion MC being considered as parallel to the refracting Plane, let the
1837 other Motion AC be distinguished into two Motions AD and DC, one of
1838 which AD is parallel, and the other DC perpendicular to the refracting
1839 Surface. In like manner, let the Motions of the emerging Rays be
1840 distinguish'd into two, whereof the perpendicular ones are MC/NG × CG
1841 and AD/EF × CF. And if the force of the refracting Plane begins to act
1842 upon the Rays either in that Plane or at a certain distance from it on
1843 the one side, and ends at a certain distance from it on the other side,
1844 and in all places between those two limits acts upon the Rays in Lines
1845 perpendicular to that refracting Plane, and the Actions upon the Rays at
1846 equal distances from the refracting Plane be equal, and at unequal ones
1847 either equal or unequal according to any rate whatever; that Motion of
1848 the Ray which is parallel to the refracting Plane, will suffer no
1849 Alteration by that Force; and that Motion which is perpendicular to it
1850 will be altered according to the rule of the foregoing Proposition. If
1851 therefore for the perpendicular velocity of the emerging Ray CN you
1852 write MC/NG × CG as above, then the perpendicular velocity of any other
1853 emerging Ray CE which was AD/EF × CF, will be equal to the square Root
1854 of CD_q_ + (_MCq/NGq_ × CG_q_). And by squaring these Equals, and adding
1855 to them the Equals AD_q_ and MC_q_ - CD_q_, and dividing the Sums by the
1856 Equals CF_q_ + EF_q_ and CG_q_ + NG_q_, you will have _MCq/NGq_ equal to
1857 _ADq/EFq_. Whence AD, the Sine of Incidence, is to EF the Sine of
1858 Refraction, as MC to NG, that is, in a given _ratio_. And this
1859 Demonstration being general, without determining what Light is, or by
1860 what kind of Force it is refracted, or assuming any thing farther than
1861 that the refracting Body acts upon the Rays in Lines perpendicular to
1862 its Surface; I take it to be a very convincing Argument of the full
1863 truth of this Proposition.
1864
1865 So then, if the _ratio_ of the Sines of Incidence and Refraction of any
1866 sort of Rays be found in any one case, 'tis given in all cases; and this
1867 may be readily found by the Method in the following Proposition.
1868
1869
1870 _PROP._ VII. THEOR. VI.
1871
1872 _The Perfection of Telescopes is impeded by the different Refrangibility
1873 of the Rays of Light._
1874
1875 The Imperfection of Telescopes is vulgarly attributed to the spherical
1876 Figures of the Glasses, and therefore Mathematicians have propounded to
1877 figure them by the conical Sections. To shew that they are mistaken, I
1878 have inserted this Proposition; the truth of which will appear by the
1879 measure of the Refractions of the several sorts of Rays; and these
1880 measures I thus determine.
1881
1882 In the third Experiment of this first Part, where the refracting Angle
1883 of the Prism was 62-1/2 Degrees, the half of that Angle 31 deg. 15 min.
1884 is the Angle of Incidence of the Rays at their going out of the Glass
1885 into the Air[F]; and the Sine of this Angle is 5188, the Radius being
1886 10000. When the Axis of this Prism was parallel to the Horizon, and the
1887 Refraction of the Rays at their Incidence on this Prism equal to that at
1888 their Emergence out of it, I observed with a Quadrant the Angle which
1889 the mean refrangible Rays, (that is those which went to the middle of
1890 the Sun's coloured Image) made with the Horizon, and by this Angle and
1891 the Sun's altitude observed at the same time, I found the Angle which
1892 the emergent Rays contained with the incident to be 44 deg. and 40 min.
1893 and the half of this Angle added to the Angle of Incidence 31 deg. 15
1894 min. makes the Angle of Refraction, which is therefore 53 deg. 35 min.
1895 and its Sine 8047. These are the Sines of Incidence and Refraction of
1896 the mean refrangible Rays, and their Proportion in round Numbers is 20
1897 to 31. This Glass was of a Colour inclining to green. The last of the
1898 Prisms mentioned in the third Experiment was of clear white Glass. Its
1899 refracting Angle 63-1/2 Degrees. The Angle which the emergent Rays
1900 contained, with the incident 45 deg. 50 min. The Sine of half the first
1901 Angle 5262. The Sine of half the Sum of the Angles 8157. And their
1902 Proportion in round Numbers 20 to 31, as before.
1903
1904 From the Length of the Image, which was about 9-3/4 or 10 Inches,
1905 subduct its Breadth, which was 2-1/8 Inches, and the Remainder 7-3/4
1906 Inches would be the Length of the Image were the Sun but a Point, and
1907 therefore subtends the Angle which the most and least refrangible Rays,
1908 when incident on the Prism in the same Lines, do contain with one
1909 another after their Emergence. Whence this Angle is 2 deg. 0´. 7´´. For
1910 the distance between the Image and the Prism where this Angle is made,
1911 was 18-1/2 Feet, and at that distance the Chord 7-3/4 Inches subtends an
1912 Angle of 2 deg. 0´. 7´´. Now half this Angle is the Angle which these
1913 emergent Rays contain with the emergent mean refrangible Rays, and a
1914 quarter thereof, that is 30´. 2´´. may be accounted the Angle which they
1915 would contain with the same emergent mean refrangible Rays, were they
1916 co-incident to them within the Glass, and suffered no other Refraction
1917 than that at their Emergence. For, if two equal Refractions, the one at
1918 the Incidence of the Rays on the Prism, the other at their Emergence,
1919 make half the Angle 2 deg. 0´. 7´´. then one of those Refractions will
1920 make about a quarter of that Angle, and this quarter added to, and
1921 subducted from the Angle of Refraction of the mean refrangible Rays,
1922 which was 53 deg. 35´, gives the Angles of Refraction of the most and
1923 least refrangible Rays 54 deg. 5´ 2´´, and 53 deg. 4´ 58´´, whose Sines
1924 are 8099 and 7995, the common Angle of Incidence being 31 deg. 15´, and
1925 its Sine 5188; and these Sines in the least round Numbers are in
1926 proportion to one another, as 78 and 77 to 50.
1927
1928 Now, if you subduct the common Sine of Incidence 50 from the Sines of
1929 Refraction 77 and 78, the Remainders 27 and 28 shew, that in small
1930 Refractions the Refraction of the least refrangible Rays is to the
1931 Refraction of the most refrangible ones, as 27 to 28 very nearly, and
1932 that the difference of the Refractions of the least refrangible and most
1933 refrangible Rays is about the 27-1/2th Part of the whole Refraction of
1934 the mean refrangible Rays.
1935
1936 Whence they that are skilled in Opticks will easily understand,[G] that
1937 the Breadth of the least circular Space, into which Object-glasses of
1938 Telescopes can collect all sorts of Parallel Rays, is about the 27-1/2th
1939 Part of half the Aperture of the Glass, or 55th Part of the whole
1940 Aperture; and that the Focus of the most refrangible Rays is nearer to
1941 the Object-glass than the Focus of the least refrangible ones, by about
1942 the 27-1/2th Part of the distance between the Object-glass and the Focus
1943 of the mean refrangible ones.
1944
1945 And if Rays of all sorts, flowing from any one lucid Point in the Axis
1946 of any convex Lens, be made by the Refraction of the Lens to converge to
1947 Points not too remote from the Lens, the Focus of the most refrangible
1948 Rays shall be nearer to the Lens than the Focus of the least refrangible
1949 ones, by a distance which is to the 27-1/2th Part of the distance of the
1950 Focus of the mean refrangible Rays from the Lens, as the distance
1951 between that Focus and the lucid Point, from whence the Rays flow, is to
1952 the distance between that lucid Point and the Lens very nearly.
1953
1954 Now to examine whether the Difference between the Refractions, which the
1955 most refrangible and the least refrangible Rays flowing from the same
1956 Point suffer in the Object-glasses of Telescopes and such-like Glasses,
1957 be so great as is here described, I contrived the following Experiment.
1958
1959 _Exper._ 16. The Lens which I used in the second and eighth Experiments,
1960 being placed six Feet and an Inch distant from any Object, collected the
1961 Species of that Object by the mean refrangible Rays at the distance of
1962 six Feet and an Inch from the Lens on the other side. And therefore by
1963 the foregoing Rule, it ought to collect the Species of that Object by
1964 the least refrangible Rays at the distance of six Feet and 3-2/3 Inches
1965 from the Lens, and by the most refrangible ones at the distance of five
1966 Feet and 10-1/3 Inches from it: So that between the two Places, where
1967 these least and most refrangible Rays collect the Species, there may be
1968 the distance of about 5-1/3 Inches. For by that Rule, as six Feet and an
1969 Inch (the distance of the Lens from the lucid Object) is to twelve Feet
1970 and two Inches (the distance of the lucid Object from the Focus of the
1971 mean refrangible Rays) that is, as One is to Two; so is the 27-1/2th
1972 Part of six Feet and an Inch (the distance between the Lens and the same
1973 Focus) to the distance between the Focus of the most refrangible Rays
1974 and the Focus of the least refrangible ones, which is therefore 5-17/55
1975 Inches, that is very nearly 5-1/3 Inches. Now to know whether this
1976 Measure was true, I repeated the second and eighth Experiment with
1977 coloured Light, which was less compounded than that I there made use of:
1978 For I now separated the heterogeneous Rays from one another by the
1979 Method I described in the eleventh Experiment, so as to make a coloured
1980 Spectrum about twelve or fifteen Times longer than broad. This Spectrum
1981 I cast on a printed Book, and placing the above-mentioned Lens at the
1982 distance of six Feet and an Inch from this Spectrum to collect the
1983 Species of the illuminated Letters at the same distance on the other
1984 side, I found that the Species of the Letters illuminated with blue were
1985 nearer to the Lens than those illuminated with deep red by about three
1986 Inches, or three and a quarter; but the Species of the Letters
1987 illuminated with indigo and violet appeared so confused and indistinct,
1988 that I could not read them: Whereupon viewing the Prism, I found it was
1989 full of Veins running from one end of the Glass to the other; so that
1990 the Refraction could not be regular. I took another Prism therefore
1991 which was free from Veins, and instead of the Letters I used two or
1992 three Parallel black Lines a little broader than the Strokes of the
1993 Letters, and casting the Colours upon these Lines in such manner, that
1994 the Lines ran along the Colours from one end of the Spectrum to the
1995 other, I found that the Focus where the indigo, or confine of this
1996 Colour and violet cast the Species of the black Lines most distinctly,
1997 to be about four Inches, or 4-1/4 nearer to the Lens than the Focus,
1998 where the deepest red cast the Species of the same black Lines most
1999 distinctly. The violet was so faint and dark, that I could not discern
2000 the Species of the Lines distinctly by that Colour; and therefore
2001 considering that the Prism was made of a dark coloured Glass inclining
2002 to green, I took another Prism of clear white Glass; but the Spectrum of
2003 Colours which this Prism made had long white Streams of faint Light
2004 shooting out from both ends of the Colours, which made me conclude that
2005 something was amiss; and viewing the Prism, I found two or three little
2006 Bubbles in the Glass, which refracted the Light irregularly. Wherefore I
2007 covered that Part of the Glass with black Paper, and letting the Light
2008 pass through another Part of it which was free from such Bubbles, the
2009 Spectrum of Colours became free from those irregular Streams of Light,
2010 and was now such as I desired. But still I found the violet so dark and
2011 faint, that I could scarce see the Species of the Lines by the violet,
2012 and not at all by the deepest Part of it, which was next the end of the
2013 Spectrum. I suspected therefore, that this faint and dark Colour might
2014 be allayed by that scattering Light which was refracted, and reflected
2015 irregularly, partly by some very small Bubbles in the Glasses, and
2016 partly by the Inequalities of their Polish; which Light, tho' it was but
2017 little, yet it being of a white Colour, might suffice to affect the
2018 Sense so strongly as to disturb the Phænomena of that weak and dark
2019 Colour the violet, and therefore I tried, as in the 12th, 13th, and 14th
2020 Experiments, whether the Light of this Colour did not consist of a
2021 sensible Mixture of heterogeneous Rays, but found it did not. Nor did
2022 the Refractions cause any other sensible Colour than violet to emerge
2023 out of this Light, as they would have done out of white Light, and by
2024 consequence out of this violet Light had it been sensibly compounded
2025 with white Light. And therefore I concluded, that the reason why I could
2026 not see the Species of the Lines distinctly by this Colour, was only
2027 the Darkness of this Colour, and Thinness of its Light, and its distance
2028 from the Axis of the Lens; I divided therefore those Parallel black
2029 Lines into equal Parts, by which I might readily know the distances of
2030 the Colours in the Spectrum from one another, and noted the distances of
2031 the Lens from the Foci of such Colours, as cast the Species of the Lines
2032 distinctly, and then considered whether the difference of those
2033 distances bear such proportion to 5-1/3 Inches, the greatest Difference
2034 of the distances, which the Foci of the deepest red and violet ought to
2035 have from the Lens, as the distance of the observed Colours from one
2036 another in the Spectrum bear to the greatest distance of the deepest red
2037 and violet measured in the Rectilinear Sides of the Spectrum, that is,
2038 to the Length of those Sides, or Excess of the Length of the Spectrum
2039 above its Breadth. And my Observations were as follows.
2040
2041 When I observed and compared the deepest sensible red, and the Colour in
2042 the Confine of green and blue, which at the Rectilinear Sides of the
2043 Spectrum was distant from it half the Length of those Sides, the Focus
2044 where the Confine of green and blue cast the Species of the Lines
2045 distinctly on the Paper, was nearer to the Lens than the Focus, where
2046 the red cast those Lines distinctly on it by about 2-1/2 or 2-3/4
2047 Inches. For sometimes the Measures were a little greater, sometimes a
2048 little less, but seldom varied from one another above 1/3 of an Inch.
2049 For it was very difficult to define the Places of the Foci, without some
2050 little Errors. Now, if the Colours distant half the Length of the
2051 Image, (measured at its Rectilinear Sides) give 2-1/2 or 2-3/4
2052 Difference of the distances of their Foci from the Lens, then the
2053 Colours distant the whole Length ought to give 5 or 5-1/2 Inches
2054 difference of those distances.
2055
2056 But here it's to be noted, that I could not see the red to the full end
2057 of the Spectrum, but only to the Center of the Semicircle which bounded
2058 that end, or a little farther; and therefore I compared this red not
2059 with that Colour which was exactly in the middle of the Spectrum, or
2060 Confine of green and blue, but with that which verged a little more to
2061 the blue than to the green: And as I reckoned the whole Length of the
2062 Colours not to be the whole Length of the Spectrum, but the Length of
2063 its Rectilinear Sides, so compleating the semicircular Ends into
2064 Circles, when either of the observed Colours fell within those Circles,
2065 I measured the distance of that Colour from the semicircular End of the
2066 Spectrum, and subducting half this distance from the measured distance
2067 of the two Colours, I took the Remainder for their corrected distance;
2068 and in these Observations set down this corrected distance for the
2069 difference of the distances of their Foci from the Lens. For, as the
2070 Length of the Rectilinear Sides of the Spectrum would be the whole
2071 Length of all the Colours, were the Circles of which (as we shewed) that
2072 Spectrum consists contracted and reduced to Physical Points, so in that
2073 Case this corrected distance would be the real distance of the two
2074 observed Colours.
2075
2076 When therefore I farther observed the deepest sensible red, and that
2077 blue whose corrected distance from it was 7/12 Parts of the Length of
2078 the Rectilinear Sides of the Spectrum, the difference of the distances
2079 of their Foci from the Lens was about 3-1/4 Inches, and as 7 to 12, so
2080 is 3-1/4 to 5-4/7.
2081
2082 When I observed the deepest sensible red, and that indigo whose
2083 corrected distance was 8/12 or 2/3 of the Length of the Rectilinear
2084 Sides of the Spectrum, the difference of the distances of their Foci
2085 from the Lens, was about 3-2/3 Inches, and as 2 to 3, so is 3-2/3 to
2086 5-1/2.
2087
2088 When I observed the deepest sensible red, and that deep indigo whose
2089 corrected distance from one another was 9/12 or 3/4 of the Length of the
2090 Rectilinear Sides of the Spectrum, the difference of the distances of
2091 their Foci from the Lens was about 4 Inches; and as 3 to 4, so is 4 to
2092 5-1/3.
2093
2094 When I observed the deepest sensible red, and that Part of the violet
2095 next the indigo, whose corrected distance from the red was 10/12 or 5/6
2096 of the Length of the Rectilinear Sides of the Spectrum, the difference
2097 of the distances of their Foci from the Lens was about 4-1/2 Inches, and
2098 as 5 to 6, so is 4-1/2 to 5-2/5. For sometimes, when the Lens was
2099 advantageously placed, so that its Axis respected the blue, and all
2100 Things else were well ordered, and the Sun shone clear, and I held my
2101 Eye very near to the Paper on which the Lens cast the Species of the
2102 Lines, I could see pretty distinctly the Species of those Lines by that
2103 Part of the violet which was next the indigo; and sometimes I could see
2104 them by above half the violet, For in making these Experiments I had
2105 observed, that the Species of those Colours only appear distinct, which
2106 were in or near the Axis of the Lens: So that if the blue or indigo were
2107 in the Axis, I could see their Species distinctly; and then the red
2108 appeared much less distinct than before. Wherefore I contrived to make
2109 the Spectrum of Colours shorter than before, so that both its Ends might
2110 be nearer to the Axis of the Lens. And now its Length was about 2-1/2
2111 Inches, and Breadth about 1/5 or 1/6 of an Inch. Also instead of the
2112 black Lines on which the Spectrum was cast, I made one black Line
2113 broader than those, that I might see its Species more easily; and this
2114 Line I divided by short cross Lines into equal Parts, for measuring the
2115 distances of the observed Colours. And now I could sometimes see the
2116 Species of this Line with its Divisions almost as far as the Center of
2117 the semicircular violet End of the Spectrum, and made these farther
2118 Observations.
2119
2120 When I observed the deepest sensible red, and that Part of the violet,
2121 whose corrected distance from it was about 8/9 Parts of the Rectilinear
2122 Sides of the Spectrum, the Difference of the distances of the Foci of
2123 those Colours from the Lens, was one time 4-2/3, another time 4-3/4,
2124 another time 4-7/8 Inches; and as 8 to 9, so are 4-2/3, 4-3/4, 4-7/8, to
2125 5-1/4, 5-11/32, 5-31/64 respectively.
2126
2127 When I observed the deepest sensible red, and deepest sensible violet,
2128 (the corrected distance of which Colours, when all Things were ordered
2129 to the best Advantage, and the Sun shone very clear, was about 11/12 or
2130 15/16 Parts of the Length of the Rectilinear Sides of the coloured
2131 Spectrum) I found the Difference of the distances of their Foci from the
2132 Lens sometimes 4-3/4 sometimes 5-1/4, and for the most part 5 Inches or
2133 thereabouts; and as 11 to 12, or 15 to 16, so is five Inches to 5-2/2 or
2134 5-1/3 Inches.
2135
2136 And by this Progression of Experiments I satisfied my self, that had the
2137 Light at the very Ends of the Spectrum been strong enough to make the
2138 Species of the black Lines appear plainly on the Paper, the Focus of the
2139 deepest violet would have been found nearer to the Lens, than the Focus
2140 of the deepest red, by about 5-1/3 Inches at least. And this is a
2141 farther Evidence, that the Sines of Incidence and Refraction of the
2142 several sorts of Rays, hold the same Proportion to one another in the
2143 smallest Refractions which they do in the greatest.
2144
2145 My Progress in making this nice and troublesome Experiment I have set
2146 down more at large, that they that shall try it after me may be aware of
2147 the Circumspection requisite to make it succeed well. And if they cannot
2148 make it succeed so well as I did, they may notwithstanding collect by
2149 the Proportion of the distance of the Colours of the Spectrum, to the
2150 Difference of the distances of their Foci from the Lens, what would be
2151 the Success in the more distant Colours by a better trial. And yet, if
2152 they use a broader Lens than I did, and fix it to a long strait Staff,
2153 by means of which it may be readily and truly directed to the Colour
2154 whose Focus is desired, I question not but the Experiment will succeed
2155 better with them than it did with me. For I directed the Axis as nearly
2156 as I could to the middle of the Colours, and then the faint Ends of the
2157 Spectrum being remote from the Axis, cast their Species less distinctly
2158 on the Paper than they would have done, had the Axis been successively
2159 directed to them.
2160
2161 Now by what has been said, it's certain that the Rays which differ in
2162 Refrangibility do not converge to the same Focus; but if they flow from
2163 a lucid Point, as far from the Lens on one side as their Foci are on the
2164 other, the Focus of the most refrangible Rays shall be nearer to the
2165 Lens than that of the least refrangible, by above the fourteenth Part of
2166 the whole distance; and if they flow from a lucid Point, so very remote
2167 from the Lens, that before their Incidence they may be accounted
2168 parallel, the Focus of the most refrangible Rays shall be nearer to the
2169 Lens than the Focus of the least refrangible, by about the 27th or 28th
2170 Part of their whole distance from it. And the Diameter of the Circle in
2171 the middle Space between those two Foci which they illuminate, when they
2172 fall there on any Plane, perpendicular to the Axis (which Circle is the
2173 least into which they can all be gathered) is about the 55th Part of the
2174 Diameter of the Aperture of the Glass. So that 'tis a wonder, that
2175 Telescopes represent Objects so distinct as they do. But were all the
2176 Rays of Light equally refrangible, the Error arising only from the
2177 Sphericalness of the Figures of Glasses would be many hundred times
2178 less. For, if the Object-glass of a Telescope be Plano-convex, and the
2179 Plane side be turned towards the Object, and the Diameter of the
2180 Sphere, whereof this Glass is a Segment, be called D, and the
2181 Semi-diameter of the Aperture of the Glass be called S, and the Sine of
2182 Incidence out of Glass into Air, be to the Sine of Refraction as I to R;
2183 the Rays which come parallel to the Axis of the Glass, shall in the
2184 Place where the Image of the Object is most distinctly made, be
2185 scattered all over a little Circle, whose Diameter is _(Rq/Iq) × (S
2186 cub./D quad.)_ very nearly,[H] as I gather by computing the Errors of
2187 the Rays by the Method of infinite Series, and rejecting the Terms,
2188 whose Quantities are inconsiderable. As for instance, if the Sine of
2189 Incidence I, be to the Sine of Refraction R, as 20 to 31, and if D the
2190 Diameter of the Sphere, to which the Convex-side of the Glass is ground,
2191 be 100 Feet or 1200 Inches, and S the Semi-diameter of the Aperture be
2192 two Inches, the Diameter of the little Circle, (that is (_Rq × S
2193 cub.)/(Iq × D quad._)) will be (31 × 31 × 8)/(20 × 20 × 1200 × 1200) (or
2194 961/72000000) Parts of an Inch. But the Diameter of the little Circle,
2195 through which these Rays are scattered by unequal Refrangibility, will
2196 be about the 55th Part of the Aperture of the Object-glass, which here
2197 is four Inches. And therefore, the Error arising from the Spherical
2198 Figure of the Glass, is to the Error arising from the different
2199 Refrangibility of the Rays, as 961/72000000 to 4/55, that is as 1 to
2200 5449; and therefore being in comparison so very little, deserves not to
2201 be considered.
2202
2203 [Illustration: FIG. 27.]
2204
2205 But you will say, if the Errors caused by the different Refrangibility
2206 be so very great, how comes it to pass, that Objects appear through
2207 Telescopes so distinct as they do? I answer, 'tis because the erring
2208 Rays are not scattered uniformly over all that Circular Space, but
2209 collected infinitely more densely in the Center than in any other Part
2210 of the Circle, and in the Way from the Center to the Circumference, grow
2211 continually rarer and rarer, so as at the Circumference to become
2212 infinitely rare; and by reason of their Rarity are not strong enough to
2213 be visible, unless in the Center and very near it. Let ADE [in _Fig._
2214 27.] represent one of those Circles described with the Center C, and
2215 Semi-diameter AC, and let BFG be a smaller Circle concentrick to the
2216 former, cutting with its Circumference the Diameter AC in B, and bisect
2217 AC in N; and by my reckoning, the Density of the Light in any Place B,
2218 will be to its Density in N, as AB to BC; and the whole Light within the
2219 lesser Circle BFG, will be to the whole Light within the greater AED, as
2220 the Excess of the Square of AC above the Square of AB, is to the Square
2221 of AC. As if BC be the fifth Part of AC, the Light will be four times
2222 denser in B than in N, and the whole Light within the less Circle, will
2223 be to the whole Light within the greater, as nine to twenty-five. Whence
2224 it's evident, that the Light within the less Circle, must strike the
2225 Sense much more strongly, than that faint and dilated Light round about
2226 between it and the Circumference of the greater.
2227
2228 But it's farther to be noted, that the most luminous of the Prismatick
2229 Colours are the yellow and orange. These affect the Senses more strongly
2230 than all the rest together, and next to these in strength are the red
2231 and green. The blue compared with these is a faint and dark Colour, and
2232 the indigo and violet are much darker and fainter, so that these
2233 compared with the stronger Colours are little to be regarded. The Images
2234 of Objects are therefore to be placed, not in the Focus of the mean
2235 refrangible Rays, which are in the Confine of green and blue, but in the
2236 Focus of those Rays which are in the middle of the orange and yellow;
2237 there where the Colour is most luminous and fulgent, that is in the
2238 brightest yellow, that yellow which inclines more to orange than to
2239 green. And by the Refraction of these Rays (whose Sines of Incidence and
2240 Refraction in Glass are as 17 and 11) the Refraction of Glass and
2241 Crystal for Optical Uses is to be measured. Let us therefore place the
2242 Image of the Object in the Focus of these Rays, and all the yellow and
2243 orange will fall within a Circle, whose Diameter is about the 250th
2244 Part of the Diameter of the Aperture of the Glass. And if you add the
2245 brighter half of the red, (that half which is next the orange) and the
2246 brighter half of the green, (that half which is next the yellow) about
2247 three fifth Parts of the Light of these two Colours will fall within the
2248 same Circle, and two fifth Parts will fall without it round about; and
2249 that which falls without will be spread through almost as much more
2250 space as that which falls within, and so in the gross be almost three
2251 times rarer. Of the other half of the red and green, (that is of the
2252 deep dark red and willow green) about one quarter will fall within this
2253 Circle, and three quarters without, and that which falls without will be
2254 spread through about four or five times more space than that which falls
2255 within; and so in the gross be rarer, and if compared with the whole
2256 Light within it, will be about 25 times rarer than all that taken in the
2257 gross; or rather more than 30 or 40 times rarer, because the deep red in
2258 the end of the Spectrum of Colours made by a Prism is very thin and
2259 rare, and the willow green is something rarer than the orange and
2260 yellow. The Light of these Colours therefore being so very much rarer
2261 than that within the Circle, will scarce affect the Sense, especially
2262 since the deep red and willow green of this Light, are much darker
2263 Colours than the rest. And for the same reason the blue and violet being
2264 much darker Colours than these, and much more rarified, may be
2265 neglected. For the dense and bright Light of the Circle, will obscure
2266 the rare and weak Light of these dark Colours round about it, and
2267 render them almost insensible. The sensible Image of a lucid Point is
2268 therefore scarce broader than a Circle, whose Diameter is the 250th Part
2269 of the Diameter of the Aperture of the Object-glass of a good Telescope,
2270 or not much broader, if you except a faint and dark misty Light round
2271 about it, which a Spectator will scarce regard. And therefore in a
2272 Telescope, whose Aperture is four Inches, and Length an hundred Feet, it
2273 exceeds not 2´´ 45´´´, or 3´´. And in a Telescope whose Aperture is two
2274 Inches, and Length 20 or 30 Feet, it may be 5´´ or 6´´, and scarce
2275 above. And this answers well to Experience: For some Astronomers have
2276 found the Diameters of the fix'd Stars, in Telescopes of between 20 and
2277 60 Feet in length, to be about 5´´ or 6´´, or at most 8´´ or 10´´ in
2278 diameter. But if the Eye-Glass be tincted faintly with the Smoak of a
2279 Lamp or Torch, to obscure the Light of the Star, the fainter Light in
2280 the Circumference of the Star ceases to be visible, and the Star (if the
2281 Glass be sufficiently soiled with Smoak) appears something more like a
2282 mathematical Point. And for the same Reason, the enormous Part of the
2283 Light in the Circumference of every lucid Point ought to be less
2284 discernible in shorter Telescopes than in longer, because the shorter
2285 transmit less Light to the Eye.
2286
2287 Now, that the fix'd Stars, by reason of their immense Distance, appear
2288 like Points, unless so far as their Light is dilated by Refraction, may
2289 appear from hence; that when the Moon passes over them and eclipses
2290 them, their Light vanishes, not gradually like that of the Planets, but
2291 all at once; and in the end of the Eclipse it returns into Sight all at
2292 once, or certainly in less time than the second of a Minute; the
2293 Refraction of the Moon's Atmosphere a little protracting the time in
2294 which the Light of the Star first vanishes, and afterwards returns into
2295 Sight.
2296
2297 Now, if we suppose the sensible Image of a lucid Point, to be even 250
2298 times narrower than the Aperture of the Glass; yet this Image would be
2299 still much greater than if it were only from the spherical Figure of the
2300 Glass. For were it not for the different Refrangibility of the Rays, its
2301 breadth in an 100 Foot Telescope whose aperture is 4 Inches, would be
2302 but 961/72000000 parts of an Inch, as is manifest by the foregoing
2303 Computation. And therefore in this case the greatest Errors arising from
2304 the spherical Figure of the Glass, would be to the greatest sensible
2305 Errors arising from the different Refrangibility of the Rays as
2306 961/72000000 to 4/250 at most, that is only as 1 to 1200. And this
2307 sufficiently shews that it is not the spherical Figures of Glasses, but
2308 the different Refrangibility of the Rays which hinders the perfection of
2309 Telescopes.
2310
2311 There is another Argument by which it may appear that the different
2312 Refrangibility of Rays, is the true cause of the imperfection of
2313 Telescopes. For the Errors of the Rays arising from the spherical
2314 Figures of Object-glasses, are as the Cubes of the Apertures of the
2315 Object Glasses; and thence to make Telescopes of various Lengths magnify
2316 with equal distinctness, the Apertures of the Object-glasses, and the
2317 Charges or magnifying Powers ought to be as the Cubes of the square
2318 Roots of their lengths; which doth not answer to Experience. But the
2319 Errors of the Rays arising from the different Refrangibility, are as the
2320 Apertures of the Object-glasses; and thence to make Telescopes of
2321 various lengths, magnify with equal distinctness, their Apertures and
2322 Charges ought to be as the square Roots of their lengths; and this
2323 answers to Experience, as is well known. For Instance, a Telescope of 64
2324 Feet in length, with an Aperture of 2-2/3 Inches, magnifies about 120
2325 times, with as much distinctness as one of a Foot in length, with 1/3 of
2326 an Inch aperture, magnifies 15 times.
2327
2328 [Illustration: FIG. 28.]
2329
2330 Now were it not for this different Refrangibility of Rays, Telescopes
2331 might be brought to a greater perfection than we have yet describ'd, by
2332 composing the Object-glass of two Glasses with Water between them. Let
2333 ADFC [in _Fig._ 28.] represent the Object-glass composed of two Glasses
2334 ABED and BEFC, alike convex on the outsides AGD and CHF, and alike
2335 concave on the insides BME, BNE, with Water in the concavity BMEN. Let
2336 the Sine of Incidence out of Glass into Air be as I to R, and out of
2337 Water into Air, as K to R, and by consequence out of Glass into Water,
2338 as I to K: and let the Diameter of the Sphere to which the convex sides
2339 AGD and CHF are ground be D, and the Diameter of the Sphere to which the
2340 concave sides BME and BNE, are ground be to D, as the Cube Root of
2341 KK--KI to the Cube Root of RK--RI: and the Refractions on the concave
2342 sides of the Glasses, will very much correct the Errors of the
2343 Refractions on the convex sides, so far as they arise from the
2344 sphericalness of the Figure. And by this means might Telescopes be
2345 brought to sufficient perfection, were it not for the different
2346 Refrangibility of several sorts of Rays. But by reason of this different
2347 Refrangibility, I do not yet see any other means of improving Telescopes
2348 by Refractions alone, than that of increasing their lengths, for which
2349 end the late Contrivance of _Hugenius_ seems well accommodated. For very
2350 long Tubes are cumbersome, and scarce to be readily managed, and by
2351 reason of their length are very apt to bend, and shake by bending, so as
2352 to cause a continual trembling in the Objects, whereby it becomes
2353 difficult to see them distinctly: whereas by his Contrivance the Glasses
2354 are readily manageable, and the Object-glass being fix'd upon a strong
2355 upright Pole becomes more steady.
2356
2357 Seeing therefore the Improvement of Telescopes of given lengths by
2358 Refractions is desperate; I contrived heretofore a Perspective by
2359 Reflexion, using instead of an Object-glass a concave Metal. The
2360 diameter of the Sphere to which the Metal was ground concave was about
2361 25 _English_ Inches, and by consequence the length of the Instrument
2362 about six Inches and a quarter. The Eye-glass was Plano-convex, and the
2363 diameter of the Sphere to which the convex side was ground was about 1/5
2364 of an Inch, or a little less, and by consequence it magnified between 30
2365 and 40 times. By another way of measuring I found that it magnified
2366 about 35 times. The concave Metal bore an Aperture of an Inch and a
2367 third part; but the Aperture was limited not by an opake Circle,
2368 covering the Limb of the Metal round about, but by an opake Circle
2369 placed between the Eyeglass and the Eye, and perforated in the middle
2370 with a little round hole for the Rays to pass through to the Eye. For
2371 this Circle by being placed here, stopp'd much of the erroneous Light,
2372 which otherwise would have disturbed the Vision. By comparing it with a
2373 pretty good Perspective of four Feet in length, made with a concave
2374 Eye-glass, I could read at a greater distance with my own Instrument
2375 than with the Glass. Yet Objects appeared much darker in it than in the
2376 Glass, and that partly because more Light was lost by Reflexion in the
2377 Metal, than by Refraction in the Glass, and partly because my Instrument
2378 was overcharged. Had it magnified but 30 or 25 times, it would have made
2379 the Object appear more brisk and pleasant. Two of these I made about 16
2380 Years ago, and have one of them still by me, by which I can prove the
2381 truth of what I write. Yet it is not so good as at the first. For the
2382 concave has been divers times tarnished and cleared again, by rubbing
2383 it with very soft Leather. When I made these an Artist in _London_
2384 undertook to imitate it; but using another way of polishing them than I
2385 did, he fell much short of what I had attained to, as I afterwards
2386 understood by discoursing the Under-workman he had employed. The Polish
2387 I used was in this manner. I had two round Copper Plates, each six
2388 Inches in Diameter, the one convex, the other concave, ground very true
2389 to one another. On the convex I ground the Object-Metal or Concave which
2390 was to be polish'd, 'till it had taken the Figure of the Convex and was
2391 ready for a Polish. Then I pitched over the convex very thinly, by
2392 dropping melted Pitch upon it, and warming it to keep the Pitch soft,
2393 whilst I ground it with the concave Copper wetted to make it spread
2394 eavenly all over the convex. Thus by working it well I made it as thin
2395 as a Groat, and after the convex was cold I ground it again to give it
2396 as true a Figure as I could. Then I took Putty which I had made very
2397 fine by washing it from all its grosser Particles, and laying a little
2398 of this upon the Pitch, I ground it upon the Pitch with the concave
2399 Copper, till it had done making a Noise; and then upon the Pitch I
2400 ground the Object-Metal with a brisk motion, for about two or three
2401 Minutes of time, leaning hard upon it. Then I put fresh Putty upon the
2402 Pitch, and ground it again till it had done making a noise, and
2403 afterwards ground the Object-Metal upon it as before. And this Work I
2404 repeated till the Metal was polished, grinding it the last time with all
2405 my strength for a good while together, and frequently breathing upon
2406 the Pitch, to keep it moist without laying on any more fresh Putty. The
2407 Object-Metal was two Inches broad, and about one third part of an Inch
2408 thick, to keep it from bending. I had two of these Metals, and when I
2409 had polished them both, I tried which was best, and ground the other
2410 again, to see if I could make it better than that which I kept. And thus
2411 by many Trials I learn'd the way of polishing, till I made those two
2412 reflecting Perspectives I spake of above. For this Art of polishing will
2413 be better learn'd by repeated Practice than by my Description. Before I
2414 ground the Object-Metal on the Pitch, I always ground the Putty on it
2415 with the concave Copper, till it had done making a noise, because if the
2416 Particles of the Putty were not by this means made to stick fast in the
2417 Pitch, they would by rolling up and down grate and fret the Object-Metal
2418 and fill it full of little holes.
2419
2420 But because Metal is more difficult to polish than Glass, and is
2421 afterwards very apt to be spoiled by tarnishing, and reflects not so
2422 much Light as Glass quick-silver'd over does: I would propound to use
2423 instead of the Metal, a Glass ground concave on the foreside, and as
2424 much convex on the backside, and quick-silver'd over on the convex side.
2425 The Glass must be every where of the same thickness exactly. Otherwise
2426 it will make Objects look colour'd and indistinct. By such a Glass I
2427 tried about five or six Years ago to make a reflecting Telescope of four
2428 Feet in length to magnify about 150 times, and I satisfied my self that
2429 there wants nothing but a good Artist to bring the Design to
2430 perfection. For the Glass being wrought by one of our _London_ Artists
2431 after such a manner as they grind Glasses for Telescopes, though it
2432 seemed as well wrought as the Object-glasses use to be, yet when it was
2433 quick-silver'd, the Reflexion discovered innumerable Inequalities all
2434 over the Glass. And by reason of these Inequalities, Objects appeared
2435 indistinct in this Instrument. For the Errors of reflected Rays caused
2436 by any Inequality of the Glass, are about six times greater than the
2437 Errors of refracted Rays caused by the like Inequalities. Yet by this
2438 Experiment I satisfied my self that the Reflexion on the concave side of
2439 the Glass, which I feared would disturb the Vision, did no sensible
2440 prejudice to it, and by consequence that nothing is wanting to perfect
2441 these Telescopes, but good Workmen who can grind and polish Glasses
2442 truly spherical. An Object-glass of a fourteen Foot Telescope, made by
2443 an Artificer at _London_, I once mended considerably, by grinding it on
2444 Pitch with Putty, and leaning very easily on it in the grinding, lest
2445 the Putty should scratch it. Whether this way may not do well enough for
2446 polishing these reflecting Glasses, I have not yet tried. But he that
2447 shall try either this or any other way of polishing which he may think
2448 better, may do well to make his Glasses ready for polishing, by grinding
2449 them without that Violence, wherewith our _London_ Workmen press their
2450 Glasses in grinding. For by such violent pressure, Glasses are apt to
2451 bend a little in the grinding, and such bending will certainly spoil
2452 their Figure. To recommend therefore the consideration of these
2453 reflecting Glasses to such Artists as are curious in figuring Glasses, I
2454 shall describe this optical Instrument in the following Proposition.
2455
2456
2457 _PROP._ VIII. PROB. II.
2458
2459 _To shorten Telescopes._
2460
2461 Let ABCD [in _Fig._ 29.] represent a Glass spherically concave on the
2462 foreside AB, and as much convex on the backside CD, so that it be every
2463 where of an equal thickness. Let it not be thicker on one side than on
2464 the other, lest it make Objects appear colour'd and indistinct, and let
2465 it be very truly wrought and quick-silver'd over on the backside; and
2466 set in the Tube VXYZ which must be very black within. Let EFG represent
2467 a Prism of Glass or Crystal placed near the other end of the Tube, in
2468 the middle of it, by means of a handle of Brass or Iron FGK, to the end
2469 of which made flat it is cemented. Let this Prism be rectangular at E,
2470 and let the other two Angles at F and G be accurately equal to each
2471 other, and by consequence equal to half right ones, and let the plane
2472 sides FE and GE be square, and by consequence the third side FG a
2473 rectangular Parallelogram, whose length is to its breadth in a
2474 subduplicate proportion of two to one. Let it be so placed in the Tube,
2475 that the Axis of the Speculum may pass through the middle of the square
2476 side EF perpendicularly and by consequence through the middle of the
2477 side FG at an Angle of 45 Degrees, and let the side EF be turned towards
2478 the Speculum, and the distance of this Prism from the Speculum be such
2479 that the Rays of the Light PQ, RS, &c. which are incident upon the
2480 Speculum in Lines parallel to the Axis thereof, may enter the Prism at
2481 the side EF, and be reflected by the side FG, and thence go out of it
2482 through the side GE, to the Point T, which must be the common Focus of
2483 the Speculum ABDC, and of a Plano-convex Eye-glass H, through which
2484 those Rays must pass to the Eye. And let the Rays at their coming out of
2485 the Glass pass through a small round hole, or aperture made in a little
2486 plate of Lead, Brass, or Silver, wherewith the Glass is to be covered,
2487 which hole must be no bigger than is necessary for Light enough to pass
2488 through. For so it will render the Object distinct, the Plate in which
2489 'tis made intercepting all the erroneous part of the Light which comes
2490 from the verges of the Speculum AB. Such an Instrument well made, if it
2491 be six Foot long, (reckoning the length from the Speculum to the Prism,
2492 and thence to the Focus T) will bear an aperture of six Inches at the
2493 Speculum, and magnify between two and three hundred times. But the hole
2494 H here limits the aperture with more advantage, than if the aperture was
2495 placed at the Speculum. If the Instrument be made longer or shorter, the
2496 aperture must be in proportion as the Cube of the square-square Root of
2497 the length, and the magnifying as the aperture. But it's convenient that
2498 the Speculum be an Inch or two broader than the aperture at the least,
2499 and that the Glass of the Speculum be thick, that it bend not in the
2500 working. The Prism EFG must be no bigger than is necessary, and its back
2501 side FG must not be quick-silver'd over. For without quicksilver it will
2502 reflect all the Light incident on it from the Speculum.
2503
2504 [Illustration: FIG. 29.]
2505
2506 In this Instrument the Object will be inverted, but may be erected by
2507 making the square sides FF and EG of the Prism EFG not plane but
2508 spherically convex, that the Rays may cross as well before they come at
2509 it as afterwards between it and the Eye-glass. If it be desired that the
2510 Instrument bear a larger aperture, that may be also done by composing
2511 the Speculum of two Glasses with Water between them.
2512
2513 If the Theory of making Telescopes could at length be fully brought into
2514 Practice, yet there would be certain Bounds beyond which Telescopes
2515 could not perform. For the Air through which we look upon the Stars, is
2516 in a perpetual Tremor; as may be seen by the tremulous Motion of Shadows
2517 cast from high Towers, and by the twinkling of the fix'd Stars. But
2518 these Stars do not twinkle when viewed through Telescopes which have
2519 large apertures. For the Rays of Light which pass through divers parts
2520 of the aperture, tremble each of them apart, and by means of their
2521 various and sometimes contrary Tremors, fall at one and the same time
2522 upon different points in the bottom of the Eye, and their trembling
2523 Motions are too quick and confused to be perceived severally. And all
2524 these illuminated Points constitute one broad lucid Point, composed of
2525 those many trembling Points confusedly and insensibly mixed with one
2526 another by very short and swift Tremors, and thereby cause the Star to
2527 appear broader than it is, and without any trembling of the whole. Long
2528 Telescopes may cause Objects to appear brighter and larger than short
2529 ones can do, but they cannot be so formed as to take away that confusion
2530 of the Rays which arises from the Tremors of the Atmosphere. The only
2531 Remedy is a most serene and quiet Air, such as may perhaps be found on
2532 the tops of the highest Mountains above the grosser Clouds.
2533
2534 FOOTNOTES:
2535
2536 [C] _See our_ Author's Lectiones Opticæ § 10. _Sect. II. § 29. and Sect.
2537 III. Prop. 25._
2538
2539 [D] See our Author's _Lectiones Opticæ_, Part. I. Sect. 1. §5.
2540
2541 [E] _This is very fully treated of in our_ Author's Lect. Optic. _Part_
2542 I. _Sect._ II.
2543
2544 [F] _See our_ Author's Lect. Optic. Part I. Sect. II. § 29.
2545
2546 [G] _This is demonstrated in our_ Author's Lect. Optic. _Part_ I.
2547 _Sect._ IV. _Prop._ 37.
2548
2549 [H] _How to do this, is shewn in our_ Author's Lect. Optic. _Part_ I.
2550 _Sect._ IV. _Prop._ 31.
2551
2552
2553
2554
2555 THE FIRST BOOK OF OPTICKS
2556
2557
2558
2559
2560 _PART II._
2561
2562
2563 _PROP._ I. THEOR. I.
2564
2565 _The Phænomena of Colours in refracted or reflected Light are not caused
2566 by new Modifications of the Light variously impress'd, according to the
2567 various Terminations of the Light and Shadow_.
2568
2569 The PROOF by Experiments.
2570
2571 _Exper._ 1. For if the Sun shine into a very dark Chamber through an
2572 oblong hole F, [in _Fig._ 1.] whose breadth is the sixth or eighth part
2573 of an Inch, or something less; and his beam FH do afterwards pass first
2574 through a very large Prism ABC, distant about 20 Feet from the hole, and
2575 parallel to it, and then (with its white part) through an oblong hole H,
2576 whose breadth is about the fortieth or sixtieth part of an Inch, and
2577 which is made in a black opake Body GI, and placed at the distance of
2578 two or three Feet from the Prism, in a parallel Situation both to the
2579 Prism and to the former hole, and if this white Light thus transmitted
2580 through the hole H, fall afterwards upon a white Paper _pt_, placed
2581 after that hole H, at the distance of three or four Feet from it, and
2582 there paint the usual Colours of the Prism, suppose red at _t_, yellow
2583 at _s_, green at _r_, blue at _q_, and violet at _p_; you may with an
2584 Iron Wire, or any such like slender opake Body, whose breadth is about
2585 the tenth part of an Inch, by intercepting the Rays at _k_, _l_, _m_,
2586 _n_ or _o_, take away any one of the Colours at _t_, _s_, _r_, _q_ or
2587 _p_, whilst the other Colours remain upon the Paper as before; or with
2588 an Obstacle something bigger you may take away any two, or three, or
2589 four Colours together, the rest remaining: So that any one of the
2590 Colours as well as violet may become outmost in the Confine of the
2591 Shadow towards _p_, and any one of them as well as red may become
2592 outmost in the Confine of the Shadow towards _t_, and any one of them
2593 may also border upon the Shadow made within the Colours by the Obstacle
2594 R intercepting some intermediate part of the Light; and, lastly, any one
2595 of them by being left alone, may border upon the Shadow on either hand.
2596 All the Colours have themselves indifferently to any Confines of Shadow,
2597 and therefore the differences of these Colours from one another, do not
2598 arise from the different Confines of Shadow, whereby Light is variously
2599 modified, as has hitherto been the Opinion of Philosophers. In trying
2600 these things 'tis to be observed, that by how much the holes F and H are
2601 narrower, and the Intervals between them and the Prism greater, and the
2602 Chamber darker, by so much the better doth the Experiment succeed;
2603 provided the Light be not so far diminished, but that the Colours at
2604 _pt_ be sufficiently visible. To procure a Prism of solid Glass large
2605 enough for this Experiment will be difficult, and therefore a prismatick
2606 Vessel must be made of polish'd Glass Plates cemented together, and
2607 filled with salt Water or clear Oil.
2608
2609 [Illustration: FIG. 1.]
2610
2611 _Exper._ 2. The Sun's Light let into a dark Chamber through the round
2612 hole F, [in _Fig._ 2.] half an Inch wide, passed first through the Prism
2613 ABC placed at the hole, and then through a Lens PT something more than
2614 four Inches broad, and about eight Feet distant from the Prism, and
2615 thence converged to O the Focus of the Lens distant from it about three
2616 Feet, and there fell upon a white Paper DE. If that Paper was
2617 perpendicular to that Light incident upon it, as 'tis represented in the
2618 posture DE, all the Colours upon it at O appeared white. But if the
2619 Paper being turned about an Axis parallel to the Prism, became very much
2620 inclined to the Light, as 'tis represented in the Positions _de_ and
2621 _[Greek: de]_; the same Light in the one case appeared yellow and red,
2622 in the other blue. Here one and the same part of the Light in one and
2623 the same place, according to the various Inclinations of the Paper,
2624 appeared in one case white, in another yellow or red, in a third blue,
2625 whilst the Confine of Light and shadow, and the Refractions of the Prism
2626 in all these cases remained the same.
2627
2628 [Illustration: FIG. 2.]
2629
2630 [Illustration: FIG. 3.]
2631
2632 _Exper._ 3. Such another Experiment may be more easily tried as follows.
2633 Let a broad beam of the Sun's Light coming into a dark Chamber through a
2634 hole in the Window-shut be refracted by a large Prism ABC, [in _Fig._
2635 3.] whose refracting Angle C is more than 60 Degrees, and so soon as it
2636 comes out of the Prism, let it fall upon the white Paper DE glewed upon
2637 a stiff Plane; and this Light, when the Paper is perpendicular to it, as
2638 'tis represented in DE, will appear perfectly white upon the Paper; but
2639 when the Paper is very much inclin'd to it in such a manner as to keep
2640 always parallel to the Axis of the Prism, the whiteness of the whole
2641 Light upon the Paper will according to the inclination of the Paper this
2642 way or that way, change either into yellow and red, as in the posture
2643 _de_, or into blue and violet, as in the posture [Greek: de]. And if the
2644 Light before it fall upon the Paper be twice refracted the same way by
2645 two parallel Prisms, these Colours will become the more conspicuous.
2646 Here all the middle parts of the broad beam of white Light which fell
2647 upon the Paper, did without any Confine of Shadow to modify it, become
2648 colour'd all over with one uniform Colour, the Colour being always the
2649 same in the middle of the Paper as at the edges, and this Colour changed
2650 according to the various Obliquity of the reflecting Paper, without any
2651 change in the Refractions or Shadow, or in the Light which fell upon the
2652 Paper. And therefore these Colours are to be derived from some other
2653 Cause than the new Modifications of Light by Refractions and Shadows.
2654
2655 If it be asked, what then is their Cause? I answer, That the Paper in
2656 the posture _de_, being more oblique to the more refrangible Rays than
2657 to the less refrangible ones, is more strongly illuminated by the latter
2658 than by the former, and therefore the less refrangible Rays are
2659 predominant in the reflected Light. And where-ever they are predominant
2660 in any Light, they tinge it with red or yellow, as may in some measure
2661 appear by the first Proposition of the first Part of this Book, and will
2662 more fully appear hereafter. And the contrary happens in the posture of
2663 the Paper [Greek: de], the more refrangible Rays being then predominant
2664 which always tinge Light with blues and violets.
2665
2666 _Exper._ 4. The Colours of Bubbles with which Children play are various,
2667 and change their Situation variously, without any respect to any Confine
2668 or Shadow. If such a Bubble be cover'd with a concave Glass, to keep it
2669 from being agitated by any Wind or Motion of the Air, the Colours will
2670 slowly and regularly change their situation, even whilst the Eye and the
2671 Bubble, and all Bodies which emit any Light, or cast any Shadow, remain
2672 unmoved. And therefore their Colours arise from some regular Cause which
2673 depends not on any Confine of Shadow. What this Cause is will be shewed
2674 in the next Book.
2675
2676 To these Experiments may be added the tenth Experiment of the first Part
2677 of this first Book, where the Sun's Light in a dark Room being
2678 trajected through the parallel Superficies of two Prisms tied together
2679 in the form of a Parallelopipede, became totally of one uniform yellow
2680 or red Colour, at its emerging out of the Prisms. Here, in the
2681 production of these Colours, the Confine of Shadow can have nothing to
2682 do. For the Light changes from white to yellow, orange and red
2683 successively, without any alteration of the Confine of Shadow: And at
2684 both edges of the emerging Light where the contrary Confines of Shadow
2685 ought to produce different Effects, the Colour is one and the same,
2686 whether it be white, yellow, orange or red: And in the middle of the
2687 emerging Light, where there is no Confine of Shadow at all, the Colour
2688 is the very same as at the edges, the whole Light at its very first
2689 Emergence being of one uniform Colour, whether white, yellow, orange or
2690 red, and going on thence perpetually without any change of Colour, such
2691 as the Confine of Shadow is vulgarly supposed to work in refracted Light
2692 after its Emergence. Neither can these Colours arise from any new
2693 Modifications of the Light by Refractions, because they change
2694 successively from white to yellow, orange and red, while the Refractions
2695 remain the same, and also because the Refractions are made contrary ways
2696 by parallel Superficies which destroy one another's Effects. They arise
2697 not therefore from any Modifications of Light made by Refractions and
2698 Shadows, but have some other Cause. What that Cause is we shewed above
2699 in this tenth Experiment, and need not here repeat it.
2700
2701 There is yet another material Circumstance of this Experiment. For this
2702 emerging Light being by a third Prism HIK [in _Fig._ 22. _Part_ I.][I]
2703 refracted towards the Paper PT, and there painting the usual Colours of
2704 the Prism, red, yellow, green, blue, violet: If these Colours arose from
2705 the Refractions of that Prism modifying the Light, they would not be in
2706 the Light before its Incidence on that Prism. And yet in that Experiment
2707 we found, that when by turning the two first Prisms about their common
2708 Axis all the Colours were made to vanish but the red; the Light which
2709 makes that red being left alone, appeared of the very same red Colour
2710 before its Incidence on the third Prism. And in general we find by other
2711 Experiments, that when the Rays which differ in Refrangibility are
2712 separated from one another, and any one Sort of them is considered
2713 apart, the Colour of the Light which they compose cannot be changed by
2714 any Refraction or Reflexion whatever, as it ought to be were Colours
2715 nothing else than Modifications of Light caused by Refractions, and
2716 Reflexions, and Shadows. This Unchangeableness of Colour I am now to
2717 describe in the following Proposition.
2718
2719
2720 _PROP._ II. THEOR. II.
2721
2722 _All homogeneal Light has its proper Colour answering to its Degree of
2723 Refrangibility, and that Colour cannot be changed by Reflexions and
2724 Refractions._
2725
2726 In the Experiments of the fourth Proposition of the first Part of this
2727 first Book, when I had separated the heterogeneous Rays from one
2728 another, the Spectrum _pt_ formed by the separated Rays, did in the
2729 Progress from its End _p_, on which the most refrangible Rays fell, unto
2730 its other End _t_, on which the least refrangible Rays fell, appear
2731 tinged with this Series of Colours, violet, indigo, blue, green, yellow,
2732 orange, red, together with all their intermediate Degrees in a continual
2733 Succession perpetually varying. So that there appeared as many Degrees
2734 of Colours, as there were sorts of Rays differing in Refrangibility.
2735
2736 _Exper._ 5. Now, that these Colours could not be changed by Refraction,
2737 I knew by refracting with a Prism sometimes one very little Part of this
2738 Light, sometimes another very little Part, as is described in the
2739 twelfth Experiment of the first Part of this Book. For by this
2740 Refraction the Colour of the Light was never changed in the least. If
2741 any Part of the red Light was refracted, it remained totally of the same
2742 red Colour as before. No orange, no yellow, no green or blue, no other
2743 new Colour was produced by that Refraction. Neither did the Colour any
2744 ways change by repeated Refractions, but continued always the same red
2745 entirely as at first. The like Constancy and Immutability I found also
2746 in the blue, green, and other Colours. So also, if I looked through a
2747 Prism upon any Body illuminated with any part of this homogeneal Light,
2748 as in the fourteenth Experiment of the first Part of this Book is
2749 described; I could not perceive any new Colour generated this way. All
2750 Bodies illuminated with compound Light appear through Prisms confused,
2751 (as was said above) and tinged with various new Colours, but those
2752 illuminated with homogeneal Light appeared through Prisms neither less
2753 distinct, nor otherwise colour'd, than when viewed with the naked Eyes.
2754 Their Colours were not in the least changed by the Refraction of the
2755 interposed Prism. I speak here of a sensible Change of Colour: For the
2756 Light which I here call homogeneal, being not absolutely homogeneal,
2757 there ought to arise some little Change of Colour from its
2758 Heterogeneity. But, if that Heterogeneity was so little as it might be
2759 made by the said Experiments of the fourth Proposition, that Change was
2760 not sensible, and therefore in Experiments, where Sense is Judge, ought
2761 to be accounted none at all.
2762
2763 _Exper._ 6. And as these Colours were not changeable by Refractions, so
2764 neither were they by Reflexions. For all white, grey, red, yellow,
2765 green, blue, violet Bodies, as Paper, Ashes, red Lead, Orpiment, Indico
2766 Bise, Gold, Silver, Copper, Grass, blue Flowers, Violets, Bubbles of
2767 Water tinged with various Colours, Peacock's Feathers, the Tincture of
2768 _Lignum Nephriticum_, and such-like, in red homogeneal Light appeared
2769 totally red, in blue Light totally blue, in green Light totally green,
2770 and so of other Colours. In the homogeneal Light of any Colour they all
2771 appeared totally of that same Colour, with this only Difference, that
2772 some of them reflected that Light more strongly, others more faintly. I
2773 never yet found any Body, which by reflecting homogeneal Light could
2774 sensibly change its Colour.
2775
2776 From all which it is manifest, that if the Sun's Light consisted of but
2777 one sort of Rays, there would be but one Colour in the whole World, nor
2778 would it be possible to produce any new Colour by Reflexions and
2779 Refractions, and by consequence that the variety of Colours depends upon
2780 the Composition of Light.
2781
2782
2783 _DEFINITION._
2784
2785 The homogeneal Light and Rays which appear red, or rather make Objects
2786 appear so, I call Rubrifick or Red-making; those which make Objects
2787 appear yellow, green, blue, and violet, I call Yellow-making,
2788 Green-making, Blue-making, Violet-making, and so of the rest. And if at
2789 any time I speak of Light and Rays as coloured or endued with Colours, I
2790 would be understood to speak not philosophically and properly, but
2791 grossly, and accordingly to such Conceptions as vulgar People in seeing
2792 all these Experiments would be apt to frame. For the Rays to speak
2793 properly are not coloured. In them there is nothing else than a certain
2794 Power and Disposition to stir up a Sensation of this or that Colour.
2795 For as Sound in a Bell or musical String, or other sounding Body, is
2796 nothing but a trembling Motion, and in the Air nothing but that Motion
2797 propagated from the Object, and in the Sensorium 'tis a Sense of that
2798 Motion under the Form of Sound; so Colours in the Object are nothing but
2799 a Disposition to reflect this or that sort of Rays more copiously than
2800 the rest; in the Rays they are nothing but their Dispositions to
2801 propagate this or that Motion into the Sensorium, and in the Sensorium
2802 they are Sensations of those Motions under the Forms of Colours.
2803
2804
2805 _PROP._ III. PROB. I.
2806
2807 _To define the Refrangibility of the several sorts of homogeneal Light
2808 answering to the several Colours._
2809
2810 For determining this Problem I made the following Experiment.[J]
2811
2812 _Exper._ 7. When I had caused the Rectilinear Sides AF, GM, [in _Fig._
2813 4.] of the Spectrum of Colours made by the Prism to be distinctly
2814 defined, as in the fifth Experiment of the first Part of this Book is
2815 described, there were found in it all the homogeneal Colours in the same
2816 Order and Situation one among another as in the Spectrum of simple
2817 Light, described in the fourth Proposition of that Part. For the Circles
2818 of which the Spectrum of compound Light PT is composed, and which in
2819 the middle Parts of the Spectrum interfere, and are intermix'd with one
2820 another, are not intermix'd in their outmost Parts where they touch
2821 those Rectilinear Sides AF and GM. And therefore, in those Rectilinear
2822 Sides when distinctly defined, there is no new Colour generated by
2823 Refraction. I observed also, that if any where between the two outmost
2824 Circles TMF and PGA a Right Line, as [Greek: gd], was cross to the
2825 Spectrum, so as both Ends to fall perpendicularly upon its Rectilinear
2826 Sides, there appeared one and the same Colour, and degree of Colour from
2827 one End of this Line to the other. I delineated therefore in a Paper the
2828 Perimeter of the Spectrum FAP GMT, and in trying the third Experiment of
2829 the first Part of this Book, I held the Paper so that the Spectrum might
2830 fall upon this delineated Figure, and agree with it exactly, whilst an
2831 Assistant, whose Eyes for distinguishing Colours were more critical than
2832 mine, did by Right Lines [Greek: ab, gd, ez,] &c. drawn cross the
2833 Spectrum, note the Confines of the Colours, that is of the red M[Greek:
2834 ab]F, of the orange [Greek: agdb], of the yellow [Greek: gezd], of the
2835 green [Greek: eêthz], of the blue [Greek: êikth], of the indico [Greek:
2836 ilmk], and of the violet [Greek: l]GA[Greek: m]. And this Operation
2837 being divers times repeated both in the same, and in several Papers, I
2838 found that the Observations agreed well enough with one another, and
2839 that the Rectilinear Sides MG and FA were by the said cross Lines
2840 divided after the manner of a Musical Chord. Let GM be produced to X,
2841 that MX may be equal to GM, and conceive GX, [Greek: l]X, [Greek: i]X,
2842 [Greek: ê]X, [Greek: e]X, [Greek: g]X, [Greek: a]X, MX, to be in
2843 proportion to one another, as the Numbers, 1, 8/9, 5/6, 3/4, 2/3, 3/5,
2844 9/16, 1/2, and so to represent the Chords of the Key, and of a Tone, a
2845 third Minor, a fourth, a fifth, a sixth Major, a seventh and an eighth
2846 above that Key: And the Intervals M[Greek: a], [Greek: ag], [Greek: ge],
2847 [Greek: eê], [Greek: êi], [Greek: il], and [Greek: l]G, will be the
2848 Spaces which the several Colours (red, orange, yellow, green, blue,
2849 indigo, violet) take up.
2850
2851 [Illustration: FIG. 4.]
2852
2853 [Illustration: FIG. 5.]
2854
2855 Now these Intervals or Spaces subtending the Differences of the
2856 Refractions of the Rays going to the Limits of those Colours, that is,
2857 to the Points M, [Greek: a], [Greek: g], [Greek: e], [Greek: ê], [Greek:
2858 i], [Greek: l], G, may without any sensible Error be accounted
2859 proportional to the Differences of the Sines of Refraction of those Rays
2860 having one common Sine of Incidence, and therefore since the common Sine
2861 of Incidence of the most and least refrangible Rays out of Glass into
2862 Air was (by a Method described above) found in proportion to their Sines
2863 of Refraction, as 50 to 77 and 78, divide the Difference between the
2864 Sines of Refraction 77 and 78, as the Line GM is divided by those
2865 Intervals, and you will have 77, 77-1/8, 77-1/5, 77-1/3, 77-1/2, 77-2/3,
2866 77-7/9, 78, the Sines of Refraction of those Rays out of Glass into Air,
2867 their common Sine of Incidence being 50. So then the Sines of the
2868 Incidences of all the red-making Rays out of Glass into Air, were to the
2869 Sines of their Refractions, not greater than 50 to 77, nor less than 50
2870 to 77-1/8, but they varied from one another according to all
2871 intermediate Proportions. And the Sines of the Incidences of the
2872 green-making Rays were to the Sines of their Refractions in all
2873 Proportions from that of 50 to 77-1/3, unto that of 50 to 77-1/2. And
2874 by the like Limits above-mentioned were the Refractions of the Rays
2875 belonging to the rest of the Colours defined, the Sines of the
2876 red-making Rays extending from 77 to 77-1/8, those of the orange-making
2877 from 77-1/8 to 77-1/5, those of the yellow-making from 77-1/5 to 77-1/3,
2878 those of the green-making from 77-1/3 to 77-1/2, those of the
2879 blue-making from 77-1/2 to 77-2/3, those of the indigo-making from
2880 77-2/3 to 77-7/9, and those of the violet from 77-7/9, to 78.
2881
2882 These are the Laws of the Refractions made out of Glass into Air, and
2883 thence by the third Axiom of the first Part of this Book, the Laws of
2884 the Refractions made out of Air into Glass are easily derived.
2885
2886 _Exper._ 8. I found moreover, that when Light goes out of Air through
2887 several contiguous refracting Mediums as through Water and Glass, and
2888 thence goes out again into Air, whether the refracting Superficies be
2889 parallel or inclin'd to one another, that Light as often as by contrary
2890 Refractions 'tis so corrected, that it emergeth in Lines parallel to
2891 those in which it was incident, continues ever after to be white. But if
2892 the emergent Rays be inclined to the incident, the Whiteness of the
2893 emerging Light will by degrees in passing on from the Place of
2894 Emergence, become tinged in its Edges with Colours. This I try'd by
2895 refracting Light with Prisms of Glass placed within a Prismatick Vessel
2896 of Water. Now those Colours argue a diverging and separation of the
2897 heterogeneous Rays from one another by means of their unequal
2898 Refractions, as in what follows will more fully appear. And, on the
2899 contrary, the permanent whiteness argues, that in like Incidences of the
2900 Rays there is no such separation of the emerging Rays, and by
2901 consequence no inequality of their whole Refractions. Whence I seem to
2902 gather the two following Theorems.
2903
2904 1. The Excesses of the Sines of Refraction of several sorts of Rays
2905 above their common Sine of Incidence when the Refractions are made out
2906 of divers denser Mediums immediately into one and the same rarer Medium,
2907 suppose of Air, are to one another in a given Proportion.
2908
2909 2. The Proportion of the Sine of Incidence to the Sine of Refraction of
2910 one and the same sort of Rays out of one Medium into another, is
2911 composed of the Proportion of the Sine of Incidence to the Sine of
2912 Refraction out of the first Medium into any third Medium, and of the
2913 Proportion of the Sine of Incidence to the Sine of Refraction out of
2914 that third Medium into the second Medium.
2915
2916 By the first Theorem the Refractions of the Rays of every sort made out
2917 of any Medium into Air are known by having the Refraction of the Rays of
2918 any one sort. As for instance, if the Refractions of the Rays of every
2919 sort out of Rain-water into Air be desired, let the common Sine of
2920 Incidence out of Glass into Air be subducted from the Sines of
2921 Refraction, and the Excesses will be 27, 27-1/8, 27-1/5, 27-1/3, 27-1/2,
2922 27-2/3, 27-7/9, 28. Suppose now that the Sine of Incidence of the least
2923 refrangible Rays be to their Sine of Refraction out of Rain-water into
2924 Air as 3 to 4, and say as 1 the difference of those Sines is to 3 the
2925 Sine of Incidence, so is 27 the least of the Excesses above-mentioned to
2926 a fourth Number 81; and 81 will be the common Sine of Incidence out of
2927 Rain-water into Air, to which Sine if you add all the above-mentioned
2928 Excesses, you will have the desired Sines of the Refractions 108,
2929 108-1/8, 108-1/5, 108-1/3, 108-1/2, 108-2/3, 108-7/9, 109.
2930
2931 By the latter Theorem the Refraction out of one Medium into another is
2932 gathered as often as you have the Refractions out of them both into any
2933 third Medium. As if the Sine of Incidence of any Ray out of Glass into
2934 Air be to its Sine of Refraction, as 20 to 31, and the Sine of Incidence
2935 of the same Ray out of Air into Water, be to its Sine of Refraction as 4
2936 to 3; the Sine of Incidence of that Ray out of Glass into Water will be
2937 to its Sine of Refraction as 20 to 31 and 4 to 3 jointly, that is, as
2938 the Factum of 20 and 4 to the Factum of 31 and 3, or as 80 to 93.
2939
2940 And these Theorems being admitted into Opticks, there would be scope
2941 enough of handling that Science voluminously after a new manner,[K] not
2942 only by teaching those things which tend to the perfection of Vision,
2943 but also by determining mathematically all kinds of Phænomena of Colours
2944 which could be produced by Refractions. For to do this, there is nothing
2945 else requisite than to find out the Separations of heterogeneous Rays,
2946 and their various Mixtures and Proportions in every Mixture. By this
2947 way of arguing I invented almost all the Phænomena described in these
2948 Books, beside some others less necessary to the Argument; and by the
2949 successes I met with in the Trials, I dare promise, that to him who
2950 shall argue truly, and then try all things with good Glasses and
2951 sufficient Circumspection, the expected Event will not be wanting. But
2952 he is first to know what Colours will arise from any others mix'd in any
2953 assigned Proportion.
2954
2955
2956 _PROP._ IV. THEOR. III.
2957
2958 _Colours may be produced by Composition which shall be like to the
2959 Colours of homogeneal Light as to the Appearance of Colour, but not as
2960 to the Immutability of Colour and Constitution of Light. And those
2961 Colours by how much they are more compounded by so much are they less
2962 full and intense, and by too much Composition they maybe diluted and
2963 weaken'd till they cease, and the Mixture becomes white or grey. There
2964 may be also Colours produced by Composition, which are not fully like
2965 any of the Colours of homogeneal Light._
2966
2967 For a Mixture of homogeneal red and yellow compounds an Orange, like in
2968 appearance of Colour to that orange which in the series of unmixed
2969 prismatick Colours lies between them; but the Light of one orange is
2970 homogeneal as to Refrangibility, and that of the other is heterogeneal,
2971 and the Colour of the one, if viewed through a Prism, remains unchanged,
2972 that of the other is changed and resolved into its component Colours red
2973 and yellow. And after the same manner other neighbouring homogeneal
2974 Colours may compound new Colours, like the intermediate homogeneal ones,
2975 as yellow and green, the Colour between them both, and afterwards, if
2976 blue be added, there will be made a green the middle Colour of the three
2977 which enter the Composition. For the yellow and blue on either hand, if
2978 they are equal in quantity they draw the intermediate green equally
2979 towards themselves in Composition, and so keep it as it were in
2980 Æquilibrion, that it verge not more to the yellow on the one hand, and
2981 to the blue on the other, but by their mix'd Actions remain still a
2982 middle Colour. To this mix'd green there may be farther added some red
2983 and violet, and yet the green will not presently cease, but only grow
2984 less full and vivid, and by increasing the red and violet, it will grow
2985 more and more dilute, until by the prevalence of the added Colours it be
2986 overcome and turned into whiteness, or some other Colour. So if to the
2987 Colour of any homogeneal Light, the Sun's white Light composed of all
2988 sorts of Rays be added, that Colour will not vanish or change its
2989 Species, but be diluted, and by adding more and more white it will be
2990 diluted more and more perpetually. Lastly, If red and violet be mingled,
2991 there will be generated according to their various Proportions various
2992 Purples, such as are not like in appearance to the Colour of any
2993 homogeneal Light, and of these Purples mix'd with yellow and blue may be
2994 made other new Colours.
2995
2996
2997 _PROP._ V. THEOR. IV.
2998
2999 _Whiteness and all grey Colours between white and black, may be
3000 compounded of Colours, and the whiteness of the Sun's Light is
3001 compounded of all the primary Colours mix'd in a due Proportion._
3002
3003 The PROOF by Experiments.
3004
3005 _Exper._ 9. The Sun shining into a dark Chamber through a little round
3006 hole in the Window-shut, and his Light being there refracted by a Prism
3007 to cast his coloured Image PT [in _Fig._ 5.] upon the opposite Wall: I
3008 held a white Paper V to that image in such manner that it might be
3009 illuminated by the colour'd Light reflected from thence, and yet not
3010 intercept any part of that Light in its passage from the Prism to the
3011 Spectrum. And I found that when the Paper was held nearer to any Colour
3012 than to the rest, it appeared of that Colour to which it approached
3013 nearest; but when it was equally or almost equally distant from all the
3014 Colours, so that it might be equally illuminated by them all it appeared
3015 white. And in this last situation of the Paper, if some Colours were
3016 intercepted, the Paper lost its white Colour, and appeared of the Colour
3017 of the rest of the Light which was not intercepted. So then the Paper
3018 was illuminated with Lights of various Colours, namely, red, yellow,
3019 green, blue and violet, and every part of the Light retained its proper
3020 Colour, until it was incident on the Paper, and became reflected thence
3021 to the Eye; so that if it had been either alone (the rest of the Light
3022 being intercepted) or if it had abounded most, and been predominant in
3023 the Light reflected from the Paper, it would have tinged the Paper with
3024 its own Colour; and yet being mixed with the rest of the Colours in a
3025 due proportion, it made the Paper look white, and therefore by a
3026 Composition with the rest produced that Colour. The several parts of the
3027 coloured Light reflected from the Spectrum, whilst they are propagated
3028 from thence through the Air, do perpetually retain their proper Colours,
3029 because wherever they fall upon the Eyes of any Spectator, they make the
3030 several parts of the Spectrum to appear under their proper Colours. They
3031 retain therefore their proper Colours when they fall upon the Paper V,
3032 and so by the confusion and perfect mixture of those Colours compound
3033 the whiteness of the Light reflected from thence.
3034
3035 _Exper._ 10. Let that Spectrum or solar Image PT [in _Fig._ 6.] fall now
3036 upon the Lens MN above four Inches broad, and about six Feet distant
3037 from the Prism ABC and so figured that it may cause the coloured Light
3038 which divergeth from the Prism to converge and meet again at its Focus
3039 G, about six or eight Feet distant from the Lens, and there to fall
3040 perpendicularly upon a white Paper DE. And if you move this Paper to and
3041 fro, you will perceive that near the Lens, as at _de_, the whole solar
3042 Image (suppose at _pt_) will appear upon it intensely coloured after the
3043 manner above-explained, and that by receding from the Lens those Colours
3044 will perpetually come towards one another, and by mixing more and more
3045 dilute one another continually, until at length the Paper come to the
3046 Focus G, where by a perfect mixture they will wholly vanish and be
3047 converted into whiteness, the whole Light appearing now upon the Paper
3048 like a little white Circle. And afterwards by receding farther from the
3049 Lens, the Rays which before converged will now cross one another in the
3050 Focus G, and diverge from thence, and thereby make the Colours to appear
3051 again, but yet in a contrary order; suppose at [Greek: de], where the
3052 red _t_ is now above which before was below, and the violet _p_ is below
3053 which before was above.
3054
3055 Let us now stop the Paper at the Focus G, where the Light appears
3056 totally white and circular, and let us consider its whiteness. I say,
3057 that this is composed of the converging Colours. For if any of those
3058 Colours be intercepted at the Lens, the whiteness will cease and
3059 degenerate into that Colour which ariseth from the composition of the
3060 other Colours which are not intercepted. And then if the intercepted
3061 Colours be let pass and fall upon that compound Colour, they mix with
3062 it, and by their mixture restore the whiteness. So if the violet, blue
3063 and green be intercepted, the remaining yellow, orange and red will
3064 compound upon the Paper an orange, and then if the intercepted Colours
3065 be let pass, they will fall upon this compounded orange, and together
3066 with it decompound a white. So also if the red and violet be
3067 intercepted, the remaining yellow, green and blue, will compound a green
3068 upon the Paper, and then the red and violet being let pass will fall
3069 upon this green, and together with it decompound a white. And that in
3070 this Composition of white the several Rays do not suffer any Change in
3071 their colorific Qualities by acting upon one another, but are only
3072 mixed, and by a mixture of their Colours produce white, may farther
3073 appear by these Arguments.
3074
3075 [Illustration: FIG. 6.]
3076
3077 If the Paper be placed beyond the Focus G, suppose at [Greek: de], and
3078 then the red Colour at the Lens be alternately intercepted, and let pass
3079 again, the violet Colour on the Paper will not suffer any Change
3080 thereby, as it ought to do if the several sorts of Rays acted upon one
3081 another in the Focus G, where they cross. Neither will the red upon the
3082 Paper be changed by any alternate stopping, and letting pass the violet
3083 which crosseth it.
3084
3085 And if the Paper be placed at the Focus G, and the white round Image at
3086 G be viewed through the Prism HIK, and by the Refraction of that Prism
3087 be translated to the place _rv_, and there appear tinged with various
3088 Colours, namely, the violet at _v_ and red at _r_, and others between,
3089 and then the red Colours at the Lens be often stopp'd and let pass by
3090 turns, the red at _r_ will accordingly disappear, and return as often,
3091 but the violet at _v_ will not thereby suffer any Change. And so by
3092 stopping and letting pass alternately the blue at the Lens, the blue at
3093 _v_ will accordingly disappear and return, without any Change made in
3094 the red at _r_. The red therefore depends on one sort of Rays, and the
3095 blue on another sort, which in the Focus G where they are commix'd, do
3096 not act on one another. And there is the same Reason of the other
3097 Colours.
3098
3099 I considered farther, that when the most refrangible Rays P_p_, and the
3100 least refrangible ones T_t_, are by converging inclined to one another,
3101 the Paper, if held very oblique to those Rays in the Focus G, might
3102 reflect one sort of them more copiously than the other sort, and by that
3103 Means the reflected Light would be tinged in that Focus with the Colour
3104 of the predominant Rays, provided those Rays severally retained their
3105 Colours, or colorific Qualities in the Composition of White made by them
3106 in that Focus. But if they did not retain them in that White, but became
3107 all of them severally endued there with a Disposition to strike the
3108 Sense with the Perception of White, then they could never lose their
3109 Whiteness by such Reflexions. I inclined therefore the Paper to the Rays
3110 very obliquely, as in the second Experiment of this second Part of the
3111 first Book, that the most refrangible Rays, might be more copiously
3112 reflected than the rest, and the Whiteness at Length changed
3113 successively into blue, indigo, and violet. Then I inclined it the
3114 contrary Way, that the least refrangible Rays might be more copious in
3115 the reflected Light than the rest, and the Whiteness turned successively
3116 to yellow, orange, and red.
3117
3118 Lastly, I made an Instrument XY in fashion of a Comb, whose Teeth being
3119 in number sixteen, were about an Inch and a half broad, and the
3120 Intervals of the Teeth about two Inches wide. Then by interposing
3121 successively the Teeth of this Instrument near the Lens, I intercepted
3122 Part of the Colours by the interposed Tooth, whilst the rest of them
3123 went on through the Interval of the Teeth to the Paper DE, and there
3124 painted a round Solar Image. But the Paper I had first placed so, that
3125 the Image might appear white as often as the Comb was taken away; and
3126 then the Comb being as was said interposed, that Whiteness by reason of
3127 the intercepted Part of the Colours at the Lens did always change into
3128 the Colour compounded of those Colours which were not intercepted, and
3129 that Colour was by the Motion of the Comb perpetually varied so, that in
3130 the passing of every Tooth over the Lens all these Colours, red, yellow,
3131 green, blue, and purple, did always succeed one another. I caused
3132 therefore all the Teeth to pass successively over the Lens, and when the
3133 Motion was slow, there appeared a perpetual Succession of the Colours
3134 upon the Paper: But if I so much accelerated the Motion, that the
3135 Colours by reason of their quick Succession could not be distinguished
3136 from one another, the Appearance of the single Colours ceased. There was
3137 no red, no yellow, no green, no blue, nor purple to be seen any longer,
3138 but from a Confusion of them all there arose one uniform white Colour.
3139 Of the Light which now by the Mixture of all the Colours appeared white,
3140 there was no Part really white. One Part was red, another yellow, a
3141 third green, a fourth blue, a fifth purple, and every Part retains its
3142 proper Colour till it strike the Sensorium. If the Impressions follow
3143 one another slowly, so that they may be severally perceived, there is
3144 made a distinct Sensation of all the Colours one after another in a
3145 continual Succession. But if the Impressions follow one another so
3146 quickly, that they cannot be severally perceived, there ariseth out of
3147 them all one common Sensation, which is neither of this Colour alone nor
3148 of that alone, but hath it self indifferently to 'em all, and this is a
3149 Sensation of Whiteness. By the Quickness of the Successions, the
3150 Impressions of the several Colours are confounded in the Sensorium, and
3151 out of that Confusion ariseth a mix'd Sensation. If a burning Coal be
3152 nimbly moved round in a Circle with Gyrations continually repeated, the
3153 whole Circle will appear like Fire; the reason of which is, that the
3154 Sensation of the Coal in the several Places of that Circle remains
3155 impress'd on the Sensorium, until the Coal return again to the same
3156 Place. And so in a quick Consecution of the Colours the Impression of
3157 every Colour remains in the Sensorium, until a Revolution of all the
3158 Colours be compleated, and that first Colour return again. The
3159 Impressions therefore of all the successive Colours are at once in the
3160 Sensorium, and jointly stir up a Sensation of them all; and so it is
3161 manifest by this Experiment, that the commix'd Impressions of all the
3162 Colours do stir up and beget a Sensation of white, that is, that
3163 Whiteness is compounded of all the Colours.
3164
3165 And if the Comb be now taken away, that all the Colours may at once pass
3166 from the Lens to the Paper, and be there intermixed, and together
3167 reflected thence to the Spectator's Eyes; their Impressions on the
3168 Sensorium being now more subtilly and perfectly commixed there, ought
3169 much more to stir up a Sensation of Whiteness.
3170
3171 You may instead of the Lens use two Prisms HIK and LMN, which by
3172 refracting the coloured Light the contrary Way to that of the first
3173 Refraction, may make the diverging Rays converge and meet again in G, as
3174 you see represented in the seventh Figure. For where they meet and mix,
3175 they will compose a white Light, as when a Lens is used.
3176
3177 _Exper._ 11. Let the Sun's coloured Image PT [in _Fig._ 8.] fall upon
3178 the Wall of a dark Chamber, as in the third Experiment of the first
3179 Book, and let the same be viewed through a Prism _abc_, held parallel to
3180 the Prism ABC, by whose Refraction that Image was made, and let it now
3181 appear lower than before, suppose in the Place S over-against the red
3182 Colour T. And if you go near to the Image PT, the Spectrum S will appear
3183 oblong and coloured like the Image PT; but if you recede from it, the
3184 Colours of the spectrum S will be contracted more and more, and at
3185 length vanish, that Spectrum S becoming perfectly round and white; and
3186 if you recede yet farther, the Colours will emerge again, but in a
3187 contrary Order. Now that Spectrum S appears white in that Case, when the
3188 Rays of several sorts which converge from the several Parts of the Image
3189 PT, to the Prism _abc_, are so refracted unequally by it, that in their
3190 Passage from the Prism to the Eye they may diverge from one and the same
3191 Point of the Spectrum S, and so fall afterwards upon one and the same
3192 Point in the bottom of the Eye, and there be mingled.
3193
3194 [Illustration: FIG. 7.]
3195
3196 [Illustration: FIG. 8.]
3197
3198 And farther, if the Comb be here made use of, by whose Teeth the Colours
3199 at the Image PT may be successively intercepted; the Spectrum S, when
3200 the Comb is moved slowly, will be perpetually tinged with successive
3201 Colours: But when by accelerating the Motion of the Comb, the Succession
3202 of the Colours is so quick that they cannot be severally seen, that
3203 Spectrum S, by a confused and mix'd Sensation of them all, will appear
3204 white.
3205
3206 _Exper._ 12. The Sun shining through a large Prism ABC [in _Fig._ 9.]
3207 upon a Comb XY, placed immediately behind the Prism, his Light which
3208 passed through the Interstices of the Teeth fell upon a white Paper DE.
3209 The Breadths of the Teeth were equal to their Interstices, and seven
3210 Teeth together with their Interstices took up an Inch in Breadth. Now,
3211 when the Paper was about two or three Inches distant from the Comb, the
3212 Light which passed through its several Interstices painted so many
3213 Ranges of Colours, _kl_, _mn_, _op_, _qr_, &c. which were parallel to
3214 one another, and contiguous, and without any Mixture of white. And these
3215 Ranges of Colours, if the Comb was moved continually up and down with a
3216 reciprocal Motion, ascended and descended in the Paper, and when the
3217 Motion of the Comb was so quick, that the Colours could not be
3218 distinguished from one another, the whole Paper by their Confusion and
3219 Mixture in the Sensorium appeared white.
3220
3221 [Illustration: FIG. 9.]
3222
3223 Let the Comb now rest, and let the Paper be removed farther from the
3224 Prism, and the several Ranges of Colours will be dilated and expanded
3225 into one another more and more, and by mixing their Colours will dilute
3226 one another, and at length, when the distance of the Paper from the Comb
3227 is about a Foot, or a little more (suppose in the Place 2D 2E) they will
3228 so far dilute one another, as to become white.
3229
3230 With any Obstacle, let all the Light be now stopp'd which passes through
3231 any one Interval of the Teeth, so that the Range of Colours which comes
3232 from thence may be taken away, and you will see the Light of the rest of
3233 the Ranges to be expanded into the Place of the Range taken away, and
3234 there to be coloured. Let the intercepted Range pass on as before, and
3235 its Colours falling upon the Colours of the other Ranges, and mixing
3236 with them, will restore the Whiteness.
3237
3238 Let the Paper 2D 2E be now very much inclined to the Rays, so that the
3239 most refrangible Rays may be more copiously reflected than the rest, and
3240 the white Colour of the Paper through the Excess of those Rays will be
3241 changed into blue and violet. Let the Paper be as much inclined the
3242 contrary way, that the least refrangible Rays may be now more copiously
3243 reflected than the rest, and by their Excess the Whiteness will be
3244 changed into yellow and red. The several Rays therefore in that white
3245 Light do retain their colorific Qualities, by which those of any sort,
3246 whenever they become more copious than the rest, do by their Excess and
3247 Predominance cause their proper Colour to appear.
3248
3249 And by the same way of arguing, applied to the third Experiment of this
3250 second Part of the first Book, it may be concluded, that the white
3251 Colour of all refracted Light at its very first Emergence, where it
3252 appears as white as before its Incidence, is compounded of various
3253 Colours.
3254
3255 [Illustration: FIG. 10.]
3256
3257 _Exper._ 13. In the foregoing Experiment the several Intervals of the
3258 Teeth of the Comb do the Office of so many Prisms, every Interval
3259 producing the Phænomenon of one Prism. Whence instead of those Intervals
3260 using several Prisms, I try'd to compound Whiteness by mixing their
3261 Colours, and did it by using only three Prisms, as also by using only
3262 two as follows. Let two Prisms ABC and _abc_, [in _Fig._ 10.] whose
3263 refracting Angles B and _b_ are equal, be so placed parallel to one
3264 another, that the refracting Angle B of the one may touch the Angle _c_
3265 at the Base of the other, and their Planes CB and _cb_, at which the
3266 Rays emerge, may lie in Directum. Then let the Light trajected through
3267 them fall upon the Paper MN, distant about 8 or 12 Inches from the
3268 Prisms. And the Colours generated by the interior Limits B and _c_ of
3269 the two Prisms, will be mingled at PT, and there compound white. For if
3270 either Prism be taken away, the Colours made by the other will appear in
3271 that Place PT, and when the Prism is restored to its Place again, so
3272 that its Colours may there fall upon the Colours of the other, the
3273 Mixture of them both will restore the Whiteness.
3274
3275 This Experiment succeeds also, as I have tried, when the Angle _b_ of
3276 the lower Prism, is a little greater than the Angle B of the upper, and
3277 between the interior Angles B and _c_, there intercedes some Space B_c_,
3278 as is represented in the Figure, and the refracting Planes BC and _bc_,
3279 are neither in Directum, nor parallel to one another. For there is
3280 nothing more requisite to the Success of this Experiment, than that the
3281 Rays of all sorts may be uniformly mixed upon the Paper in the Place PT.
3282 If the most refrangible Rays coming from the superior Prism take up all
3283 the Space from M to P, the Rays of the same sort which come from the
3284 inferior Prism ought to begin at P, and take up all the rest of the
3285 Space from thence towards N. If the least refrangible Rays coming from
3286 the superior Prism take up the Space MT, the Rays of the same kind which
3287 come from the other Prism ought to begin at T, and take up the
3288 remaining Space TN. If one sort of the Rays which have intermediate
3289 Degrees of Refrangibility, and come from the superior Prism be extended
3290 through the Space MQ, and another sort of those Rays through the Space
3291 MR, and a third sort of them through the Space MS, the same sorts of
3292 Rays coming from the lower Prism, ought to illuminate the remaining
3293 Spaces QN, RN, SN, respectively. And the same is to be understood of all
3294 the other sorts of Rays. For thus the Rays of every sort will be
3295 scattered uniformly and evenly through the whole Space MN, and so being
3296 every where mix'd in the same Proportion, they must every where produce
3297 the same Colour. And therefore, since by this Mixture they produce white
3298 in the Exterior Spaces MP and TN, they must also produce white in the
3299 Interior Space PT. This is the reason of the Composition by which
3300 Whiteness was produced in this Experiment, and by what other way soever
3301 I made the like Composition, the Result was Whiteness.
3302
3303 Lastly, If with the Teeth of a Comb of a due Size, the coloured Lights
3304 of the two Prisms which fall upon the Space PT be alternately
3305 intercepted, that Space PT, when the Motion of the Comb is slow, will
3306 always appear coloured, but by accelerating the Motion of the Comb so
3307 much that the successive Colours cannot be distinguished from one
3308 another, it will appear white.
3309
3310 _Exper._ 14. Hitherto I have produced Whiteness by mixing the Colours of
3311 Prisms. If now the Colours of natural Bodies are to be mingled, let
3312 Water a little thicken'd with Soap be agitated to raise a Froth, and
3313 after that Froth has stood a little, there will appear to one that shall
3314 view it intently various Colours every where in the Surfaces of the
3315 several Bubbles; but to one that shall go so far off, that he cannot
3316 distinguish the Colours from one another, the whole Froth will grow
3317 white with a perfect Whiteness.
3318
3319 _Exper._ 15. Lastly, In attempting to compound a white, by mixing the
3320 coloured Powders which Painters use, I consider'd that all colour'd
3321 Powders do suppress and stop in them a very considerable Part of the
3322 Light by which they are illuminated. For they become colour'd by
3323 reflecting the Light of their own Colours more copiously, and that of
3324 all other Colours more sparingly, and yet they do not reflect the Light
3325 of their own Colours so copiously as white Bodies do. If red Lead, for
3326 instance, and a white Paper, be placed in the red Light of the colour'd
3327 Spectrum made in a dark Chamber by the Refraction of a Prism, as is
3328 described in the third Experiment of the first Part of this Book; the
3329 Paper will appear more lucid than the red Lead, and therefore reflects
3330 the red-making Rays more copiously than red Lead doth. And if they be
3331 held in the Light of any other Colour, the Light reflected by the Paper
3332 will exceed the Light reflected by the red Lead in a much greater
3333 Proportion. And the like happens in Powders of other Colours. And
3334 therefore by mixing such Powders, we are not to expect a strong and
3335 full White, such as is that of Paper, but some dusky obscure one, such
3336 as might arise from a Mixture of Light and Darkness, or from white and
3337 black, that is, a grey, or dun, or russet brown, such as are the Colours
3338 of a Man's Nail, of a Mouse, of Ashes, of ordinary Stones, of Mortar, of
3339 Dust and Dirt in High-ways, and the like. And such a dark white I have
3340 often produced by mixing colour'd Powders. For thus one Part of red
3341 Lead, and five Parts of _Viride Æris_, composed a dun Colour like that
3342 of a Mouse. For these two Colours were severally so compounded of
3343 others, that in both together were a Mixture of all Colours; and there
3344 was less red Lead used than _Viride Æris_, because of the Fulness of its
3345 Colour. Again, one Part of red Lead, and four Parts of blue Bise,
3346 composed a dun Colour verging a little to purple, and by adding to this
3347 a certain Mixture of Orpiment and _Viride Æris_ in a due Proportion, the
3348 Mixture lost its purple Tincture, and became perfectly dun. But the
3349 Experiment succeeded best without Minium thus. To Orpiment I added by
3350 little and little a certain full bright purple, which Painters use,
3351 until the Orpiment ceased to be yellow, and became of a pale red. Then I
3352 diluted that red by adding a little _Viride Æris_, and a little more
3353 blue Bise than _Viride Æris_, until it became of such a grey or pale
3354 white, as verged to no one of the Colours more than to another. For thus
3355 it became of a Colour equal in Whiteness to that of Ashes, or of Wood
3356 newly cut, or of a Man's Skin. The Orpiment reflected more Light than
3357 did any other of the Powders, and therefore conduced more to the
3358 Whiteness of the compounded Colour than they. To assign the Proportions
3359 accurately may be difficult, by reason of the different Goodness of
3360 Powders of the same kind. Accordingly, as the Colour of any Powder is
3361 more or less full and luminous, it ought to be used in a less or greater
3362 Proportion.
3363
3364 Now, considering that these grey and dun Colours may be also produced by
3365 mixing Whites and Blacks, and by consequence differ from perfect Whites,
3366 not in Species of Colours, but only in degree of Luminousness, it is
3367 manifest that there is nothing more requisite to make them perfectly
3368 white than to increase their Light sufficiently; and, on the contrary,
3369 if by increasing their Light they can be brought to perfect Whiteness,
3370 it will thence also follow, that they are of the same Species of Colour
3371 with the best Whites, and differ from them only in the Quantity of
3372 Light. And this I tried as follows. I took the third of the
3373 above-mention'd grey Mixtures, (that which was compounded of Orpiment,
3374 Purple, Bise, and _Viride Æris_) and rubbed it thickly upon the Floor of
3375 my Chamber, where the Sun shone upon it through the opened Casement; and
3376 by it, in the shadow, I laid a Piece of white Paper of the same Bigness.
3377 Then going from them to the distance of 12 or 18 Feet, so that I could
3378 not discern the Unevenness of the Surface of the Powder, nor the little
3379 Shadows let fall from the gritty Particles thereof; the Powder appeared
3380 intensely white, so as to transcend even the Paper it self in Whiteness,
3381 especially if the Paper were a little shaded from the Light of the
3382 Clouds, and then the Paper compared with the Powder appeared of such a
3383 grey Colour as the Powder had done before. But by laying the Paper where
3384 the Sun shines through the Glass of the Window, or by shutting the
3385 Window that the Sun might shine through the Glass upon the Powder, and
3386 by such other fit Means of increasing or decreasing the Lights wherewith
3387 the Powder and Paper were illuminated, the Light wherewith the Powder is
3388 illuminated may be made stronger in such a due Proportion than the Light
3389 wherewith the Paper is illuminated, that they shall both appear exactly
3390 alike in Whiteness. For when I was trying this, a Friend coming to visit
3391 me, I stopp'd him at the Door, and before I told him what the Colours
3392 were, or what I was doing; I asked him, Which of the two Whites were the
3393 best, and wherein they differed? And after he had at that distance
3394 viewed them well, he answer'd, that they were both good Whites, and that
3395 he could not say which was best, nor wherein their Colours differed.
3396 Now, if you consider, that this White of the Powder in the Sun-shine was
3397 compounded of the Colours which the component Powders (Orpiment, Purple,
3398 Bise, and _Viride Æris_) have in the same Sun-shine, you must
3399 acknowledge by this Experiment, as well as by the former, that perfect
3400 Whiteness may be compounded of Colours.
3401
3402 From what has been said it is also evident, that the Whiteness of the
3403 Sun's Light is compounded of all the Colours wherewith the several sorts
3404 of Rays whereof that Light consists, when by their several
3405 Refrangibilities they are separated from one another, do tinge Paper or
3406 any other white Body whereon they fall. For those Colours (by _Prop._
3407 II. _Part_ 2.) are unchangeable, and whenever all those Rays with those
3408 their Colours are mix'd again, they reproduce the same white Light as
3409 before.
3410
3411
3412 _PROP._ VI. PROB. II.
3413
3414 _In a mixture of Primary Colours, the Quantity and Quality of each being
3415 given, to know the Colour of the Compound._
3416
3417 [Illustration: FIG. 11.]
3418
3419 With the Center O [in _Fig._ 11.] and Radius OD describe a Circle ADF,
3420 and distinguish its Circumference into seven Parts DE, EF, FG, GA, AB,
3421 BC, CD, proportional to the seven Musical Tones or Intervals of the
3422 eight Sounds, _Sol_, _la_, _fa_, _sol_, _la_, _mi_, _fa_, _sol_,
3423 contained in an eight, that is, proportional to the Number 1/9, 1/16,
3424 1/10, 1/9, 1/16, 1/16, 1/9. Let the first Part DE represent a red
3425 Colour, the second EF orange, the third FG yellow, the fourth CA green,
3426 the fifth AB blue, the sixth BC indigo, and the seventh CD violet. And
3427 conceive that these are all the Colours of uncompounded Light gradually
3428 passing into one another, as they do when made by Prisms; the
3429 Circumference DEFGABCD, representing the whole Series of Colours from
3430 one end of the Sun's colour'd Image to the other, so that from D to E be
3431 all degrees of red, at E the mean Colour between red and orange, from E
3432 to F all degrees of orange, at F the mean between orange and yellow,
3433 from F to G all degrees of yellow, and so on. Let _p_ be the Center of
3434 Gravity of the Arch DE, and _q_, _r_, _s_, _t_, _u_, _x_, the Centers of
3435 Gravity of the Arches EF, FG, GA, AB, BC, and CD respectively, and about
3436 those Centers of Gravity let Circles proportional to the Number of Rays
3437 of each Colour in the given Mixture be describ'd: that is, the Circle
3438 _p_ proportional to the Number of the red-making Rays in the Mixture,
3439 the Circle _q_ proportional to the Number of the orange-making Rays in
3440 the Mixture, and so of the rest. Find the common Center of Gravity of
3441 all those Circles, _p_, _q_, _r_, _s_, _t_, _u_, _x_. Let that Center be
3442 Z; and from the Center of the Circle ADF, through Z to the
3443 Circumference, drawing the Right Line OY, the Place of the Point Y in
3444 the Circumference shall shew the Colour arising from the Composition of
3445 all the Colours in the given Mixture, and the Line OZ shall be
3446 proportional to the Fulness or Intenseness of the Colour, that is, to
3447 its distance from Whiteness. As if Y fall in the middle between F and G,
3448 the compounded Colour shall be the best yellow; if Y verge from the
3449 middle towards F or G, the compound Colour shall accordingly be a
3450 yellow, verging towards orange or green. If Z fall upon the
3451 Circumference, the Colour shall be intense and florid in the highest
3452 Degree; if it fall in the mid-way between the Circumference and Center,
3453 it shall be but half so intense, that is, it shall be such a Colour as
3454 would be made by diluting the intensest yellow with an equal quantity of
3455 whiteness; and if it fall upon the center O, the Colour shall have lost
3456 all its intenseness, and become a white. But it is to be noted, That if
3457 the point Z fall in or near the line OD, the main ingredients being the
3458 red and violet, the Colour compounded shall not be any of the prismatick
3459 Colours, but a purple, inclining to red or violet, accordingly as the
3460 point Z lieth on the side of the line DO towards E or towards C, and in
3461 general the compounded violet is more bright and more fiery than the
3462 uncompounded. Also if only two of the primary Colours which in the
3463 circle are opposite to one another be mixed in an equal proportion, the
3464 point Z shall fall upon the center O, and yet the Colour compounded of
3465 those two shall not be perfectly white, but some faint anonymous Colour.
3466 For I could never yet by mixing only two primary Colours produce a
3467 perfect white. Whether it may be compounded of a mixture of three taken
3468 at equal distances in the circumference I do not know, but of four or
3469 five I do not much question but it may. But these are Curiosities of
3470 little or no moment to the understanding the Phænomena of Nature. For in
3471 all whites produced by Nature, there uses to be a mixture of all sorts
3472 of Rays, and by consequence a composition of all Colours.
3473
3474 To give an instance of this Rule; suppose a Colour is compounded of
3475 these homogeneal Colours, of violet one part, of indigo one part, of
3476 blue two parts, of green three parts, of yellow five parts, of orange
3477 six parts, and of red ten parts. Proportional to these parts describe
3478 the Circles _x_, _v_, _t_, _s_, _r_, _q_, _p_, respectively, that is, so
3479 that if the Circle _x_ be one, the Circle _v_ may be one, the Circle _t_
3480 two, the Circle _s_ three, and the Circles _r_, _q_ and _p_, five, six
3481 and ten. Then I find Z the common center of gravity of these Circles,
3482 and through Z drawing the Line OY, the Point Y falls upon the
3483 circumference between E and F, something nearer to E than to F, and
3484 thence I conclude, that the Colour compounded of these Ingredients will
3485 be an orange, verging a little more to red than to yellow. Also I find
3486 that OZ is a little less than one half of OY, and thence I conclude,
3487 that this orange hath a little less than half the fulness or intenseness
3488 of an uncompounded orange; that is to say, that it is such an orange as
3489 may be made by mixing an homogeneal orange with a good white in the
3490 proportion of the Line OZ to the Line ZY, this Proportion being not of
3491 the quantities of mixed orange and white Powders, but of the quantities
3492 of the Lights reflected from them.
3493
3494 This Rule I conceive accurate enough for practice, though not
3495 mathematically accurate; and the truth of it may be sufficiently proved
3496 to Sense, by stopping any of the Colours at the Lens in the tenth
3497 Experiment of this Book. For the rest of the Colours which are not
3498 stopp'd, but pass on to the Focus of the Lens, will there compound
3499 either accurately or very nearly such a Colour, as by this Rule ought to
3500 result from their Mixture.
3501
3502
3503 _PROP._ VII. THEOR. V.
3504
3505 _All the Colours in the Universe which are made by Light, and depend not
3506 on the Power of Imagination, are either the Colours of homogeneal
3507 Lights, or compounded of these, and that either accurately or very
3508 nearly, according to the Rule of the foregoing Problem._
3509
3510 For it has been proved (in _Prop. 1. Part 2._) that the changes of
3511 Colours made by Refractions do not arise from any new Modifications of
3512 the Rays impress'd by those Refractions, and by the various Terminations
3513 of Light and Shadow, as has been the constant and general Opinion of
3514 Philosophers. It has also been proved that the several Colours of the
3515 homogeneal Rays do constantly answer to their degrees of Refrangibility,
3516 (_Prop._ 1. _Part_ 1. and _Prop._ 2. _Part_ 2.) and that their degrees
3517 of Refrangibility cannot be changed by Refractions and Reflexions
3518 (_Prop._ 2. _Part_ 1.) and by consequence that those their Colours are
3519 likewise immutable. It has also been proved directly by refracting and
3520 reflecting homogeneal Lights apart, that their Colours cannot be
3521 changed, (_Prop._ 2. _Part_ 2.) It has been proved also, that when the
3522 several sorts of Rays are mixed, and in crossing pass through the same
3523 space, they do not act on one another so as to change each others
3524 colorific qualities. (_Exper._ 10. _Part_ 2.) but by mixing their
3525 Actions in the Sensorium beget a Sensation differing from what either
3526 would do apart, that is a Sensation of a mean Colour between their
3527 proper Colours; and particularly when by the concourse and mixtures of
3528 all sorts of Rays, a white Colour is produced, the white is a mixture of
3529 all the Colours which the Rays would have apart, (_Prop._ 5. _Part_ 2.)
3530 The Rays in that mixture do not lose or alter their several colorific
3531 qualities, but by all their various kinds of Actions mix'd in the
3532 Sensorium, beget a Sensation of a middling Colour between all their
3533 Colours, which is whiteness. For whiteness is a mean between all
3534 Colours, having it self indifferently to them all, so as with equal
3535 facility to be tinged with any of them. A red Powder mixed with a little
3536 blue, or a blue with a little red, doth not presently lose its Colour,
3537 but a white Powder mix'd with any Colour is presently tinged with that
3538 Colour, and is equally capable of being tinged with any Colour whatever.
3539 It has been shewed also, that as the Sun's Light is mix'd of all sorts
3540 of Rays, so its whiteness is a mixture of the Colours of all sorts of
3541 Rays; those Rays having from the beginning their several colorific
3542 qualities as well as their several Refrangibilities, and retaining them
3543 perpetually unchanged notwithstanding any Refractions or Reflexions they
3544 may at any time suffer, and that whenever any sort of the Sun's Rays is
3545 by any means (as by Reflexion in _Exper._ 9, and 10. _Part_ 1. or by
3546 Refraction as happens in all Refractions) separated from the rest, they
3547 then manifest their proper Colours. These things have been prov'd, and
3548 the sum of all this amounts to the Proposition here to be proved. For if
3549 the Sun's Light is mix'd of several sorts of Rays, each of which have
3550 originally their several Refrangibilities and colorific Qualities, and
3551 notwithstanding their Refractions and Reflexions, and their various
3552 Separations or Mixtures, keep those their original Properties
3553 perpetually the same without alteration; then all the Colours in the
3554 World must be such as constantly ought to arise from the original
3555 colorific qualities of the Rays whereof the Lights consist by which
3556 those Colours are seen. And therefore if the reason of any Colour
3557 whatever be required, we have nothing else to do than to consider how
3558 the Rays in the Sun's Light have by Reflexions or Refractions, or other
3559 causes, been parted from one another, or mixed together; or otherwise to
3560 find out what sorts of Rays are in the Light by which that Colour is
3561 made, and in what Proportion; and then by the last Problem to learn the
3562 Colour which ought to arise by mixing those Rays (or their Colours) in
3563 that proportion. I speak here of Colours so far as they arise from
3564 Light. For they appear sometimes by other Causes, as when by the power
3565 of Phantasy we see Colours in a Dream, or a Mad-man sees things before
3566 him which are not there; or when we see Fire by striking the Eye, or see
3567 Colours like the Eye of a Peacock's Feather, by pressing our Eyes in
3568 either corner whilst we look the other way. Where these and such like
3569 Causes interpose not, the Colour always answers to the sort or sorts of
3570 the Rays whereof the Light consists, as I have constantly found in
3571 whatever Phænomena of Colours I have hitherto been able to examine. I
3572 shall in the following Propositions give instances of this in the
3573 Phænomena of chiefest note.
3574
3575
3576 _PROP._ VIII. PROB. III.
3577
3578 _By the discovered Properties of Light to explain the Colours made by
3579 Prisms._
3580
3581 Let ABC [in _Fig._ 12.] represent a Prism refracting the Light of the
3582 Sun, which comes into a dark Chamber through a hole F[Greek: ph] almost
3583 as broad as the Prism, and let MN represent a white Paper on which the
3584 refracted Light is cast, and suppose the most refrangible or deepest
3585 violet-making Rays fall upon the Space P[Greek: p], the least
3586 refrangible or deepest red-making Rays upon the Space T[Greek: t], the
3587 middle sort between the indigo-making and blue-making Rays upon the
3588 Space Q[Greek: ch], the middle sort of the green-making Rays upon the
3589 Space R, the middle sort between the yellow-making and orange-making
3590 Rays upon the Space S[Greek: s], and other intermediate sorts upon
3591 intermediate Spaces. For so the Spaces upon which the several sorts
3592 adequately fall will by reason of the different Refrangibility of those
3593 sorts be one lower than another. Now if the Paper MN be so near the
3594 Prism that the Spaces PT and [Greek: pt] do not interfere with one
3595 another, the distance between them T[Greek: p] will be illuminated by
3596 all the sorts of Rays in that proportion to one another which they have
3597 at their very first coming out of the Prism, and consequently be white.
3598 But the Spaces PT and [Greek: pt] on either hand, will not be
3599 illuminated by them all, and therefore will appear coloured. And
3600 particularly at P, where the outmost violet-making Rays fall alone, the
3601 Colour must be the deepest violet. At Q where the violet-making and
3602 indigo-making Rays are mixed, it must be a violet inclining much to
3603 indigo. At R where the violet-making, indigo-making, blue-making, and
3604 one half of the green-making Rays are mixed, their Colours must (by the
3605 construction of the second Problem) compound a middle Colour between
3606 indigo and blue. At S where all the Rays are mixed, except the
3607 red-making and orange-making, their Colours ought by the same Rule to
3608 compound a faint blue, verging more to green than indigo. And in the
3609 progress from S to T, this blue will grow more and more faint and
3610 dilute, till at T, where all the Colours begin to be mixed, it ends in
3611 whiteness.
3612
3613 [Illustration: FIG. 12.]
3614
3615 So again, on the other side of the white at [Greek: t], where the least
3616 refrangible or utmost red-making Rays are alone, the Colour must be the
3617 deepest red. At [Greek: s] the mixture of red and orange will compound a
3618 red inclining to orange. At [Greek: r] the mixture of red, orange,
3619 yellow, and one half of the green must compound a middle Colour between
3620 orange and yellow. At [Greek: ch] the mixture of all Colours but violet
3621 and indigo will compound a faint yellow, verging more to green than to
3622 orange. And this yellow will grow more faint and dilute continually in
3623 its progress from [Greek: ch] to [Greek: p], where by a mixture of all
3624 sorts of Rays it will become white.
3625
3626 These Colours ought to appear were the Sun's Light perfectly white: But
3627 because it inclines to yellow, the Excess of the yellow-making Rays
3628 whereby 'tis tinged with that Colour, being mixed with the faint blue
3629 between S and T, will draw it to a faint green. And so the Colours in
3630 order from P to [Greek: t] ought to be violet, indigo, blue, very faint
3631 green, white, faint yellow, orange, red. Thus it is by the computation:
3632 And they that please to view the Colours made by a Prism will find it so
3633 in Nature.
3634
3635 These are the Colours on both sides the white when the Paper is held
3636 between the Prism and the Point X where the Colours meet, and the
3637 interjacent white vanishes. For if the Paper be held still farther off
3638 from the Prism, the most refrangible and least refrangible Rays will be
3639 wanting in the middle of the Light, and the rest of the Rays which are
3640 found there, will by mixture produce a fuller green than before. Also
3641 the yellow and blue will now become less compounded, and by consequence
3642 more intense than before. And this also agrees with experience.
3643
3644 And if one look through a Prism upon a white Object encompassed with
3645 blackness or darkness, the reason of the Colours arising on the edges is
3646 much the same, as will appear to one that shall a little consider it. If
3647 a black Object be encompassed with a white one, the Colours which appear
3648 through the Prism are to be derived from the Light of the white one,
3649 spreading into the Regions of the black, and therefore they appear in a
3650 contrary order to that, when a white Object is surrounded with black.
3651 And the same is to be understood when an Object is viewed, whose parts
3652 are some of them less luminous than others. For in the borders of the
3653 more and less luminous Parts, Colours ought always by the same
3654 Principles to arise from the Excess of the Light of the more luminous,
3655 and to be of the same kind as if the darker parts were black, but yet to
3656 be more faint and dilute.
3657
3658 What is said of Colours made by Prisms may be easily applied to Colours
3659 made by the Glasses of Telescopes or Microscopes, or by the Humours of
3660 the Eye. For if the Object-glass of a Telescope be thicker on one side
3661 than on the other, or if one half of the Glass, or one half of the Pupil
3662 of the Eye be cover'd with any opake substance; the Object-glass, or
3663 that part of it or of the Eye which is not cover'd, may be consider'd as
3664 a Wedge with crooked Sides, and every Wedge of Glass or other pellucid
3665 Substance has the effect of a Prism in refracting the Light which passes
3666 through it.[L]
3667
3668 How the Colours in the ninth and tenth Experiments of the first Part
3669 arise from the different Reflexibility of Light, is evident by what was
3670 there said. But it is observable in the ninth Experiment, that whilst
3671 the Sun's direct Light is yellow, the Excess of the blue-making Rays in
3672 the reflected beam of Light MN, suffices only to bring that yellow to a
3673 pale white inclining to blue, and not to tinge it with a manifestly blue
3674 Colour. To obtain therefore a better blue, I used instead of the yellow
3675 Light of the Sun the white Light of the Clouds, by varying a little the
3676 Experiment, as follows.
3677
3678 [Illustration: FIG. 13.]
3679
3680 _Exper._ 16 Let HFG [in _Fig._ 13.] represent a Prism in the open Air,
3681 and S the Eye of the Spectator, viewing the Clouds by their Light coming
3682 into the Prism at the Plane Side FIGK, and reflected in it by its Base
3683 HEIG, and thence going out through its Plane Side HEFK to the Eye. And
3684 when the Prism and Eye are conveniently placed, so that the Angles of
3685 Incidence and Reflexion at the Base may be about 40 Degrees, the
3686 Spectator will see a Bow MN of a blue Colour, running from one End of
3687 the Base to the other, with the Concave Side towards him, and the Part
3688 of the Base IMNG beyond this Bow will be brighter than the other Part
3689 EMNH on the other Side of it. This blue Colour MN being made by nothing
3690 else than by Reflexion of a specular Superficies, seems so odd a
3691 Phænomenon, and so difficult to be explained by the vulgar Hypothesis of
3692 Philosophers, that I could not but think it deserved to be taken Notice
3693 of. Now for understanding the Reason of it, suppose the Plane ABC to cut
3694 the Plane Sides and Base of the Prism perpendicularly. From the Eye to
3695 the Line BC, wherein that Plane cuts the Base, draw the Lines S_p_ and
3696 S_t_, in the Angles S_pc_ 50 degr. 1/9, and S_tc_ 49 degr. 1/28, and the
3697 Point _p_ will be the Limit beyond which none of the most refrangible
3698 Rays can pass through the Base of the Prism, and be refracted, whose
3699 Incidence is such that they may be reflected to the Eye; and the Point
3700 _t_ will be the like Limit for the least refrangible Rays, that is,
3701 beyond which none of them can pass through the Base, whose Incidence is
3702 such that by Reflexion they may come to the Eye. And the Point _r_ taken
3703 in the middle Way between _p_ and _t_, will be the like Limit for the
3704 meanly refrangible Rays. And therefore all the least refrangible Rays
3705 which fall upon the Base beyond _t_, that is, between _t_ and B, and can
3706 come from thence to the Eye, will be reflected thither: But on this side
3707 _t_, that is, between _t_ and _c_, many of these Rays will be
3708 transmitted through the Base. And all the most refrangible Rays which
3709 fall upon the Base beyond _p_, that is, between, _p_ and B, and can by
3710 Reflexion come from thence to the Eye, will be reflected thither, but
3711 every where between _p_ and _c_, many of these Rays will get through the
3712 Base, and be refracted; and the same is to be understood of the meanly
3713 refrangible Rays on either side of the Point _r_. Whence it follows,
3714 that the Base of the Prism must every where between _t_ and B, by a
3715 total Reflexion of all sorts of Rays to the Eye, look white and bright.
3716 And every where between _p_ and C, by reason of the Transmission of many
3717 Rays of every sort, look more pale, obscure, and dark. But at _r_, and
3718 in other Places between _p_ and _t_, where all the more refrangible Rays
3719 are reflected to the Eye, and many of the less refrangible are
3720 transmitted, the Excess of the most refrangible in the reflected Light
3721 will tinge that Light with their Colour, which is violet and blue. And
3722 this happens by taking the Line C _prt_ B any where between the Ends of
3723 the Prism HG and EI.
3724
3725
3726 _PROP._ IX. PROB. IV.
3727
3728 _By the discovered Properties of Light to explain the Colours of the
3729 Rain-bow._
3730
3731 [Illustration: FIG. 14.]
3732
3733 This Bow never appears, but where it rains in the Sun-shine, and may be
3734 made artificially by spouting up Water which may break aloft, and
3735 scatter into Drops, and fall down like Rain. For the Sun shining upon
3736 these Drops certainly causes the Bow to appear to a Spectator standing
3737 in a due Position to the Rain and Sun. And hence it is now agreed upon,
3738 that this Bow is made by Refraction of the Sun's Light in drops of
3739 falling Rain. This was understood by some of the Antients, and of late
3740 more fully discover'd and explain'd by the famous _Antonius de Dominis_
3741 Archbishop of _Spalato_, in his book _De Radiis Visûs & Lucis_,
3742 published by his Friend _Bartolus_ at _Venice_, in the Year 1611, and
3743 written above 20 Years before. For he teaches there how the interior Bow
3744 is made in round Drops of Rain by two Refractions of the Sun's Light,
3745 and one Reflexion between them, and the exterior by two Refractions, and
3746 two sorts of Reflexions between them in each Drop of Water, and proves
3747 his Explications by Experiments made with a Phial full of Water, and
3748 with Globes of Glass filled with Water, and placed in the Sun to make
3749 the Colours of the two Bows appear in them. The same Explication
3750 _Des-Cartes_ hath pursued in his Meteors, and mended that of the
3751 exterior Bow. But whilst they understood not the true Origin of Colours,
3752 it's necessary to pursue it here a little farther. For understanding
3753 therefore how the Bow is made, let a Drop of Rain, or any other
3754 spherical transparent Body be represented by the Sphere BNFG, [in _Fig._
3755 14.] described with the Center C, and Semi-diameter CN. And let AN be
3756 one of the Sun's Rays incident upon it at N, and thence refracted to F,
3757 where let it either go out of the Sphere by Refraction towards V, or be
3758 reflected to G; and at G let it either go out by Refraction to R, or be
3759 reflected to H; and at H let it go out by Refraction towards S, cutting
3760 the incident Ray in Y. Produce AN and RG, till they meet in X, and upon
3761 AX and NF, let fall the Perpendiculars CD and CE, and produce CD till it
3762 fall upon the Circumference at L. Parallel to the incident Ray AN draw
3763 the Diameter BQ, and let the Sine of Incidence out of Air into Water be
3764 to the Sine of Refraction as I to R. Now, if you suppose the Point of
3765 Incidence N to move from the Point B, continually till it come to L, the
3766 Arch QF will first increase and then decrease, and so will the Angle AXR
3767 which the Rays AN and GR contain; and the Arch QF and Angle AXR will be
3768 biggest when ND is to CN as sqrt(II - RR) to sqrt(3)RR, in which
3769 case NE will be to ND as 2R to I. Also the Angle AYS, which the Rays AN
3770 and HS contain will first decrease, and then increase and grow least
3771 when ND is to CN as sqrt(II - RR) to sqrt(8)RR, in which case NE
3772 will be to ND, as 3R to I. And so the Angle which the next emergent Ray
3773 (that is, the emergent Ray after three Reflexions) contains with the
3774 incident Ray AN will come to its Limit when ND is to CN as sqrt(II -
3775 RR) to sqrt(15)RR, in which case NE will be to ND as 4R to I. And the
3776 Angle which the Ray next after that Emergent, that is, the Ray emergent
3777 after four Reflexions, contains with the Incident, will come to its
3778 Limit, when ND is to CN as sqrt(II - RR) to sqrt(24)RR, in which
3779 case NE will be to ND as 5R to I; and so on infinitely, the Numbers 3,
3780 8, 15, 24, &c. being gather'd by continual Addition of the Terms of the
3781 arithmetical Progression 3, 5, 7, 9, &c. The Truth of all this
3782 Mathematicians will easily examine.[M]
3783
3784 Now it is to be observed, that as when the Sun comes to his Tropicks,
3785 Days increase and decrease but a very little for a great while together;
3786 so when by increasing the distance CD, these Angles come to their
3787 Limits, they vary their quantity but very little for some time together,
3788 and therefore a far greater number of the Rays which fall upon all the
3789 Points N in the Quadrant BL, shall emerge in the Limits of these Angles,
3790 than in any other Inclinations. And farther it is to be observed, that
3791 the Rays which differ in Refrangibility will have different Limits of
3792 their Angles of Emergence, and by consequence according to their
3793 different Degrees of Refrangibility emerge most copiously in different
3794 Angles, and being separated from one another appear each in their proper
3795 Colours. And what those Angles are may be easily gather'd from the
3796 foregoing Theorem by Computation.
3797
3798 For in the least refrangible Rays the Sines I and R (as was found above)
3799 are 108 and 81, and thence by Computation the greatest Angle AXR will be
3800 found 42 Degrees and 2 Minutes, and the least Angle AYS, 50 Degrees and
3801 57 Minutes. And in the most refrangible Rays the Sines I and R are 109
3802 and 81, and thence by Computation the greatest Angle AXR will be found
3803 40 Degrees and 17 Minutes, and the least Angle AYS 54 Degrees and 7
3804 Minutes.
3805
3806 Suppose now that O [in _Fig._ 15.] is the Spectator's Eye, and OP a Line
3807 drawn parallel to the Sun's Rays and let POE, POF, POG, POH, be Angles
3808 of 40 Degr. 17 Min. 42 Degr. 2 Min. 50 Degr. 57 Min. and 54 Degr. 7 Min.
3809 respectively, and these Angles turned about their common Side OP, shall
3810 with their other Sides OE, OF; OG, OH, describe the Verges of two
3811 Rain-bows AF, BE and CHDG. For if E, F, G, H, be drops placed any where
3812 in the conical Superficies described by OE, OF, OG, OH, and be
3813 illuminated by the Sun's Rays SE, SF, SG, SH; the Angle SEO being equal
3814 to the Angle POE, or 40 Degr. 17 Min. shall be the greatest Angle in
3815 which the most refrangible Rays can after one Reflexion be refracted to
3816 the Eye, and therefore all the Drops in the Line OE shall send the most
3817 refrangible Rays most copiously to the Eye, and thereby strike the
3818 Senses with the deepest violet Colour in that Region. And in like
3819 manner the Angle SFO being equal to the Angle POF, or 42 Degr. 2 Min.
3820 shall be the greatest in which the least refrangible Rays after one
3821 Reflexion can emerge out of the Drops, and therefore those Rays shall
3822 come most copiously to the Eye from the Drops in the Line OF, and strike
3823 the Senses with the deepest red Colour in that Region. And by the same
3824 Argument, the Rays which have intermediate Degrees of Refrangibility
3825 shall come most copiously from Drops between E and F, and strike the
3826 Senses with the intermediate Colours, in the Order which their Degrees
3827 of Refrangibility require, that is in the Progress from E to F, or from
3828 the inside of the Bow to the outside in this order, violet, indigo,
3829 blue, green, yellow, orange, red. But the violet, by the mixture of the
3830 white Light of the Clouds, will appear faint and incline to purple.
3831
3832 [Illustration: FIG. 15.]
3833
3834 Again, the Angle SGO being equal to the Angle POG, or 50 Gr. 51 Min.
3835 shall be the least Angle in which the least refrangible Rays can after
3836 two Reflexions emerge out of the Drops, and therefore the least
3837 refrangible Rays shall come most copiously to the Eye from the Drops in
3838 the Line OG, and strike the Sense with the deepest red in that Region.
3839 And the Angle SHO being equal to the Angle POH, or 54 Gr. 7 Min. shall
3840 be the least Angle, in which the most refrangible Rays after two
3841 Reflexions can emerge out of the Drops; and therefore those Rays shall
3842 come most copiously to the Eye from the Drops in the Line OH, and strike
3843 the Senses with the deepest violet in that Region. And by the same
3844 Argument, the Drops in the Regions between G and H shall strike the
3845 Sense with the intermediate Colours in the Order which their Degrees of
3846 Refrangibility require, that is, in the Progress from G to H, or from
3847 the inside of the Bow to the outside in this order, red, orange, yellow,
3848 green, blue, indigo, violet. And since these four Lines OE, OF, OG, OH,
3849 may be situated any where in the above-mention'd conical Superficies;
3850 what is said of the Drops and Colours in these Lines is to be understood
3851 of the Drops and Colours every where in those Superficies.
3852
3853 Thus shall there be made two Bows of Colours, an interior and stronger,
3854 by one Reflexion in the Drops, and an exterior and fainter by two; for
3855 the Light becomes fainter by every Reflexion. And their Colours shall
3856 lie in a contrary Order to one another, the red of both Bows bordering
3857 upon the Space GF, which is between the Bows. The Breadth of the
3858 interior Bow EOF measured cross the Colours shall be 1 Degr. 45 Min. and
3859 the Breadth of the exterior GOH shall be 3 Degr. 10 Min. and the
3860 distance between them GOF shall be 8 Gr. 15 Min. the greatest
3861 Semi-diameter of the innermost, that is, the Angle POF being 42 Gr. 2
3862 Min. and the least Semi-diameter of the outermost POG, being 50 Gr. 57
3863 Min. These are the Measures of the Bows, as they would be were the Sun
3864 but a Point; for by the Breadth of his Body, the Breadth of the Bows
3865 will be increased, and their Distance decreased by half a Degree, and so
3866 the breadth of the interior Iris will be 2 Degr. 15 Min. that of the
3867 exterior 3 Degr. 40 Min. their distance 8 Degr. 25 Min. the greatest
3868 Semi-diameter of the interior Bow 42 Degr. 17 Min. and the least of the
3869 exterior 50 Degr. 42 Min. And such are the Dimensions of the Bows in the
3870 Heavens found to be very nearly, when their Colours appear strong and
3871 perfect. For once, by such means as I then had, I measured the greatest
3872 Semi-diameter of the interior Iris about 42 Degrees, and the breadth of
3873 the red, yellow and green in that Iris 63 or 64 Minutes, besides the
3874 outmost faint red obscured by the brightness of the Clouds, for which we
3875 may allow 3 or 4 Minutes more. The breadth of the blue was about 40
3876 Minutes more besides the violet, which was so much obscured by the
3877 brightness of the Clouds, that I could not measure its breadth. But
3878 supposing the breadth of the blue and violet together to equal that of
3879 the red, yellow and green together, the whole breadth of this Iris will
3880 be about 2-1/4 Degrees, as above. The least distance between this Iris
3881 and the exterior Iris was about 8 Degrees and 30 Minutes. The exterior
3882 Iris was broader than the interior, but so faint, especially on the blue
3883 side, that I could not measure its breadth distinctly. At another time
3884 when both Bows appeared more distinct, I measured the breadth of the
3885 interior Iris 2 Gr. 10´, and the breadth of the red, yellow and green in
3886 the exterior Iris, was to the breadth of the same Colours in the
3887 interior as 3 to 2.
3888
3889 This Explication of the Rain-bow is yet farther confirmed by the known
3890 Experiment (made by _Antonius de Dominis_ and _Des-Cartes_) of hanging
3891 up any where in the Sun-shine a Glass Globe filled with Water, and
3892 viewing it in such a posture, that the Rays which come from the Globe to
3893 the Eye may contain with the Sun's Rays an Angle of either 42 or 50
3894 Degrees. For if the Angle be about 42 or 43 Degrees, the Spectator
3895 (suppose at O) shall see a full red Colour in that side of the Globe
3896 opposed to the Sun as 'tis represented at F, and if that Angle become
3897 less (suppose by depressing the Globe to E) there will appear other
3898 Colours, yellow, green and blue successive in the same side of the
3899 Globe. But if the Angle be made about 50 Degrees (suppose by lifting up
3900 the Globe to G) there will appear a red Colour in that side of the Globe
3901 towards the Sun, and if the Angle be made greater (suppose by lifting
3902 up the Globe to H) the red will turn successively to the other Colours,
3903 yellow, green and blue. The same thing I have tried, by letting a Globe
3904 rest, and raising or depressing the Eye, or otherwise moving it to make
3905 the Angle of a just magnitude.
3906
3907 I have heard it represented, that if the Light of a Candle be refracted
3908 by a Prism to the Eye; when the blue Colour falls upon the Eye, the
3909 Spectator shall see red in the Prism, and when the red falls upon the
3910 Eye he shall see blue; and if this were certain, the Colours of the
3911 Globe and Rain-bow ought to appear in a contrary order to what we find.
3912 But the Colours of the Candle being very faint, the mistake seems to
3913 arise from the difficulty of discerning what Colours fall on the Eye.
3914 For, on the contrary, I have sometimes had occasion to observe in the
3915 Sun's Light refracted by a Prism, that the Spectator always sees that
3916 Colour in the Prism which falls upon his Eye. And the same I have found
3917 true also in Candle-light. For when the Prism is moved slowly from the
3918 Line which is drawn directly from the Candle to the Eye, the red appears
3919 first in the Prism and then the blue, and therefore each of them is seen
3920 when it falls upon the Eye. For the red passes over the Eye first, and
3921 then the blue.
3922
3923 The Light which comes through drops of Rain by two Refractions without
3924 any Reflexion, ought to appear strongest at the distance of about 26
3925 Degrees from the Sun, and to decay gradually both ways as the distance
3926 from him increases and decreases. And the same is to be understood of
3927 Light transmitted through spherical Hail-stones. And if the Hail be a
3928 little flatted, as it often is, the Light transmitted may grow so strong
3929 at a little less distance than that of 26 Degrees, as to form a Halo
3930 about the Sun or Moon; which Halo, as often as the Hail-stones are duly
3931 figured may be colour'd, and then it must be red within by the least
3932 refrangible Rays, and blue without by the most refrangible ones,
3933 especially if the Hail-stones have opake Globules of Snow in their
3934 center to intercept the Light within the Halo (as _Hugenius_ has
3935 observ'd) and make the inside thereof more distinctly defined than it
3936 would otherwise be. For such Hail-stones, though spherical, by
3937 terminating the Light by the Snow, may make a Halo red within and
3938 colourless without, and darker in the red than without, as Halos used to
3939 be. For of those Rays which pass close by the Snow the Rubriform will be
3940 least refracted, and so come to the Eye in the directest Lines.
3941
3942 The Light which passes through a drop of Rain after two Refractions, and
3943 three or more Reflexions, is scarce strong enough to cause a sensible
3944 Bow; but in those Cylinders of Ice by which _Hugenius_ explains the
3945 _Parhelia_, it may perhaps be sensible.
3946
3947
3948 _PROP._ X. PROB. V.
3949
3950 _By the discovered Properties of Light to explain the permanent Colours
3951 of Natural Bodies._
3952
3953 These Colours arise from hence, that some natural Bodies reflect some
3954 sorts of Rays, others other sorts more copiously than the rest. Minium
3955 reflects the least refrangible or red-making Rays most copiously, and
3956 thence appears red. Violets reflect the most refrangible most copiously,
3957 and thence have their Colour, and so of other Bodies. Every Body
3958 reflects the Rays of its own Colour more copiously than the rest, and
3959 from their excess and predominance in the reflected Light has its
3960 Colour.
3961
3962 _Exper._ 17. For if in the homogeneal Lights obtained by the solution of
3963 the Problem proposed in the fourth Proposition of the first Part of this
3964 Book, you place Bodies of several Colours, you will find, as I have
3965 done, that every Body looks most splendid and luminous in the Light of
3966 its own Colour. Cinnaber in the homogeneal red Light is most
3967 resplendent, in the green Light it is manifestly less resplendent, and
3968 in the blue Light still less. Indigo in the violet blue Light is most
3969 resplendent, and its splendor is gradually diminish'd, as it is removed
3970 thence by degrees through the green and yellow Light to the red. By a
3971 Leek the green Light, and next that the blue and yellow which compound
3972 green, are more strongly reflected than the other Colours red and
3973 violet, and so of the rest. But to make these Experiments the more
3974 manifest, such Bodies ought to be chosen as have the fullest and most
3975 vivid Colours, and two of those Bodies are to be compared together.
3976 Thus, for instance, if Cinnaber and _ultra_-marine blue, or some other
3977 full blue be held together in the red homogeneal Light, they will both
3978 appear red, but the Cinnaber will appear of a strongly luminous and
3979 resplendent red, and the _ultra_-marine blue of a faint obscure and dark
3980 red; and if they be held together in the blue homogeneal Light, they
3981 will both appear blue, but the _ultra_-marine will appear of a strongly
3982 luminous and resplendent blue, and the Cinnaber of a faint and dark
3983 blue. Which puts it out of dispute that the Cinnaber reflects the red
3984 Light much more copiously than the _ultra_-marine doth, and the
3985 _ultra_-marine reflects the blue Light much more copiously than the
3986 Cinnaber doth. The same Experiment may be tried successfully with red
3987 Lead and Indigo, or with any other two colour'd Bodies, if due allowance
3988 be made for the different strength or weakness of their Colour and
3989 Light.
3990
3991 And as the reason of the Colours of natural Bodies is evident by these
3992 Experiments, so it is farther confirmed and put past dispute by the two
3993 first Experiments of the first Part, whereby 'twas proved in such Bodies
3994 that the reflected Lights which differ in Colours do differ also in
3995 degrees of Refrangibility. For thence it's certain, that some Bodies
3996 reflect the more refrangible, others the less refrangible Rays more
3997 copiously.
3998
3999 And that this is not only a true reason of these Colours, but even the
4000 only reason, may appear farther from this Consideration, that the Colour
4001 of homogeneal Light cannot be changed by the Reflexion of natural
4002 Bodies.
4003
4004 For if Bodies by Reflexion cannot in the least change the Colour of any
4005 one sort of Rays, they cannot appear colour'd by any other means than by
4006 reflecting those which either are of their own Colour, or which by
4007 mixture must produce it.
4008
4009 But in trying Experiments of this kind care must be had that the Light
4010 be sufficiently homogeneal. For if Bodies be illuminated by the ordinary
4011 prismatick Colours, they will appear neither of their own Day-light
4012 Colours, nor of the Colour of the Light cast on them, but of some middle
4013 Colour between both, as I have found by Experience. Thus red Lead (for
4014 instance) illuminated with the ordinary prismatick green will not appear
4015 either red or green, but orange or yellow, or between yellow and green,
4016 accordingly as the green Light by which 'tis illuminated is more or less
4017 compounded. For because red Lead appears red when illuminated with white
4018 Light, wherein all sorts of Rays are equally mix'd, and in the green
4019 Light all sorts of Rays are not equally mix'd, the Excess of the
4020 yellow-making, green-making and blue-making Rays in the incident green
4021 Light, will cause those Rays to abound so much in the reflected Light,
4022 as to draw the Colour from red towards their Colour. And because the red
4023 Lead reflects the red-making Rays most copiously in proportion to their
4024 number, and next after them the orange-making and yellow-making Rays;
4025 these Rays in the reflected Light will be more in proportion to the
4026 Light than they were in the incident green Light, and thereby will draw
4027 the reflected Light from green towards their Colour. And therefore the
4028 red Lead will appear neither red nor green, but of a Colour between
4029 both.
4030
4031 In transparently colour'd Liquors 'tis observable, that their Colour
4032 uses to vary with their thickness. Thus, for instance, a red Liquor in a
4033 conical Glass held between the Light and the Eye, looks of a pale and
4034 dilute yellow at the bottom where 'tis thin, and a little higher where
4035 'tis thicker grows orange, and where 'tis still thicker becomes red, and
4036 where 'tis thickest the red is deepest and darkest. For it is to be
4037 conceiv'd that such a Liquor stops the indigo-making and violet-making
4038 Rays most easily, the blue-making Rays more difficultly, the
4039 green-making Rays still more difficultly, and the red-making most
4040 difficultly: And that if the thickness of the Liquor be only so much as
4041 suffices to stop a competent number of the violet-making and
4042 indigo-making Rays, without diminishing much the number of the rest, the
4043 rest must (by _Prop._ 6. _Part_ 2.) compound a pale yellow. But if the
4044 Liquor be so much thicker as to stop also a great number of the
4045 blue-making Rays, and some of the green-making, the rest must compound
4046 an orange; and where it is so thick as to stop also a great number of
4047 the green-making and a considerable number of the yellow-making, the
4048 rest must begin to compound a red, and this red must grow deeper and
4049 darker as the yellow-making and orange-making Rays are more and more
4050 stopp'd by increasing the thickness of the Liquor, so that few Rays
4051 besides the red-making can get through.
4052
4053 Of this kind is an Experiment lately related to me by Mr. _Halley_, who,
4054 in diving deep into the Sea in a diving Vessel, found in a clear
4055 Sun-shine Day, that when he was sunk many Fathoms deep into the Water
4056 the upper part of his Hand on which the Sun shone directly through the
4057 Water and through a small Glass Window in the Vessel appeared of a red
4058 Colour, like that of a Damask Rose, and the Water below and the under
4059 part of his Hand illuminated by Light reflected from the Water below
4060 look'd green. For thence it may be gather'd, that the Sea-Water reflects
4061 back the violet and blue-making Rays most easily, and lets the
4062 red-making Rays pass most freely and copiously to great Depths. For
4063 thereby the Sun's direct Light at all great Depths, by reason of the
4064 predominating red-making Rays, must appear red; and the greater the
4065 Depth is, the fuller and intenser must that red be. And at such Depths
4066 as the violet-making Rays scarce penetrate unto, the blue-making,
4067 green-making, and yellow-making Rays being reflected from below more
4068 copiously than the red-making ones, must compound a green.
4069
4070 Now, if there be two Liquors of full Colours, suppose a red and blue,
4071 and both of them so thick as suffices to make their Colours sufficiently
4072 full; though either Liquor be sufficiently transparent apart, yet will
4073 you not be able to see through both together. For, if only the
4074 red-making Rays pass through one Liquor, and only the blue-making
4075 through the other, no Rays can pass through both. This Mr. _Hook_ tried
4076 casually with Glass Wedges filled with red and blue Liquors, and was
4077 surprized at the unexpected Event, the reason of it being then unknown;
4078 which makes me trust the more to his Experiment, though I have not tried
4079 it my self. But he that would repeat it, must take care the Liquors be
4080 of very good and full Colours.
4081
4082 Now, whilst Bodies become coloured by reflecting or transmitting this or
4083 that sort of Rays more copiously than the rest, it is to be conceived
4084 that they stop and stifle in themselves the Rays which they do not
4085 reflect or transmit. For, if Gold be foliated and held between your Eye
4086 and the Light, the Light looks of a greenish blue, and therefore massy
4087 Gold lets into its Body the blue-making Rays to be reflected to and fro
4088 within it till they be stopp'd and stifled, whilst it reflects the
4089 yellow-making outwards, and thereby looks yellow. And much after the
4090 same manner that Leaf Gold is yellow by reflected, and blue by
4091 transmitted Light, and massy Gold is yellow in all Positions of the Eye;
4092 there are some Liquors, as the Tincture of _Lignum Nephriticum_, and
4093 some sorts of Glass which transmit one sort of Light most copiously, and
4094 reflect another sort, and thereby look of several Colours, according to
4095 the Position of the Eye to the Light. But, if these Liquors or Glasses
4096 were so thick and massy that no Light could get through them, I question
4097 not but they would like all other opake Bodies appear of one and the
4098 same Colour in all Positions of the Eye, though this I cannot yet affirm
4099 by Experience. For all colour'd Bodies, so far as my Observation
4100 reaches, may be seen through if made sufficiently thin, and therefore
4101 are in some measure transparent, and differ only in degrees of
4102 Transparency from tinged transparent Liquors; these Liquors, as well as
4103 those Bodies, by a sufficient Thickness becoming opake. A transparent
4104 Body which looks of any Colour by transmitted Light, may also look of
4105 the same Colour by reflected Light, the Light of that Colour being
4106 reflected by the farther Surface of the Body, or by the Air beyond it.
4107 And then the reflected Colour will be diminished, and perhaps cease, by
4108 making the Body very thick, and pitching it on the backside to diminish
4109 the Reflexion of its farther Surface, so that the Light reflected from
4110 the tinging Particles may predominate. In such Cases, the Colour of the
4111 reflected Light will be apt to vary from that of the Light transmitted.
4112 But whence it is that tinged Bodies and Liquors reflect some sort of
4113 Rays, and intromit or transmit other sorts, shall be said in the next
4114 Book. In this Proposition I content my self to have put it past dispute,
4115 that Bodies have such Properties, and thence appear colour'd.
4116
4117
4118 _PROP._ XI. PROB. VI.
4119
4120 _By mixing colour'd Lights to compound a beam of Light of the same
4121 Colour and Nature with a beam of the Sun's direct Light, and therein to
4122 experience the Truth of the foregoing Propositions._
4123
4124 [Illustration: FIG. 16.]
4125
4126 Let ABC _abc_ [in _Fig._ 16.] represent a Prism, by which the Sun's
4127 Light let into a dark Chamber through the Hole F, may be refracted
4128 towards the Lens MN, and paint upon it at _p_, _q_, _r_, _s_, and _t_,
4129 the usual Colours violet, blue, green, yellow, and red, and let the
4130 diverging Rays by the Refraction of this Lens converge again towards X,
4131 and there, by the mixture of all those their Colours, compound a white
4132 according to what was shewn above. Then let another Prism DEG _deg_,
4133 parallel to the former, be placed at X, to refract that white Light
4134 upwards towards Y. Let the refracting Angles of the Prisms, and their
4135 distances from the Lens be equal, so that the Rays which converged from
4136 the Lens towards X, and without Refraction, would there have crossed and
4137 diverged again, may by the Refraction of the second Prism be reduced
4138 into Parallelism and diverge no more. For then those Rays will recompose
4139 a beam of white Light XY. If the refracting Angle of either Prism be the
4140 bigger, that Prism must be so much the nearer to the Lens. You will know
4141 when the Prisms and the Lens are well set together, by observing if the
4142 beam of Light XY, which comes out of the second Prism be perfectly white
4143 to the very edges of the Light, and at all distances from the Prism
4144 continue perfectly and totally white like a beam of the Sun's Light. For
4145 till this happens, the Position of the Prisms and Lens to one another
4146 must be corrected; and then if by the help of a long beam of Wood, as is
4147 represented in the Figure, or by a Tube, or some other such Instrument,
4148 made for that Purpose, they be made fast in that Situation, you may try
4149 all the same Experiments in this compounded beam of Light XY, which have
4150 been made in the Sun's direct Light. For this compounded beam of Light
4151 has the same appearance, and is endow'd with all the same Properties
4152 with a direct beam of the Sun's Light, so far as my Observation reaches.
4153 And in trying Experiments in this beam you may by stopping any of the
4154 Colours, _p_, _q_, _r_, _s_, and _t_, at the Lens, see how the Colours
4155 produced in the Experiments are no other than those which the Rays had
4156 at the Lens before they entered the Composition of this Beam: And by
4157 consequence, that they arise not from any new Modifications of the Light
4158 by Refractions and Reflexions, but from the various Separations and
4159 Mixtures of the Rays originally endow'd with their colour-making
4160 Qualities.
4161
4162 So, for instance, having with a Lens 4-1/4 Inches broad, and two Prisms
4163 on either hand 6-1/4 Feet distant from the Lens, made such a beam of
4164 compounded Light; to examine the reason of the Colours made by Prisms, I
4165 refracted this compounded beam of Light XY with another Prism HIK _kh_,
4166 and thereby cast the usual Prismatick Colours PQRST upon the Paper LV
4167 placed behind. And then by stopping any of the Colours _p_, _q_, _r_,
4168 _s_, _t_, at the Lens, I found that the same Colour would vanish at the
4169 Paper. So if the Purple _p_ was stopp'd at the Lens, the Purple P upon
4170 the Paper would vanish, and the rest of the Colours would remain
4171 unalter'd, unless perhaps the blue, so far as some purple latent in it
4172 at the Lens might be separated from it by the following Refractions. And
4173 so by intercepting the green upon the Lens, the green R upon the Paper
4174 would vanish, and so of the rest; which plainly shews, that as the white
4175 beam of Light XY was compounded of several Lights variously colour'd at
4176 the Lens, so the Colours which afterwards emerge out of it by new
4177 Refractions are no other than those of which its Whiteness was
4178 compounded. The Refraction of the Prism HIK _kh_ generates the Colours
4179 PQRST upon the Paper, not by changing the colorific Qualities of the
4180 Rays, but by separating the Rays which had the very same colorific
4181 Qualities before they enter'd the Composition of the refracted beam of
4182 white Light XY. For otherwise the Rays which were of one Colour at the
4183 Lens might be of another upon the Paper, contrary to what we find.
4184
4185 So again, to examine the reason of the Colours of natural Bodies, I
4186 placed such Bodies in the Beam of Light XY, and found that they all
4187 appeared there of those their own Colours which they have in Day-light,
4188 and that those Colours depend upon the Rays which had the same Colours
4189 at the Lens before they enter'd the Composition of that beam. Thus, for
4190 instance, Cinnaber illuminated by this beam appears of the same red
4191 Colour as in Day-light; and if at the Lens you intercept the
4192 green-making and blue-making Rays, its redness will become more full and
4193 lively: But if you there intercept the red-making Rays, it will not any
4194 longer appear red, but become yellow or green, or of some other Colour,
4195 according to the sorts of Rays which you do not intercept. So Gold in
4196 this Light XY appears of the same yellow Colour as in Day-light, but by
4197 intercepting at the Lens a due Quantity of the yellow-making Rays it
4198 will appear white like Silver (as I have tried) which shews that its
4199 yellowness arises from the Excess of the intercepted Rays tinging that
4200 Whiteness with their Colour when they are let pass. So the Infusion of
4201 _Lignum Nephriticum_ (as I have also tried) when held in this beam of
4202 Light XY, looks blue by the reflected Part of the Light, and red by the
4203 transmitted Part of it, as when 'tis view'd in Day-light; but if you
4204 intercept the blue at the Lens the Infusion will lose its reflected blue
4205 Colour, whilst its transmitted red remains perfect, and by the loss of
4206 some blue-making Rays, wherewith it was allay'd, becomes more intense
4207 and full. And, on the contrary, if the red and orange-making Rays be
4208 intercepted at the Lens, the Infusion will lose its transmitted red,
4209 whilst its blue will remain and become more full and perfect. Which
4210 shews, that the Infusion does not tinge the Rays with blue and red, but
4211 only transmits those most copiously which were red-making before, and
4212 reflects those most copiously which were blue-making before. And after
4213 the same manner may the Reasons of other Phænomena be examined, by
4214 trying them in this artificial beam of Light XY.
4215
4216 FOOTNOTES:
4217
4218 [I] See p. 59.
4219
4220 [J] _See our_ Author's Lect. Optic. _Part_ II. _Sect._ II. _p._ 239.
4221
4222 [K] _As is done in our_ Author's Lect. Optic. _Part_ I. _Sect._ III.
4223 _and_ IV. _and Part_ II. _Sect._ II.
4224
4225 [L] _See our_ Author's Lect. Optic. _Part_ II. _Sect._ II. _pag._ 269,
4226 &c.
4227
4228 [M] _This is demonstrated in our_ Author's Lect. Optic. _Part_ I.
4229 _Sect._ IV. _Prop._ 35 _and_ 36.
4230
4231
4232
4233
4234 THE
4235
4236 SECOND BOOK
4237
4238 OF
4239
4240 OPTICKS
4241
4242
4243
4244
4245 _PART I._
4246
4247 _Observations concerning the Reflexions, Refractions, and Colours of
4248 thin transparent Bodies._
4249
4250
4251 It has been observed by others, that transparent Substances, as Glass,
4252 Water, Air, &c. when made very thin by being blown into Bubbles, or
4253 otherwise formed into Plates, do exhibit various Colours according to
4254 their various thinness, altho' at a greater thickness they appear very
4255 clear and colourless. In the former Book I forbore to treat of these
4256 Colours, because they seemed of a more difficult Consideration, and were
4257 not necessary for establishing the Properties of Light there discoursed
4258 of. But because they may conduce to farther Discoveries for compleating
4259 the Theory of Light, especially as to the constitution of the parts of
4260 natural Bodies, on which their Colours or Transparency depend; I have
4261 here set down an account of them. To render this Discourse short and
4262 distinct, I have first described the principal of my Observations, and
4263 then consider'd and made use of them. The Observations are these.
4264
4265 _Obs._ 1. Compressing two Prisms hard together that their sides (which
4266 by chance were a very little convex) might somewhere touch one another:
4267 I found the place in which they touched to become absolutely
4268 transparent, as if they had there been one continued piece of Glass. For
4269 when the Light fell so obliquely on the Air, which in other places was
4270 between them, as to be all reflected; it seemed in that place of contact
4271 to be wholly transmitted, insomuch that when look'd upon, it appeared
4272 like a black or dark spot, by reason that little or no sensible Light
4273 was reflected from thence, as from other places; and when looked through
4274 it seemed (as it were) a hole in that Air which was formed into a thin
4275 Plate, by being compress'd between the Glasses. And through this hole
4276 Objects that were beyond might be seen distinctly, which could not at
4277 all be seen through other parts of the Glasses where the Air was
4278 interjacent. Although the Glasses were a little convex, yet this
4279 transparent spot was of a considerable breadth, which breadth seemed
4280 principally to proceed from the yielding inwards of the parts of the
4281 Glasses, by reason of their mutual pressure. For by pressing them very
4282 hard together it would become much broader than otherwise.
4283
4284 _Obs._ 2. When the Plate of Air, by turning the Prisms about their
4285 common Axis, became so little inclined to the incident Rays, that some
4286 of them began to be transmitted, there arose in it many slender Arcs of
4287 Colours which at first were shaped almost like the Conchoid, as you see
4288 them delineated in the first Figure. And by continuing the Motion of the
4289 Prisms, these Arcs increased and bended more and more about the said
4290 transparent spot, till they were compleated into Circles or Rings
4291 incompassing it, and afterwards continually grew more and more
4292 contracted.
4293
4294 [Illustration: FIG. 1.]
4295
4296 These Arcs at their first appearance were of a violet and blue Colour,
4297 and between them were white Arcs of Circles, which presently by
4298 continuing the Motion of the Prisms became a little tinged in their
4299 inward Limbs with red and yellow, and to their outward Limbs the blue
4300 was adjacent. So that the order of these Colours from the central dark
4301 spot, was at that time white, blue, violet; black, red, orange, yellow,
4302 white, blue, violet, &c. But the yellow and red were much fainter than
4303 the blue and violet.
4304
4305 The Motion of the Prisms about their Axis being continued, these Colours
4306 contracted more and more, shrinking towards the whiteness on either
4307 side of it, until they totally vanished into it. And then the Circles in
4308 those parts appear'd black and white, without any other Colours
4309 intermix'd. But by farther moving the Prisms about, the Colours again
4310 emerged out of the whiteness, the violet and blue at its inward Limb,
4311 and at its outward Limb the red and yellow. So that now their order from
4312 the central Spot was white, yellow, red; black; violet, blue, white,
4313 yellow, red, &c. contrary to what it was before.
4314
4315 _Obs._ 3. When the Rings or some parts of them appeared only black and
4316 white, they were very distinct and well defined, and the blackness
4317 seemed as intense as that of the central Spot. Also in the Borders of
4318 the Rings, where the Colours began to emerge out of the whiteness, they
4319 were pretty distinct, which made them visible to a very great multitude.
4320 I have sometimes number'd above thirty Successions (reckoning every
4321 black and white Ring for one Succession) and seen more of them, which by
4322 reason of their smalness I could not number. But in other Positions of
4323 the Prisms, at which the Rings appeared of many Colours, I could not
4324 distinguish above eight or nine of them, and the Exterior of those were
4325 very confused and dilute.
4326
4327 In these two Observations to see the Rings distinct, and without any
4328 other Colour than Black and white, I found it necessary to hold my Eye
4329 at a good distance from them. For by approaching nearer, although in the
4330 same inclination of my Eye to the Plane of the Rings, there emerged a
4331 bluish Colour out of the white, which by dilating it self more and more
4332 into the black, render'd the Circles less distinct, and left the white a
4333 little tinged with red and yellow. I found also by looking through a
4334 slit or oblong hole, which was narrower than the pupil of my Eye, and
4335 held close to it parallel to the Prisms, I could see the Circles much
4336 distincter and visible to a far greater number than otherwise.
4337
4338 _Obs._ 4. To observe more nicely the order of the Colours which arose
4339 out of the white Circles as the Rays became less and less inclined to
4340 the Plate of Air; I took two Object-glasses, the one a Plano-convex for
4341 a fourteen Foot Telescope, and the other a large double Convex for one
4342 of about fifty Foot; and upon this, laying the other with its plane side
4343 downwards, I pressed them slowly together, to make the Colours
4344 successively emerge in the middle of the Circles, and then slowly lifted
4345 the upper Glass from the lower to make them successively vanish again in
4346 the same place. The Colour, which by pressing the Glasses together,
4347 emerged last in the middle of the other Colours, would upon its first
4348 appearance look like a Circle of a Colour almost uniform from the
4349 circumference to the center and by compressing the Glasses still more,
4350 grow continually broader until a new Colour emerged in its center, and
4351 thereby it became a Ring encompassing that new Colour. And by
4352 compressing the Glasses still more, the diameter of this Ring would
4353 increase, and the breadth of its Orbit or Perimeter decrease until
4354 another new Colour emerged in the center of the last: And so on until a
4355 third, a fourth, a fifth, and other following new Colours successively
4356 emerged there, and became Rings encompassing the innermost Colour, the
4357 last of which was the black Spot. And, on the contrary, by lifting up
4358 the upper Glass from the lower, the diameter of the Rings would
4359 decrease, and the breadth of their Orbit increase, until their Colours
4360 reached successively to the center; and then they being of a
4361 considerable breadth, I could more easily discern and distinguish their
4362 Species than before. And by this means I observ'd their Succession and
4363 Quantity to be as followeth.
4364
4365 Next to the pellucid central Spot made by the contact of the Glasses
4366 succeeded blue, white, yellow, and red. The blue was so little in
4367 quantity, that I could not discern it in the Circles made by the Prisms,
4368 nor could I well distinguish any violet in it, but the yellow and red
4369 were pretty copious, and seemed about as much in extent as the white,
4370 and four or five times more than the blue. The next Circuit in order of
4371 Colours immediately encompassing these were violet, blue, green, yellow,
4372 and red: and these were all of them copious and vivid, excepting the
4373 green, which was very little in quantity, and seemed much more faint and
4374 dilute than the other Colours. Of the other four, the violet was the
4375 least in extent, and the blue less than the yellow or red. The third
4376 Circuit or Order was purple, blue, green, yellow, and red; in which the
4377 purple seemed more reddish than the violet in the former Circuit, and
4378 the green was much more conspicuous, being as brisk and copious as any
4379 of the other Colours, except the yellow, but the red began to be a
4380 little faded, inclining very much to purple. After this succeeded the
4381 fourth Circuit of green and red. The green was very copious and lively,
4382 inclining on the one side to blue, and on the other side to yellow. But
4383 in this fourth Circuit there was neither violet, blue, nor yellow, and
4384 the red was very imperfect and dirty. Also the succeeding Colours became
4385 more and more imperfect and dilute, till after three or four revolutions
4386 they ended in perfect whiteness. Their form, when the Glasses were most
4387 compress'd so as to make the black Spot appear in the center, is
4388 delineated in the second Figure; where _a_, _b_, _c_, _d_, _e_: _f_,
4389 _g_, _h_, _i_, _k_: _l_, _m_, _n_, _o_, _p_: _q_, _r_: _s_, _t_: _v_,
4390 _x_: _y_, _z_, denote the Colours reckon'd in order from the center,
4391 black, blue, white, yellow, red: violet, blue, green, yellow, red:
4392 purple, blue, green, yellow, red: green, red: greenish blue, red:
4393 greenish blue, pale red: greenish blue, reddish white.
4394
4395 [Illustration: FIG. 2.]
4396
4397 _Obs._ 5. To determine the interval of the Glasses, or thickness of the
4398 interjacent Air, by which each Colour was produced, I measured the
4399 Diameters of the first six Rings at the most lucid part of their Orbits,
4400 and squaring them, I found their Squares to be in the arithmetical
4401 Progression of the odd Numbers, 1, 3, 5, 7, 9, 11. And since one of
4402 these Glasses was plane, and the other spherical, their Intervals at
4403 those Rings must be in the same Progression. I measured also the
4404 Diameters of the dark or faint Rings between the more lucid Colours, and
4405 found their Squares to be in the arithmetical Progression of the even
4406 Numbers, 2, 4, 6, 8, 10, 12. And it being very nice and difficult to
4407 take these measures exactly; I repeated them divers times at divers
4408 parts of the Glasses, that by their Agreement I might be confirmed in
4409 them. And the same method I used in determining some others of the
4410 following Observations.
4411
4412 _Obs._ 6. The Diameter of the sixth Ring at the most lucid part of its
4413 Orbit was 58/100 parts of an Inch, and the Diameter of the Sphere on
4414 which the double convex Object-glass was ground was about 102 Feet, and
4415 hence I gathered the thickness of the Air or Aereal Interval of the
4416 Glasses at that Ring. But some time after, suspecting that in making
4417 this Observation I had not determined the Diameter of the Sphere with
4418 sufficient accurateness, and being uncertain whether the Plano-convex
4419 Glass was truly plane, and not something concave or convex on that side
4420 which I accounted plane; and whether I had not pressed the Glasses
4421 together, as I often did, to make them touch; (For by pressing such
4422 Glasses together their parts easily yield inwards, and the Rings thereby
4423 become sensibly broader than they would be, did the Glasses keep their
4424 Figures.) I repeated the Experiment, and found the Diameter of the sixth
4425 lucid Ring about 55/100 parts of an Inch. I repeated the Experiment also
4426 with such an Object-glass of another Telescope as I had at hand. This
4427 was a double Convex ground on both sides to one and the same Sphere, and
4428 its Focus was distant from it 83-2/5 Inches. And thence, if the Sines of
4429 Incidence and Refraction of the bright yellow Light be assumed in
4430 proportion as 11 to 17, the Diameter of the Sphere to which the Glass
4431 was figured will by computation be found 182 Inches. This Glass I laid
4432 upon a flat one, so that the black Spot appeared in the middle of the
4433 Rings of Colours without any other Pressure than that of the weight of
4434 the Glass. And now measuring the Diameter of the fifth dark Circle as
4435 accurately as I could, I found it the fifth part of an Inch precisely.
4436 This Measure was taken with the points of a pair of Compasses on the
4437 upper Surface on the upper Glass, and my Eye was about eight or nine
4438 Inches distance from the Glass, almost perpendicularly over it, and the
4439 Glass was 1/6 of an Inch thick, and thence it is easy to collect that
4440 the true Diameter of the Ring between the Glasses was greater than its
4441 measur'd Diameter above the Glasses in the Proportion of 80 to 79, or
4442 thereabouts, and by consequence equal to 16/79 parts of an Inch, and its
4443 true Semi-diameter equal to 8/79 parts. Now as the Diameter of the
4444 Sphere (182 Inches) is to the Semi-diameter of this fifth dark Ring
4445 (8/79 parts of an Inch) so is this Semi-diameter to the thickness of the
4446 Air at this fifth dark Ring; which is therefore 32/567931 or
4447 100/1774784. Parts of an Inch; and the fifth Part thereof, _viz._ the
4448 1/88739 Part of an Inch, is the Thickness of the Air at the first of
4449 these dark Rings.
4450
4451 The same Experiment I repeated with another double convex Object-glass
4452 ground on both sides to one and the same Sphere. Its Focus was distant
4453 from it 168-1/2 Inches, and therefore the Diameter of that Sphere was
4454 184 Inches. This Glass being laid upon the same plain Glass, the
4455 Diameter of the fifth of the dark Rings, when the black Spot in their
4456 Center appear'd plainly without pressing the Glasses, was by the measure
4457 of the Compasses upon the upper Glass 121/600 Parts of an Inch, and by
4458 consequence between the Glasses it was 1222/6000: For the upper Glass
4459 was 1/8 of an Inch thick, and my Eye was distant from it 8 Inches. And a
4460 third proportional to half this from the Diameter of the Sphere is
4461 5/88850 Parts of an Inch. This is therefore the Thickness of the Air at
4462 this Ring, and a fifth Part thereof, _viz._ the 1/88850th Part of an
4463 Inch is the Thickness thereof at the first of the Rings, as above.
4464
4465 I tried the same Thing, by laying these Object-glasses upon flat Pieces
4466 of a broken Looking-glass, and found the same Measures of the Rings:
4467 Which makes me rely upon them till they can be determin'd more
4468 accurately by Glasses ground to larger Spheres, though in such Glasses
4469 greater care must be taken of a true Plane.
4470
4471 These Dimensions were taken, when my Eye was placed almost
4472 perpendicularly over the Glasses, being about an Inch, or an Inch and a
4473 quarter, distant from the incident Rays, and eight Inches distant from
4474 the Glass; so that the Rays were inclined to the Glass in an Angle of
4475 about four Degrees. Whence by the following Observation you will
4476 understand, that had the Rays been perpendicular to the Glasses, the
4477 Thickness of the Air at these Rings would have been less in the
4478 Proportion of the Radius to the Secant of four Degrees, that is, of
4479 10000 to 10024. Let the Thicknesses found be therefore diminish'd in
4480 this Proportion, and they will become 1/88952 and 1/89063, or (to use
4481 the nearest round Number) the 1/89000th Part of an Inch. This is the
4482 Thickness of the Air at the darkest Part of the first dark Ring made by
4483 perpendicular Rays; and half this Thickness multiplied by the
4484 Progression, 1, 3, 5, 7, 9, 11, &c. gives the Thicknesses of the Air at
4485 the most luminous Parts of all the brightest Rings, _viz._ 1/178000,
4486 3/178000, 5/178000, 7/178000, &c. their arithmetical Means 2/178000,
4487 4/178000, 6/178000, &c. being its Thicknesses at the darkest Parts of
4488 all the dark ones.
4489
4490 _Obs._ 7. The Rings were least, when my Eye was placed perpendicularly
4491 over the Glasses in the Axis of the Rings: And when I view'd them
4492 obliquely they became bigger, continually swelling as I removed my Eye
4493 farther from the Axis. And partly by measuring the Diameter of the same
4494 Circle at several Obliquities of my Eye, partly by other Means, as also
4495 by making use of the two Prisms for very great Obliquities, I found its
4496 Diameter, and consequently the Thickness of the Air at its Perimeter in
4497 all those Obliquities to be very nearly in the Proportions express'd in
4498 this Table.
4499
4500 -------------------+--------------------+----------+----------
4501 Angle of Incidence |Angle of Refraction |Diameter |Thickness
4502 on | into | of the | of the
4503 the Air. | the Air. | Ring. | Air.
4504 -------------------+--------------------+----------+----------
4505 Deg. Min. | | |
4506 | | |
4507 00 00 | 00 00 | 10 | 10
4508 | | |
4509 06 26 | 10 00 | 10-1/13 | 10-2/13
4510 | | |
4511 12 45 | 20 00 | 10-1/3 | 10-2/3
4512 | | |
4513 18 49 | 30 00 | 10-3/4 | 11-1/2
4514 | | |
4515 24 30 | 40 00 | 11-2/5 | 13
4516 | | |
4517 29 37 | 50 00 | 12-1/2 | 15-1/2
4518 | | |
4519 33 58 | 60 00 | 14 | 20
4520 | | |
4521 35 47 | 65 00 | 15-1/4 | 23-1/4
4522 | | |
4523 37 19 | 70 00 | 16-4/5 | 28-1/4
4524 | | |
4525 38 33 | 75 00 | 19-1/4 | 37
4526 | | |
4527 39 27 | 80 00 | 22-6/7 | 52-1/4
4528 | | |
4529 40 00 | 85 00 | 29 | 84-1/12
4530 | | |
4531 40 11 | 90 00 | 35 | 122-1/2
4532 -------------------+--------------------+----------+----------
4533
4534 In the two first Columns are express'd the Obliquities of the incident
4535 and emergent Rays to the Plate of the Air, that is, their Angles of
4536 Incidence and Refraction. In the third Column the Diameter of any
4537 colour'd Ring at those Obliquities is expressed in Parts, of which ten
4538 constitute that Diameter when the Rays are perpendicular. And in the
4539 fourth Column the Thickness of the Air at the Circumference of that Ring
4540 is expressed in Parts, of which also ten constitute its Thickness when
4541 the Rays are perpendicular.
4542
4543 And from these Measures I seem to gather this Rule: That the Thickness
4544 of the Air is proportional to the Secant of an Angle, whose Sine is a
4545 certain mean Proportional between the Sines of Incidence and Refraction.
4546 And that mean Proportional, so far as by these Measures I can determine
4547 it, is the first of an hundred and six arithmetical mean Proportionals
4548 between those Sines counted from the bigger Sine, that is, from the Sine
4549 of Refraction when the Refraction is made out of the Glass into the
4550 Plate of Air, or from the Sine of Incidence when the Refraction is made
4551 out of the Plate of Air into the Glass.
4552
4553 _Obs._ 8. The dark Spot in the middle of the Rings increased also by the
4554 Obliquation of the Eye, although almost insensibly. But, if instead of
4555 the Object-glasses the Prisms were made use of, its Increase was more
4556 manifest when viewed so obliquely that no Colours appear'd about it. It
4557 was least when the Rays were incident most obliquely on the interjacent
4558 Air, and as the obliquity decreased it increased more and more until the
4559 colour'd Rings appear'd, and then decreased again, but not so much as it
4560 increased before. And hence it is evident, that the Transparency was
4561 not only at the absolute Contact of the Glasses, but also where they had
4562 some little Interval. I have sometimes observed the Diameter of that
4563 Spot to be between half and two fifth parts of the Diameter of the
4564 exterior Circumference of the red in the first Circuit or Revolution of
4565 Colours when view'd almost perpendicularly; whereas when view'd
4566 obliquely it hath wholly vanish'd and become opake and white like the
4567 other parts of the Glass; whence it may be collected that the Glasses
4568 did then scarcely, or not at all, touch one another, and that their
4569 Interval at the perimeter of that Spot when view'd perpendicularly was
4570 about a fifth or sixth part of their Interval at the circumference of
4571 the said red.
4572
4573 _Obs._ 9. By looking through the two contiguous Object-glasses, I found
4574 that the interjacent Air exhibited Rings of Colours, as well by
4575 transmitting Light as by reflecting it. The central Spot was now white,
4576 and from it the order of the Colours were yellowish red; black, violet,
4577 blue, white, yellow, red; violet, blue, green, yellow, red, &c. But
4578 these Colours were very faint and dilute, unless when the Light was
4579 trajected very obliquely through the Glasses: For by that means they
4580 became pretty vivid. Only the first yellowish red, like the blue in the
4581 fourth Observation, was so little and faint as scarcely to be discern'd.
4582 Comparing the colour'd Rings made by Reflexion, with these made by
4583 transmission of the Light; I found that white was opposite to black, red
4584 to blue, yellow to violet, and green to a Compound of red and violet.
4585 That is, those parts of the Glass were black when looked through, which
4586 when looked upon appeared white, and on the contrary. And so those which
4587 in one case exhibited blue, did in the other case exhibit red. And the
4588 like of the other Colours. The manner you have represented in the third
4589 Figure, where AB, CD, are the Surfaces of the Glasses contiguous at E,
4590 and the black Lines between them are their Distances in arithmetical
4591 Progression, and the Colours written above are seen by reflected Light,
4592 and those below by Light transmitted (p. 209).
4593
4594 _Obs._ 10. Wetting the Object-glasses a little at their edges, the Water
4595 crept in slowly between them, and the Circles thereby became less and
4596 the Colours more faint: Insomuch that as the Water crept along, one half
4597 of them at which it first arrived would appear broken off from the other
4598 half, and contracted into a less Room. By measuring them I found the
4599 Proportions of their Diameters to the Diameters of the like Circles made
4600 by Air to be about seven to eight, and consequently the Intervals of the
4601 Glasses at like Circles, caused by those two Mediums Water and Air, are
4602 as about three to four. Perhaps it may be a general Rule, That if any
4603 other Medium more or less dense than Water be compress'd between the
4604 Glasses, their Intervals at the Rings caused thereby will be to their
4605 Intervals caused by interjacent Air, as the Sines are which measure the
4606 Refraction made out of that Medium into Air.
4607
4608 _Obs._ 11. When the Water was between the Glasses, if I pressed the
4609 upper Glass variously at its edges to make the Rings move nimbly from
4610 one place to another, a little white Spot would immediately follow the
4611 center of them, which upon creeping in of the ambient Water into that
4612 place would presently vanish. Its appearance was such as interjacent Air
4613 would have caused, and it exhibited the same Colours. But it was not
4614 air, for where any Bubbles of Air were in the Water they would not
4615 vanish. The Reflexion must have rather been caused by a subtiler Medium,
4616 which could recede through the Glasses at the creeping in of the Water.
4617
4618 _Obs._ 12. These Observations were made in the open Air. But farther to
4619 examine the Effects of colour'd Light falling on the Glasses, I darken'd
4620 the Room, and view'd them by Reflexion of the Colours of a Prism cast on
4621 a Sheet of white Paper, my Eye being so placed that I could see the
4622 colour'd Paper by Reflexion in the Glasses, as in a Looking-glass. And
4623 by this means the Rings became distincter and visible to a far greater
4624 number than in the open Air. I have sometimes seen more than twenty of
4625 them, whereas in the open Air I could not discern above eight or nine.
4626
4627 [Illustration: FIG. 3.]
4628
4629 _Obs._ 13. Appointing an Assistant to move the Prism to and fro about
4630 its Axis, that all the Colours might successively fall on that part of
4631 the Paper which I saw by Reflexion from that part of the Glasses, where
4632 the Circles appear'd, so that all the Colours might be successively
4633 reflected from the Circles to my Eye, whilst I held it immovable, I
4634 found the Circles which the red Light made to be manifestly bigger than
4635 those which were made by the blue and violet. And it was very pleasant
4636 to see them gradually swell or contract accordingly as the Colour of the
4637 Light was changed. The Interval of the Glasses at any of the Rings when
4638 they were made by the utmost red Light, was to their Interval at the
4639 same Ring when made by the utmost violet, greater than as 3 to 2, and
4640 less than as 13 to 8. By the most of my Observations it was as 14 to 9.
4641 And this Proportion seem'd very nearly the same in all Obliquities of my
4642 Eye; unless when two Prisms were made use of instead of the
4643 Object-glasses. For then at a certain great obliquity of my Eye, the
4644 Rings made by the several Colours seem'd equal, and at a greater
4645 obliquity those made by the violet would be greater than the same Rings
4646 made by the red: the Refraction of the Prism in this case causing the
4647 most refrangible Rays to fall more obliquely on that plate of the Air
4648 than the least refrangible ones. Thus the Experiment succeeded in the
4649 colour'd Light, which was sufficiently strong and copious to make the
4650 Rings sensible. And thence it may be gather'd, that if the most
4651 refrangible and least refrangible Rays had been copious enough to make
4652 the Rings sensible without the mixture of other Rays, the Proportion
4653 which here was 14 to 9 would have been a little greater, suppose 14-1/4
4654 or 14-1/3 to 9.
4655
4656 _Obs._ 14. Whilst the Prism was turn'd about its Axis with an uniform
4657 Motion, to make all the several Colours fall successively upon the
4658 Object-glasses, and thereby to make the Rings contract and dilate: The
4659 Contraction or Dilatation of each Ring thus made by the variation of its
4660 Colour was swiftest in the red, and slowest in the violet, and in the
4661 intermediate Colours it had intermediate degrees of Celerity. Comparing
4662 the quantity of Contraction and Dilatation made by all the degrees of
4663 each Colour, I found that it was greatest in the red; less in the
4664 yellow, still less in the blue, and least in the violet. And to make as
4665 just an Estimation as I could of the Proportions of their Contractions
4666 or Dilatations, I observ'd that the whole Contraction or Dilatation of
4667 the Diameter of any Ring made by all the degrees of red, was to that of
4668 the Diameter of the same Ring made by all the degrees of violet, as
4669 about four to three, or five to four, and that when the Light was of the
4670 middle Colour between yellow and green, the Diameter of the Ring was
4671 very nearly an arithmetical Mean between the greatest Diameter of the
4672 same Ring made by the outmost red, and the least Diameter thereof made
4673 by the outmost violet: Contrary to what happens in the Colours of the
4674 oblong Spectrum made by the Refraction of a Prism, where the red is most
4675 contracted, the violet most expanded, and in the midst of all the
4676 Colours is the Confine of green and blue. And hence I seem to collect
4677 that the thicknesses of the Air between the Glasses there, where the
4678 Ring is successively made by the limits of the five principal Colours
4679 (red, yellow, green, blue, violet) in order (that is, by the extreme
4680 red, by the limit of red and yellow in the middle of the orange, by the
4681 limit of yellow and green, by the limit of green and blue, by the limit
4682 of blue and violet in the middle of the indigo, and by the extreme
4683 violet) are to one another very nearly as the sixth lengths of a Chord
4684 which found the Notes in a sixth Major, _sol_, _la_, _mi_, _fa_, _sol_,
4685 _la_. But it agrees something better with the Observation to say, that
4686 the thicknesses of the Air between the Glasses there, where the Rings
4687 are successively made by the limits of the seven Colours, red, orange,
4688 yellow, green, blue, indigo, violet in order, are to one another as the
4689 Cube Roots of the Squares of the eight lengths of a Chord, which found
4690 the Notes in an eighth, _sol_, _la_, _fa_, _sol_, _la_, _mi_, _fa_,
4691 _sol_; that is, as the Cube Roots of the Squares of the Numbers, 1, 8/9,
4692 5/6, 3/4, 2/3, 3/5, 9/16, 1/2.
4693
4694 _Obs._ 15. These Rings were not of various Colours like those made in
4695 the open Air, but appeared all over of that prismatick Colour only with
4696 which they were illuminated. And by projecting the prismatick Colours
4697 immediately upon the Glasses, I found that the Light which fell on the
4698 dark Spaces which were between the Colour'd Rings was transmitted
4699 through the Glasses without any variation of Colour. For on a white
4700 Paper placed behind, it would paint Rings of the same Colour with those
4701 which were reflected, and of the bigness of their immediate Spaces. And
4702 from thence the origin of these Rings is manifest; namely, that the Air
4703 between the Glasses, according to its various thickness, is disposed in
4704 some places to reflect, and in others to transmit the Light of any one
4705 Colour (as you may see represented in the fourth Figure) and in the same
4706 place to reflect that of one Colour where it transmits that of another.
4707
4708 [Illustration: FIG. 4.]
4709
4710 _Obs._ 16. The Squares of the Diameters of these Rings made by any
4711 prismatick Colour were in arithmetical Progression, as in the fifth
4712 Observation. And the Diameter of the sixth Circle, when made by the
4713 citrine yellow, and viewed almost perpendicularly was about 58/100 parts
4714 of an Inch, or a little less, agreeable to the sixth Observation.
4715
4716 The precedent Observations were made with a rarer thin Medium,
4717 terminated by a denser, such as was Air or Water compress'd between two
4718 Glasses. In those that follow are set down the Appearances of a denser
4719 Medium thin'd within a rarer, such as are Plates of Muscovy Glass,
4720 Bubbles of Water, and some other thin Substances terminated on all sides
4721 with air.
4722
4723 _Obs._ 17. If a Bubble be blown with Water first made tenacious by
4724 dissolving a little Soap in it, 'tis a common Observation, that after a
4725 while it will appear tinged with a great variety of Colours. To defend
4726 these Bubbles from being agitated by the external Air (whereby their
4727 Colours are irregularly moved one among another, so that no accurate
4728 Observation can be made of them,) as soon as I had blown any of them I
4729 cover'd it with a clear Glass, and by that means its Colours emerged in
4730 a very regular order, like so many concentrick Rings encompassing the
4731 top of the Bubble. And as the Bubble grew thinner by the continual
4732 subsiding of the Water, these Rings dilated slowly and overspread the
4733 whole Bubble, descending in order to the bottom of it, where they
4734 vanish'd successively. In the mean while, after all the Colours were
4735 emerged at the top, there grew in the center of the Rings a small round
4736 black Spot, like that in the first Observation, which continually
4737 dilated it self till it became sometimes more than 1/2 or 3/4 of an Inch
4738 in breadth before the Bubble broke. At first I thought there had been no
4739 Light reflected from the Water in that place, but observing it more
4740 curiously, I saw within it several smaller round Spots, which appeared
4741 much blacker and darker than the rest, whereby I knew that there was
4742 some Reflexion at the other places which were not so dark as those
4743 Spots. And by farther Tryal I found that I could see the Images of some
4744 things (as of a Candle or the Sun) very faintly reflected, not only from
4745 the great black Spot, but also from the little darker Spots which were
4746 within it.
4747
4748 Besides the aforesaid colour'd Rings there would often appear small
4749 Spots of Colours, ascending and descending up and down the sides of the
4750 Bubble, by reason of some Inequalities in the subsiding of the Water.
4751 And sometimes small black Spots generated at the sides would ascend up
4752 to the larger black Spot at the top of the Bubble, and unite with it.
4753
4754 _Obs._ 18. Because the Colours of these Bubbles were more extended and
4755 lively than those of the Air thinn'd between two Glasses, and so more
4756 easy to be distinguish'd, I shall here give you a farther description of
4757 their order, as they were observ'd in viewing them by Reflexion of the
4758 Skies when of a white Colour, whilst a black substance was placed
4759 behind the Bubble. And they were these, red, blue; red, blue; red, blue;
4760 red, green; red, yellow, green, blue, purple; red, yellow, green, blue,
4761 violet; red, yellow, white, blue, black.
4762
4763 The three first Successions of red and blue were very dilute and dirty,
4764 especially the first, where the red seem'd in a manner to be white.
4765 Among these there was scarce any other Colour sensible besides red and
4766 blue, only the blues (and principally the second blue) inclined a little
4767 to green.
4768
4769 The fourth red was also dilute and dirty, but not so much as the former
4770 three; after that succeeded little or no yellow, but a copious green,
4771 which at first inclined a little to yellow, and then became a pretty
4772 brisk and good willow green, and afterwards changed to a bluish Colour;
4773 but there succeeded neither blue nor violet.
4774
4775 The fifth red at first inclined very much to purple, and afterwards
4776 became more bright and brisk, but yet not very pure. This was succeeded
4777 with a very bright and intense yellow, which was but little in quantity,
4778 and soon chang'd to green: But that green was copious and something more
4779 pure, deep and lively, than the former green. After that follow'd an
4780 excellent blue of a bright Sky-colour, and then a purple, which was less
4781 in quantity than the blue, and much inclined to red.
4782
4783 The sixth red was at first of a very fair and lively scarlet, and soon
4784 after of a brighter Colour, being very pure and brisk, and the best of
4785 all the reds. Then after a lively orange follow'd an intense bright and
4786 copious yellow, which was also the best of all the yellows, and this
4787 changed first to a greenish yellow, and then to a greenish blue; but the
4788 green between the yellow and the blue, was very little and dilute,
4789 seeming rather a greenish white than a green. The blue which succeeded
4790 became very good, and of a very bright Sky-colour, but yet something
4791 inferior to the former blue; and the violet was intense and deep with
4792 little or no redness in it. And less in quantity than the blue.
4793
4794 In the last red appeared a tincture of scarlet next to violet, which
4795 soon changed to a brighter Colour, inclining to an orange; and the
4796 yellow which follow'd was at first pretty good and lively, but
4797 afterwards it grew more dilute until by degrees it ended in perfect
4798 whiteness. And this whiteness, if the Water was very tenacious and
4799 well-temper'd, would slowly spread and dilate it self over the greater
4800 part of the Bubble; continually growing paler at the top, where at
4801 length it would crack in many places, and those cracks, as they dilated,
4802 would appear of a pretty good, but yet obscure and dark Sky-colour; the
4803 white between the blue Spots diminishing, until it resembled the Threds
4804 of an irregular Net-work, and soon after vanish'd, and left all the
4805 upper part of the Bubble of the said dark blue Colour. And this Colour,
4806 after the aforesaid manner, dilated it self downwards, until sometimes
4807 it hath overspread the whole Bubble. In the mean while at the top, which
4808 was of a darker blue than the bottom, and appear'd also full of many
4809 round blue Spots, something darker than the rest, there would emerge
4810 one or more very black Spots, and within those, other Spots of an
4811 intenser blackness, which I mention'd in the former Observation; and
4812 these continually dilated themselves until the Bubble broke.
4813
4814 If the Water was not very tenacious, the black Spots would break forth
4815 in the white, without any sensible intervention of the blue. And
4816 sometimes they would break forth within the precedent yellow, or red, or
4817 perhaps within the blue of the second order, before the intermediate
4818 Colours had time to display themselves.
4819
4820 By this description you may perceive how great an affinity these Colours
4821 have with those of Air described in the fourth Observation, although set
4822 down in a contrary order, by reason that they begin to appear when the
4823 Bubble is thickest, and are most conveniently reckon'd from the lowest
4824 and thickest part of the Bubble upwards.
4825
4826 _Obs._ 19. Viewing in several oblique Positions of my Eye the Rings of
4827 Colours emerging on the top of the Bubble, I found that they were
4828 sensibly dilated by increasing the obliquity, but yet not so much by far
4829 as those made by thinn'd Air in the seventh Observation. For there they
4830 were dilated so much as, when view'd most obliquely, to arrive at a part
4831 of the Plate more than twelve times thicker than that where they
4832 appear'd when viewed perpendicularly; whereas in this case the thickness
4833 of the Water, at which they arrived when viewed most obliquely, was to
4834 that thickness which exhibited them by perpendicular Rays, something
4835 less than as 8 to 5. By the best of my Observations it was between 15
4836 and 15-1/2 to 10; an increase about 24 times less than in the other
4837 case.
4838
4839 Sometimes the Bubble would become of an uniform thickness all over,
4840 except at the top of it near the black Spot, as I knew, because it would
4841 exhibit the same appearance of Colours in all Positions of the Eye. And
4842 then the Colours which were seen at its apparent circumference by the
4843 obliquest Rays, would be different from those that were seen in other
4844 places, by Rays less oblique to it. And divers Spectators might see the
4845 same part of it of differing Colours, by viewing it at very differing
4846 Obliquities. Now observing how much the Colours at the same places of
4847 the Bubble, or at divers places of equal thickness, were varied by the
4848 several Obliquities of the Rays; by the assistance of the 4th, 14th,
4849 16th and 18th Observations, as they are hereafter explain'd, I collect
4850 the thickness of the Water requisite to exhibit any one and the same
4851 Colour, at several Obliquities, to be very nearly in the Proportion
4852 expressed in this Table.
4853
4854 -----------------+------------------+----------------
4855 Incidence on | Refraction into | Thickness of
4856 the Water. | the Water. | the Water.
4857 -----------------+------------------+----------------
4858 Deg. Min. | Deg. Min. |
4859 | |
4860 00 00 | 00 00 | 10
4861 | |
4862 15 00 | 11 11 | 10-1/4
4863 | |
4864 30 00 | 22 1 | 10-4/5
4865 | |
4866 45 00 | 32 2 | 11-4/5
4867 | |
4868 60 00 | 40 30 | 13
4869 | |
4870 75 00 | 46 25 | 14-1/2
4871 | |
4872 90 00 | 48 35 | 15-1/5
4873 -----------------+------------------+----------------
4874
4875 In the two first Columns are express'd the Obliquities of the Rays to
4876 the Superficies of the Water, that is, their Angles of Incidence and
4877 Refraction. Where I suppose, that the Sines which measure them are in
4878 round Numbers, as 3 to 4, though probably the Dissolution of Soap in the
4879 Water, may a little alter its refractive Virtue. In the third Column,
4880 the Thickness of the Bubble, at which any one Colour is exhibited in
4881 those several Obliquities, is express'd in Parts, of which ten
4882 constitute its Thickness when the Rays are perpendicular. And the Rule
4883 found by the seventh Observation agrees well with these Measures, if
4884 duly apply'd; namely, that the Thickness of a Plate of Water requisite
4885 to exhibit one and the same Colour at several Obliquities of the Eye, is
4886 proportional to the Secant of an Angle, whose Sine is the first of an
4887 hundred and six arithmetical mean Proportionals between the Sines of
4888 Incidence and Refraction counted from the lesser Sine, that is, from the
4889 Sine of Refraction when the Refraction is made out of Air into Water,
4890 otherwise from the Sine of Incidence.
4891
4892 I have sometimes observ'd, that the Colours which arise on polish'd
4893 Steel by heating it, or on Bell-metal, and some other metalline
4894 Substances, when melted and pour'd on the Ground, where they may cool in
4895 the open Air, have, like the Colours of Water-bubbles, been a little
4896 changed by viewing them at divers Obliquities, and particularly that a
4897 deep blue, or violet, when view'd very obliquely, hath been changed to a
4898 deep red. But the Changes of these Colours are not so great and
4899 sensible as of those made by Water. For the Scoria, or vitrified Part of
4900 the Metal, which most Metals when heated or melted do continually
4901 protrude, and send out to their Surface, and which by covering the
4902 Metals in form of a thin glassy Skin, causes these Colours, is much
4903 denser than Water; and I find that the Change made by the Obliquation of
4904 the Eye is least in Colours of the densest thin Substances.
4905
4906 _Obs._ 20. As in the ninth Observation, so here, the Bubble, by
4907 transmitted Light, appear'd of a contrary Colour to that, which it
4908 exhibited by Reflexion. Thus when the Bubble being look'd on by the
4909 Light of the Clouds reflected from it, seemed red at its apparent
4910 Circumference, if the Clouds at the same time, or immediately after,
4911 were view'd through it, the Colour at its Circumference would be blue.
4912 And, on the contrary, when by reflected Light it appeared blue, it would
4913 appear red by transmitted Light.
4914
4915 _Obs._ 21. By wetting very thin Plates of _Muscovy_ Glass, whose
4916 thinness made the like Colours appear, the Colours became more faint and
4917 languid, especially by wetting the Plates on that side opposite to the
4918 Eye: But I could not perceive any variation of their Species. So then
4919 the thickness of a Plate requisite to produce any Colour, depends only
4920 on the density of the Plate, and not on that of the ambient Medium. And
4921 hence, by the 10th and 16th Observations, may be known the thickness
4922 which Bubbles of Water, or Plates of _Muscovy_ Glass, or other
4923 Substances, have at any Colour produced by them.
4924
4925 _Obs._ 22. A thin transparent Body, which is denser than its ambient
4926 Medium, exhibits more brisk and vivid Colours than that which is so much
4927 rarer; as I have particularly observed in the Air and Glass. For blowing
4928 Glass very thin at a Lamp Furnace, those Plates encompassed with Air did
4929 exhibit Colours much more vivid than those of Air made thin between two
4930 Glasses.
4931
4932 _Obs._ 23. Comparing the quantity of Light reflected from the several
4933 Rings, I found that it was most copious from the first or inmost, and in
4934 the exterior Rings became gradually less and less. Also the whiteness of
4935 the first Ring was stronger than that reflected from those parts of the
4936 thin Medium or Plate which were without the Rings; as I could manifestly
4937 perceive by viewing at a distance the Rings made by the two
4938 Object-glasses; or by comparing two Bubbles of Water blown at distant
4939 Times, in the first of which the Whiteness appear'd, which succeeded all
4940 the Colours, and in the other, the Whiteness which preceded them all.
4941
4942 _Obs._ 24. When the two Object-glasses were lay'd upon one another, so
4943 as to make the Rings of the Colours appear, though with my naked Eye I
4944 could not discern above eight or nine of those Rings, yet by viewing
4945 them through a Prism I have seen a far greater Multitude, insomuch that
4946 I could number more than forty, besides many others, that were so very
4947 small and close together, that I could not keep my Eye steady on them
4948 severally so as to number them, but by their Extent I have sometimes
4949 estimated them to be more than an hundred. And I believe the Experiment
4950 may be improved to the Discovery of far greater Numbers. For they seem
4951 to be really unlimited, though visible only so far as they can be
4952 separated by the Refraction of the Prism, as I shall hereafter explain.
4953
4954 [Illustration: FIG. 5.]
4955
4956 But it was but one side of these Rings, namely, that towards which the
4957 Refraction was made, which by that Refraction was render'd distinct, and
4958 the other side became more confused than when view'd by the naked Eye,
4959 insomuch that there I could not discern above one or two, and sometimes
4960 none of those Rings, of which I could discern eight or nine with my
4961 naked Eye. And their Segments or Arcs, which on the other side appear'd
4962 so numerous, for the most part exceeded not the third Part of a Circle.
4963 If the Refraction was very great, or the Prism very distant from the
4964 Object-glasses, the middle Part of those Arcs became also confused, so
4965 as to disappear and constitute an even Whiteness, whilst on either side
4966 their Ends, as also the whole Arcs farthest from the Center, became
4967 distincter than before, appearing in the Form as you see them design'd
4968 in the fifth Figure.
4969
4970 The Arcs, where they seem'd distinctest, were only white and black
4971 successively, without any other Colours intermix'd. But in other Places
4972 there appeared Colours, whose Order was inverted by the refraction in
4973 such manner, that if I first held the Prism very near the
4974 Object-glasses, and then gradually removed it farther off towards my
4975 Eye, the Colours of the 2d, 3d, 4th, and following Rings, shrunk towards
4976 the white that emerged between them, until they wholly vanish'd into it
4977 at the middle of the Arcs, and afterwards emerged again in a contrary
4978 Order. But at the Ends of the Arcs they retain'd their Order unchanged.
4979
4980 I have sometimes so lay'd one Object-glass upon the other, that to the
4981 naked Eye they have all over seem'd uniformly white, without the least
4982 Appearance of any of the colour'd Rings; and yet by viewing them through
4983 a Prism, great Multitudes of those Rings have discover'd themselves. And
4984 in like manner Plates of _Muscovy_ Glass, and Bubbles of Glass blown at
4985 a Lamp-Furnace, which were not so thin as to exhibit any Colours to the
4986 naked Eye, have through the Prism exhibited a great Variety of them
4987 ranged irregularly up and down in the Form of Waves. And so Bubbles of
4988 Water, before they began to exhibit their Colours to the naked Eye of a
4989 Bystander, have appeared through a Prism, girded about with many
4990 parallel and horizontal Rings; to produce which Effect, it was necessary
4991 to hold the Prism parallel, or very nearly parallel to the Horizon, and
4992 to dispose it so that the Rays might be refracted upwards.
4993
4994
4995
4996
4997 THE
4998
4999 SECOND BOOK
5000
5001 OF
5002
5003 OPTICKS
5004
5005
5006 _PART II._
5007
5008 _Remarks upon the foregoing Observations._
5009
5010
5011 Having given my Observations of these Colours, before I make use of them
5012 to unfold the Causes of the Colours of natural Bodies, it is convenient
5013 that by the simplest of them, such as are the 2d, 3d, 4th, 9th, 12th,
5014 18th, 20th, and 24th, I first explain the more compounded. And first to
5015 shew how the Colours in the fourth and eighteenth Observations are
5016 produced, let there be taken in any Right Line from the Point Y, [in
5017 _Fig._ 6.] the Lengths YA, YB, YC, YD, YE, YF, YG, YH, in proportion to
5018 one another, as the Cube-Roots of the Squares of the Numbers, 1/2, 9/16,
5019 3/5, 2/3, 3/4, 5/6, 8/9, 1, whereby the Lengths of a Musical Chord to
5020 sound all the Notes in an eighth are represented; that is, in the
5021 Proportion of the Numbers 6300, 6814, 7114, 7631, 8255, 8855, 9243,
5022 10000. And at the Points A, B, C, D, E, F, G, H, let Perpendiculars
5023 A[Greek: a], B[Greek: b], &c. be erected, by whose Intervals the Extent
5024 of the several Colours set underneath against them, is to be
5025 represented. Then divide the Line _A[Greek: a]_ in such Proportion as
5026 the Numbers 1, 2, 3, 5, 6, 7, 9, 10, 11, &c. set at the Points of
5027 Division denote. And through those Divisions from Y draw Lines 1I, 2K,
5028 3L, 5M, 6N, 7O, &c.
5029
5030 Now, if A2 be supposed to represent the Thickness of any thin
5031 transparent Body, at which the outmost Violet is most copiously
5032 reflected in the first Ring, or Series of Colours, then by the 13th
5033 Observation, HK will represent its Thickness, at which the utmost Red is
5034 most copiously reflected in the same Series. Also by the 5th and 16th
5035 Observations, A6 and HN will denote the Thicknesses at which those
5036 extreme Colours are most copiously reflected in the second Series, and
5037 A10 and HQ the Thicknesses at which they are most copiously reflected in
5038 the third Series, and so on. And the Thickness at which any of the
5039 intermediate Colours are reflected most copiously, will, according to
5040 the 14th Observation, be defined by the distance of the Line AH from the
5041 intermediate parts of the Lines 2K, 6N, 10Q, &c. against which the Names
5042 of those Colours are written below.
5043
5044 [Illustration: FIG. 6.]
5045
5046 But farther, to define the Latitude of these Colours in each Ring or
5047 Series, let A1 design the least thickness, and A3 the greatest
5048 thickness, at which the extreme violet in the first Series is reflected,
5049 and let HI, and HL, design the like limits for the extreme red, and let
5050 the intermediate Colours be limited by the intermediate parts of the
5051 Lines 1I, and 3L, against which the Names of those Colours are written,
5052 and so on: But yet with this caution, that the Reflexions be supposed
5053 strongest at the intermediate Spaces, 2K, 6N, 10Q, &c. and from thence
5054 to decrease gradually towards these limits, 1I, 3L, 5M, 7O, &c. on
5055 either side; where you must not conceive them to be precisely limited,
5056 but to decay indefinitely. And whereas I have assign'd the same Latitude
5057 to every Series, I did it, because although the Colours in the first
5058 Series seem to be a little broader than the rest, by reason of a
5059 stronger Reflexion there, yet that inequality is so insensible as
5060 scarcely to be determin'd by Observation.
5061
5062 Now according to this Description, conceiving that the Rays originally
5063 of several Colours are by turns reflected at the Spaces 1I, L3, 5M, O7,
5064 9PR11, &c. and transmitted at the Spaces AHI1, 3LM5, 7OP9, &c. it is
5065 easy to know what Colour must in the open Air be exhibited at any
5066 thickness of a transparent thin Body. For if a Ruler be applied parallel
5067 to AH, at that distance from it by which the thickness of the Body is
5068 represented, the alternate Spaces 1IL3, 5MO7, &c. which it crosseth will
5069 denote the reflected original Colours, of which the Colour exhibited in
5070 the open Air is compounded. Thus if the constitution of the green in the
5071 third Series of Colours be desired, apply the Ruler as you see at
5072 [Greek: prsph], and by its passing through some of the blue at [Greek:
5073 p] and yellow at [Greek: s], as well as through the green at [Greek: r],
5074 you may conclude that the green exhibited at that thickness of the Body
5075 is principally constituted of original green, but not without a mixture
5076 of some blue and yellow.
5077
5078 By this means you may know how the Colours from the center of the Rings
5079 outward ought to succeed in order as they were described in the 4th and
5080 18th Observations. For if you move the Ruler gradually from AH through
5081 all distances, having pass'd over the first Space which denotes little
5082 or no Reflexion to be made by thinnest Substances, it will first arrive
5083 at 1 the violet, and then very quickly at the blue and green, which
5084 together with that violet compound blue, and then at the yellow and red,
5085 by whose farther addition that blue is converted into whiteness, which
5086 whiteness continues during the transit of the edge of the Ruler from I
5087 to 3, and after that by the successive deficience of its component
5088 Colours, turns first to compound yellow, and then to red, and last of
5089 all the red ceaseth at L. Then begin the Colours of the second Series,
5090 which succeed in order during the transit of the edge of the Ruler from
5091 5 to O, and are more lively than before, because more expanded and
5092 severed. And for the same reason instead of the former white there
5093 intercedes between the blue and yellow a mixture of orange, yellow,
5094 green, blue and indigo, all which together ought to exhibit a dilute and
5095 imperfect green. So the Colours of the third Series all succeed in
5096 order; first, the violet, which a little interferes with the red of the
5097 second order, and is thereby inclined to a reddish purple; then the blue
5098 and green, which are less mix'd with other Colours, and consequently
5099 more lively than before, especially the green: Then follows the yellow,
5100 some of which towards the green is distinct and good, but that part of
5101 it towards the succeeding red, as also that red is mix'd with the violet
5102 and blue of the fourth Series, whereby various degrees of red very much
5103 inclining to purple are compounded. This violet and blue, which should
5104 succeed this red, being mixed with, and hidden in it, there succeeds a
5105 green. And this at first is much inclined to blue, but soon becomes a
5106 good green, the only unmix'd and lively Colour in this fourth Series.
5107 For as it verges towards the yellow, it begins to interfere with the
5108 Colours of the fifth Series, by whose mixture the succeeding yellow and
5109 red are very much diluted and made dirty, especially the yellow, which
5110 being the weaker Colour is scarce able to shew it self. After this the
5111 several Series interfere more and more, and their Colours become more
5112 and more intermix'd, till after three or four more revolutions (in which
5113 the red and blue predominate by turns) all sorts of Colours are in all
5114 places pretty equally blended, and compound an even whiteness.
5115
5116 And since by the 15th Observation the Rays endued with one Colour are
5117 transmitted, where those of another Colour are reflected, the reason of
5118 the Colours made by the transmitted Light in the 9th and 20th
5119 Observations is from hence evident.
5120
5121 If not only the Order and Species of these Colours, but also the precise
5122 thickness of the Plate, or thin Body at which they are exhibited, be
5123 desired in parts of an Inch, that may be also obtained by assistance of
5124 the 6th or 16th Observations. For according to those Observations the
5125 thickness of the thinned Air, which between two Glasses exhibited the
5126 most luminous parts of the first six Rings were 1/178000, 3/178000,
5127 5/178000, 7/178000, 9/178000, 11/178000 parts of an Inch. Suppose the
5128 Light reflected most copiously at these thicknesses be the bright
5129 citrine yellow, or confine of yellow and orange, and these thicknesses
5130 will be F[Greek: l], F[Greek: m], F[Greek: u], F[Greek: x], F[Greek: o],
5131 F[Greek: t]. And this being known, it is easy to determine what
5132 thickness of Air is represented by G[Greek: ph], or by any other
5133 distance of the Ruler from AH.
5134
5135 But farther, since by the 10th Observation the thickness of Air was to
5136 the thickness of Water, which between the same Glasses exhibited the
5137 same Colour, as 4 to 3, and by the 21st Observation the Colours of thin
5138 Bodies are not varied by varying the ambient Medium; the thickness of a
5139 Bubble of Water, exhibiting any Colour, will be 3/4 of the thickness of
5140 Air producing the same Colour. And so according to the same 10th and
5141 21st Observations, the thickness of a Plate of Glass, whose Refraction
5142 of the mean refrangible Ray, is measured by the proportion of the Sines
5143 31 to 20, may be 20/31 of the thickness of Air producing the same
5144 Colours; and the like of other Mediums. I do not affirm, that this
5145 proportion of 20 to 31, holds in all the Rays; for the Sines of other
5146 sorts of Rays have other Proportions. But the differences of those
5147 Proportions are so little that I do not here consider them. On these
5148 Grounds I have composed the following Table, wherein the thickness of
5149 Air, Water, and Glass, at which each Colour is most intense and
5150 specifick, is expressed in parts of an Inch divided into ten hundred
5151 thousand equal parts.
5152
5153 Now if this Table be compared with the 6th Scheme, you will there see
5154 the constitution of each Colour, as to its Ingredients, or the original
5155 Colours of which it is compounded, and thence be enabled to judge of its
5156 Intenseness or Imperfection; which may suffice in explication of the 4th
5157 and 18th Observations, unless it be farther desired to delineate the
5158 manner how the Colours appear, when the two Object-glasses are laid upon
5159 one another. To do which, let there be described a large Arc of a
5160 Circle, and a streight Line which may touch that Arc, and parallel to
5161 that Tangent several occult Lines, at such distances from it, as the
5162 Numbers set against the several Colours in the Table denote. For the
5163 Arc, and its Tangent, will represent the Superficies of the Glasses
5164 terminating the interjacent Air; and the places where the occult Lines
5165 cut the Arc will show at what distances from the center, or Point of
5166 contact, each Colour is reflected.
5167
5168 _The thickness of colour'd Plates and Particles of_
5169 _____________|_______________
5170 / \
5171 Air. Water. Glass.
5172 |---------+----------+----------+
5173 {Very black | 1/2 | 3/8 | 10/31 |
5174 {Black | 1 | 3/4 | 20/31 |
5175 {Beginning of | | | |
5176 { Black | 2 | 1-1/2 | 1-2/7 |
5177 Their Colours of the {Blue | 2-2/5 | 1-4/5 | 1-11/22 |
5178 first Order, {White | 5-1/4 | 3-7/8 | 3-2/5 |
5179 {Yellow | 7-1/9 | 5-1/3 | 4-3/5 |
5180 {Orange | 8 | 6 | 5-1/6 |
5181 {Red | 9 | 6-3/4 | 5-4/5 |
5182 |---------+----------+----------|
5183 {Violet | 11-1/6 | 8-3/8 | 7-1/5 |
5184 {Indigo | 12-5/6 | 9-5/8 | 8-2/11 |
5185 {Blue | 14 | 10-1/2 | 9 |
5186 {Green | 15-1/8 | 11-2/3 | 9-5/7 |
5187 Of the second order, {Yellow | 16-2/7 | 12-1/5 | 10-2/5 |
5188 {Orange | 17-2/9 | 13 | 11-1/9 |
5189 {Bright red | 18-1/3 | 13-3/4 | 11-5/6 |
5190 {Scarlet | 19-2/3 | 14-3/4 | 12-2/3 |
5191 |---------+----------+----------|
5192 {Purple | 21 | 15-3/4 | 13-11/20 |
5193 {Indigo | 22-1/10 | 16-4/7 | 14-1/4 |
5194 {Blue | 23-2/5 | 17-11/20 | 15-1/10 |
5195 Of the third Order, {Green | 25-1/5 | 18-9/10 | 16-1/4 |
5196 {Yellow | 27-1/7 | 20-1/3 | 17-1/2 |
5197 {Red | 29 | 21-3/4 | 18-5/7 |
5198 {Bluish red | 32 | 24 | 20-2/3 |
5199 |---------+----------+----------|
5200 {Bluish green | 34 | 25-1/2 | 22 |
5201 {Green | 35-2/7 | 26-1/2 | 22-3/4 |
5202 Of the fourth Order, {Yellowish green | 36 | 27 | 23-2/9 |
5203 {Red | 40-1/3 | 30-1/4 | 26 |
5204 |---------+----------+----------|
5205 {Greenish blue | 46 | 34-1/2 | 29-2/3 |
5206 Of the fifth Order, {Red | 52-1/2 | 39-3/8 | 34 |
5207 |---------+----------+----------|
5208 {Greenish blue | 58-3/4 | 44 | 38 |
5209 Of the sixth Order, {Red | 65 | 48-3/4 | 42 |
5210 |---------+----------+----------|
5211 Of the seventh Order, {Greenish blue | 71 | 53-1/4 | 45-4/5 |
5212 {Ruddy White | 77 | 57-3/4 | 49-2/3 |
5213 |---------+----------+----------|
5214
5215 There are also other Uses of this Table: For by its assistance the
5216 thickness of the Bubble in the 19th Observation was determin'd by the
5217 Colours which it exhibited. And so the bigness of the parts of natural
5218 Bodies may be conjectured by their Colours, as shall be hereafter shewn.
5219 Also, if two or more very thin Plates be laid one upon another, so as to
5220 compose one Plate equalling them all in thickness, the resulting Colour
5221 may be hereby determin'd. For instance, Mr. _Hook_ observed, as is
5222 mentioned in his _Micrographia_, that a faint yellow Plate of _Muscovy_
5223 Glass laid upon a blue one, constituted a very deep purple. The yellow
5224 of the first Order is a faint one, and the thickness of the Plate
5225 exhibiting it, according to the Table is 4-3/5, to which add 9, the
5226 thickness exhibiting blue of the second Order, and the Sum will be
5227 13-3/5, which is the thickness exhibiting the purple of the third Order.
5228
5229 To explain, in the next place, the circumstances of the 2d and 3d
5230 Observations; that is, how the Rings of the Colours may (by turning the
5231 Prisms about their common Axis the contrary way to that expressed in
5232 those Observations) be converted into white and black Rings, and
5233 afterwards into Rings of Colours again, the Colours of each Ring lying
5234 now in an inverted order; it must be remember'd, that those Rings of
5235 Colours are dilated by the obliquation of the Rays to the Air which
5236 intercedes the Glasses, and that according to the Table in the 7th
5237 Observation, their Dilatation or Increase of their Diameter is most
5238 manifest and speedy when they are obliquest. Now the Rays of yellow
5239 being more refracted by the first Superficies of the said Air than those
5240 of red, are thereby made more oblique to the second Superficies, at
5241 which they are reflected to produce the colour'd Rings, and consequently
5242 the yellow Circle in each Ring will be more dilated than the red; and
5243 the Excess of its Dilatation will be so much the greater, by how much
5244 the greater is the obliquity of the Rays, until at last it become of
5245 equal extent with the red of the same Ring. And for the same reason the
5246 green, blue and violet, will be also so much dilated by the still
5247 greater obliquity of their Rays, as to become all very nearly of equal
5248 extent with the red, that is, equally distant from the center of the
5249 Rings. And then all the Colours of the same Ring must be co-incident,
5250 and by their mixture exhibit a white Ring. And these white Rings must
5251 have black and dark Rings between them, because they do not spread and
5252 interfere with one another, as before. And for that reason also they
5253 must become distincter, and visible to far greater numbers. But yet the
5254 violet being obliquest will be something more dilated, in proportion to
5255 its extent, than the other Colours, and so very apt to appear at the
5256 exterior Verges of the white.
5257
5258 Afterwards, by a greater obliquity of the Rays, the violet and blue
5259 become more sensibly dilated than the red and yellow, and so being
5260 farther removed from the center of the Rings, the Colours must emerge
5261 out of the white in an order contrary to that which they had before; the
5262 violet and blue at the exterior Limbs of each Ring, and the red and
5263 yellow at the interior. And the violet, by reason of the greatest
5264 obliquity of its Rays, being in proportion most of all expanded, will
5265 soonest appear at the exterior Limb of each white Ring, and become more
5266 conspicuous than the rest. And the several Series of Colours belonging
5267 to the several Rings, will, by their unfolding and spreading, begin
5268 again to interfere, and thereby render the Rings less distinct, and not
5269 visible to so great numbers.
5270
5271 If instead of the Prisms the Object-glasses be made use of, the Rings
5272 which they exhibit become not white and distinct by the obliquity of the
5273 Eye, by reason that the Rays in their passage through that Air which
5274 intercedes the Glasses are very nearly parallel to those Lines in which
5275 they were first incident on the Glasses, and consequently the Rays
5276 endued with several Colours are not inclined one more than another to
5277 that Air, as it happens in the Prisms.
5278
5279 There is yet another circumstance of these Experiments to be consider'd,
5280 and that is why the black and white Rings which when view'd at a
5281 distance appear distinct, should not only become confused by viewing
5282 them near at hand, but also yield a violet Colour at both the edges of
5283 every white Ring. And the reason is, that the Rays which enter the Eye
5284 at several parts of the Pupil, have several Obliquities to the Glasses,
5285 and those which are most oblique, if consider'd apart, would represent
5286 the Rings bigger than those which are the least oblique. Whence the
5287 breadth of the Perimeter of every white Ring is expanded outwards by the
5288 obliquest Rays, and inwards by the least oblique. And this Expansion is
5289 so much the greater by how much the greater is the difference of the
5290 Obliquity; that is, by how much the Pupil is wider, or the Eye nearer to
5291 the Glasses. And the breadth of the violet must be most expanded,
5292 because the Rays apt to excite a Sensation of that Colour are most
5293 oblique to a second or farther Superficies of the thinn'd Air at which
5294 they are reflected, and have also the greatest variation of Obliquity,
5295 which makes that Colour soonest emerge out of the edges of the white.
5296 And as the breadth of every Ring is thus augmented, the dark Intervals
5297 must be diminish'd, until the neighbouring Rings become continuous, and
5298 are blended, the exterior first, and then those nearer the center; so
5299 that they can no longer be distinguish'd apart, but seem to constitute
5300 an even and uniform whiteness.
5301
5302 Among all the Observations there is none accompanied with so odd
5303 circumstances as the twenty-fourth. Of those the principal are, that in
5304 thin Plates, which to the naked Eye seem of an even and uniform
5305 transparent whiteness, without any terminations of Shadows, the
5306 Refraction of a Prism should make Rings of Colours appear, whereas it
5307 usually makes Objects appear colour'd only there where they are
5308 terminated with Shadows, or have parts unequally luminous; and that it
5309 should make those Rings exceedingly distinct and white, although it
5310 usually renders Objects confused and coloured. The Cause of these things
5311 you will understand by considering, that all the Rings of Colours are
5312 really in the Plate, when view'd with the naked Eye, although by reason
5313 of the great breadth of their Circumferences they so much interfere and
5314 are blended together, that they seem to constitute an uniform whiteness.
5315 But when the Rays pass through the Prism to the Eye, the Orbits of the
5316 several Colours in every Ring are refracted, some more than others,
5317 according to their degrees of Refrangibility: By which means the Colours
5318 on one side of the Ring (that is in the circumference on one side of its
5319 center), become more unfolded and dilated, and those on the other side
5320 more complicated and contracted. And where by a due Refraction they are
5321 so much contracted, that the several Rings become narrower than to
5322 interfere with one another, they must appear distinct, and also white,
5323 if the constituent Colours be so much contracted as to be wholly
5324 co-incident. But on the other side, where the Orbit of every Ring is
5325 made broader by the farther unfolding of its Colours, it must interfere
5326 more with other Rings than before, and so become less distinct.
5327
5328 [Illustration: FIG. 7.]
5329
5330 To explain this a little farther, suppose the concentrick Circles AV,
5331 and BX, [in _Fig._ 7.] represent the red and violet of any Order, which,
5332 together with the intermediate Colours, constitute any one of these
5333 Rings. Now these being view'd through a Prism, the violet Circle BX,
5334 will, by a greater Refraction, be farther translated from its place than
5335 the red AV, and so approach nearer to it on that side of the Circles,
5336 towards which the Refractions are made. For instance, if the red be
5337 translated to _av_, the violet may be translated to _bx_, so as to
5338 approach nearer to it at _x_ than before; and if the red be farther
5339 translated to av, the violet may be so much farther translated to bx as
5340 to convene with it at x; and if the red be yet farther translated to
5341 [Greek: aY], the violet may be still so much farther translated to
5342 [Greek: bx] as to pass beyond it at [Greek: x], and convene with it at
5343 _e_ and _f_. And this being understood not only of the red and violet,
5344 but of all the other intermediate Colours, and also of every revolution
5345 of those Colours, you will easily perceive how those of the same
5346 revolution or order, by their nearness at _xv_ and [Greek: Yx], and
5347 their coincidence at xv, _e_ and _f_, ought to constitute pretty
5348 distinct Arcs of Circles, especially at xv, or at _e_ and _f_; and that
5349 they will appear severally at _x_[Greek: u] and at xv exhibit whiteness
5350 by their coincidence, and again appear severally at [Greek: Yx], but yet
5351 in a contrary order to that which they had before, and still retain
5352 beyond _e_ and _f_. But on the other side, at _ab_, ab, or [Greek: ab],
5353 these Colours must become much more confused by being dilated and spread
5354 so as to interfere with those of other Orders. And the same confusion
5355 will happen at [Greek: Ux] between _e_ and _f_, if the Refraction be
5356 very great, or the Prism very distant from the Object-glasses: In which
5357 case no parts of the Rings will be seen, save only two little Arcs at
5358 _e_ and _f_, whose distance from one another will be augmented by
5359 removing the Prism still farther from the Object-glasses: And these
5360 little Arcs must be distinctest and whitest at their middle, and at
5361 their ends, where they begin to grow confused, they must be colour'd.
5362 And the Colours at one end of every Arc must be in a contrary order to
5363 those at the other end, by reason that they cross in the intermediate
5364 white; namely, their ends, which verge towards [Greek: Ux], will be red
5365 and yellow on that side next the center, and blue and violet on the
5366 other side. But their other ends which verge from [Greek: Ux], will on
5367 the contrary be blue and violet on that side towards the center, and on
5368 the other side red and yellow.
5369
5370 Now as all these things follow from the properties of Light by a
5371 mathematical way of reasoning, so the truth of them may be manifested by
5372 Experiments. For in a dark Room, by viewing these Rings through a Prism,
5373 by reflexion of the several prismatick Colours, which an assistant
5374 causes to move to and fro upon a Wall or Paper from whence they are
5375 reflected, whilst the Spectator's Eye, the Prism, and the
5376 Object-glasses, (as in the 13th Observation,) are placed steady; the
5377 Position of the Circles made successively by the several Colours, will
5378 be found such, in respect of one another, as I have described in the
5379 Figures _abxv_, or abxv, or _[Greek: abxU]_. And by the same method the
5380 truth of the Explications of other Observations may be examined.
5381
5382 By what hath been said, the like Phænomena of Water and thin Plates of
5383 Glass may be understood. But in small fragments of those Plates there is
5384 this farther observable, that where they lie flat upon a Table, and are
5385 turned about their centers whilst they are view'd through a Prism, they
5386 will in some postures exhibit Waves of various Colours; and some of them
5387 exhibit these Waves in one or two Positions only, but the most of them
5388 do in all Positions exhibit them, and make them for the most part appear
5389 almost all over the Plates. The reason is, that the Superficies of such
5390 Plates are not even, but have many Cavities and Swellings, which, how
5391 shallow soever, do a little vary the thickness of the Plate. For at the
5392 several sides of those Cavities, for the Reasons newly described, there
5393 ought to be produced Waves in several postures of the Prism. Now though
5394 it be but some very small and narrower parts of the Glass, by which
5395 these Waves for the most part are caused, yet they may seem to extend
5396 themselves over the whole Glass, because from the narrowest of those
5397 parts there are Colours of several Orders, that is, of several Rings,
5398 confusedly reflected, which by Refraction of the Prism are unfolded,
5399 separated, and, according to their degrees of Refraction, dispersed to
5400 several places, so as to constitute so many several Waves, as there were
5401 divers orders of Colours promiscuously reflected from that part of the
5402 Glass.
5403
5404 These are the principal Phænomena of thin Plates or Bubbles, whose
5405 Explications depend on the properties of Light, which I have heretofore
5406 deliver'd. And these you see do necessarily follow from them, and agree
5407 with them, even to their very least circumstances; and not only so, but
5408 do very much tend to their proof. Thus, by the 24th Observation it
5409 appears, that the Rays of several Colours, made as well by thin Plates
5410 or Bubbles, as by Refractions of a Prism, have several degrees of
5411 Refrangibility; whereby those of each order, which at the reflexion from
5412 the Plate or Bubble are intermix'd with those of other orders, are
5413 separated from them by Refraction, and associated together so as to
5414 become visible by themselves like Arcs of Circles. For if the Rays were
5415 all alike refrangible, 'tis impossible that the whiteness, which to the
5416 naked Sense appears uniform, should by Refraction have its parts
5417 transposed and ranged into those black and white Arcs.
5418
5419 It appears also that the unequal Refractions of difform Rays proceed not
5420 from any contingent irregularities; such as are Veins, an uneven Polish,
5421 or fortuitous Position of the Pores of Glass; unequal and casual Motions
5422 in the Air or Æther, the spreading, breaking, or dividing the same Ray
5423 into many diverging parts; or the like. For, admitting any such
5424 irregularities, it would be impossible for Refractions to render those
5425 Rings so very distinct, and well defined, as they do in the 24th
5426 Observation. It is necessary therefore that every Ray have its proper
5427 and constant degree of Refrangibility connate with it, according to
5428 which its refraction is ever justly and regularly perform'd; and that
5429 several Rays have several of those degrees.
5430
5431 And what is said of their Refrangibility may be also understood of their
5432 Reflexibility, that is, of their Dispositions to be reflected, some at a
5433 greater, and others at a less thickness of thin Plates or Bubbles;
5434 namely, that those Dispositions are also connate with the Rays, and
5435 immutable; as may appear by the 13th, 14th, and 15th Observations,
5436 compared with the fourth and eighteenth.
5437
5438 By the Precedent Observations it appears also, that whiteness is a
5439 dissimilar mixture of all Colours, and that Light is a mixture of Rays
5440 endued with all those Colours. For, considering the multitude of the
5441 Rings of Colours in the 3d, 12th, and 24th Observations, it is manifest,
5442 that although in the 4th and 18th Observations there appear no more than
5443 eight or nine of those Rings, yet there are really a far greater number,
5444 which so much interfere and mingle with one another, as after those
5445 eight or nine revolutions to dilute one another wholly, and constitute
5446 an even and sensibly uniform whiteness. And consequently that whiteness
5447 must be allow'd a mixture of all Colours, and the Light which conveys it
5448 to the Eye must be a mixture of Rays endued with all those Colours.
5449
5450 But farther; by the 24th Observation it appears, that there is a
5451 constant relation between Colours and Refrangibility; the most
5452 refrangible Rays being violet, the least refrangible red, and those of
5453 intermediate Colours having proportionably intermediate degrees of
5454 Refrangibility. And by the 13th, 14th, and 15th Observations, compared
5455 with the 4th or 18th there appears to be the same constant relation
5456 between Colour and Reflexibility; the violet being in like circumstances
5457 reflected at least thicknesses of any thin Plate or Bubble, the red at
5458 greatest thicknesses, and the intermediate Colours at intermediate
5459 thicknesses. Whence it follows, that the colorifick Dispositions of
5460 Rays are also connate with them, and immutable; and by consequence, that
5461 all the Productions and Appearances of Colours in the World are derived,
5462 not from any physical Change caused in Light by Refraction or Reflexion,
5463 but only from the various Mixtures or Separations of Rays, by virtue of
5464 their different Refrangibility or Reflexibility. And in this respect the
5465 Science of Colours becomes a Speculation as truly mathematical as any
5466 other part of Opticks. I mean, so far as they depend on the Nature of
5467 Light, and are not produced or alter'd by the Power of Imagination, or
5468 by striking or pressing the Eye.
5469
5470
5471
5472
5473 THE
5474
5475 SECOND BOOK
5476
5477 OF
5478
5479 OPTICKS
5480
5481
5482 _PART III._
5483
5484 _Of the permanent Colours of natural Bodies, and the Analogy between
5485 them and the Colours of thin transparent Plates._
5486
5487 I am now come to another part of this Design, which is to consider how
5488 the Phænomena of thin transparent Plates stand related to those of all
5489 other natural Bodies. Of these Bodies I have already told you that they
5490 appear of divers Colours, accordingly as they are disposed to reflect
5491 most copiously the Rays originally endued with those Colours. But their
5492 Constitutions, whereby they reflect some Rays more copiously than
5493 others, remain to be discover'd; and these I shall endeavour to manifest
5494 in the following Propositions.
5495
5496
5497 PROP. I.
5498
5499 _Those Superficies of transparent Bodies reflect the greatest quantity
5500 of Light, which have the greatest refracting Power; that is, which
5501 intercede Mediums that differ most in their refractive Densities. And in
5502 the Confines of equally refracting Mediums there is no Reflexion._
5503
5504 The Analogy between Reflexion and Refraction will appear by considering,
5505 that when Light passeth obliquely out of one Medium into another which
5506 refracts from the perpendicular, the greater is the difference of their
5507 refractive Density, the less Obliquity of Incidence is requisite to
5508 cause a total Reflexion. For as the Sines are which measure the
5509 Refraction, so is the Sine of Incidence at which the total Reflexion
5510 begins, to the Radius of the Circle; and consequently that Angle of
5511 Incidence is least where there is the greatest difference of the Sines.
5512 Thus in the passing of Light out of Water into Air, where the Refraction
5513 is measured by the Ratio of the Sines 3 to 4, the total Reflexion begins
5514 when the Angle of Incidence is about 48 Degrees 35 Minutes. In passing
5515 out of Glass into Air, where the Refraction is measured by the Ratio of
5516 the Sines 20 to 31, the total Reflexion begins when the Angle of
5517 Incidence is 40 Degrees 10 Minutes; and so in passing out of Crystal, or
5518 more strongly refracting Mediums into Air, there is still a less
5519 obliquity requisite to cause a total reflexion. Superficies therefore
5520 which refract most do soonest reflect all the Light which is incident on
5521 them, and so must be allowed most strongly reflexive.
5522
5523 But the truth of this Proposition will farther appear by observing, that
5524 in the Superficies interceding two transparent Mediums, (such as are
5525 Air, Water, Oil, common Glass, Crystal, metalline Glasses, Island
5526 Glasses, white transparent Arsenick, Diamonds, &c.) the Reflexion is
5527 stronger or weaker accordingly, as the Superficies hath a greater or
5528 less refracting Power. For in the Confine of Air and Sal-gem 'tis
5529 stronger than in the Confine of Air and Water, and still stronger in the
5530 Confine of Air and common Glass or Crystal, and stronger in the Confine
5531 of Air and a Diamond. If any of these, and such like transparent Solids,
5532 be immerged in Water, its Reflexion becomes, much weaker than before;
5533 and still weaker if they be immerged in the more strongly refracting
5534 Liquors of well rectified Oil of Vitriol or Spirit of Turpentine. If
5535 Water be distinguish'd into two parts by any imaginary Surface, the
5536 Reflexion in the Confine of those two parts is none at all. In the
5537 Confine of Water and Ice 'tis very little; in that of Water and Oil 'tis
5538 something greater; in that of Water and Sal-gem still greater; and in
5539 that of Water and Glass, or Crystal or other denser Substances still
5540 greater, accordingly as those Mediums differ more or less in their
5541 refracting Powers. Hence in the Confine of common Glass and Crystal,
5542 there ought to be a weak Reflexion, and a stronger Reflexion in the
5543 Confine of common and metalline Glass; though I have not yet tried
5544 this. But in the Confine of two Glasses of equal density, there is not
5545 any sensible Reflexion; as was shewn in the first Observation. And the
5546 same may be understood of the Superficies interceding two Crystals, or
5547 two Liquors, or any other Substances in which no Refraction is caused.
5548 So then the reason why uniform pellucid Mediums (such as Water, Glass,
5549 or Crystal,) have no sensible Reflexion but in their external
5550 Superficies, where they are adjacent to other Mediums of a different
5551 density, is because all their contiguous parts have one and the same
5552 degree of density.
5553
5554
5555 PROP. II.
5556
5557 _The least parts of almost all natural Bodies are in some measure
5558 transparent: And the Opacity of those Bodies ariseth from the multitude
5559 of Reflexions caused in their internal Parts._
5560
5561 That this is so has been observed by others, and will easily be granted
5562 by them that have been conversant with Microscopes. And it may be also
5563 tried by applying any substance to a hole through which some Light is
5564 immitted into a dark Room. For how opake soever that Substance may seem
5565 in the open Air, it will by that means appear very manifestly
5566 transparent, if it be of a sufficient thinness. Only white metalline
5567 Bodies must be excepted, which by reason of their excessive density seem
5568 to reflect almost all the Light incident on their first Superficies;
5569 unless by solution in Menstruums they be reduced into very small
5570 Particles, and then they become transparent.
5571
5572
5573 PROP. III.
5574
5575 _Between the parts of opake and colour'd Bodies are many Spaces, either
5576 empty, or replenish'd with Mediums of other Densities; as Water between
5577 the tinging Corpuscles wherewith any Liquor is impregnated, Air between
5578 the aqueous Globules that constitute Clouds or Mists; and for the most
5579 part Spaces void of both Air and Water, but yet perhaps not wholly void
5580 of all Substance, between the parts of hard Bodies._
5581
5582 The truth of this is evinced by the two precedent Propositions: For by
5583 the second Proposition there are many Reflexions made by the internal
5584 parts of Bodies, which, by the first Proposition, would not happen if
5585 the parts of those Bodies were continued without any such Interstices
5586 between them; because Reflexions are caused only in Superficies, which
5587 intercede Mediums of a differing density, by _Prop._ 1.
5588
5589 But farther, that this discontinuity of parts is the principal Cause of
5590 the opacity of Bodies, will appear by considering, that opake Substances
5591 become transparent by filling their Pores with any Substance of equal or
5592 almost equal density with their parts. Thus Paper dipped in Water or
5593 Oil, the _Oculus Mundi_ Stone steep'd in Water, Linnen Cloth oiled or
5594 varnish'd, and many other Substances soaked in such Liquors as will
5595 intimately pervade their little Pores, become by that means more
5596 transparent than otherwise; so, on the contrary, the most transparent
5597 Substances, may, by evacuating their Pores, or separating their parts,
5598 be render'd sufficiently opake; as Salts or wet Paper, or the _Oculus
5599 Mundi_ Stone by being dried, Horn by being scraped, Glass by being
5600 reduced to Powder, or otherwise flawed; Turpentine by being stirred
5601 about with Water till they mix imperfectly, and Water by being form'd
5602 into many small Bubbles, either alone in the form of Froth, or by
5603 shaking it together with Oil of Turpentine, or Oil Olive, or with some
5604 other convenient Liquor, with which it will not perfectly incorporate.
5605 And to the increase of the opacity of these Bodies, it conduces
5606 something, that by the 23d Observation the Reflexions of very thin
5607 transparent Substances are considerably stronger than those made by the
5608 same Substances of a greater thickness.
5609
5610
5611 PROP. IV.
5612
5613 _The Parts of Bodies and their Interstices must not be less than of some
5614 definite bigness, to render them opake and colour'd._
5615
5616 For the opakest Bodies, if their parts be subtilly divided, (as Metals,
5617 by being dissolved in acid Menstruums, &c.) become perfectly
5618 transparent. And you may also remember, that in the eighth Observation
5619 there was no sensible reflexion at the Superficies of the
5620 Object-glasses, where they were very near one another, though they did
5621 not absolutely touch. And in the 17th Observation the Reflexion of the
5622 Water-bubble where it became thinnest was almost insensible, so as to
5623 cause very black Spots to appear on the top of the Bubble, by the want
5624 of reflected Light.
5625
5626 On these grounds I perceive it is that Water, Salt, Glass, Stones, and
5627 such like Substances, are transparent. For, upon divers Considerations,
5628 they seem to be as full of Pores or Interstices between their parts as
5629 other Bodies are, but yet their Parts and Interstices to be too small to
5630 cause Reflexions in their common Surfaces.
5631
5632
5633 PROP. V.
5634
5635 _The transparent parts of Bodies, according to their several sizes,
5636 reflect Rays of one Colour, and transmit those of another, on the same
5637 grounds that thin Plates or Bubbles do reflect or transmit those Rays.
5638 And this I take to be the ground of all their Colours._
5639
5640 For if a thinn'd or plated Body, which being of an even thickness,
5641 appears all over of one uniform Colour, should be slit into Threads, or
5642 broken into Fragments, of the same thickness with the Plate; I see no
5643 reason why every Thread or Fragment should not keep its Colour, and by
5644 consequence why a heap of those Threads or Fragments should not
5645 constitute a Mass or Powder of the same Colour, which the Plate
5646 exhibited before it was broken. And the parts of all natural Bodies
5647 being like so many Fragments of a Plate, must on the same grounds
5648 exhibit the same Colours.
5649
5650 Now, that they do so will appear by the affinity of their Properties.
5651 The finely colour'd Feathers of some Birds, and particularly those of
5652 Peacocks Tails, do, in the very same part of the Feather, appear of
5653 several Colours in several Positions of the Eye, after the very same
5654 manner that thin Plates were found to do in the 7th and 19th
5655 Observations, and therefore their Colours arise from the thinness of the
5656 transparent parts of the Feathers; that is, from the slenderness of the
5657 very fine Hairs, or _Capillamenta_, which grow out of the sides of the
5658 grosser lateral Branches or Fibres of those Feathers. And to the same
5659 purpose it is, that the Webs of some Spiders, by being spun very fine,
5660 have appeared colour'd, as some have observ'd, and that the colour'd
5661 Fibres of some Silks, by varying the Position of the Eye, do vary their
5662 Colour. Also the Colours of Silks, Cloths, and other Substances, which
5663 Water or Oil can intimately penetrate, become more faint and obscure by
5664 being immerged in those Liquors, and recover their Vigor again by being
5665 dried; much after the manner declared of thin Bodies in the 10th and
5666 21st Observations. Leaf-Gold, some sorts of painted Glass, the Infusion
5667 of _Lignum Nephriticum_, and some other Substances, reflect one Colour,
5668 and transmit another; like thin Bodies in the 9th and 20th Observations.
5669 And some of those colour'd Powders which Painters use, may have their
5670 Colours a little changed, by being very elaborately and finely ground.
5671 Where I see not what can be justly pretended for those changes, besides
5672 the breaking of their parts into less parts by that contrition, after
5673 the same manner that the Colour of a thin Plate is changed by varying
5674 its thickness. For which reason also it is that the colour'd Flowers of
5675 Plants and Vegetables, by being bruised, usually become more transparent
5676 than before, or at least in some degree or other change their Colours.
5677 Nor is it much less to my purpose, that, by mixing divers Liquors, very
5678 odd and remarkable Productions and Changes of Colours may be effected,
5679 of which no cause can be more obvious and rational than that the saline
5680 Corpuscles of one Liquor do variously act upon or unite with the tinging
5681 Corpuscles of another, so as to make them swell, or shrink, (whereby not
5682 only their bulk but their density also may be changed,) or to divide
5683 them into smaller Corpuscles, (whereby a colour'd Liquor may become
5684 transparent,) or to make many of them associate into one cluster,
5685 whereby two transparent Liquors may compose a colour'd one. For we see
5686 how apt those saline Menstruums are to penetrate and dissolve Substances
5687 to which they are applied, and some of them to precipitate what others
5688 dissolve. In like manner, if we consider the various Phænomena of the
5689 Atmosphere, we may observe, that when Vapours are first raised, they
5690 hinder not the transparency of the Air, being divided into parts too
5691 small to cause any Reflexion in their Superficies. But when in order to
5692 compose drops of Rain they begin to coalesce and constitute Globules of
5693 all intermediate sizes, those Globules, when they become of convenient
5694 size to reflect some Colours and transmit others, may constitute Clouds
5695 of various Colours according to their sizes. And I see not what can be
5696 rationally conceived in so transparent a Substance as Water for the
5697 production of these Colours, besides the various sizes of its fluid and
5698 globular Parcels.
5699
5700
5701 PROP. VI.
5702
5703 _The parts of Bodies on which their Colours depend, are denser than the
5704 Medium which pervades their Interstices._
5705
5706 This will appear by considering, that the Colour of a Body depends not
5707 only on the Rays which are incident perpendicularly on its parts, but on
5708 those also which are incident at all other Angles. And that according to
5709 the 7th Observation, a very little variation of obliquity will change
5710 the reflected Colour, where the thin Body or small Particles is rarer
5711 than the ambient Medium, insomuch that such a small Particle will at
5712 diversly oblique Incidences reflect all sorts of Colours, in so great a
5713 variety that the Colour resulting from them all, confusedly reflected
5714 from a heap of such Particles, must rather be a white or grey than any
5715 other Colour, or at best it must be but a very imperfect and dirty
5716 Colour. Whereas if the thin Body or small Particle be much denser than
5717 the ambient Medium, the Colours, according to the 19th Observation, are
5718 so little changed by the variation of obliquity, that the Rays which
5719 are reflected least obliquely may predominate over the rest, so much as
5720 to cause a heap of such Particles to appear very intensely of their
5721 Colour.
5722
5723 It conduces also something to the confirmation of this Proposition,
5724 that, according to the 22d Observation, the Colours exhibited by the
5725 denser thin Body within the rarer, are more brisk than those exhibited
5726 by the rarer within the denser.
5727
5728
5729 PROP. VII.
5730
5731 _The bigness of the component parts of natural Bodies may be conjectured
5732 by their Colours._
5733
5734 For since the parts of these Bodies, by _Prop._ 5. do most probably
5735 exhibit the same Colours with a Plate of equal thickness, provided they
5736 have the same refractive density; and since their parts seem for the
5737 most part to have much the same density with Water or Glass, as by many
5738 circumstances is obvious to collect; to determine the sizes of those
5739 parts, you need only have recourse to the precedent Tables, in which the
5740 thickness of Water or Glass exhibiting any Colour is expressed. Thus if
5741 it be desired to know the diameter of a Corpuscle, which being of equal
5742 density with Glass shall reflect green of the third Order; the Number
5743 16-1/4 shews it to be (16-1/4)/10000 parts of an Inch.
5744
5745 The greatest difficulty is here to know of what Order the Colour of any
5746 Body is. And for this end we must have recourse to the 4th and 18th
5747 Observations; from whence may be collected these particulars.
5748
5749 _Scarlets_, and other _reds_, _oranges_, and _yellows_, if they be pure
5750 and intense, are most probably of the second order. Those of the first
5751 and third order also may be pretty good; only the yellow of the first
5752 order is faint, and the orange and red of the third Order have a great
5753 Mixture of violet and blue.
5754
5755 There may be good _Greens_ of the fourth Order, but the purest are of
5756 the third. And of this Order the green of all Vegetables seems to be,
5757 partly by reason of the Intenseness of their Colours, and partly because
5758 when they wither some of them turn to a greenish yellow, and others to a
5759 more perfect yellow or orange, or perhaps to red, passing first through
5760 all the aforesaid intermediate Colours. Which Changes seem to be
5761 effected by the exhaling of the Moisture which may leave the tinging
5762 Corpuscles more dense, and something augmented by the Accretion of the
5763 oily and earthy Part of that Moisture. Now the green, without doubt, is
5764 of the same Order with those Colours into which it changeth, because the
5765 Changes are gradual, and those Colours, though usually not very full,
5766 yet are often too full and lively to be of the fourth Order.
5767
5768 _Blues_ and _Purples_ may be either of the second or third Order, but
5769 the best are of the third. Thus the Colour of Violets seems to be of
5770 that Order, because their Syrup by acid Liquors turns red, and by
5771 urinous and alcalizate turns green. For since it is of the Nature of
5772 Acids to dissolve or attenuate, and of Alcalies to precipitate or
5773 incrassate, if the Purple Colour of the Syrup was of the second Order,
5774 an acid Liquor by attenuating its tinging Corpuscles would change it to
5775 a red of the first Order, and an Alcali by incrassating them would
5776 change it to a green of the second Order; which red and green,
5777 especially the green, seem too imperfect to be the Colours produced by
5778 these Changes. But if the said Purple be supposed of the third Order,
5779 its Change to red of the second, and green of the third, may without any
5780 Inconvenience be allow'd.
5781
5782 If there be found any Body of a deeper and less reddish Purple than that
5783 of the Violets, its Colour most probably is of the second Order. But yet
5784 there being no Body commonly known whose Colour is constantly more deep
5785 than theirs, I have made use of their Name to denote the deepest and
5786 least reddish Purples, such as manifestly transcend their Colour in
5787 purity.
5788
5789 The _blue_ of the first Order, though very faint and little, may
5790 possibly be the Colour of some Substances; and particularly the azure
5791 Colour of the Skies seems to be of this Order. For all Vapours when they
5792 begin to condense and coalesce into small Parcels, become first of that
5793 Bigness, whereby such an Azure must be reflected before they can
5794 constitute Clouds of other Colours. And so this being the first Colour
5795 which Vapours begin to reflect, it ought to be the Colour of the finest
5796 and most transparent Skies, in which Vapours are not arrived to that
5797 Grossness requisite to reflect other Colours, as we find it is by
5798 Experience.
5799
5800 _Whiteness_, if most intense and luminous, is that of the first Order,
5801 if less strong and luminous, a Mixture of the Colours of several Orders.
5802 Of this last kind is the Whiteness of Froth, Paper, Linnen, and most
5803 white Substances; of the former I reckon that of white Metals to be. For
5804 whilst the densest of Metals, Gold, if foliated, is transparent, and all
5805 Metals become transparent if dissolved in Menstruums or vitrified, the
5806 Opacity of white Metals ariseth not from their Density alone. They being
5807 less dense than Gold would be more transparent than it, did not some
5808 other Cause concur with their Density to make them opake. And this Cause
5809 I take to be such a Bigness of their Particles as fits them to reflect
5810 the white of the first order. For, if they be of other Thicknesses they
5811 may reflect other Colours, as is manifest by the Colours which appear
5812 upon hot Steel in tempering it, and sometimes upon the Surface of melted
5813 Metals in the Skin or Scoria which arises upon them in their cooling.
5814 And as the white of the first order is the strongest which can be made
5815 by Plates of transparent Substances, so it ought to be stronger in the
5816 denser Substances of Metals than in the rarer of Air, Water, and Glass.
5817 Nor do I see but that metallick Substances of such a Thickness as may
5818 fit them to reflect the white of the first order, may, by reason of
5819 their great Density (according to the Tenor of the first of these
5820 Propositions) reflect all the Light incident upon them, and so be as
5821 opake and splendent as it's possible for any Body to be. Gold, or Copper
5822 mix'd with less than half their Weight of Silver, or Tin, or Regulus of
5823 Antimony, in fusion, or amalgamed with a very little Mercury, become
5824 white; which shews both that the Particles of white Metals have much
5825 more Superficies, and so are smaller, than those of Gold and Copper, and
5826 also that they are so opake as not to suffer the Particles of Gold or
5827 Copper to shine through them. Now it is scarce to be doubted but that
5828 the Colours of Gold and Copper are of the second and third order, and
5829 therefore the Particles of white Metals cannot be much bigger than is
5830 requisite to make them reflect the white of the first order. The
5831 Volatility of Mercury argues that they are not much bigger, nor may they
5832 be much less, lest they lose their Opacity, and become either
5833 transparent as they do when attenuated by Vitrification, or by Solution
5834 in Menstruums, or black as they do when ground smaller, by rubbing
5835 Silver, or Tin, or Lead, upon other Substances to draw black Lines. The
5836 first and only Colour which white Metals take by grinding their
5837 Particles smaller, is black, and therefore their white ought to be that
5838 which borders upon the black Spot in the Center of the Rings of Colours,
5839 that is, the white of the first order. But, if you would hence gather
5840 the Bigness of metallick Particles, you must allow for their Density.
5841 For were Mercury transparent, its Density is such that the Sine of
5842 Incidence upon it (by my Computation) would be to the Sine of its
5843 Refraction, as 71 to 20, or 7 to 2. And therefore the Thickness of its
5844 Particles, that they may exhibit the same Colours with those of Bubbles
5845 of Water, ought to be less than the Thickness of the Skin of those
5846 Bubbles in the Proportion of 2 to 7. Whence it's possible, that the
5847 Particles of Mercury may be as little as the Particles of some
5848 transparent and volatile Fluids, and yet reflect the white of the first
5849 order.
5850
5851 Lastly, for the production of _black_, the Corpuscles must be less than
5852 any of those which exhibit Colours. For at all greater sizes there is
5853 too much Light reflected to constitute this Colour. But if they be
5854 supposed a little less than is requisite to reflect the white and very
5855 faint blue of the first order, they will, according to the 4th, 8th,
5856 17th and 18th Observations, reflect so very little Light as to appear
5857 intensely black, and yet may perhaps variously refract it to and fro
5858 within themselves so long, until it happen to be stifled and lost, by
5859 which means they will appear black in all positions of the Eye without
5860 any transparency. And from hence may be understood why Fire, and the
5861 more subtile dissolver Putrefaction, by dividing the Particles of
5862 Substances, turn them to black, why small quantities of black Substances
5863 impart their Colour very freely and intensely to other Substances to
5864 which they are applied; the minute Particles of these, by reason of
5865 their very great number, easily overspreading the gross Particles of
5866 others; why Glass ground very elaborately with Sand on a Copper Plate,
5867 'till it be well polish'd, makes the Sand, together with what is worn
5868 off from the Glass and Copper, become very black: why black Substances
5869 do soonest of all others become hot in the Sun's Light and burn, (which
5870 Effect may proceed partly from the multitude of Refractions in a little
5871 room, and partly from the easy Commotion of so very small Corpuscles;)
5872 and why blacks are usually a little inclined to a bluish Colour. For
5873 that they are so may be seen by illuminating white Paper by Light
5874 reflected from black Substances. For the Paper will usually appear of a
5875 bluish white; and the reason is, that black borders in the obscure blue
5876 of the order described in the 18th Observation, and therefore reflects
5877 more Rays of that Colour than of any other.
5878
5879 In these Descriptions I have been the more particular, because it is not
5880 impossible but that Microscopes may at length be improved to the
5881 discovery of the Particles of Bodies on which their Colours depend, if
5882 they are not already in some measure arrived to that degree of
5883 perfection. For if those Instruments are or can be so far improved as
5884 with sufficient distinctness to represent Objects five or six hundred
5885 times bigger than at a Foot distance they appear to our naked Eyes, I
5886 should hope that we might be able to discover some of the greatest of
5887 those Corpuscles. And by one that would magnify three or four thousand
5888 times perhaps they might all be discover'd, but those which produce
5889 blackness. In the mean while I see nothing material in this Discourse
5890 that may rationally be doubted of, excepting this Position: That
5891 transparent Corpuscles of the same thickness and density with a Plate,
5892 do exhibit the same Colour. And this I would have understood not without
5893 some Latitude, as well because those Corpuscles may be of irregular
5894 Figures, and many Rays must be obliquely incident on them, and so have
5895 a shorter way through them than the length of their Diameters, as
5896 because the straitness of the Medium put in on all sides within such
5897 Corpuscles may a little alter its Motions or other qualities on which
5898 the Reflexion depends. But yet I cannot much suspect the last, because I
5899 have observed of some small Plates of Muscovy Glass which were of an
5900 even thickness, that through a Microscope they have appeared of the same
5901 Colour at their edges and corners where the included Medium was
5902 terminated, which they appeared of in other places. However it will add
5903 much to our Satisfaction, if those Corpuscles can be discover'd with
5904 Microscopes; which if we shall at length attain to, I fear it will be
5905 the utmost improvement of this Sense. For it seems impossible to see the
5906 more secret and noble Works of Nature within the Corpuscles by reason of
5907 their transparency.
5908
5909
5910 PROP. VIII.
5911
5912 _The Cause of Reflexion is not the impinging of Light on the solid or
5913 impervious parts of Bodies, as is commonly believed._
5914
5915 This will appear by the following Considerations. First, That in the
5916 passage of Light out of Glass into Air there is a Reflexion as strong as
5917 in its passage out of Air into Glass, or rather a little stronger, and
5918 by many degrees stronger than in its passage out of Glass into Water.
5919 And it seems not probable that Air should have more strongly reflecting
5920 parts than Water or Glass. But if that should possibly be supposed, yet
5921 it will avail nothing; for the Reflexion is as strong or stronger when
5922 the Air is drawn away from the Glass, (suppose by the Air-Pump invented
5923 by _Otto Gueriet_, and improved and made useful by Mr. _Boyle_) as when
5924 it is adjacent to it. Secondly, If Light in its passage out of Glass
5925 into Air be incident more obliquely than at an Angle of 40 or 41 Degrees
5926 it is wholly reflected, if less obliquely it is in great measure
5927 transmitted. Now it is not to be imagined that Light at one degree of
5928 obliquity should meet with Pores enough in the Air to transmit the
5929 greater part of it, and at another degree of obliquity should meet with
5930 nothing but parts to reflect it wholly, especially considering that in
5931 its passage out of Air into Glass, how oblique soever be its Incidence,
5932 it finds Pores enough in the Glass to transmit a great part of it. If
5933 any Man suppose that it is not reflected by the Air, but by the outmost
5934 superficial parts of the Glass, there is still the same difficulty:
5935 Besides, that such a Supposition is unintelligible, and will also appear
5936 to be false by applying Water behind some part of the Glass instead of
5937 Air. For so in a convenient obliquity of the Rays, suppose of 45 or 46
5938 Degrees, at which they are all reflected where the Air is adjacent to
5939 the Glass, they shall be in great measure transmitted where the Water is
5940 adjacent to it; which argues, that their Reflexion or Transmission
5941 depends on the constitution of the Air and Water behind the Glass, and
5942 not on the striking of the Rays upon the parts of the Glass. Thirdly,
5943 If the Colours made by a Prism placed at the entrance of a Beam of Light
5944 into a darken'd Room be successively cast on a second Prism placed at a
5945 greater distance from the former, in such manner that they are all alike
5946 incident upon it, the second Prism may be so inclined to the incident
5947 Rays, that those which are of a blue Colour shall be all reflected by
5948 it, and yet those of a red Colour pretty copiously transmitted. Now if
5949 the Reflexion be caused by the parts of Air or Glass, I would ask, why
5950 at the same Obliquity of Incidence the blue should wholly impinge on
5951 those parts, so as to be all reflected, and yet the red find Pores
5952 enough to be in a great measure transmitted. Fourthly, Where two Glasses
5953 touch one another, there is no sensible Reflexion, as was declared in
5954 the first Observation; and yet I see no reason why the Rays should not
5955 impinge on the parts of Glass, as much when contiguous to other Glass as
5956 when contiguous to Air. Fifthly, When the top of a Water-Bubble (in the
5957 17th Observation,) by the continual subsiding and exhaling of the Water
5958 grew very thin, there was such a little and almost insensible quantity
5959 of Light reflected from it, that it appeared intensely black; whereas
5960 round about that black Spot, where the Water was thicker, the Reflexion
5961 was so strong as to make the Water seem very white. Nor is it only at
5962 the least thickness of thin Plates or Bubbles, that there is no manifest
5963 Reflexion, but at many other thicknesses continually greater and
5964 greater. For in the 15th Observation the Rays of the same Colour were by
5965 turns transmitted at one thickness, and reflected at another thickness,
5966 for an indeterminate number of Successions. And yet in the Superficies
5967 of the thinned Body, where it is of any one thickness, there are as many
5968 parts for the Rays to impinge on, as where it is of any other thickness.
5969 Sixthly, If Reflexion were caused by the parts of reflecting Bodies, it
5970 would be impossible for thin Plates or Bubbles, at one and the same
5971 place, to reflect the Rays of one Colour, and transmit those of another,
5972 as they do according to the 13th and 15th Observations. For it is not to
5973 be imagined that at one place the Rays which, for instance, exhibit a
5974 blue Colour, should have the fortune to dash upon the parts, and those
5975 which exhibit a red to hit upon the Pores of the Body; and then at
5976 another place, where the Body is either a little thicker or a little
5977 thinner, that on the contrary the blue should hit upon its pores, and
5978 the red upon its parts. Lastly, Were the Rays of Light reflected by
5979 impinging on the solid parts of Bodies, their Reflexions from polish'd
5980 Bodies could not be so regular as they are. For in polishing Glass with
5981 Sand, Putty, or Tripoly, it is not to be imagined that those Substances
5982 can, by grating and fretting the Glass, bring all its least Particles to
5983 an accurate Polish; so that all their Surfaces shall be truly plain or
5984 truly spherical, and look all the same way, so as together to compose
5985 one even Surface. The smaller the Particles of those Substances are, the
5986 smaller will be the Scratches by which they continually fret and wear
5987 away the Glass until it be polish'd; but be they never so small they can
5988 wear away the Glass no otherwise than by grating and scratching it, and
5989 breaking the Protuberances; and therefore polish it no otherwise than by
5990 bringing its roughness to a very fine Grain, so that the Scratches and
5991 Frettings of the Surface become too small to be visible. And therefore
5992 if Light were reflected by impinging upon the solid parts of the Glass,
5993 it would be scatter'd as much by the most polish'd Glass as by the
5994 roughest. So then it remains a Problem, how Glass polish'd by fretting
5995 Substances can reflect Light so regularly as it does. And this Problem
5996 is scarce otherwise to be solved, than by saying, that the Reflexion of
5997 a Ray is effected, not by a single point of the reflecting Body, but by
5998 some power of the Body which is evenly diffused all over its Surface,
5999 and by which it acts upon the Ray without immediate Contact. For that
6000 the parts of Bodies do act upon Light at a distance shall be shewn
6001 hereafter.
6002
6003 Now if Light be reflected, not by impinging on the solid parts of
6004 Bodies, but by some other principle; it's probable that as many of its
6005 Rays as impinge on the solid parts of Bodies are not reflected but
6006 stifled and lost in the Bodies. For otherwise we must allow two sorts of
6007 Reflexions. Should all the Rays be reflected which impinge on the
6008 internal parts of clear Water or Crystal, those Substances would rather
6009 have a cloudy Colour than a clear Transparency. To make Bodies look
6010 black, it's necessary that many Rays be stopp'd, retained, and lost in
6011 them; and it seems not probable that any Rays can be stopp'd and
6012 stifled in them which do not impinge on their parts.
6013
6014 And hence we may understand that Bodies are much more rare and porous
6015 than is commonly believed. Water is nineteen times lighter, and by
6016 consequence nineteen times rarer than Gold; and Gold is so rare as very
6017 readily and without the least opposition to transmit the magnetick
6018 Effluvia, and easily to admit Quicksilver into its Pores, and to let
6019 Water pass through it. For a concave Sphere of Gold filled with Water,
6020 and solder'd up, has, upon pressing the Sphere with great force, let the
6021 Water squeeze through it, and stand all over its outside in multitudes
6022 of small Drops, like Dew, without bursting or cracking the Body of the
6023 Gold, as I have been inform'd by an Eye witness. From all which we may
6024 conclude, that Gold has more Pores than solid parts, and by consequence
6025 that Water has above forty times more Pores than Parts. And he that
6026 shall find out an Hypothesis, by which Water may be so rare, and yet not
6027 be capable of compression by force, may doubtless by the same Hypothesis
6028 make Gold, and Water, and all other Bodies, as much rarer as he pleases;
6029 so that Light may find a ready passage through transparent Substances.
6030
6031 The Magnet acts upon Iron through all dense Bodies not magnetick nor red
6032 hot, without any diminution of its Virtue; as for instance, through
6033 Gold, Silver, Lead, Glass, Water. The gravitating Power of the Sun is
6034 transmitted through the vast Bodies of the Planets without any
6035 diminution, so as to act upon all their parts to their very centers
6036 with the same Force and according to the same Laws, as if the part upon
6037 which it acts were not surrounded with the Body of the Planet, The Rays
6038 of Light, whether they be very small Bodies projected, or only Motion or
6039 Force propagated, are moved in right Lines; and whenever a Ray of Light
6040 is by any Obstacle turned out of its rectilinear way, it will never
6041 return into the same rectilinear way, unless perhaps by very great
6042 accident. And yet Light is transmitted through pellucid solid Bodies in
6043 right Lines to very great distances. How Bodies can have a sufficient
6044 quantity of Pores for producing these Effects is very difficult to
6045 conceive, but perhaps not altogether impossible. For the Colours of
6046 Bodies arise from the Magnitudes of the Particles which reflect them, as
6047 was explained above. Now if we conceive these Particles of Bodies to be
6048 so disposed amongst themselves, that the Intervals or empty Spaces
6049 between them may be equal in magnitude to them all; and that these
6050 Particles may be composed of other Particles much smaller, which have as
6051 much empty Space between them as equals all the Magnitudes of these
6052 smaller Particles: And that in like manner these smaller Particles are
6053 again composed of others much smaller, all which together are equal to
6054 all the Pores or empty Spaces between them; and so on perpetually till
6055 you come to solid Particles, such as have no Pores or empty Spaces
6056 within them: And if in any gross Body there be, for instance, three such
6057 degrees of Particles, the least of which are solid; this Body will have
6058 seven times more Pores than solid Parts. But if there be four such
6059 degrees of Particles, the least of which are solid, the Body will have
6060 fifteen times more Pores than solid Parts. If there be five degrees, the
6061 Body will have one and thirty times more Pores than solid Parts. If six
6062 degrees, the Body will have sixty and three times more Pores than solid
6063 Parts. And so on perpetually. And there are other ways of conceiving how
6064 Bodies may be exceeding porous. But what is really their inward Frame is
6065 not yet known to us.
6066
6067
6068 PROP. IX.
6069
6070 _Bodies reflect and refract Light by one and the same power, variously
6071 exercised in various Circumstances._
6072
6073 This appears by several Considerations. First, Because when Light goes
6074 out of Glass into Air, as obliquely as it can possibly do. If its
6075 Incidence be made still more oblique, it becomes totally reflected. For
6076 the power of the Glass after it has refracted the Light as obliquely as
6077 is possible, if the Incidence be still made more oblique, becomes too
6078 strong to let any of its Rays go through, and by consequence causes
6079 total Reflexions. Secondly, Because Light is alternately reflected and
6080 transmitted by thin Plates of Glass for many Successions, accordingly as
6081 the thickness of the Plate increases in an arithmetical Progression. For
6082 here the thickness of the Glass determines whether that Power by which
6083 Glass acts upon Light shall cause it to be reflected, or suffer it to
6084 be transmitted. And, Thirdly, because those Surfaces of transparent
6085 Bodies which have the greatest refracting power, reflect the greatest
6086 quantity of Light, as was shewn in the first Proposition.
6087
6088
6089 PROP. X.
6090
6091 _If Light be swifter in Bodies than in Vacuo, in the proportion of the
6092 Sines which measure the Refraction of the Bodies, the Forces of the
6093 Bodies to reflect and refract Light, are very nearly proportional to the
6094 densities of the same Bodies; excepting that unctuous and sulphureous
6095 Bodies refract more than others of this same density._
6096
6097 [Illustration: FIG. 8.]
6098
6099 Let AB represent the refracting plane Surface of any Body, and IC a Ray
6100 incident very obliquely upon the Body in C, so that the Angle ACI may be
6101 infinitely little, and let CR be the refracted Ray. From a given Point B
6102 perpendicular to the refracting Surface erect BR meeting with the
6103 refracting Ray CR in R, and if CR represent the Motion of the refracted
6104 Ray, and this Motion be distinguish'd into two Motions CB and BR,
6105 whereof CB is parallel to the refracting Plane, and BR perpendicular to
6106 it: CB shall represent the Motion of the incident Ray, and BR the
6107 Motion generated by the Refraction, as Opticians have of late explain'd.
6108
6109 Now if any Body or Thing, in moving through any Space of a given breadth
6110 terminated on both sides by two parallel Planes, be urged forward in all
6111 parts of that Space by Forces tending directly forwards towards the last
6112 Plane, and before its Incidence on the first Plane, had no Motion
6113 towards it, or but an infinitely little one; and if the Forces in all
6114 parts of that Space, between the Planes, be at equal distances from the
6115 Planes equal to one another, but at several distances be bigger or less
6116 in any given Proportion, the Motion generated by the Forces in the whole
6117 passage of the Body or thing through that Space shall be in a
6118 subduplicate Proportion of the Forces, as Mathematicians will easily
6119 understand. And therefore, if the Space of activity of the refracting
6120 Superficies of the Body be consider'd as such a Space, the Motion of the
6121 Ray generated by the refracting Force of the Body, during its passage
6122 through that Space, that is, the Motion BR, must be in subduplicate
6123 Proportion of that refracting Force. I say therefore, that the Square of
6124 the Line BR, and by consequence the refracting Force of the Body, is
6125 very nearly as the density of the same Body. For this will appear by the
6126 following Table, wherein the Proportion of the Sines which measure the
6127 Refractions of several Bodies, the Square of BR, supposing CB an unite,
6128 the Densities of the Bodies estimated by their Specifick Gravities, and
6129 their Refractive Power in respect of their Densities are set down in
6130 several Columns.
6131
6132 ---------------------+----------------+----------------+----------+-----------
6133 | | | |
6134 | | The Square | The | The
6135 | | of BR, to | density | refractive
6136 | The Proportion | which the | and | Power of
6137 | of the Sines of| refracting | specifick| the Body
6138 | Incidence and | force of the | gravity | in respect
6139 The refracting | Refraction of | Body is | of the | of its
6140 Bodies. | yellow Light. | proportionate. | Body. | density.
6141 ---------------------+----------------+----------------+----------+-----------
6142 A Pseudo-Topazius, | | | |
6143 being a natural, | | | |
6144 pellucid, brittle, | 23 to 14 | 1'699 | 4'27 | 3979
6145 hairy Stone, of a | | | |
6146 yellow Colour. | | | |
6147 Air. | 3201 to 3200 | 0'000625 | 0'0012 | 5208
6148 Glass of Antimony. | 17 to 9 | 2'568 | 5'28 | 4864
6149 A Selenitis. | 61 to 41 | 1'213 | 2'252 | 5386
6150 Glass vulgar. | 31 to 20 | 1'4025 | 2'58 | 5436
6151 Crystal of the Rock. | 25 to 16 | 1'445 | 2'65 | 5450
6152 Island Crystal. | 5 to 3 | 1'778 | 2'72 | 6536
6153 Sal Gemmæ. | 17 to 11 | 1'388 | 2'143 | 6477
6154 Alume. | 35 to 24 | 1'1267 | 1'714 | 6570
6155 Borax. | 22 to 15 | 1'1511 | 1'714 | 6716
6156 Niter. | 32 to 21 | 1'345 | 1'9 | 7079
6157 Dantzick Vitriol. | 303 to 200 | 1'295 | 1'715 | 7551
6158 Oil of Vitriol. | 10 to 7 | 1'041 | 1'7 | 6124
6159 Rain Water. | 529 to 396 | 0'7845 | 1' | 7845
6160 Gum Arabick. | 31 to 21 | 1'179 | 1'375 | 8574
6161 Spirit of Wine well | | | |
6162 rectified. | 100 to 73 | 0'8765 | 0'866 | 10121
6163 Camphire. | 3 to 2 | 1'25 | 0'996 | 12551
6164 Oil Olive. | 22 to 15 | 1'1511 | 0'913 | 12607
6165 Linseed Oil. | 40 to 27 | 1'1948 | 0'932 | 12819
6166 Spirit of Turpentine.| 25 to 17 | 1'1626 | 0'874 | 13222
6167 Amber. | 14 to 9 | 1'42 | 1'04 | 13654
6168 A Diamond. | 100 to 41 | 4'949 | 3'4 | 14556
6169 ---------------------+----------------+----------------+----------+-----------
6170
6171 The Refraction of the Air in this Table is determin'd by that of the
6172 Atmosphere observed by Astronomers. For, if Light pass through many
6173 refracting Substances or Mediums gradually denser and denser, and
6174 terminated with parallel Surfaces, the Sum of all the Refractions will
6175 be equal to the single Refraction which it would have suffer'd in
6176 passing immediately out of the first Medium into the last. And this
6177 holds true, though the Number of the refracting Substances be increased
6178 to Infinity, and the Distances from one another as much decreased, so
6179 that the Light may be refracted in every Point of its Passage, and by
6180 continual Refractions bent into a Curve-Line. And therefore the whole
6181 Refraction of Light in passing through the Atmosphere from the highest
6182 and rarest Part thereof down to the lowest and densest Part, must be
6183 equal to the Refraction which it would suffer in passing at like
6184 Obliquity out of a Vacuum immediately into Air of equal Density with
6185 that in the lowest Part of the Atmosphere.
6186
6187 Now, although a Pseudo-Topaz, a Selenitis, Rock Crystal, Island Crystal,
6188 Vulgar Glass (that is, Sand melted together) and Glass of Antimony,
6189 which are terrestrial stony alcalizate Concretes, and Air which probably
6190 arises from such Substances by Fermentation, be Substances very
6191 differing from one another in Density, yet by this Table, they have
6192 their refractive Powers almost in the same Proportion to one another as
6193 their Densities are, excepting that the Refraction of that strange
6194 Substance, Island Crystal is a little bigger than the rest. And
6195 particularly Air, which is 3500 Times rarer than the Pseudo-Topaz, and
6196 4400 Times rarer than Glass of Antimony, and 2000 Times rarer than the
6197 Selenitis, Glass vulgar, or Crystal of the Rock, has notwithstanding its
6198 rarity the same refractive Power in respect of its Density which those
6199 very dense Substances have in respect of theirs, excepting so far as
6200 those differ from one another.
6201
6202 Again, the Refraction of Camphire, Oil Olive, Linseed Oil, Spirit of
6203 Turpentine and Amber, which are fat sulphureous unctuous Bodies, and a
6204 Diamond, which probably is an unctuous Substance coagulated, have their
6205 refractive Powers in Proportion to one another as their Densities
6206 without any considerable Variation. But the refractive Powers of these
6207 unctuous Substances are two or three Times greater in respect of their
6208 Densities than the refractive Powers of the former Substances in respect
6209 of theirs.
6210
6211 Water has a refractive Power in a middle degree between those two sorts
6212 of Substances, and probably is of a middle nature. For out of it grow
6213 all vegetable and animal Substances, which consist as well of
6214 sulphureous fat and inflamable Parts, as of earthy lean and alcalizate
6215 ones.
6216
6217 Salts and Vitriols have refractive Powers in a middle degree between
6218 those of earthy Substances and Water, and accordingly are composed of
6219 those two sorts of Substances. For by distillation and rectification of
6220 their Spirits a great Part of them goes into Water, and a great Part
6221 remains behind in the form of a dry fix'd Earth capable of
6222 Vitrification.
6223
6224 Spirit of Wine has a refractive Power in a middle degree between those
6225 of Water and oily Substances, and accordingly seems to be composed of
6226 both, united by Fermentation; the Water, by means of some saline Spirits
6227 with which 'tis impregnated, dissolving the Oil, and volatizing it by
6228 the Action. For Spirit of Wine is inflamable by means of its oily Parts,
6229 and being distilled often from Salt of Tartar, grow by every
6230 distillation more and more aqueous and phlegmatick. And Chymists
6231 observe, that Vegetables (as Lavender, Rue, Marjoram, &c.) distilled
6232 _per se_, before fermentation yield Oils without any burning Spirits,
6233 but after fermentation yield ardent Spirits without Oils: Which shews,
6234 that their Oil is by fermentation converted into Spirit. They find also,
6235 that if Oils be poured in a small quantity upon fermentating Vegetables,
6236 they distil over after fermentation in the form of Spirits.
6237
6238 So then, by the foregoing Table, all Bodies seem to have their
6239 refractive Powers proportional to their Densities, (or very nearly;)
6240 excepting so far as they partake more or less of sulphureous oily
6241 Particles, and thereby have their refractive Power made greater or less.
6242 Whence it seems rational to attribute the refractive Power of all Bodies
6243 chiefly, if not wholly, to the sulphureous Parts with which they abound.
6244 For it's probable that all Bodies abound more or less with Sulphurs. And
6245 as Light congregated by a Burning-glass acts most upon sulphureous
6246 Bodies, to turn them into Fire and Flame; so, since all Action is
6247 mutual, Sulphurs ought to act most upon Light. For that the action
6248 between Light and Bodies is mutual, may appear from this Consideration;
6249 That the densest Bodies which refract and reflect Light most strongly,
6250 grow hottest in the Summer Sun, by the action of the refracted or
6251 reflected Light.
6252
6253 I have hitherto explain'd the power of Bodies to reflect and refract,
6254 and shew'd, that thin transparent Plates, Fibres, and Particles, do,
6255 according to their several thicknesses and densities, reflect several
6256 sorts of Rays, and thereby appear of several Colours; and by consequence
6257 that nothing more is requisite for producing all the Colours of natural
6258 Bodies, than the several sizes and densities of their transparent
6259 Particles. But whence it is that these Plates, Fibres, and Particles,
6260 do, according to their several thicknesses and densities, reflect
6261 several sorts of Rays, I have not yet explain'd. To give some insight
6262 into this matter, and make way for understanding the next part of this
6263 Book, I shall conclude this part with a few more Propositions. Those
6264 which preceded respect the nature of Bodies, these the nature of Light:
6265 For both must be understood, before the reason of their Actions upon one
6266 another can be known. And because the last Proposition depended upon the
6267 velocity of Light, I will begin with a Proposition of that kind.
6268
6269
6270 PROP. XI.
6271
6272 _Light is propagated from luminous Bodies in time, and spends about
6273 seven or eight Minutes of an Hour in passing from the Sun to the Earth._
6274
6275 This was observed first by _Roemer_, and then by others, by means of the
6276 Eclipses of the Satellites of _Jupiter_. For these Eclipses, when the
6277 Earth is between the Sun and _Jupiter_, happen about seven or eight
6278 Minutes sooner than they ought to do by the Tables, and when the Earth
6279 is beyond the Sun they happen about seven or eight Minutes later than
6280 they ought to do; the reason being, that the Light of the Satellites has
6281 farther to go in the latter case than in the former by the Diameter of
6282 the Earth's Orbit. Some inequalities of time may arise from the
6283 Excentricities of the Orbs of the Satellites; but those cannot answer in
6284 all the Satellites, and at all times to the Position and Distance of the
6285 Earth from the Sun. The mean motions of _Jupiter_'s Satellites is also
6286 swifter in his descent from his Aphelium to his Perihelium, than in his
6287 ascent in the other half of his Orb. But this inequality has no respect
6288 to the position of the Earth, and in the three interior Satellites is
6289 insensible, as I find by computation from the Theory of their Gravity.
6290
6291
6292 PROP. XII.
6293
6294 _Every Ray of Light in its passage through any refracting Surface is put
6295 into a certain transient Constitution or State, which in the progress of
6296 the Ray returns at equal Intervals, and disposes the Ray at every return
6297 to be easily transmitted through the next refracting Surface, and
6298 between the returns to be easily reflected by it._
6299
6300 This is manifest by the 5th, 9th, 12th, and 15th Observations. For by
6301 those Observations it appears, that one and the same sort of Rays at
6302 equal Angles of Incidence on any thin transparent Plate, is alternately
6303 reflected and transmitted for many Successions accordingly as the
6304 thickness of the Plate increases in arithmetical Progression of the
6305 Numbers, 0, 1, 2, 3, 4, 5, 6, 7, 8, &c. so that if the first Reflexion
6306 (that which makes the first or innermost of the Rings of Colours there
6307 described) be made at the thickness 1, the Rays shall be transmitted at
6308 the thicknesses 0, 2, 4, 6, 8, 10, 12, &c. and thereby make the central
6309 Spot and Rings of Light, which appear by transmission, and be reflected
6310 at the thickness 1, 3, 5, 7, 9, 11, &c. and thereby make the Rings which
6311 appear by Reflexion. And this alternate Reflexion and Transmission, as I
6312 gather by the 24th Observation, continues for above an hundred
6313 vicissitudes, and by the Observations in the next part of this Book, for
6314 many thousands, being propagated from one Surface of a Glass Plate to
6315 the other, though the thickness of the Plate be a quarter of an Inch or
6316 above: So that this alternation seems to be propagated from every
6317 refracting Surface to all distances without end or limitation.
6318
6319 This alternate Reflexion and Refraction depends on both the Surfaces of
6320 every thin Plate, because it depends on their distance. By the 21st
6321 Observation, if either Surface of a thin Plate of _Muscovy_ Glass be
6322 wetted, the Colours caused by the alternate Reflexion and Refraction
6323 grow faint, and therefore it depends on them both.
6324
6325 It is therefore perform'd at the second Surface; for if it were
6326 perform'd at the first, before the Rays arrive at the second, it would
6327 not depend on the second.
6328
6329 It is also influenced by some action or disposition, propagated from the
6330 first to the second, because otherwise at the second it would not depend
6331 on the first. And this action or disposition, in its propagation,
6332 intermits and returns by equal Intervals, because in all its progress it
6333 inclines the Ray at one distance from the first Surface to be reflected
6334 by the second, at another to be transmitted by it, and that by equal
6335 Intervals for innumerable vicissitudes. And because the Ray is disposed
6336 to Reflexion at the distances 1, 3, 5, 7, 9, &c. and to Transmission at
6337 the distances 0, 2, 4, 6, 8, 10, &c. (for its transmission through the
6338 first Surface, is at the distance 0, and it is transmitted through both
6339 together, if their distance be infinitely little or much less than 1)
6340 the disposition to be transmitted at the distances 2, 4, 6, 8, 10, &c.
6341 is to be accounted a return of the same disposition which the Ray first
6342 had at the distance 0, that is at its transmission through the first
6343 refracting Surface. All which is the thing I would prove.
6344
6345 What kind of action or disposition this is; Whether it consists in a
6346 circulating or a vibrating motion of the Ray, or of the Medium, or
6347 something else, I do not here enquire. Those that are averse from
6348 assenting to any new Discoveries, but such as they can explain by an
6349 Hypothesis, may for the present suppose, that as Stones by falling upon
6350 Water put the Water into an undulating Motion, and all Bodies by
6351 percussion excite vibrations in the Air; so the Rays of Light, by
6352 impinging on any refracting or reflecting Surface, excite vibrations in
6353 the refracting or reflecting Medium or Substance, and by exciting them
6354 agitate the solid parts of the refracting or reflecting Body, and by
6355 agitating them cause the Body to grow warm or hot; that the vibrations
6356 thus excited are propagated in the refracting or reflecting Medium or
6357 Substance, much after the manner that vibrations are propagated in the
6358 Air for causing Sound, and move faster than the Rays so as to overtake
6359 them; and that when any Ray is in that part of the vibration which
6360 conspires with its Motion, it easily breaks through a refracting
6361 Surface, but when it is in the contrary part of the vibration which
6362 impedes its Motion, it is easily reflected; and, by consequence, that
6363 every Ray is successively disposed to be easily reflected, or easily
6364 transmitted, by every vibration which overtakes it. But whether this
6365 Hypothesis be true or false I do not here consider. I content my self
6366 with the bare Discovery, that the Rays of Light are by some cause or
6367 other alternately disposed to be reflected or refracted for many
6368 vicissitudes.
6369
6370
6371 DEFINITION.
6372
6373 _The returns of the disposition of any Ray to be reflected I will call
6374 its_ Fits of easy Reflexion, _and those of its disposition to be
6375 transmitted its_ Fits of easy Transmission, _and the space it passes
6376 between every return and the next return, the_ Interval of its Fits.
6377
6378
6379 PROP. XIII.
6380
6381 _The reason why the Surfaces of all thick transparent Bodies reflect
6382 part of the Light incident on them, and refract the rest, is, that some
6383 Rays at their Incidence are in Fits of easy Reflexion, and others in
6384 Fits of easy Transmission._
6385
6386 This may be gather'd from the 24th Observation, where the Light
6387 reflected by thin Plates of Air and Glass, which to the naked Eye
6388 appear'd evenly white all over the Plate, did through a Prism appear
6389 waved with many Successions of Light and Darkness made by alternate Fits
6390 of easy Reflexion and easy Transmission, the Prism severing and
6391 distinguishing the Waves of which the white reflected Light was
6392 composed, as was explain'd above.
6393
6394 And hence Light is in Fits of easy Reflexion and easy Transmission,
6395 before its Incidence on transparent Bodies. And probably it is put into
6396 such fits at its first emission from luminous Bodies, and continues in
6397 them during all its progress. For these Fits are of a lasting nature, as
6398 will appear by the next part of this Book.
6399
6400 In this Proposition I suppose the transparent Bodies to be thick;
6401 because if the thickness of the Body be much less than the Interval of
6402 the Fits of easy Reflexion and Transmission of the Rays, the Body loseth
6403 its reflecting power. For if the Rays, which at their entering into the
6404 Body are put into Fits of easy Transmission, arrive at the farthest
6405 Surface of the Body before they be out of those Fits, they must be
6406 transmitted. And this is the reason why Bubbles of Water lose their
6407 reflecting power when they grow very thin; and why all opake Bodies,
6408 when reduced into very small parts, become transparent.
6409
6410
6411 PROP. XIV.
6412
6413 _Those Surfaces of transparent Bodies, which if the Ray be in a Fit of
6414 Refraction do refract it most strongly, if the Ray be in a Fit of
6415 Reflexion do reflect it most easily._
6416
6417 For we shewed above, in _Prop._ 8. that the cause of Reflexion is not
6418 the impinging of Light on the solid impervious parts of Bodies, but some
6419 other power by which those solid parts act on Light at a distance. We
6420 shewed also in _Prop._ 9. that Bodies reflect and refract Light by one
6421 and the same power, variously exercised in various circumstances; and in
6422 _Prop._ 1. that the most strongly refracting Surfaces reflect the most
6423 Light: All which compared together evince and rarify both this and the
6424 last Proposition.
6425
6426
6427 PROP. XV.
6428
6429 _In any one and the same sort of Rays, emerging in any Angle out of any
6430 refracting Surface into one and the same Medium, the Interval of the
6431 following Fits of easy Reflexion and Transmission are either accurately
6432 or very nearly, as the Rectangle of the Secant of the Angle of
6433 Refraction, and of the Secant of another Angle, whose Sine is the first
6434 of 106 arithmetical mean Proportionals, between the Sines of Incidence
6435 and Refraction, counted from the Sine of Refraction._
6436
6437 This is manifest by the 7th and 19th Observations.
6438
6439
6440 PROP. XVI.
6441
6442 _In several sorts of Rays emerging in equal Angles out of any refracting
6443 Surface into the same Medium, the Intervals of the following Fits of
6444 easy Reflexion and easy Transmission are either accurately, or very
6445 nearly, as the Cube-Roots of the Squares of the lengths of a Chord,
6446 which found the Notes in an Eight_, sol, la, fa, sol, la, mi, fa, sol,
6447 _with all their intermediate degrees answering to the Colours of those
6448 Rays, according to the Analogy described in the seventh Experiment of
6449 the second Part of the first Book._
6450
6451 This is manifest by the 13th and 14th Observations.
6452
6453
6454 PROP. XVII.
6455
6456 _If Rays of any sort pass perpendicularly into several Mediums, the
6457 Intervals of the Fits of easy Reflexion and Transmission in any one
6458 Medium, are to those Intervals in any other, as the Sine of Incidence to
6459 the Sine of Refraction, when the Rays pass out of the first of those two
6460 Mediums into the second._
6461
6462 This is manifest by the 10th Observation.
6463
6464
6465 PROP. XVIII.
6466
6467 _If the Rays which paint the Colour in the Confine of yellow and orange
6468 pass perpendicularly out of any Medium into Air, the Intervals of their
6469 Fits of easy Reflexion are the 1/89000th part of an Inch. And of the
6470 same length are the Intervals of their Fits of easy Transmission._
6471
6472 This is manifest by the 6th Observation. From these Propositions it is
6473 easy to collect the Intervals of the Fits of easy Reflexion and easy
6474 Transmission of any sort of Rays refracted in any angle into any Medium;
6475 and thence to know, whether the Rays shall be reflected or transmitted
6476 at their subsequent Incidence upon any other pellucid Medium. Which
6477 thing, being useful for understanding the next part of this Book, was
6478 here to be set down. And for the same reason I add the two following
6479 Propositions.
6480
6481
6482 PROP. XIX.
6483
6484 _If any sort of Rays falling on the polite Surface of any pellucid
6485 Medium be reflected back, the Fits of easy Reflexion, which they have at
6486 the point of Reflexion, shall still continue to return; and the Returns
6487 shall be at distances from the point of Reflexion in the arithmetical
6488 progression of the Numbers 2, 4, 6, 8, 10, 12, &c. and between these
6489 Fits the Rays shall be in Fits of easy Transmission._
6490
6491 For since the Fits of easy Reflexion and easy Transmission are of a
6492 returning nature, there is no reason why these Fits, which continued
6493 till the Ray arrived at the reflecting Medium, and there inclined the
6494 Ray to Reflexion, should there cease. And if the Ray at the point of
6495 Reflexion was in a Fit of easy Reflexion, the progression of the
6496 distances of these Fits from that point must begin from 0, and so be of
6497 the Numbers 0, 2, 4, 6, 8, &c. And therefore the progression of the
6498 distances of the intermediate Fits of easy Transmission, reckon'd from
6499 the same point, must be in the progression of the odd Numbers 1, 3, 5,
6500 7, 9, &c. contrary to what happens when the Fits are propagated from
6501 points of Refraction.
6502
6503
6504 PROP. XX.
6505
6506 _The Intervals of the Fits of easy Reflexion and easy Transmission,
6507 propagated from points of Reflexion into any Medium, are equal to the
6508 Intervals of the like Fits, which the same Rays would have, if refracted
6509 into the same Medium in Angles of Refraction equal to their Angles of
6510 Reflexion._
6511
6512 For when Light is reflected by the second Surface of thin Plates, it
6513 goes out afterwards freely at the first Surface to make the Rings of
6514 Colours which appear by Reflexion; and, by the freedom of its egress,
6515 makes the Colours of these Rings more vivid and strong than those which
6516 appear on the other side of the Plates by the transmitted Light. The
6517 reflected Rays are therefore in Fits of easy Transmission at their
6518 egress; which would not always happen, if the Intervals of the Fits
6519 within the Plate after Reflexion were not equal, both in length and
6520 number, to their Intervals before it. And this confirms also the
6521 proportions set down in the former Proposition. For if the Rays both in
6522 going in and out at the first Surface be in Fits of easy Transmission,
6523 and the Intervals and Numbers of those Fits between the first and second
6524 Surface, before and after Reflexion, be equal, the distances of the Fits
6525 of easy Transmission from either Surface, must be in the same
6526 progression after Reflexion as before; that is, from the first Surface
6527 which transmitted them in the progression of the even Numbers 0, 2, 4,
6528 6, 8, &c. and from the second which reflected them, in that of the odd
6529 Numbers 1, 3, 5, 7, &c. But these two Propositions will become much more
6530 evident by the Observations in the following part of this Book.
6531
6532
6533
6534
6535 THE
6536
6537 SECOND BOOK
6538
6539 OF
6540
6541 OPTICKS
6542
6543
6544 _PART IV._
6545
6546 _Observations concerning the Reflexions and Colours of thick transparent
6547 polish'd Plates._
6548
6549 There is no Glass or Speculum how well soever polished, but, besides the
6550 Light which it refracts or reflects regularly, scatters every way
6551 irregularly a faint Light, by means of which the polish'd Surface, when
6552 illuminated in a dark room by a beam of the Sun's Light, may be easily
6553 seen in all positions of the Eye. There are certain Phænomena of this
6554 scatter'd Light, which when I first observed them, seem'd very strange
6555 and surprizing to me. My Observations were as follows.
6556
6557 _Obs._ 1. The Sun shining into my darken'd Chamber through a hole one
6558 third of an Inch wide, I let the intromitted beam of Light fall
6559 perpendicularly upon a Glass Speculum ground concave on one side and
6560 convex on the other, to a Sphere of five Feet and eleven Inches Radius,
6561 and Quick-silver'd over on the convex side. And holding a white opake
6562 Chart, or a Quire of Paper at the center of the Spheres to which the
6563 Speculum was ground, that is, at the distance of about five Feet and
6564 eleven Inches from the Speculum, in such manner, that the beam of Light
6565 might pass through a little hole made in the middle of the Chart to the
6566 Speculum, and thence be reflected back to the same hole: I observed upon
6567 the Chart four or five concentric Irises or Rings of Colours, like
6568 Rain-bows, encompassing the hole much after the manner that those, which
6569 in the fourth and following Observations of the first part of this Book
6570 appear'd between the Object-glasses, encompassed the black Spot, but yet
6571 larger and fainter than those. These Rings as they grew larger and
6572 larger became diluter and fainter, so that the fifth was scarce visible.
6573 Yet sometimes, when the Sun shone very clear, there appear'd faint
6574 Lineaments of a sixth and seventh. If the distance of the Chart from the
6575 Speculum was much greater or much less than that of six Feet, the Rings
6576 became dilute and vanish'd. And if the distance of the Speculum from the
6577 Window was much greater than that of six Feet, the reflected beam of
6578 Light would be so broad at the distance of six Feet from the Speculum
6579 where the Rings appear'd, as to obscure one or two of the innermost
6580 Rings. And therefore I usually placed the Speculum at about six Feet
6581 from the Window; so that its Focus might there fall in with the center
6582 of its concavity at the Rings upon the Chart. And this Posture is always
6583 to be understood in the following Observations where no other is
6584 express'd.
6585
6586 _Obs._ 2. The Colours of these Rain-bows succeeded one another from the
6587 center outwards, in the same form and order with those which were made
6588 in the ninth Observation of the first Part of this Book by Light not
6589 reflected, but transmitted through the two Object-glasses. For, first,
6590 there was in their common center a white round Spot of faint Light,
6591 something broader than the reflected beam of Light, which beam sometimes
6592 fell upon the middle of the Spot, and sometimes by a little inclination
6593 of the Speculum receded from the middle, and left the Spot white to the
6594 center.
6595
6596 This white Spot was immediately encompassed with a dark grey or russet,
6597 and that dark grey with the Colours of the first Iris; which Colours on
6598 the inside next the dark grey were a little violet and indigo, and next
6599 to that a blue, which on the outside grew pale, and then succeeded a
6600 little greenish yellow, and after that a brighter yellow, and then on
6601 the outward edge of the Iris a red which on the outside inclined to
6602 purple.
6603
6604 This Iris was immediately encompassed with a second, whose Colours were
6605 in order from the inside outwards, purple, blue, green, yellow, light
6606 red, a red mix'd with purple.
6607
6608 Then immediately follow'd the Colours of the third Iris, which were in
6609 order outwards a green inclining to purple, a good green, and a red more
6610 bright than that of the former Iris.
6611
6612 The fourth and fifth Iris seem'd of a bluish green within, and red
6613 without, but so faintly that it was difficult to discern the Colours.
6614
6615 _Obs._ 3. Measuring the Diameters of these Rings upon the Chart as
6616 accurately as I could, I found them also in the same proportion to one
6617 another with the Rings made by Light transmitted through the two
6618 Object-glasses. For the Diameters of the four first of the bright Rings
6619 measured between the brightest parts of their Orbits, at the distance of
6620 six Feet from the Speculum were 1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches,
6621 whose Squares are in arithmetical progression of the numbers 1, 2, 3, 4.
6622 If the white circular Spot in the middle be reckon'd amongst the Rings,
6623 and its central Light, where it seems to be most luminous, be put
6624 equipollent to an infinitely little Ring; the Squares of the Diameters
6625 of the Rings will be in the progression 0, 1, 2, 3, 4, &c. I measured
6626 also the Diameters of the dark Circles between these luminous ones, and
6627 found their Squares in the progression of the numbers 1/2, 1-1/2, 2-1/2,
6628 3-1/2, &c. the Diameters of the first four at the distance of six Feet
6629 from the Speculum, being 1-3/16, 2-1/16, 2-2/3, 3-3/20 Inches. If the
6630 distance of the Chart from the Speculum was increased or diminished, the
6631 Diameters of the Circles were increased or diminished proportionally.
6632
6633 _Obs._ 4. By the analogy between these Rings and those described in the
6634 Observations of the first Part of this Book, I suspected that there
6635 were many more of them which spread into one another, and by interfering
6636 mix'd their Colours, and diluted one another so that they could not be
6637 seen apart. I viewed them therefore through a Prism, as I did those in
6638 the 24th Observation of the first Part of this Book. And when the Prism
6639 was so placed as by refracting the Light of their mix'd Colours to
6640 separate them, and distinguish the Rings from one another, as it did
6641 those in that Observation, I could then see them distincter than before,
6642 and easily number eight or nine of them, and sometimes twelve or
6643 thirteen. And had not their Light been so very faint, I question not but
6644 that I might have seen many more.
6645
6646 _Obs._ 5. Placing a Prism at the Window to refract the intromitted beam
6647 of Light, and cast the oblong Spectrum of Colours on the Speculum: I
6648 covered the Speculum with a black Paper which had in the middle of it a
6649 hole to let any one of the Colours pass through to the Speculum, whilst
6650 the rest were intercepted by the Paper. And now I found Rings of that
6651 Colour only which fell upon the Speculum. If the Speculum was
6652 illuminated with red, the Rings were totally red with dark Intervals, if
6653 with blue they were totally blue, and so of the other Colours. And when
6654 they were illuminated with any one Colour, the Squares of their
6655 Diameters measured between their most luminous Parts, were in the
6656 arithmetical Progression of the Numbers, 0, 1, 2, 3, 4 and the Squares
6657 of the Diameters of their dark Intervals in the Progression of the
6658 intermediate Numbers 1/2, 1-1/2, 2-1/2, 3-1/2. But if the Colour was
6659 varied, they varied their Magnitude. In the red they were largest, in
6660 the indigo and violet least, and in the intermediate Colours yellow,
6661 green, and blue, they were of several intermediate Bignesses answering
6662 to the Colour, that is, greater in yellow than in green, and greater in
6663 green than in blue. And hence I knew, that when the Speculum was
6664 illuminated with white Light, the red and yellow on the outside of the
6665 Rings were produced by the least refrangible Rays, and the blue and
6666 violet by the most refrangible, and that the Colours of each Ring spread
6667 into the Colours of the neighbouring Rings on either side, after the
6668 manner explain'd in the first and second Part of this Book, and by
6669 mixing diluted one another so that they could not be distinguish'd,
6670 unless near the Center where they were least mix'd. For in this
6671 Observation I could see the Rings more distinctly, and to a greater
6672 Number than before, being able in the yellow Light to number eight or
6673 nine of them, besides a faint shadow of a tenth. To satisfy my self how
6674 much the Colours of the several Rings spread into one another, I
6675 measured the Diameters of the second and third Rings, and found them
6676 when made by the Confine of the red and orange to be to the same
6677 Diameters when made by the Confine of blue and indigo, as 9 to 8, or
6678 thereabouts. For it was hard to determine this Proportion accurately.
6679 Also the Circles made successively by the red, yellow, and green,
6680 differ'd more from one another than those made successively by the
6681 green, blue, and indigo. For the Circle made by the violet was too dark
6682 to be seen. To carry on the Computation, let us therefore suppose that
6683 the Differences of the Diameters of the Circles made by the outmost red,
6684 the Confine of red and orange, the Confine of orange and yellow, the
6685 Confine of yellow and green, the Confine of green and blue, the Confine
6686 of blue and indigo, the Confine of indigo and violet, and outmost
6687 violet, are in proportion as the Differences of the Lengths of a
6688 Monochord which sound the Tones in an Eight; _sol_, _la_, _fa_, _sol_,
6689 _la_, _mi_, _fa_, _sol_, that is, as the Numbers 1/9, 1/18, 1/12, 1/12,
6690 2/27, 1/27, 1/18. And if the Diameter of the Circle made by the Confine
6691 of red and orange be 9A, and that of the Circle made by the Confine of
6692 blue and indigo be 8A as above; their difference 9A-8A will be to the
6693 difference of the Diameters of the Circles made by the outmost red, and
6694 by the Confine of red and orange, as 1/18 + 1/12 + 1/12 + 2/27 to 1/9,
6695 that is as 8/27 to 1/9, or 8 to 3, and to the difference of the Circles
6696 made by the outmost violet, and by the Confine of blue and indigo, as
6697 1/18 + 1/12 + 1/12 + 2/27 to 1/27 + 1/18, that is, as 8/27 to 5/54, or
6698 as 16 to 5. And therefore these differences will be 3/8A and 5/16A. Add
6699 the first to 9A and subduct the last from 8A, and you will have the
6700 Diameters of the Circles made by the least and most refrangible Rays
6701 75/8A and ((61-1/2)/8)A. These diameters are therefore to one another as
6702 75 to 61-1/2 or 50 to 41, and their Squares as 2500 to 1681, that is, as
6703 3 to 2 very nearly. Which proportion differs not much from the
6704 proportion of the Diameters of the Circles made by the outmost red and
6705 outmost violet, in the 13th Observation of the first part of this Book.
6706
6707 _Obs._ 6. Placing my Eye where these Rings appear'd plainest, I saw the
6708 Speculum tinged all over with Waves of Colours, (red, yellow, green,
6709 blue;) like those which in the Observations of the first part of this
6710 Book appeared between the Object-glasses, and upon Bubbles of Water, but
6711 much larger. And after the manner of those, they were of various
6712 magnitudes in various Positions of the Eye, swelling and shrinking as I
6713 moved my Eye this way and that way. They were formed like Arcs of
6714 concentrick Circles, as those were; and when my Eye was over against the
6715 center of the concavity of the Speculum, (that is, 5 Feet and 10 Inches
6716 distant from the Speculum,) their common center was in a right Line with
6717 that center of concavity, and with the hole in the Window. But in other
6718 postures of my Eye their center had other positions. They appear'd by
6719 the Light of the Clouds propagated to the Speculum through the hole in
6720 the Window; and when the Sun shone through that hole upon the Speculum,
6721 his Light upon it was of the Colour of the Ring whereon it fell, but by
6722 its splendor obscured the Rings made by the Light of the Clouds, unless
6723 when the Speculum was removed to a great distance from the Window, so
6724 that his Light upon it might be broad and faint. By varying the position
6725 of my Eye, and moving it nearer to or farther from the direct beam of
6726 the Sun's Light, the Colour of the Sun's reflected Light constantly
6727 varied upon the Speculum, as it did upon my Eye, the same Colour always
6728 appearing to a Bystander upon my Eye which to me appear'd upon the
6729 Speculum. And thence I knew that the Rings of Colours upon the Chart
6730 were made by these reflected Colours, propagated thither from the
6731 Speculum in several Angles, and that their production depended not upon
6732 the termination of Light and Shadow.
6733
6734 _Obs._ 7. By the Analogy of all these Phænomena with those of the like
6735 Rings of Colours described in the first part of this Book, it seemed to
6736 me that these Colours were produced by this thick Plate of Glass, much
6737 after the manner that those were produced by very thin Plates. For, upon
6738 trial, I found that if the Quick-silver were rubb'd off from the
6739 backside of the Speculum, the Glass alone would cause the same Rings of
6740 Colours, but much more faint than before; and therefore the Phænomenon
6741 depends not upon the Quick-silver, unless so far as the Quick-silver by
6742 increasing the Reflexion of the backside of the Glass increases the
6743 Light of the Rings of Colours. I found also that a Speculum of Metal
6744 without Glass made some Years since for optical uses, and very well
6745 wrought, produced none of those Rings; and thence I understood that
6746 these Rings arise not from one specular Surface alone, but depend upon
6747 the two Surfaces of the Plate of Glass whereof the Speculum was made,
6748 and upon the thickness of the Glass between them. For as in the 7th and
6749 19th Observations of the first part of this Book a thin Plate of Air,
6750 Water, or Glass of an even thickness appeared of one Colour when the
6751 Rays were perpendicular to it, of another when they were a little
6752 oblique, of another when more oblique, of another when still more
6753 oblique, and so on; so here, in the sixth Observation, the Light which
6754 emerged out of the Glass in several Obliquities, made the Glass appear
6755 of several Colours, and being propagated in those Obliquities to the
6756 Chart, there painted Rings of those Colours. And as the reason why a
6757 thin Plate appeared of several Colours in several Obliquities of the
6758 Rays, was, that the Rays of one and the same sort are reflected by the
6759 thin Plate at one obliquity and transmitted at another, and those of
6760 other sorts transmitted where these are reflected, and reflected where
6761 these are transmitted: So the reason why the thick Plate of Glass
6762 whereof the Speculum was made did appear of various Colours in various
6763 Obliquities, and in those Obliquities propagated those Colours to the
6764 Chart, was, that the Rays of one and the same sort did at one Obliquity
6765 emerge out of the Glass, at another did not emerge, but were reflected
6766 back towards the Quick-silver by the hither Surface of the Glass, and
6767 accordingly as the Obliquity became greater and greater, emerged and
6768 were reflected alternately for many Successions; and that in one and the
6769 same Obliquity the Rays of one sort were reflected, and those of another
6770 transmitted. This is manifest by the fifth Observation of this part of
6771 this Book. For in that Observation, when the Speculum was illuminated by
6772 any one of the prismatick Colours, that Light made many Rings of the
6773 same Colour upon the Chart with dark Intervals, and therefore at its
6774 emergence out of the Speculum was alternately transmitted and not
6775 transmitted from the Speculum to the Chart for many Successions,
6776 according to the various Obliquities of its Emergence. And when the
6777 Colour cast on the Speculum by the Prism was varied, the Rings became of
6778 the Colour cast on it, and varied their bigness with their Colour, and
6779 therefore the Light was now alternately transmitted and not transmitted
6780 from the Speculum to the Chart at other Obliquities than before. It
6781 seemed to me therefore that these Rings were of one and the same
6782 original with those of thin Plates, but yet with this difference, that
6783 those of thin Plates are made by the alternate Reflexions and
6784 Transmissions of the Rays at the second Surface of the Plate, after one
6785 passage through it; but here the Rays go twice through the Plate before
6786 they are alternately reflected and transmitted. First, they go through
6787 it from the first Surface to the Quick-silver, and then return through
6788 it from the Quick-silver to the first Surface, and there are either
6789 transmitted to the Chart or reflected back to the Quick-silver,
6790 accordingly as they are in their Fits of easy Reflexion or Transmission
6791 when they arrive at that Surface. For the Intervals of the Fits of the
6792 Rays which fall perpendicularly on the Speculum, and are reflected back
6793 in the same perpendicular Lines, by reason of the equality of these
6794 Angles and Lines, are of the same length and number within the Glass
6795 after Reflexion as before, by the 19th Proposition of the third part of
6796 this Book. And therefore since all the Rays that enter through the
6797 first Surface are in their Fits of easy Transmission at their entrance,
6798 and as many of these as are reflected by the second are in their Fits of
6799 easy Reflexion there, all these must be again in their Fits of easy
6800 Transmission at their return to the first, and by consequence there go
6801 out of the Glass to the Chart, and form upon it the white Spot of Light
6802 in the center of the Rings. For the reason holds good in all sorts of
6803 Rays, and therefore all sorts must go out promiscuously to that Spot,
6804 and by their mixture cause it to be white. But the Intervals of the Fits
6805 of those Rays which are reflected more obliquely than they enter, must
6806 be greater after Reflexion than before, by the 15th and 20th
6807 Propositions. And thence it may happen that the Rays at their return to
6808 the first Surface, may in certain Obliquities be in Fits of easy
6809 Reflexion, and return back to the Quick-silver, and in other
6810 intermediate Obliquities be again in Fits of easy Transmission, and so
6811 go out to the Chart, and paint on it the Rings of Colours about the
6812 white Spot. And because the Intervals of the Fits at equal obliquities
6813 are greater and fewer in the less refrangible Rays, and less and more
6814 numerous in the more refrangible, therefore the less refrangible at
6815 equal obliquities shall make fewer Rings than the more refrangible, and
6816 the Rings made by those shall be larger than the like number of Rings
6817 made by these; that is, the red Rings shall be larger than the yellow,
6818 the yellow than the green, the green than the blue, and the blue than
6819 the violet, as they were really found to be in the fifth Observation.
6820 And therefore the first Ring of all Colours encompassing the white Spot
6821 of Light shall be red without any violet within, and yellow, and green,
6822 and blue in the middle, as it was found in the second Observation; and
6823 these Colours in the second Ring, and those that follow, shall be more
6824 expanded, till they spread into one another, and blend one another by
6825 interfering.
6826
6827 These seem to be the reasons of these Rings in general; and this put me
6828 upon observing the thickness of the Glass, and considering whether the
6829 dimensions and proportions of the Rings may be truly derived from it by
6830 computation.
6831
6832 _Obs._ 8. I measured therefore the thickness of this concavo-convex
6833 Plate of Glass, and found it every where 1/4 of an Inch precisely. Now,
6834 by the sixth Observation of the first Part of this Book, a thin Plate of
6835 Air transmits the brightest Light of the first Ring, that is, the bright
6836 yellow, when its thickness is the 1/89000th part of an Inch; and by the
6837 tenth Observation of the same Part, a thin Plate of Glass transmits the
6838 same Light of the same Ring, when its thickness is less in proportion of
6839 the Sine of Refraction to the Sine of Incidence, that is, when its
6840 thickness is the 11/1513000th or 1/137545th part of an Inch, supposing
6841 the Sines are as 11 to 17. And if this thickness be doubled, it
6842 transmits the same bright Light of the second Ring; if tripled, it
6843 transmits that of the third, and so on; the bright yellow Light in all
6844 these cases being in its Fits of Transmission. And therefore if its
6845 thickness be multiplied 34386 times, so as to become 1/4 of an Inch, it
6846 transmits the same bright Light of the 34386th Ring. Suppose this be the
6847 bright yellow Light transmitted perpendicularly from the reflecting
6848 convex side of the Glass through the concave side to the white Spot in
6849 the center of the Rings of Colours on the Chart: And by a Rule in the
6850 7th and 19th Observations in the first Part of this Book, and by the
6851 15th and 20th Propositions of the third Part of this Book, if the Rays
6852 be made oblique to the Glass, the thickness of the Glass requisite to
6853 transmit the same bright Light of the same Ring in any obliquity, is to
6854 this thickness of 1/4 of an Inch, as the Secant of a certain Angle to
6855 the Radius, the Sine of which Angle is the first of an hundred and six
6856 arithmetical Means between the Sines of Incidence and Refraction,
6857 counted from the Sine of Incidence when the Refraction is made out of
6858 any plated Body into any Medium encompassing it; that is, in this case,
6859 out of Glass into Air. Now if the thickness of the Glass be increased by
6860 degrees, so as to bear to its first thickness, (_viz._ that of a quarter
6861 of an Inch,) the Proportions which 34386 (the number of Fits of the
6862 perpendicular Rays in going through the Glass towards the white Spot in
6863 the center of the Rings,) hath to 34385, 34384, 34383, and 34382, (the
6864 numbers of the Fits of the oblique Rays in going through the Glass
6865 towards the first, second, third, and fourth Rings of Colours,) and if
6866 the first thickness be divided into 100000000 equal parts, the increased
6867 thicknesses will be 100002908, 100005816, 100008725, and 100011633, and
6868 the Angles of which these thicknesses are Secants will be 26´ 13´´, 37´
6869 5´´, 45´ 6´´, and 52´ 26´´, the Radius being 100000000; and the Sines of
6870 these Angles are 762, 1079, 1321, and 1525, and the proportional Sines
6871 of Refraction 1172, 1659, 2031, and 2345, the Radius being 100000. For
6872 since the Sines of Incidence out of Glass into Air are to the Sines of
6873 Refraction as 11 to 17, and to the above-mentioned Secants as 11 to the
6874 first of 106 arithmetical Means between 11 and 17, that is, as 11 to
6875 11-6/106, those Secants will be to the Sines of Refraction as 11-6/106,
6876 to 17, and by this Analogy will give these Sines. So then, if the
6877 obliquities of the Rays to the concave Surface of the Glass be such that
6878 the Sines of their Refraction in passing out of the Glass through that
6879 Surface into the Air be 1172, 1659, 2031, 2345, the bright Light of the
6880 34386th Ring shall emerge at the thicknesses of the Glass, which are to
6881 1/4 of an Inch as 34386 to 34385, 34384, 34383, 34382, respectively. And
6882 therefore, if the thickness in all these Cases be 1/4 of an Inch (as it
6883 is in the Glass of which the Speculum was made) the bright Light of the
6884 34385th Ring shall emerge where the Sine of Refraction is 1172, and that
6885 of the 34384th, 34383th, and 34382th Ring where the Sine is 1659, 2031,
6886 and 2345 respectively. And in these Angles of Refraction the Light of
6887 these Rings shall be propagated from the Speculum to the Chart, and
6888 there paint Rings about the white central round Spot of Light which we
6889 said was the Light of the 34386th Ring. And the Semidiameters of these
6890 Rings shall subtend the Angles of Refraction made at the
6891 Concave-Surface of the Speculum, and by consequence their Diameters
6892 shall be to the distance of the Chart from the Speculum as those Sines
6893 of Refraction doubled are to the Radius, that is, as 1172, 1659, 2031,
6894 and 2345, doubled are to 100000. And therefore, if the distance of the
6895 Chart from the Concave-Surface of the Speculum be six Feet (as it was in
6896 the third of these Observations) the Diameters of the Rings of this
6897 bright yellow Light upon the Chart shall be 1'688, 2'389, 2'925, 3'375
6898 Inches: For these Diameters are to six Feet, as the above-mention'd
6899 Sines doubled are to the Radius. Now, these Diameters of the bright
6900 yellow Rings, thus found by Computation are the very same with those
6901 found in the third of these Observations by measuring them, _viz._ with
6902 1-11/16, 2-3/8, 2-11/12, and 3-3/8 Inches, and therefore the Theory of
6903 deriving these Rings from the thickness of the Plate of Glass of which
6904 the Speculum was made, and from the Obliquity of the emerging Rays
6905 agrees with the Observation. In this Computation I have equalled the
6906 Diameters of the bright Rings made by Light of all Colours, to the
6907 Diameters of the Rings made by the bright yellow. For this yellow makes
6908 the brightest Part of the Rings of all Colours. If you desire the
6909 Diameters of the Rings made by the Light of any other unmix'd Colour,
6910 you may find them readily by putting them to the Diameters of the bright
6911 yellow ones in a subduplicate Proportion of the Intervals of the Fits of
6912 the Rays of those Colours when equally inclined to the refracting or
6913 reflecting Surface which caused those Fits, that is, by putting the
6914 Diameters of the Rings made by the Rays in the Extremities and Limits of
6915 the seven Colours, red, orange, yellow, green, blue, indigo, violet,
6916 proportional to the Cube-roots of the Numbers, 1, 8/9, 5/6, 3/4, 2/3,
6917 3/5, 9/16, 1/2, which express the Lengths of a Monochord sounding the
6918 Notes in an Eighth: For by this means the Diameters of the Rings of
6919 these Colours will be found pretty nearly in the same Proportion to one
6920 another, which they ought to have by the fifth of these Observations.
6921
6922 And thus I satisfy'd my self, that these Rings were of the same kind and
6923 Original with those of thin Plates, and by consequence that the Fits or
6924 alternate Dispositions of the Rays to be reflected and transmitted are
6925 propagated to great distances from every reflecting and refracting
6926 Surface. But yet to put the matter out of doubt, I added the following
6927 Observation.
6928
6929 _Obs._ 9. If these Rings thus depend on the thickness of the Plate of
6930 Glass, their Diameters at equal distances from several Speculums made of
6931 such concavo-convex Plates of Glass as are ground on the same Sphere,
6932 ought to be reciprocally in a subduplicate Proportion of the thicknesses
6933 of the Plates of Glass. And if this Proportion be found true by
6934 experience it will amount to a demonstration that these Rings (like
6935 those formed in thin Plates) do depend on the thickness of the Glass. I
6936 procured therefore another concavo-convex Plate of Glass ground on both
6937 sides to the same Sphere with the former Plate. Its thickness was 5/62
6938 Parts of an Inch; and the Diameters of the three first bright Rings
6939 measured between the brightest Parts of their Orbits at the distance of
6940 six Feet from the Glass were 3·4-1/6·5-1/8· Inches. Now, the thickness
6941 of the other Glass being 1/4 of an Inch was to the thickness of this
6942 Glass as 1/4 to 5/62, that is as 31 to 10, or 310000000 to 100000000,
6943 and the Roots of these Numbers are 17607 and 10000, and in the
6944 Proportion of the first of these Roots to the second are the Diameters
6945 of the bright Rings made in this Observation by the thinner Glass,
6946 3·4-1/6·5-1/8, to the Diameters of the same Rings made in the third of
6947 these Observations by the thicker Glass 1-11/16, 2-3/8. 2-11/12, that
6948 is, the Diameters of the Rings are reciprocally in a subduplicate
6949 Proportion of the thicknesses of the Plates of Glass.
6950
6951 So then in Plates of Glass which are alike concave on one side, and
6952 alike convex on the other side, and alike quick-silver'd on the convex
6953 sides, and differ in nothing but their thickness, the Diameters of the
6954 Rings are reciprocally in a subduplicate Proportion of the thicknesses
6955 of the Plates. And this shews sufficiently that the Rings depend on both
6956 the Surfaces of the Glass. They depend on the convex Surface, because
6957 they are more luminous when that Surface is quick-silver'd over than
6958 when it is without Quick-silver. They depend also upon the concave
6959 Surface, because without that Surface a Speculum makes them not. They
6960 depend on both Surfaces, and on the distances between them, because
6961 their bigness is varied by varying only that distance. And this
6962 dependence is of the same kind with that which the Colours of thin
6963 Plates have on the distance of the Surfaces of those Plates, because the
6964 bigness of the Rings, and their Proportion to one another, and the
6965 variation of their bigness arising from the variation of the thickness
6966 of the Glass, and the Orders of their Colours, is such as ought to
6967 result from the Propositions in the end of the third Part of this Book,
6968 derived from the Phænomena of the Colours of thin Plates set down in the
6969 first Part.
6970
6971 There are yet other Phænomena of these Rings of Colours, but such as
6972 follow from the same Propositions, and therefore confirm both the Truth
6973 of those Propositions, and the Analogy between these Rings and the Rings
6974 of Colours made by very thin Plates. I shall subjoin some of them.
6975
6976 _Obs._ 10. When the beam of the Sun's Light was reflected back from the
6977 Speculum not directly to the hole in the Window, but to a place a little
6978 distant from it, the common center of that Spot, and of all the Rings of
6979 Colours fell in the middle way between the beam of the incident Light,
6980 and the beam of the reflected Light, and by consequence in the center of
6981 the spherical concavity of the Speculum, whenever the Chart on which the
6982 Rings of Colours fell was placed at that center. And as the beam of
6983 reflected Light by inclining the Speculum receded more and more from the
6984 beam of incident Light and from the common center of the colour'd Rings
6985 between them, those Rings grew bigger and bigger, and so also did the
6986 white round Spot, and new Rings of Colours emerged successively out of
6987 their common center, and the white Spot became a white Ring
6988 encompassing them; and the incident and reflected beams of Light always
6989 fell upon the opposite parts of this white Ring, illuminating its
6990 Perimeter like two mock Suns in the opposite parts of an Iris. So then
6991 the Diameter of this Ring, measured from the middle of its Light on one
6992 side to the middle of its Light on the other side, was always equal to
6993 the distance between the middle of the incident beam of Light, and the
6994 middle of the reflected beam measured at the Chart on which the Rings
6995 appeared: And the Rays which form'd this Ring were reflected by the
6996 Speculum in Angles equal to their Angles of Incidence, and by
6997 consequence to their Angles of Refraction at their entrance into the
6998 Glass, but yet their Angles of Reflexion were not in the same Planes
6999 with their Angles of Incidence.
7000
7001 _Obs._ 11. The Colours of the new Rings were in a contrary order to
7002 those of the former, and arose after this manner. The white round Spot
7003 of Light in the middle of the Rings continued white to the center till
7004 the distance of the incident and reflected beams at the Chart was about
7005 7/8 parts of an Inch, and then it began to grow dark in the middle. And
7006 when that distance was about 1-3/16 of an Inch, the white Spot was
7007 become a Ring encompassing a dark round Spot which in the middle
7008 inclined to violet and indigo. And the luminous Rings encompassing it
7009 were grown equal to those dark ones which in the four first Observations
7010 encompassed them, that is to say, the white Spot was grown a white Ring
7011 equal to the first of those dark Rings, and the first of those luminous
7012 Rings was now grown equal to the second of those dark ones, and the
7013 second of those luminous ones to the third of those dark ones, and so
7014 on. For the Diameters of the luminous Rings were now 1-3/16, 2-1/16,
7015 2-2/3, 3-3/20, &c. Inches.
7016
7017 When the distance between the incident and reflected beams of Light
7018 became a little bigger, there emerged out of the middle of the dark Spot
7019 after the indigo a blue, and then out of that blue a pale green, and
7020 soon after a yellow and red. And when the Colour at the center was
7021 brightest, being between yellow and red, the bright Rings were grown
7022 equal to those Rings which in the four first Observations next
7023 encompassed them; that is to say, the white Spot in the middle of those
7024 Rings was now become a white Ring equal to the first of those bright
7025 Rings, and the first of those bright ones was now become equal to the
7026 second of those, and so on. For the Diameters of the white Ring, and of
7027 the other luminous Rings encompassing it, were now 1-11/16, 2-3/8,
7028 2-11/12, 3-3/8, &c. or thereabouts.
7029
7030 When the distance of the two beams of Light at the Chart was a little
7031 more increased, there emerged out of the middle in order after the red,
7032 a purple, a blue, a green, a yellow, and a red inclining much to purple,
7033 and when the Colour was brightest being between yellow and red, the
7034 former indigo, blue, green, yellow and red, were become an Iris or Ring
7035 of Colours equal to the first of those luminous Rings which appeared in
7036 the four first Observations, and the white Ring which was now become
7037 the second of the luminous Rings was grown equal to the second of those,
7038 and the first of those which was now become the third Ring was become
7039 equal to the third of those, and so on. For their Diameters were
7040 1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches, the distance of the two beams of
7041 Light, and the Diameter of the white Ring being 2-3/8 Inches.
7042
7043 When these two beams became more distant there emerged out of the middle
7044 of the purplish red, first a darker round Spot, and then out of the
7045 middle of that Spot a brighter. And now the former Colours (purple,
7046 blue, green, yellow, and purplish red) were become a Ring equal to the
7047 first of the bright Rings mentioned in the four first Observations, and
7048 the Rings about this Ring were grown equal to the Rings about that
7049 respectively; the distance between the two beams of Light and the
7050 Diameter of the white Ring (which was now become the third Ring) being
7051 about 3 Inches.
7052
7053 The Colours of the Rings in the middle began now to grow very dilute,
7054 and if the distance between the two Beams was increased half an Inch, or
7055 an Inch more, they vanish'd whilst the white Ring, with one or two of
7056 the Rings next it on either side, continued still visible. But if the
7057 distance of the two beams of Light was still more increased, these also
7058 vanished: For the Light which coming from several parts of the hole in
7059 the Window fell upon the Speculum in several Angles of Incidence, made
7060 Rings of several bignesses, which diluted and blotted out one another,
7061 as I knew by intercepting some part of that Light. For if I intercepted
7062 that part which was nearest to the Axis of the Speculum the Rings would
7063 be less, if the other part which was remotest from it they would be
7064 bigger.
7065
7066 _Obs._ 12. When the Colours of the Prism were cast successively on the
7067 Speculum, that Ring which in the two last Observations was white, was of
7068 the same bigness in all the Colours, but the Rings without it were
7069 greater in the green than in the blue, and still greater in the yellow,
7070 and greatest in the red. And, on the contrary, the Rings within that
7071 white Circle were less in the green than in the blue, and still less in
7072 the yellow, and least in the red. For the Angles of Reflexion of those
7073 Rays which made this Ring, being equal to their Angles of Incidence, the
7074 Fits of every reflected Ray within the Glass after Reflexion are equal
7075 in length and number to the Fits of the same Ray within the Glass before
7076 its Incidence on the reflecting Surface. And therefore since all the
7077 Rays of all sorts at their entrance into the Glass were in a Fit of
7078 Transmission, they were also in a Fit of Transmission at their returning
7079 to the same Surface after Reflexion; and by consequence were
7080 transmitted, and went out to the white Ring on the Chart. This is the
7081 reason why that Ring was of the same bigness in all the Colours, and why
7082 in a mixture of all it appears white. But in Rays which are reflected in
7083 other Angles, the Intervals of the Fits of the least refrangible being
7084 greatest, make the Rings of their Colour in their progress from this
7085 white Ring, either outwards or inwards, increase or decrease by the
7086 greatest steps; so that the Rings of this Colour without are greatest,
7087 and within least. And this is the reason why in the last Observation,
7088 when the Speculum was illuminated with white Light, the exterior Rings
7089 made by all Colours appeared red without and blue within, and the
7090 interior blue without and red within.
7091
7092 These are the Phænomena of thick convexo-concave Plates of Glass, which
7093 are every where of the same thickness. There are yet other Phænomena
7094 when these Plates are a little thicker on one side than on the other,
7095 and others when the Plates are more or less concave than convex, or
7096 plano-convex, or double-convex. For in all these cases the Plates make
7097 Rings of Colours, but after various manners; all which, so far as I have
7098 yet observed, follow from the Propositions in the end of the third part
7099 of this Book, and so conspire to confirm the truth of those
7100 Propositions. But the Phænomena are too various, and the Calculations
7101 whereby they follow from those Propositions too intricate to be here
7102 prosecuted. I content my self with having prosecuted this kind of
7103 Phænomena so far as to discover their Cause, and by discovering it to
7104 ratify the Propositions in the third Part of this Book.
7105
7106 _Obs._ 13. As Light reflected by a Lens quick-silver'd on the backside
7107 makes the Rings of Colours above described, so it ought to make the like
7108 Rings of Colours in passing through a drop of Water. At the first
7109 Reflexion of the Rays within the drop, some Colours ought to be
7110 transmitted, as in the case of a Lens, and others to be reflected back
7111 to the Eye. For instance, if the Diameter of a small drop or globule of
7112 Water be about the 500th part of an Inch, so that a red-making Ray in
7113 passing through the middle of this globule has 250 Fits of easy
7114 Transmission within the globule, and that all the red-making Rays which
7115 are at a certain distance from this middle Ray round about it have 249
7116 Fits within the globule, and all the like Rays at a certain farther
7117 distance round about it have 248 Fits, and all those at a certain
7118 farther distance 247 Fits, and so on; these concentrick Circles of Rays
7119 after their transmission, falling on a white Paper, will make
7120 concentrick Rings of red upon the Paper, supposing the Light which
7121 passes through one single globule, strong enough to be sensible. And, in
7122 like manner, the Rays of other Colours will make Rings of other Colours.
7123 Suppose now that in a fair Day the Sun shines through a thin Cloud of
7124 such globules of Water or Hail, and that the globules are all of the
7125 same bigness; and the Sun seen through this Cloud shall appear
7126 encompassed with the like concentrick Rings of Colours, and the Diameter
7127 of the first Ring of red shall be 7-1/4 Degrees, that of the second
7128 10-1/4 Degrees, that of the third 12 Degrees 33 Minutes. And accordingly
7129 as the Globules of Water are bigger or less, the Rings shall be less or
7130 bigger. This is the Theory, and Experience answers it. For in _June_
7131 1692, I saw by reflexion in a Vessel of stagnating Water three Halos,
7132 Crowns, or Rings of Colours about the Sun, like three little Rain-bows,
7133 concentrick to his Body. The Colours of the first or innermost Crown
7134 were blue next the Sun, red without, and white in the middle between the
7135 blue and red. Those of the second Crown were purple and blue within, and
7136 pale red without, and green in the middle. And those of the third were
7137 pale blue within, and pale red without; these Crowns enclosed one
7138 another immediately, so that their Colours proceeded in this continual
7139 order from the Sun outward: blue, white, red; purple, blue, green, pale
7140 yellow and red; pale blue, pale red. The Diameter of the second Crown
7141 measured from the middle of the yellow and red on one side of the Sun,
7142 to the middle of the same Colour on the other side was 9-1/3 Degrees, or
7143 thereabouts. The Diameters of the first and third I had not time to
7144 measure, but that of the first seemed to be about five or six Degrees,
7145 and that of the third about twelve. The like Crowns appear sometimes
7146 about the Moon; for in the beginning of the Year 1664, _Febr._ 19th at
7147 Night, I saw two such Crowns about her. The Diameter of the first or
7148 innermost was about three Degrees, and that of the second about five
7149 Degrees and an half. Next about the Moon was a Circle of white, and next
7150 about that the inner Crown, which was of a bluish green within next the
7151 white, and of a yellow and red without, and next about these Colours
7152 were blue and green on the inside of the outward Crown, and red on the
7153 outside of it. At the same time there appear'd a Halo about 22 Degrees
7154 35´ distant from the center of the Moon. It was elliptical, and its long
7155 Diameter was perpendicular to the Horizon, verging below farthest from
7156 the Moon. I am told that the Moon has sometimes three or more
7157 concentrick Crowns of Colours encompassing one another next about her
7158 Body. The more equal the globules of Water or Ice are to one another,
7159 the more Crowns of Colours will appear, and the Colours will be the more
7160 lively. The Halo at the distance of 22-1/2 Degrees from the Moon is of
7161 another sort. By its being oval and remoter from the Moon below than
7162 above, I conclude, that it was made by Refraction in some sort of Hail
7163 or Snow floating in the Air in an horizontal posture, the refracting
7164 Angle being about 58 or 60 Degrees.
7165
7166
7167
7168
7169 THE
7170
7171 THIRD BOOK
7172
7173 OF
7174
7175 OPTICKS
7176
7177
7178 _PART I._
7179
7180 _Observations concerning the Inflexions of the Rays of Light, and the
7181 Colours made thereby._
7182
7183 Grimaldo has inform'd us, that if a beam of the Sun's Light be let into
7184 a dark Room through a very small hole, the Shadows of things in this
7185 Light will be larger than they ought to be if the Rays went on by the
7186 Bodies in straight Lines, and that these Shadows have three parallel
7187 Fringes, Bands or Ranks of colour'd Light adjacent to them. But if the
7188 Hole be enlarged the Fringes grow broad and run into one another, so
7189 that they cannot be distinguish'd. These broad Shadows and Fringes have
7190 been reckon'd by some to proceed from the ordinary refraction of the
7191 Air, but without due examination of the Matter. For the circumstances of
7192 the Phænomenon, so far as I have observed them, are as follows.
7193
7194 _Obs._ 1. I made in a piece of Lead a small Hole with a Pin, whose
7195 breadth was the 42d part of an Inch. For 21 of those Pins laid together
7196 took up the breadth of half an Inch. Through this Hole I let into my
7197 darken'd Chamber a beam of the Sun's Light, and found that the Shadows
7198 of Hairs, Thred, Pins, Straws, and such like slender Substances placed
7199 in this beam of Light, were considerably broader than they ought to be,
7200 if the Rays of Light passed on by these Bodies in right Lines. And
7201 particularly a Hair of a Man's Head, whose breadth was but the 280th
7202 part of an Inch, being held in this Light, at the distance of about
7203 twelve Feet from the Hole, did cast a Shadow which at the distance of
7204 four Inches from the Hair was the sixtieth part of an Inch broad, that
7205 is, above four times broader than the Hair, and at the distance of two
7206 Feet from the Hair was about the eight and twentieth part of an Inch
7207 broad, that is, ten times broader than the Hair, and at the distance of
7208 ten Feet was the eighth part of an Inch broad, that is 35 times broader.
7209
7210 Nor is it material whether the Hair be encompassed with Air, or with any
7211 other pellucid Substance. For I wetted a polish'd Plate of Glass, and
7212 laid the Hair in the Water upon the Glass, and then laying another
7213 polish'd Plate of Glass upon it, so that the Water might fill up the
7214 space between the Glasses, I held them in the aforesaid beam of Light,
7215 so that the Light might pass through them perpendicularly, and the
7216 Shadow of the Hair was at the same distances as big as before. The
7217 Shadows of Scratches made in polish'd Plates of Glass were also much
7218 broader than they ought to be, and the Veins in polish'd Plates of Glass
7219 did also cast the like broad Shadows. And therefore the great breadth of
7220 these Shadows proceeds from some other cause than the Refraction of the
7221 Air.
7222
7223 Let the Circle X [in _Fig._ 1.] represent the middle of the Hair; ADG,
7224 BEH, CFI, three Rays passing by one side of the Hair at several
7225 distances; KNQ, LOR, MPS, three other Rays passing by the other side of
7226 the Hair at the like distances; D, E, F, and N, O, P, the places where
7227 the Rays are bent in their passage by the Hair; G, H, I, and Q, R, S,
7228 the places where the Rays fall on a Paper GQ; IS the breadth of the
7229 Shadow of the Hair cast on the Paper, and TI, VS, two Rays passing to
7230 the Points I and S without bending when the Hair is taken away. And it's
7231 manifest that all the Light between these two Rays TI and VS is bent in
7232 passing by the Hair, and turned aside from the Shadow IS, because if any
7233 part of this Light were not bent it would fall on the Paper within the
7234 Shadow, and there illuminate the Paper, contrary to experience. And
7235 because when the Paper is at a great distance from the Hair, the Shadow
7236 is broad, and therefore the Rays TI and VS are at a great distance from
7237 one another, it follows that the Hair acts upon the Rays of Light at a
7238 good distance in their passing by it. But the Action is strongest on the
7239 Rays which pass by at least distances, and grows weaker and weaker
7240 accordingly as the Rays pass by at distances greater and greater, as is
7241 represented in the Scheme: For thence it comes to pass, that the Shadow
7242 of the Hair is much broader in proportion to the distance of the Paper
7243 from the Hair, when the Paper is nearer the Hair, than when it is at a
7244 great distance from it.
7245
7246 _Obs._ 2. The Shadows of all Bodies (Metals, Stones, Glass, Wood, Horn,
7247 Ice, &c.) in this Light were border'd with three Parallel Fringes or
7248 Bands of colour'd Light, whereof that which was contiguous to the Shadow
7249 was broadest and most luminous, and that which was remotest from it was
7250 narrowest, and so faint, as not easily to be visible. It was difficult
7251 to distinguish the Colours, unless when the Light fell very obliquely
7252 upon a smooth Paper, or some other smooth white Body, so as to make them
7253 appear much broader than they would otherwise do. And then the Colours
7254 were plainly visible in this Order: The first or innermost Fringe was
7255 violet and deep blue next the Shadow, and then light blue, green, and
7256 yellow in the middle, and red without. The second Fringe was almost
7257 contiguous to the first, and the third to the second, and both were blue
7258 within, and yellow and red without, but their Colours were very faint,
7259 especially those of the third. The Colours therefore proceeded in this
7260 order from the Shadow; violet, indigo, pale blue, green, yellow, red;
7261 blue, yellow, red; pale blue, pale yellow and red. The Shadows made by
7262 Scratches and Bubbles in polish'd Plates of Glass were border'd with the
7263 like Fringes of colour'd Light. And if Plates of Looking-glass sloop'd
7264 off near the edges with a Diamond-cut, be held in the same beam of
7265 Light, the Light which passes through the parallel Planes of the Glass
7266 will be border'd with the like Fringes of Colours where those Planes
7267 meet with the Diamond-cut, and by this means there will sometimes appear
7268 four or five Fringes of Colours. Let AB, CD [in _Fig._ 2.] represent the
7269 parallel Planes of a Looking-glass, and BD the Plane of the Diamond-cut,
7270 making at B a very obtuse Angle with the Plane AB. And let all the Light
7271 between the Rays ENI and FBM pass directly through the parallel Planes
7272 of the Glass, and fall upon the Paper between I and M, and all the Light
7273 between the Rays GO and HD be refracted by the oblique Plane of the
7274 Diamond-cut BD, and fall upon the Paper between K and L; and the Light
7275 which passes directly through the parallel Planes of the Glass, and
7276 falls upon the Paper between I and M, will be border'd with three or
7277 more Fringes at M.
7278
7279 [Illustration: FIG. 1.]
7280
7281 [Illustration: FIG. 2.]
7282
7283 So by looking on the Sun through a Feather or black Ribband held close
7284 to the Eye, several Rain-bows will appear; the Shadows which the Fibres
7285 or Threds cast on the _Tunica Retina_, being border'd with the like
7286 Fringes of Colours.
7287
7288 _Obs._ 3. When the Hair was twelve Feet distant from this Hole, and its
7289 Shadow fell obliquely upon a flat white Scale of Inches and Parts of an
7290 Inch placed half a Foot beyond it, and also when the Shadow fell
7291 perpendicularly upon the same Scale placed nine Feet beyond it; I
7292 measured the breadth of the Shadow and Fringes as accurately as I could,
7293 and found them in Parts of an Inch as follows.
7294
7295 -------------------------------------------+-----------+--------
7296 | half a | Nine
7297 At the Distance of | Foot | Feet
7298 -------------------------------------------+-----------+--------
7299 The breadth of the Shadow | 1/54 | 1/9
7300 -------------------------------------------+-----------+--------
7301 The breadth between the Middles of the | 1/38 |
7302 brightest Light of the innermost Fringes | or |
7303 on either side the Shadow | 1/39 | 7/50
7304 -------------------------------------------+-----------+--------
7305 The breadth between the Middles of the | |
7306 brightest Light of the middlemost Fringes| |
7307 on either side the Shadow | 1/23-1/2 | 4/17
7308 -------------------------------------------+-----------+--------
7309 The breadth between the Middles of the | 1/18 |
7310 brightest Light of the outmost Fringes | or |
7311 on either side the Shadow | 1/18-1/2 | 3/10
7312 -------------------------------------------+-----------+--------
7313 The distance between the Middles of the | |
7314 brightest Light of the first and second | |
7315 Fringes | 1/120 | 1/21
7316 -------------------------------------------+-----------+--------
7317 The distance between the Middles of the | |
7318 brightest Light of the second and third | |
7319 Fringes | 1/170 | 1/31
7320 -------------------------------------------+-----------+--------
7321 The breadth of the luminous Part (green, | |
7322 white, yellow, and red) of the first | |
7323 Fringe | 1/170 | 1/32
7324 -------------------------------------------+-----------+--------
7325 The breadth of the darker Space between | |
7326 the first and second Fringes | 1/240 | 1/45
7327 -------------------------------------------+-----------+--------
7328 The breadth of the luminous Part of the | |
7329 second Fringe | 1/290 | 1/55
7330 -------------------------------------------+-----------+--------
7331 The breadth of the darker Space between | |
7332 the second and third Fringes | 1/340 | 1/63
7333 -------------------------------------------+-----------+--------
7334
7335 These Measures I took by letting the Shadow of the Hair, at half a Foot
7336 distance, fall so obliquely on the Scale, as to appear twelve times
7337 broader than when it fell perpendicularly on it at the same distance,
7338 and setting down in this Table the twelfth part of the Measures I then
7339 took.
7340
7341 _Obs._ 4. When the Shadow and Fringes were cast obliquely upon a smooth
7342 white Body, and that Body was removed farther and farther from the Hair,
7343 the first Fringe began to appear and look brighter than the rest of the
7344 Light at the distance of less than a quarter of an Inch from the Hair,
7345 and the dark Line or Shadow between that and the second Fringe began to
7346 appear at a less distance from the Hair than that of the third part of
7347 an Inch. The second Fringe began to appear at a distance from the Hair
7348 of less than half an Inch, and the Shadow between that and the third
7349 Fringe at a distance less than an inch, and the third Fringe at a
7350 distance less than three Inches. At greater distances they became much
7351 more sensible, but kept very nearly the same proportion of their
7352 breadths and intervals which they had at their first appearing. For the
7353 distance between the middle of the first, and middle of the second
7354 Fringe, was to the distance between the middle of the second and middle
7355 of the third Fringe, as three to two, or ten to seven. And the last of
7356 these two distances was equal to the breadth of the bright Light or
7357 luminous part of the first Fringe. And this breadth was to the breadth
7358 of the bright Light of the second Fringe as seven to four, and to the
7359 dark Interval of the first and second Fringe as three to two, and to
7360 the like dark Interval between the second and third as two to one. For
7361 the breadths of the Fringes seem'd to be in the progression of the
7362 Numbers 1, sqrt(1/3), sqrt(1/5), and their Intervals to be in the
7363 same progression with them; that is, the Fringes and their Intervals
7364 together to be in the continual progression of the Numbers 1,
7365 sqrt(1/2), sqrt(1/3), sqrt(1/4), sqrt(1/5), or thereabouts. And
7366 these Proportions held the same very nearly at all distances from the
7367 Hair; the dark Intervals of the Fringes being as broad in proportion to
7368 the breadth of the Fringes at their first appearance as afterwards at
7369 great distances from the Hair, though not so dark and distinct.
7370
7371 _Obs._ 5. The Sun shining into my darken'd Chamber through a hole a
7372 quarter of an Inch broad, I placed at the distance of two or three Feet
7373 from the Hole a Sheet of Pasteboard, which was black'd all over on both
7374 sides, and in the middle of it had a hole about three quarters of an
7375 Inch square for the Light to pass through. And behind the hole I
7376 fasten'd to the Pasteboard with Pitch the blade of a sharp Knife, to
7377 intercept some part of the Light which passed through the hole. The
7378 Planes of the Pasteboard and blade of the Knife were parallel to one
7379 another, and perpendicular to the Rays. And when they were so placed
7380 that none of the Sun's Light fell on the Pasteboard, but all of it
7381 passed through the hole to the Knife, and there part of it fell upon the
7382 blade of the Knife, and part of it passed by its edge; I let this part
7383 of the Light which passed by, fall on a white Paper two or three Feet
7384 beyond the Knife, and there saw two streams of faint Light shoot out
7385 both ways from the beam of Light into the shadow, like the Tails of
7386 Comets. But because the Sun's direct Light by its brightness upon the
7387 Paper obscured these faint streams, so that I could scarce see them, I
7388 made a little hole in the midst of the Paper for that Light to pass
7389 through and fall on a black Cloth behind it; and then I saw the two
7390 streams plainly. They were like one another, and pretty nearly equal in
7391 length, and breadth, and quantity of Light. Their Light at that end next
7392 the Sun's direct Light was pretty strong for the space of about a
7393 quarter of an Inch, or half an Inch, and in all its progress from that
7394 direct Light decreased gradually till it became insensible. The whole
7395 length of either of these streams measured upon the paper at the
7396 distance of three Feet from the Knife was about six or eight Inches; so
7397 that it subtended an Angle at the edge of the Knife of about 10 or 12,
7398 or at most 14 Degrees. Yet sometimes I thought I saw it shoot three or
7399 four Degrees farther, but with a Light so very faint that I could scarce
7400 perceive it, and suspected it might (in some measure at least) arise
7401 from some other cause than the two streams did. For placing my Eye in
7402 that Light beyond the end of that stream which was behind the Knife, and
7403 looking towards the Knife, I could see a line of Light upon its edge,
7404 and that not only when my Eye was in the line of the Streams, but also
7405 when it was without that line either towards the point of the Knife, or
7406 towards the handle. This line of Light appear'd contiguous to the edge
7407 of the Knife, and was narrower than the Light of the innermost Fringe,
7408 and narrowest when my Eye was farthest from the direct Light, and
7409 therefore seem'd to pass between the Light of that Fringe and the edge
7410 of the Knife, and that which passed nearest the edge to be most bent,
7411 though not all of it.
7412
7413 _Obs._ 6. I placed another Knife by this, so that their edges might be
7414 parallel, and look towards one another, and that the beam of Light might
7415 fall upon both the Knives, and some part of it pass between their edges.
7416 And when the distance of their edges was about the 400th part of an
7417 Inch, the stream parted in the middle, and left a Shadow between the two
7418 parts. This Shadow was so black and dark that all the Light which passed
7419 between the Knives seem'd to be bent, and turn'd aside to the one hand
7420 or to the other. And as the Knives still approach'd one another the
7421 Shadow grew broader, and the streams shorter at their inward ends which
7422 were next the Shadow, until upon the contact of the Knives the whole
7423 Light vanish'd, leaving its place to the Shadow.
7424
7425 And hence I gather that the Light which is least bent, and goes to the
7426 inward ends of the streams, passes by the edges of the Knives at the
7427 greatest distance, and this distance when the Shadow begins to appear
7428 between the streams, is about the 800th part of an Inch. And the Light
7429 which passes by the edges of the Knives at distances still less and
7430 less, is more and more bent, and goes to those parts of the streams
7431 which are farther and farther from the direct Light; because when the
7432 Knives approach one another till they touch, those parts of the streams
7433 vanish last which are farthest from the direct Light.
7434
7435 _Obs._ 7. In the fifth Observation the Fringes did not appear, but by
7436 reason of the breadth of the hole in the Window became so broad as to
7437 run into one another, and by joining, to make one continued Light in the
7438 beginning of the streams. But in the sixth, as the Knives approached one
7439 another, a little before the Shadow appeared between the two streams,
7440 the Fringes began to appear on the inner ends of the Streams on either
7441 side of the direct Light; three on one side made by the edge of one
7442 Knife, and three on the other side made by the edge of the other Knife.
7443 They were distinctest when the Knives were placed at the greatest
7444 distance from the hole in the Window, and still became more distinct by
7445 making the hole less, insomuch that I could sometimes see a faint
7446 lineament of a fourth Fringe beyond the three above mention'd. And as
7447 the Knives continually approach'd one another, the Fringes grew
7448 distincter and larger, until they vanish'd. The outmost Fringe vanish'd
7449 first, and the middlemost next, and the innermost last. And after they
7450 were all vanish'd, and the line of Light which was in the middle between
7451 them was grown very broad, enlarging it self on both sides into the
7452 streams of Light described in the fifth Observation, the above-mention'd
7453 Shadow began to appear in the middle of this line, and divide it along
7454 the middle into two lines of Light, and increased until the whole Light
7455 vanish'd. This enlargement of the Fringes was so great that the Rays
7456 which go to the innermost Fringe seem'd to be bent above twenty times
7457 more when this Fringe was ready to vanish, than when one of the Knives
7458 was taken away.
7459
7460 And from this and the former Observation compared, I gather, that the
7461 Light of the first Fringe passed by the edge of the Knife at a distance
7462 greater than the 800th part of an Inch, and the Light of the second
7463 Fringe passed by the edge of the Knife at a greater distance than the
7464 Light of the first Fringe did, and that of the third at a greater
7465 distance than that of the second, and that of the streams of Light
7466 described in the fifth and sixth Observations passed by the edges of the
7467 Knives at less distances than that of any of the Fringes.
7468
7469 _Obs._ 8. I caused the edges of two Knives to be ground truly strait,
7470 and pricking their points into a Board so that their edges might look
7471 towards one another, and meeting near their points contain a rectilinear
7472 Angle, I fasten'd their Handles together with Pitch to make this Angle
7473 invariable. The distance of the edges of the Knives from one another at
7474 the distance of four Inches from the angular Point, where the edges of
7475 the Knives met, was the eighth part of an Inch; and therefore the Angle
7476 contain'd by the edges was about one Degree 54: The Knives thus fix'd
7477 together I placed in a beam of the Sun's Light, let into my darken'd
7478 Chamber through a Hole the 42d Part of an Inch wide, at the distance of
7479 10 or 15 Feet from the Hole, and let the Light which passed between
7480 their edges fall very obliquely upon a smooth white Ruler at the
7481 distance of half an Inch, or an Inch from the Knives, and there saw the
7482 Fringes by the two edges of the Knives run along the edges of the
7483 Shadows of the Knives in Lines parallel to those edges without growing
7484 sensibly broader, till they met in Angles equal to the Angle contained
7485 by the edges of the Knives, and where they met and joined they ended
7486 without crossing one another. But if the Ruler was held at a much
7487 greater distance from the Knives, the Fringes where they were farther
7488 from the Place of their Meeting, were a little narrower, and became
7489 something broader and broader as they approach'd nearer and nearer to
7490 one another, and after they met they cross'd one another, and then
7491 became much broader than before.
7492
7493 Whence I gather that the distances at which the Fringes pass by the
7494 Knives are not increased nor alter'd by the approach of the Knives, but
7495 the Angles in which the Rays are there bent are much increased by that
7496 approach; and that the Knife which is nearest any Ray determines which
7497 way the Ray shall be bent, and the other Knife increases the bent.
7498
7499 _Obs._ 9. When the Rays fell very obliquely upon the Ruler at the
7500 distance of the third Part of an Inch from the Knives, the dark Line
7501 between the first and second Fringe of the Shadow of one Knife, and the
7502 dark Line between the first and second Fringe of the Shadow of the other
7503 knife met with one another, at the distance of the fifth Part of an Inch
7504 from the end of the Light which passed between the Knives at the
7505 concourse of their edges. And therefore the distance of the edges of the
7506 Knives at the meeting of these dark Lines was the 160th Part of an Inch.
7507 For as four Inches to the eighth Part of an Inch, so is any Length of
7508 the edges of the Knives measured from the point of their concourse to
7509 the distance of the edges of the Knives at the end of that Length, and
7510 so is the fifth Part of an Inch to the 160th Part. So then the dark
7511 Lines above-mention'd meet in the middle of the Light which passes
7512 between the Knives where they are distant the 160th Part of an Inch, and
7513 the one half of that Light passes by the edge of one Knife at a distance
7514 not greater than the 320th Part of an Inch, and falling upon the Paper
7515 makes the Fringes of the Shadow of that Knife, and the other half passes
7516 by the edge of the other Knife, at a distance not greater than the 320th
7517 Part of an Inch, and falling upon the Paper makes the Fringes of the
7518 Shadow of the other Knife. But if the Paper be held at a distance from
7519 the Knives greater than the third Part of an Inch, the dark Lines
7520 above-mention'd meet at a greater distance than the fifth Part of an
7521 Inch from the end of the Light which passed between the Knives at the
7522 concourse of their edges; and therefore the Light which falls upon the
7523 Paper where those dark Lines meet passes between the Knives where the
7524 edges are distant above the 160th part of an Inch.
7525
7526 For at another time, when the two Knives were distant eight Feet and
7527 five Inches from the little hole in the Window, made with a small Pin as
7528 above, the Light which fell upon the Paper where the aforesaid dark
7529 lines met, passed between the Knives, where the distance between their
7530 edges was as in the following Table, when the distance of the Paper from
7531 the Knives was also as follows.
7532
7533 -----------------------------+------------------------------
7534 | Distances between the edges
7535 Distances of the Paper | of the Knives in millesimal
7536 from the Knives in Inches. | parts of an Inch.
7537 -----------------------------+------------------------------
7538 1-1/2. | 0'012
7539 3-1/3. | 0'020
7540 8-3/5. | 0'034
7541 32. | 0'057
7542 96. | 0'081
7543 131. | 0'087
7544 _____________________________|______________________________
7545
7546 And hence I gather, that the Light which makes the Fringes upon the
7547 Paper is not the same Light at all distances of the Paper from the
7548 Knives, but when the Paper is held near the Knives, the Fringes are made
7549 by Light which passes by the edges of the Knives at a less distance, and
7550 is more bent than when the Paper is held at a greater distance from the
7551 Knives.
7552
7553 [Illustration: FIG. 3.]
7554
7555 _Obs._ 10. When the Fringes of the Shadows of the Knives fell
7556 perpendicularly upon a Paper at a great distance from the Knives, they
7557 were in the form of Hyperbola's, and their Dimensions were as follows.
7558 Let CA, CB [in _Fig._ 3.] represent Lines drawn upon the Paper parallel
7559 to the edges of the Knives, and between which all the Light would fall,
7560 if it passed between the edges of the Knives without inflexion; DE a
7561 Right Line drawn through C making the Angles ACD, BCE, equal to one
7562 another, and terminating all the Light which falls upon the Paper from
7563 the point where the edges of the Knives meet; _eis_, _fkt_, and _glv_,
7564 three hyperbolical Lines representing the Terminus of the Shadow of one
7565 of the Knives, the dark Line between the first and second Fringes of
7566 that Shadow, and the dark Line between the second and third Fringes of
7567 the same Shadow; _xip_, _ykq_, and _zlr_, three other hyperbolical Lines
7568 representing the Terminus of the Shadow of the other Knife, the dark
7569 Line between the first and second Fringes of that Shadow, and the dark
7570 line between the second and third Fringes of the same Shadow. And
7571 conceive that these three Hyperbola's are like and equal to the former
7572 three, and cross them in the points _i_, _k_, and _l_, and that the
7573 Shadows of the Knives are terminated and distinguish'd from the first
7574 luminous Fringes by the lines _eis_ and _xip_, until the meeting and
7575 crossing of the Fringes, and then those lines cross the Fringes in the
7576 form of dark lines, terminating the first luminous Fringes within side,
7577 and distinguishing them from another Light which begins to appear at
7578 _i_, and illuminates all the triangular space _ip_DE_s_ comprehended by
7579 these dark lines, and the right line DE. Of these Hyperbola's one
7580 Asymptote is the line DE, and their other Asymptotes are parallel to the
7581 lines CA and CB. Let _rv_ represent a line drawn any where upon the
7582 Paper parallel to the Asymptote DE, and let this line cross the right
7583 lines AC in _m_, and BC in _n_, and the six dark hyperbolical lines in
7584 _p_, _q_, _r_; _s_, _t_, _v_; and by measuring the distances _ps_, _qt_,
7585 _rv_, and thence collecting the lengths of the Ordinates _np_, _nq_,
7586 _nr_ or _ms_, _mt_, _mv_, and doing this at several distances of the
7587 line _rv_ from the Asymptote DD, you may find as many points of these
7588 Hyperbola's as you please, and thereby know that these curve lines are
7589 Hyperbola's differing little from the conical Hyperbola. And by
7590 measuring the lines C_i_, C_k_, C_l_, you may find other points of these
7591 Curves.
7592
7593 For instance; when the Knives were distant from the hole in the Window
7594 ten Feet, and the Paper from the Knives nine Feet, and the Angle
7595 contained by the edges of the Knives to which the Angle ACB is equal,
7596 was subtended by a Chord which was to the Radius as 1 to 32, and the
7597 distance of the line _rv_ from the Asymptote DE was half an Inch: I
7598 measured the lines _ps_, _qt_, _rv_, and found them 0'35, 0'65, 0'98
7599 Inches respectively; and by adding to their halfs the line 1/2 _mn_,
7600 (which here was the 128th part of an Inch, or 0'0078 Inches,) the Sums
7601 _np_, _nq_, _nr_, were 0'1828, 0'3328, 0'4978 Inches. I measured also
7602 the distances of the brightest parts of the Fringes which run between
7603 _pq_ and _st_, _qr_ and _tv_, and next beyond _r_ and _v_, and found
7604 them 0'5, 0'8, and 1'17 Inches.
7605
7606 _Obs._ 11. The Sun shining into my darken'd Room through a small round
7607 hole made in a Plate of Lead with a slender Pin, as above; I placed at
7608 the hole a Prism to refract the Light, and form on the opposite Wall the
7609 Spectrum of Colours, described in the third Experiment of the first
7610 Book. And then I found that the Shadows of all Bodies held in the
7611 colour'd Light between the Prism and the Wall, were border'd with
7612 Fringes of the Colour of that Light in which they were held. In the full
7613 red Light they were totally red without any sensible blue or violet, and
7614 in the deep blue Light they were totally blue without any sensible red
7615 or yellow; and so in the green Light they were totally green, excepting
7616 a little yellow and blue, which were mixed in the green Light of the
7617 Prism. And comparing the Fringes made in the several colour'd Lights, I
7618 found that those made in the red Light were largest, those made in the
7619 violet were least, and those made in the green were of a middle bigness.
7620 For the Fringes with which the Shadow of a Man's Hair were bordered,
7621 being measured cross the Shadow at the distance of six Inches from the
7622 Hair, the distance between the middle and most luminous part of the
7623 first or innermost Fringe on one side of the Shadow, and that of the
7624 like Fringe on the other side of the Shadow, was in the full red Light
7625 1/37-1/4 of an Inch, and in the full violet 7/46. And the like distance
7626 between the middle and most luminous parts of the second Fringes on
7627 either side the Shadow was in the full red Light 1/22, and in the violet
7628 1/27 of an Inch. And these distances of the Fringes held the same
7629 proportion at all distances from the Hair without any sensible
7630 variation.
7631
7632 So then the Rays which made these Fringes in the red Light passed by the
7633 Hair at a greater distance than those did which made the like Fringes in
7634 the violet; and therefore the Hair in causing these Fringes acted alike
7635 upon the red Light or least refrangible Rays at a greater distance, and
7636 upon the violet or most refrangible Rays at a less distance, and by
7637 those actions disposed the red Light into Larger Fringes, and the violet
7638 into smaller, and the Lights of intermediate Colours into Fringes of
7639 intermediate bignesses without changing the Colour of any sort of Light.
7640
7641 When therefore the Hair in the first and second of these Observations
7642 was held in the white beam of the Sun's Light, and cast a Shadow which
7643 was border'd with three Fringes of coloured Light, those Colours arose
7644 not from any new modifications impress'd upon the Rays of Light by the
7645 Hair, but only from the various inflexions whereby the several Sorts of
7646 Rays were separated from one another, which before separation, by the
7647 mixture of all their Colours, composed the white beam of the Sun's
7648 Light, but whenever separated compose Lights of the several Colours
7649 which they are originally disposed to exhibit. In this 11th Observation,
7650 where the Colours are separated before the Light passes by the Hair, the
7651 least refrangible Rays, which when separated from the rest make red,
7652 were inflected at a greater distance from the Hair, so as to make three
7653 red Fringes at a greater distance from the middle of the Shadow of the
7654 Hair; and the most refrangible Rays which when separated make violet,
7655 were inflected at a less distance from the Hair, so as to make three
7656 violet Fringes at a less distance from the middle of the Shadow of the
7657 Hair. And other Rays of intermediate degrees of Refrangibility were
7658 inflected at intermediate distances from the Hair, so as to make Fringes
7659 of intermediate Colours at intermediate distances from the middle of the
7660 Shadow of the Hair. And in the second Observation, where all the Colours
7661 are mix'd in the white Light which passes by the Hair, these Colours are
7662 separated by the various inflexions of the Rays, and the Fringes which
7663 they make appear all together, and the innermost Fringes being
7664 contiguous make one broad Fringe composed of all the Colours in due
7665 order, the violet lying on the inside of the Fringe next the Shadow, the
7666 red on the outside farthest from the Shadow, and the blue, green, and
7667 yellow, in the middle. And, in like manner, the middlemost Fringes of
7668 all the Colours lying in order, and being contiguous, make another broad
7669 Fringe composed of all the Colours; and the outmost Fringes of all the
7670 Colours lying in order, and being contiguous, make a third broad Fringe
7671 composed of all the Colours. These are the three Fringes of colour'd
7672 Light with which the Shadows of all Bodies are border'd in the second
7673 Observation.
7674
7675 When I made the foregoing Observations, I design'd to repeat most of
7676 them with more care and exactness, and to make some new ones for
7677 determining the manner how the Rays of Light are bent in their passage
7678 by Bodies, for making the Fringes of Colours with the dark lines between
7679 them. But I was then interrupted, and cannot now think of taking these
7680 things into farther Consideration. And since I have not finish'd this
7681 part of my Design, I shall conclude with proposing only some Queries, in
7682 order to a farther search to be made by others.
7683
7684 _Query_ 1. Do not Bodies act upon Light at a distance, and by their
7685 action bend its Rays; and is not this action (_cæteris paribus_)
7686 strongest at the least distance?
7687
7688 _Qu._ 2. Do not the Rays which differ in Refrangibility differ also in
7689 Flexibity; and are they not by their different Inflexions separated from
7690 one another, so as after separation to make the Colours in the three
7691 Fringes above described? And after what manner are they inflected to
7692 make those Fringes?
7693
7694 _Qu._ 3. Are not the Rays of Light in passing by the edges and sides of
7695 Bodies, bent several times backwards and forwards, with a motion like
7696 that of an Eel? And do not the three Fringes of colour'd Light
7697 above-mention'd arise from three such bendings?
7698
7699 _Qu._ 4. Do not the Rays of Light which fall upon Bodies, and are
7700 reflected or refracted, begin to bend before they arrive at the Bodies;
7701 and are they not reflected, refracted, and inflected, by one and the
7702 same Principle, acting variously in various Circumstances?
7703
7704 _Qu._ 5. Do not Bodies and Light act mutually upon one another; that is
7705 to say, Bodies upon Light in emitting, reflecting, refracting and
7706 inflecting it, and Light upon Bodies for heating them, and putting their
7707 parts into a vibrating motion wherein heat consists?
7708
7709 _Qu._ 6. Do not black Bodies conceive heat more easily from Light than
7710 those of other Colours do, by reason that the Light falling on them is
7711 not reflected outwards, but enters the Bodies, and is often reflected
7712 and refracted within them, until it be stifled and lost?
7713
7714 _Qu._ 7. Is not the strength and vigor of the action between Light and
7715 sulphureous Bodies observed above, one reason why sulphureous Bodies
7716 take fire more readily, and burn more vehemently than other Bodies do?
7717
7718 _Qu._ 8. Do not all fix'd Bodies, when heated beyond a certain degree,
7719 emit Light and shine; and is not this Emission perform'd by the
7720 vibrating motions of their parts? And do not all Bodies which abound
7721 with terrestrial parts, and especially with sulphureous ones, emit Light
7722 as often as those parts are sufficiently agitated; whether that
7723 agitation be made by Heat, or by Friction, or Percussion, or
7724 Putrefaction, or by any vital Motion, or any other Cause? As for
7725 instance; Sea-Water in a raging Storm; Quick-silver agitated in _vacuo_;
7726 the Back of a Cat, or Neck of a Horse, obliquely struck or rubbed in a
7727 dark place; Wood, Flesh and Fish while they putrefy; Vapours arising
7728 from putrefy'd Waters, usually call'd _Ignes Fatui_; Stacks of moist Hay
7729 or Corn growing hot by fermentation; Glow-worms and the Eyes of some
7730 Animals by vital Motions; the vulgar _Phosphorus_ agitated by the
7731 attrition of any Body, or by the acid Particles of the Air; Amber and
7732 some Diamonds by striking, pressing or rubbing them; Scrapings of Steel
7733 struck off with a Flint; Iron hammer'd very nimbly till it become so hot
7734 as to kindle Sulphur thrown upon it; the Axletrees of Chariots taking
7735 fire by the rapid rotation of the Wheels; and some Liquors mix'd with
7736 one another whose Particles come together with an Impetus, as Oil of
7737 Vitriol distilled from its weight of Nitre, and then mix'd with twice
7738 its weight of Oil of Anniseeds. So also a Globe of Glass about 8 or 10
7739 Inches in diameter, being put into a Frame where it may be swiftly
7740 turn'd round its Axis, will in turning shine where it rubs against the
7741 palm of ones Hand apply'd to it: And if at the same time a piece of
7742 white Paper or white Cloth, or the end of ones Finger be held at the
7743 distance of about a quarter of an Inch or half an Inch from that part of
7744 the Glass where it is most in motion, the electrick Vapour which is
7745 excited by the friction of the Glass against the Hand, will by dashing
7746 against the white Paper, Cloth or Finger, be put into such an agitation
7747 as to emit Light, and make the white Paper, Cloth or Finger, appear
7748 lucid like a Glowworm; and in rushing out of the Glass will sometimes
7749 push against the finger so as to be felt. And the same things have been
7750 found by rubbing a long and large Cylinder or Glass or Amber with a
7751 Paper held in ones hand, and continuing the friction till the Glass grew
7752 warm.
7753
7754 _Qu._ 9. Is not Fire a Body heated so hot as to emit Light copiously?
7755 For what else is a red hot Iron than Fire? And what else is a burning
7756 Coal than red hot Wood?
7757
7758 _Qu._ 10. Is not Flame a Vapour, Fume or Exhalation heated red hot, that
7759 is, so hot as to shine? For Bodies do not flame without emitting a
7760 copious Fume, and this Fume burns in the Flame. The _Ignis Fatuus_ is a
7761 Vapour shining without heat, and is there not the same difference
7762 between this Vapour and Flame, as between rotten Wood shining without
7763 heat and burning Coals of Fire? In distilling hot Spirits, if the Head
7764 of the Still be taken off, the Vapour which ascends out of the Still
7765 will take fire at the Flame of a Candle, and turn into Flame, and the
7766 Flame will run along the Vapour from the Candle to the Still. Some
7767 Bodies heated by Motion, or Fermentation, if the heat grow intense, fume
7768 copiously, and if the heat be great enough the Fumes will shine and
7769 become Flame. Metals in fusion do not flame for want of a copious Fume,
7770 except Spelter, which fumes copiously, and thereby flames. All flaming
7771 Bodies, as Oil, Tallow, Wax, Wood, fossil Coals, Pitch, Sulphur, by
7772 flaming waste and vanish into burning Smoke, which Smoke, if the Flame
7773 be put out, is very thick and visible, and sometimes smells strongly,
7774 but in the Flame loses its smell by burning, and according to the nature
7775 of the Smoke the Flame is of several Colours, as that of Sulphur blue,
7776 that of Copper open'd with sublimate green, that of Tallow yellow, that
7777 of Camphire white. Smoke passing through Flame cannot but grow red hot,
7778 and red hot Smoke can have no other appearance than that of Flame. When
7779 Gun-powder takes fire, it goes away into Flaming Smoke. For the Charcoal
7780 and Sulphur easily take fire, and set fire to the Nitre, and the Spirit
7781 of the Nitre being thereby rarified into Vapour, rushes out with
7782 Explosion much after the manner that the Vapour of Water rushes out of
7783 an Æolipile; the Sulphur also being volatile is converted into Vapour,
7784 and augments the Explosion. And the acid Vapour of the Sulphur (namely
7785 that which distils under a Bell into Oil of Sulphur,) entring violently
7786 into the fix'd Body of the Nitre, sets loose the Spirit of the Nitre,
7787 and excites a great Fermentation, whereby the Heat is farther augmented,
7788 and the fix'd Body of the Nitre is also rarified into Fume, and the
7789 Explosion is thereby made more vehement and quick. For if Salt of Tartar
7790 be mix'd with Gun-powder, and that Mixture be warm'd till it takes fire,
7791 the Explosion will be more violent and quick than that of Gun-powder
7792 alone; which cannot proceed from any other cause than the action of the
7793 Vapour of the Gun-powder upon the Salt of Tartar, whereby that Salt is
7794 rarified. The Explosion of Gun-powder arises therefore from the violent
7795 action whereby all the Mixture being quickly and vehemently heated, is
7796 rarified and converted into Fume and Vapour: which Vapour, by the
7797 violence of that action, becoming so hot as to shine, appears in the
7798 form of Flame.
7799
7800 _Qu._ 11. Do not great Bodies conserve their heat the longest, their
7801 parts heating one another, and may not great dense and fix'd Bodies,
7802 when heated beyond a certain degree, emit Light so copiously, as by the
7803 Emission and Re-action of its Light, and the Reflexions and Refractions
7804 of its Rays within its Pores to grow still hotter, till it comes to a
7805 certain period of heat, such as is that of the Sun? And are not the Sun
7806 and fix'd Stars great Earths vehemently hot, whose heat is conserved by
7807 the greatness of the Bodies, and the mutual Action and Reaction between
7808 them, and the Light which they emit, and whose parts are kept from
7809 fuming away, not only by their fixity, but also by the vast weight and
7810 density of the Atmospheres incumbent upon them; and very strongly
7811 compressing them, and condensing the Vapours and Exhalations which arise
7812 from them? For if Water be made warm in any pellucid Vessel emptied of
7813 Air, that Water in the _Vacuum_ will bubble and boil as vehemently as it
7814 would in the open Air in a Vessel set upon the Fire till it conceives a
7815 much greater heat. For the weight of the incumbent Atmosphere keeps down
7816 the Vapours, and hinders the Water from boiling, until it grow much
7817 hotter than is requisite to make it boil _in vacuo_. Also a mixture of
7818 Tin and Lead being put upon a red hot Iron _in vacuo_ emits a Fume and
7819 Flame, but the same Mixture in the open Air, by reason of the incumbent
7820 Atmosphere, does not so much as emit any Fume which can be perceived by
7821 Sight. In like manner the great weight of the Atmosphere which lies upon
7822 the Globe of the Sun may hinder Bodies there from rising up and going
7823 away from the Sun in the form of Vapours and Fumes, unless by means of a
7824 far greater heat than that which on the Surface of our Earth would very
7825 easily turn them into Vapours and Fumes. And the same great weight may
7826 condense those Vapours and Exhalations as soon as they shall at any time
7827 begin to ascend from the Sun, and make them presently fall back again
7828 into him, and by that action increase his Heat much after the manner
7829 that in our Earth the Air increases the Heat of a culinary Fire. And the
7830 same weight may hinder the Globe of the Sun from being diminish'd,
7831 unless by the Emission of Light, and a very small quantity of Vapours
7832 and Exhalations.
7833
7834 _Qu._ 12. Do not the Rays of Light in falling upon the bottom of the Eye
7835 excite Vibrations in the _Tunica Retina_? Which Vibrations, being
7836 propagated along the solid Fibres of the optick Nerves into the Brain,
7837 cause the Sense of seeing. For because dense Bodies conserve their Heat
7838 a long time, and the densest Bodies conserve their Heat the longest, the
7839 Vibrations of their parts are of a lasting nature, and therefore may be
7840 propagated along solid Fibres of uniform dense Matter to a great
7841 distance, for conveying into the Brain the impressions made upon all the
7842 Organs of Sense. For that Motion which can continue long in one and the
7843 same part of a Body, can be propagated a long way from one part to
7844 another, supposing the Body homogeneal, so that the Motion may not be
7845 reflected, refracted, interrupted or disorder'd by any unevenness of the
7846 Body.
7847
7848 _Qu._ 13. Do not several sorts of Rays make Vibrations of several
7849 bignesses, which according to their bignesses excite Sensations of
7850 several Colours, much after the manner that the Vibrations of the Air,
7851 according to their several bignesses excite Sensations of several
7852 Sounds? And particularly do not the most refrangible Rays excite the
7853 shortest Vibrations for making a Sensation of deep violet, the least
7854 refrangible the largest for making a Sensation of deep red, and the
7855 several intermediate sorts of Rays, Vibrations of several intermediate
7856 bignesses to make Sensations of the several intermediate Colours?
7857
7858 _Qu._ 14. May not the harmony and discord of Colours arise from the
7859 proportions of the Vibrations propagated through the Fibres of the
7860 optick Nerves into the Brain, as the harmony and discord of Sounds arise
7861 from the proportions of the Vibrations of the Air? For some Colours, if
7862 they be view'd together, are agreeable to one another, as those of Gold
7863 and Indigo, and others disagree.
7864
7865 _Qu._ 15. Are not the Species of Objects seen with both Eyes united
7866 where the optick Nerves meet before they come into the Brain, the Fibres
7867 on the right side of both Nerves uniting there, and after union going
7868 thence into the Brain in the Nerve which is on the right side of the
7869 Head, and the Fibres on the left side of both Nerves uniting in the same
7870 place, and after union going into the Brain in the Nerve which is on the
7871 left side of the Head, and these two Nerves meeting in the Brain in such
7872 a manner that their Fibres make but one entire Species or Picture, half
7873 of which on the right side of the Sensorium comes from the right side of
7874 both Eyes through the right side of both optick Nerves to the place
7875 where the Nerves meet, and from thence on the right side of the Head
7876 into the Brain, and the other half on the left side of the Sensorium
7877 comes in like manner from the left side of both Eyes. For the optick
7878 Nerves of such Animals as look the same way with both Eyes (as of Men,
7879 Dogs, Sheep, Oxen, &c.) meet before they come into the Brain, but the
7880 optick Nerves of such Animals as do not look the same way with both Eyes
7881 (as of Fishes, and of the Chameleon,) do not meet, if I am rightly
7882 inform'd.
7883
7884 _Qu._ 16. When a Man in the dark presses either corner of his Eye with
7885 his Finger, and turns his Eye away from his Finger, he will see a Circle
7886 of Colours like those in the Feather of a Peacock's Tail. If the Eye and
7887 the Finger remain quiet these Colours vanish in a second Minute of Time,
7888 but if the Finger be moved with a quavering Motion they appear again. Do
7889 not these Colours arise from such Motions excited in the bottom of the
7890 Eye by the Pressure and Motion of the Finger, as, at other times are
7891 excited there by Light for causing Vision? And do not the Motions once
7892 excited continue about a Second of Time before they cease? And when a
7893 Man by a stroke upon his Eye sees a flash of Light, are not the like
7894 Motions excited in the _Retina_ by the stroke? And when a Coal of Fire
7895 moved nimbly in the circumference of a Circle, makes the whole
7896 circumference appear like a Circle of Fire; is it not because the
7897 Motions excited in the bottom of the Eye by the Rays of Light are of a
7898 lasting nature, and continue till the Coal of Fire in going round
7899 returns to its former place? And considering the lastingness of the
7900 Motions excited in the bottom of the Eye by Light, are they not of a
7901 vibrating nature?
7902
7903 _Qu._ 17. If a stone be thrown into stagnating Water, the Waves excited
7904 thereby continue some time to arise in the place where the Stone fell
7905 into the Water, and are propagated from thence in concentrick Circles
7906 upon the Surface of the Water to great distances. And the Vibrations or
7907 Tremors excited in the Air by percussion, continue a little time to move
7908 from the place of percussion in concentrick Spheres to great distances.
7909 And in like manner, when a Ray of Light falls upon the Surface of any
7910 pellucid Body, and is there refracted or reflected, may not Waves of
7911 Vibrations, or Tremors, be thereby excited in the refracting or
7912 reflecting Medium at the point of Incidence, and continue to arise
7913 there, and to be propagated from thence as long as they continue to
7914 arise and be propagated, when they are excited in the bottom of the Eye
7915 by the Pressure or Motion of the Finger, or by the Light which comes
7916 from the Coal of Fire in the Experiments above-mention'd? and are not
7917 these Vibrations propagated from the point of Incidence to great
7918 distances? And do they not overtake the Rays of Light, and by overtaking
7919 them successively, do they not put them into the Fits of easy Reflexion
7920 and easy Transmission described above? For if the Rays endeavour to
7921 recede from the densest part of the Vibration, they may be alternately
7922 accelerated and retarded by the Vibrations overtaking them.
7923
7924 _Qu._ 18. If in two large tall cylindrical Vessels of Glass inverted,
7925 two little Thermometers be suspended so as not to touch the Vessels, and
7926 the Air be drawn out of one of these Vessels, and these Vessels thus
7927 prepared be carried out of a cold place into a warm one; the Thermometer
7928 _in vacuo_ will grow warm as much, and almost as soon as the Thermometer
7929 which is not _in vacuo_. And when the Vessels are carried back into the
7930 cold place, the Thermometer _in vacuo_ will grow cold almost as soon as
7931 the other Thermometer. Is not the Heat of the warm Room convey'd through
7932 the _Vacuum_ by the Vibrations of a much subtiler Medium than Air, which
7933 after the Air was drawn out remained in the _Vacuum_? And is not this
7934 Medium the same with that Medium by which Light is refracted and
7935 reflected, and by whose Vibrations Light communicates Heat to Bodies,
7936 and is put into Fits of easy Reflexion and easy Transmission? And do not
7937 the Vibrations of this Medium in hot Bodies contribute to the
7938 intenseness and duration of their Heat? And do not hot Bodies
7939 communicate their Heat to contiguous cold ones, by the Vibrations of
7940 this Medium propagated from them into the cold ones? And is not this
7941 Medium exceedingly more rare and subtile than the Air, and exceedingly
7942 more elastick and active? And doth it not readily pervade all Bodies?
7943 And is it not (by its elastick force) expanded through all the Heavens?
7944
7945 _Qu._ 19. Doth not the Refraction of Light proceed from the different
7946 density of this Æthereal Medium in different places, the Light receding
7947 always from the denser parts of the Medium? And is not the density
7948 thereof greater in free and open Spaces void of Air and other grosser
7949 Bodies, than within the Pores of Water, Glass, Crystal, Gems, and other
7950 compact Bodies? For when Light passes through Glass or Crystal, and
7951 falling very obliquely upon the farther Surface thereof is totally
7952 reflected, the total Reflexion ought to proceed rather from the density
7953 and vigour of the Medium without and beyond the Glass, than from the
7954 rarity and weakness thereof.
7955
7956 _Qu._ 20. Doth not this Æthereal Medium in passing out of Water, Glass,
7957 Crystal, and other compact and dense Bodies into empty Spaces, grow
7958 denser and denser by degrees, and by that means refract the Rays of
7959 Light not in a point, but by bending them gradually in curve Lines? And
7960 doth not the gradual condensation of this Medium extend to some distance
7961 from the Bodies, and thereby cause the Inflexions of the Rays of Light,
7962 which pass by the edges of dense Bodies, at some distance from the
7963 Bodies?
7964
7965 _Qu._ 21. Is not this Medium much rarer within the dense Bodies of the
7966 Sun, Stars, Planets and Comets, than in the empty celestial Spaces
7967 between them? And in passing from them to great distances, doth it not
7968 grow denser and denser perpetually, and thereby cause the gravity of
7969 those great Bodies towards one another, and of their parts towards the
7970 Bodies; every Body endeavouring to go from the denser parts of the
7971 Medium towards the rarer? For if this Medium be rarer within the Sun's
7972 Body than at its Surface, and rarer there than at the hundredth part of
7973 an Inch from its Body, and rarer there than at the fiftieth part of an
7974 Inch from its Body, and rarer there than at the Orb of _Saturn_; I see
7975 no reason why the Increase of density should stop any where, and not
7976 rather be continued through all distances from the Sun to _Saturn_, and
7977 beyond. And though this Increase of density may at great distances be
7978 exceeding slow, yet if the elastick force of this Medium be exceeding
7979 great, it may suffice to impel Bodies from the denser parts of the
7980 Medium towards the rarer, with all that power which we call Gravity. And
7981 that the elastick force of this Medium is exceeding great, may be
7982 gather'd from the swiftness of its Vibrations. Sounds move about 1140
7983 _English_ Feet in a second Minute of Time, and in seven or eight Minutes
7984 of Time they move about one hundred _English_ Miles. Light moves from
7985 the Sun to us in about seven or eight Minutes of Time, which distance is
7986 about 70,000,000 _English_ Miles, supposing the horizontal Parallax of
7987 the Sun to be about 12´´. And the Vibrations or Pulses of this Medium,
7988 that they may cause the alternate Fits of easy Transmission and easy
7989 Reflexion, must be swifter than Light, and by consequence above 700,000
7990 times swifter than Sounds. And therefore the elastick force of this
7991 Medium, in proportion to its density, must be above 700000 x 700000
7992 (that is, above 490,000,000,000) times greater than the elastick force
7993 of the Air is in proportion to its density. For the Velocities of the
7994 Pulses of elastick Mediums are in a subduplicate _Ratio_ of the
7995 Elasticities and the Rarities of the Mediums taken together.
7996
7997 As Attraction is stronger in small Magnets than in great ones in
7998 proportion to their Bulk, and Gravity is greater in the Surfaces of
7999 small Planets than in those of great ones in proportion to their bulk,
8000 and small Bodies are agitated much more by electric attraction than
8001 great ones; so the smallness of the Rays of Light may contribute very
8002 much to the power of the Agent by which they are refracted. And so if
8003 any one should suppose that _Æther_ (like our Air) may contain Particles
8004 which endeavour to recede from one another (for I do not know what this
8005 _Æther_ is) and that its Particles are exceedingly smaller than those of
8006 Air, or even than those of Light: The exceeding smallness of its
8007 Particles may contribute to the greatness of the force by which those
8008 Particles may recede from one another, and thereby make that Medium
8009 exceedingly more rare and elastick than Air, and by consequence
8010 exceedingly less able to resist the motions of Projectiles, and
8011 exceedingly more able to press upon gross Bodies, by endeavouring to
8012 expand it self.
8013
8014 _Qu._ 22. May not Planets and Comets, and all gross Bodies, perform
8015 their Motions more freely, and with less resistance in this Æthereal
8016 Medium than in any Fluid, which fills all Space adequately without
8017 leaving any Pores, and by consequence is much denser than Quick-silver
8018 or Gold? And may not its resistance be so small, as to be
8019 inconsiderable? For instance; If this _Æther_ (for so I will call it)
8020 should be supposed 700000 times more elastick than our Air, and above
8021 700000 times more rare; its resistance would be above 600,000,000 times
8022 less than that of Water. And so small a resistance would scarce make any
8023 sensible alteration in the Motions of the Planets in ten thousand
8024 Years. If any one would ask how a Medium can be so rare, let him tell me
8025 how the Air, in the upper parts of the Atmosphere, can be above an
8026 hundred thousand thousand times rarer than Gold. Let him also tell me,
8027 how an electrick Body can by Friction emit an Exhalation so rare and
8028 subtile, and yet so potent, as by its Emission to cause no sensible
8029 Diminution of the weight of the electrick Body, and to be expanded
8030 through a Sphere, whose Diameter is above two Feet, and yet to be able
8031 to agitate and carry up Leaf Copper, or Leaf Gold, at the distance of
8032 above a Foot from the electrick Body? And how the Effluvia of a Magnet
8033 can be so rare and subtile, as to pass through a Plate of Glass without
8034 any Resistance or Diminution of their Force, and yet so potent as to
8035 turn a magnetick Needle beyond the Glass?
8036
8037 _Qu._ 23. Is not Vision perform'd chiefly by the Vibrations of this
8038 Medium, excited in the bottom of the Eye by the Rays of Light, and
8039 propagated through the solid, pellucid and uniform Capillamenta of the
8040 optick Nerves into the place of Sensation? And is not Hearing perform'd
8041 by the Vibrations either of this or some other Medium, excited in the
8042 auditory Nerves by the Tremors of the Air, and propagated through the
8043 solid, pellucid and uniform Capillamenta of those Nerves into the place
8044 of Sensation? And so of the other Senses.
8045
8046 _Qu._ 24. Is not Animal Motion perform'd by the Vibrations of this
8047 Medium, excited in the Brain by the power of the Will, and propagated
8048 from thence through the solid, pellucid and uniform Capillamenta of the
8049 Nerves into the Muscles, for contracting and dilating them? I suppose
8050 that the Capillamenta of the Nerves are each of them solid and uniform,
8051 that the vibrating Motion of the Æthereal Medium may be propagated along
8052 them from one end to the other uniformly, and without interruption: For
8053 Obstructions in the Nerves create Palsies. And that they may be
8054 sufficiently uniform, I suppose them to be pellucid when view'd singly,
8055 tho' the Reflexions in their cylindrical Surfaces may make the whole
8056 Nerve (composed of many Capillamenta) appear opake and white. For
8057 opacity arises from reflecting Surfaces, such as may disturb and
8058 interrupt the Motions of this Medium.
8059
8060 [Sidenote: _See the following Scheme, p. 356._]
8061
8062 _Qu._ 25. Are there not other original Properties of the Rays of Light,
8063 besides those already described? An instance of another original
8064 Property we have in the Refraction of Island Crystal, described first by
8065 _Erasmus Bartholine_, and afterwards more exactly by _Hugenius_, in his
8066 Book _De la Lumiere_. This Crystal is a pellucid fissile Stone, clear as
8067 Water or Crystal of the Rock, and without Colour; enduring a red Heat
8068 without losing its transparency, and in a very strong Heat calcining
8069 without Fusion. Steep'd a Day or two in Water, it loses its natural
8070 Polish. Being rubb'd on Cloth, it attracts pieces of Straws and other
8071 light things, like Ambar or Glass; and with _Aqua fortis_ it makes an
8072 Ebullition. It seems to be a sort of Talk, and is found in form of an
8073 oblique Parallelopiped, with six parallelogram Sides and eight solid
8074 Angles. The obtuse Angles of the Parallelograms are each of them 101
8075 Degrees and 52 Minutes; the acute ones 78 Degrees and 8 Minutes. Two of
8076 the solid Angles opposite to one another, as C and E, are compassed each
8077 of them with three of these obtuse Angles, and each of the other six
8078 with one obtuse and two acute ones. It cleaves easily in planes parallel
8079 to any of its Sides, and not in any other Planes. It cleaves with a
8080 glossy polite Surface not perfectly plane, but with some little
8081 unevenness. It is easily scratch'd, and by reason of its softness it
8082 takes a Polish very difficultly. It polishes better upon polish'd
8083 Looking-glass than upon Metal, and perhaps better upon Pitch, Leather or
8084 Parchment. Afterwards it must be rubb'd with a little Oil or white of an
8085 Egg, to fill up its Scratches; whereby it will become very transparent
8086 and polite. But for several Experiments, it is not necessary to polish
8087 it. If a piece of this crystalline Stone be laid upon a Book, every
8088 Letter of the Book seen through it will appear double, by means of a
8089 double Refraction. And if any beam of Light falls either
8090 perpendicularly, or in any oblique Angle upon any Surface of this
8091 Crystal, it becomes divided into two beams by means of the same double
8092 Refraction. Which beams are of the same Colour with the incident beam of
8093 Light, and seem equal to one another in the quantity of their Light, or
8094 very nearly equal. One of these Refractions is perform'd by the usual
8095 Rule of Opticks, the Sine of Incidence out of Air into this Crystal
8096 being to the Sine of Refraction, as five to three. The other
8097 Refraction, which may be called the unusual Refraction, is perform'd by
8098 the following Rule.
8099
8100 [Illustration: FIG. 4.]
8101
8102 Let ADBC represent the refracting Surface of the Crystal, C the biggest
8103 solid Angle at that Surface, GEHF the opposite Surface, and CK a
8104 perpendicular on that Surface. This perpendicular makes with the edge of
8105 the Crystal CF, an Angle of 19 Degr. 3'. Join KF, and in it take KL, so
8106 that the Angle KCL be 6 Degr. 40'. and the Angle LCF 12 Degr. 23'. And
8107 if ST represent any beam of Light incident at T in any Angle upon the
8108 refracting Surface ADBC, let TV be the refracted beam determin'd by the
8109 given Portion of the Sines 5 to 3, according to the usual Rule of
8110 Opticks. Draw VX parallel and equal to KL. Draw it the same way from V
8111 in which L lieth from K; and joining TX, this line TX shall be the other
8112 refracted beam carried from T to X, by the unusual Refraction.
8113
8114 If therefore the incident beam ST be perpendicular to the refracting
8115 Surface, the two beams TV and TX, into which it shall become divided,
8116 shall be parallel to the lines CK and CL; one of those beams going
8117 through the Crystal perpendicularly, as it ought to do by the usual Laws
8118 of Opticks, and the other TX by an unusual Refraction diverging from the
8119 perpendicular, and making with it an Angle VTX of about 6-2/3 Degrees,
8120 as is found by Experience. And hence, the Plane VTX, and such like
8121 Planes which are parallel to the Plane CFK, may be called the Planes of
8122 perpendicular Refraction. And the Coast towards which the lines KL and
8123 VX are drawn, may be call'd the Coast of unusual Refraction.
8124
8125 In like manner Crystal of the Rock has a double Refraction: But the
8126 difference of the two Refractions is not so great and manifest as in
8127 Island Crystal.
8128
8129 When the beam ST incident on Island Crystal is divided into two beams TV
8130 and TX, and these two beams arrive at the farther Surface of the Glass;
8131 the beam TV, which was refracted at the first Surface after the usual
8132 manner, shall be again refracted entirely after the usual manner at the
8133 second Surface; and the beam TX, which was refracted after the unusual
8134 manner in the first Surface, shall be again refracted entirely after the
8135 unusual manner in the second Surface; so that both these beams shall
8136 emerge out of the second Surface in lines parallel to the first incident
8137 beam ST.
8138
8139 And if two pieces of Island Crystal be placed one after another, in such
8140 manner that all the Surfaces of the latter be parallel to all the
8141 corresponding Surfaces of the former: The Rays which are refracted after
8142 the usual manner in the first Surface of the first Crystal, shall be
8143 refracted after the usual manner in all the following Surfaces; and the
8144 Rays which are refracted after the unusual manner in the first Surface,
8145 shall be refracted after the unusual manner in all the following
8146 Surfaces. And the same thing happens, though the Surfaces of the
8147 Crystals be any ways inclined to one another, provided that their Planes
8148 of perpendicular Refraction be parallel to one another.
8149
8150 And therefore there is an original difference in the Rays of Light, by
8151 means of which some Rays are in this Experiment constantly refracted
8152 after the usual manner, and others constantly after the unusual manner:
8153 For if the difference be not original, but arises from new Modifications
8154 impress'd on the Rays at their first Refraction, it would be alter'd by
8155 new Modifications in the three following Refractions; whereas it suffers
8156 no alteration, but is constant, and has the same effect upon the Rays in
8157 all the Refractions. The unusual Refraction is therefore perform'd by an
8158 original property of the Rays. And it remains to be enquired, whether
8159 the Rays have not more original Properties than are yet discover'd.
8160
8161 _Qu._ 26. Have not the Rays of Light several sides, endued with several
8162 original Properties? For if the Planes of perpendicular Refraction of
8163 the second Crystal be at right Angles with the Planes of perpendicular
8164 Refraction of the first Crystal, the Rays which are refracted after the
8165 usual manner in passing through the first Crystal, will be all of them
8166 refracted after the unusual manner in passing through the second
8167 Crystal; and the Rays which are refracted after the unusual manner in
8168 passing through the first Crystal, will be all of them refracted after
8169 the usual manner in passing through the second Crystal. And therefore
8170 there are not two sorts of Rays differing in their nature from one
8171 another, one of which is constantly and in all Positions refracted after
8172 the usual manner, and the other constantly and in all Positions after
8173 the unusual manner. The difference between the two sorts of Rays in the
8174 Experiment mention'd in the 25th Question, was only in the Positions of
8175 the Sides of the Rays to the Planes of perpendicular Refraction. For one
8176 and the same Ray is here refracted sometimes after the usual, and
8177 sometimes after the unusual manner, according to the Position which its
8178 Sides have to the Crystals. If the Sides of the Ray are posited the same
8179 way to both Crystals, it is refracted after the same manner in them
8180 both: But if that side of the Ray which looks towards the Coast of the
8181 unusual Refraction of the first Crystal, be 90 Degrees from that side of
8182 the same Ray which looks toward the Coast of the unusual Refraction of
8183 the second Crystal, (which may be effected by varying the Position of
8184 the second Crystal to the first, and by consequence to the Rays of
8185 Light,) the Ray shall be refracted after several manners in the several
8186 Crystals. There is nothing more required to determine whether the Rays
8187 of Light which fall upon the second Crystal shall be refracted after
8188 the usual or after the unusual manner, but to turn about this Crystal,
8189 so that the Coast of this Crystal's unusual Refraction may be on this or
8190 on that side of the Ray. And therefore every Ray may be consider'd as
8191 having four Sides or Quarters, two of which opposite to one another
8192 incline the Ray to be refracted after the unusual manner, as often as
8193 either of them are turn'd towards the Coast of unusual Refraction; and
8194 the other two, whenever either of them are turn'd towards the Coast of
8195 unusual Refraction, do not incline it to be otherwise refracted than
8196 after the usual manner. The two first may therefore be call'd the Sides
8197 of unusual Refraction. And since these Dispositions were in the Rays
8198 before their Incidence on the second, third, and fourth Surfaces of the
8199 two Crystals, and suffered no alteration (so far as appears,) by the
8200 Refraction of the Rays in their passage through those Surfaces, and the
8201 Rays were refracted by the same Laws in all the four Surfaces; it
8202 appears that those Dispositions were in the Rays originally, and
8203 suffer'd no alteration by the first Refraction, and that by means of
8204 those Dispositions the Rays were refracted at their Incidence on the
8205 first Surface of the first Crystal, some of them after the usual, and
8206 some of them after the unusual manner, accordingly as their Sides of
8207 unusual Refraction were then turn'd towards the Coast of the unusual
8208 Refraction of that Crystal, or sideways from it.
8209
8210 Every Ray of Light has therefore two opposite Sides, originally endued
8211 with a Property on which the unusual Refraction depends, and the other
8212 two opposite Sides not endued with that Property. And it remains to be
8213 enquired, whether there are not more Properties of Light by which the
8214 Sides of the Rays differ, and are distinguished from one another.
8215
8216 In explaining the difference of the Sides of the Rays above mention'd, I
8217 have supposed that the Rays fall perpendicularly on the first Crystal.
8218 But if they fall obliquely on it, the Success is the same. Those Rays
8219 which are refracted after the usual manner in the first Crystal, will be
8220 refracted after the unusual manner in the second Crystal, supposing the
8221 Planes of perpendicular Refraction to be at right Angles with one
8222 another, as above; and on the contrary.
8223
8224 If the Planes of the perpendicular Refraction of the two Crystals be
8225 neither parallel nor perpendicular to one another, but contain an acute
8226 Angle: The two beams of Light which emerge out of the first Crystal,
8227 will be each of them divided into two more at their Incidence on the
8228 second Crystal. For in this case the Rays in each of the two beams will
8229 some of them have their Sides of unusual Refraction, and some of them
8230 their other Sides turn'd towards the Coast of the unusual Refraction of
8231 the second Crystal.
8232
8233 _Qu._ 27. Are not all Hypotheses erroneous which have hitherto been
8234 invented for explaining the Phænomena of Light, by new Modifications of
8235 the Rays? For those Phænomena depend not upon new Modifications, as has
8236 been supposed, but upon the original and unchangeable Properties of the
8237 Rays.
8238
8239 _Qu._ 28. Are not all Hypotheses erroneous, in which Light is supposed
8240 to consist in Pression or Motion, propagated through a fluid Medium? For
8241 in all these Hypotheses the Phænomena of Light have been hitherto
8242 explain'd by supposing that they arise from new Modifications of the
8243 Rays; which is an erroneous Supposition.
8244
8245 If Light consisted only in Pression propagated without actual Motion, it
8246 would not be able to agitate and heat the Bodies which refract and
8247 reflect it. If it consisted in Motion propagated to all distances in an
8248 instant, it would require an infinite force every moment, in every
8249 shining Particle, to generate that Motion. And if it consisted in
8250 Pression or Motion, propagated either in an instant or in time, it would
8251 bend into the Shadow. For Pression or Motion cannot be propagated in a
8252 Fluid in right Lines, beyond an Obstacle which stops part of the Motion,
8253 but will bend and spread every way into the quiescent Medium which lies
8254 beyond the Obstacle. Gravity tends downwards, but the Pressure of Water
8255 arising from Gravity tends every way with equal Force, and is propagated
8256 as readily, and with as much force sideways as downwards, and through
8257 crooked passages as through strait ones. The Waves on the Surface of
8258 stagnating Water, passing by the sides of a broad Obstacle which stops
8259 part of them, bend afterwards and dilate themselves gradually into the
8260 quiet Water behind the Obstacle. The Waves, Pulses or Vibrations of the
8261 Air, wherein Sounds consist, bend manifestly, though not so much as the
8262 Waves of Water. For a Bell or a Cannon may be heard beyond a Hill which
8263 intercepts the sight of the sounding Body, and Sounds are propagated as
8264 readily through crooked Pipes as through streight ones. But Light is
8265 never known to follow crooked Passages nor to bend into the Shadow. For
8266 the fix'd Stars by the Interposition of any of the Planets cease to be
8267 seen. And so do the Parts of the Sun by the Interposition of the Moon,
8268 _Mercury_ or _Venus_. The Rays which pass very near to the edges of any
8269 Body, are bent a little by the action of the Body, as we shew'd above;
8270 but this bending is not towards but from the Shadow, and is perform'd
8271 only in the passage of the Ray by the Body, and at a very small distance
8272 from it. So soon as the Ray is past the Body, it goes right on.
8273
8274 [Sidenote: _Mais pour dire comment cela se fait, je n'ay rien trove
8275 jusqu' ici qui me satisfasse._ C. H. de la lumiere, c. 5, p. 91.]
8276
8277 To explain the unusual Refraction of Island Crystal by Pression or
8278 Motion propagated, has not hitherto been attempted (to my knowledge)
8279 except by _Huygens_, who for that end supposed two several vibrating
8280 Mediums within that Crystal. But when he tried the Refractions in two
8281 successive pieces of that Crystal, and found them such as is mention'd
8282 above; he confessed himself at a loss for explaining them. For Pressions
8283 or Motions, propagated from a shining Body through an uniform Medium,
8284 must be on all sides alike; whereas by those Experiments it appears,
8285 that the Rays of Light have different Properties in their different
8286 Sides. He suspected that the Pulses of _Æther_ in passing through the
8287 first Crystal might receive certain new Modifications, which might
8288 determine them to be propagated in this or that Medium within the
8289 second Crystal, according to the Position of that Crystal. But what
8290 Modifications those might be he could not say, nor think of any thing
8291 satisfactory in that Point. And if he had known that the unusual
8292 Refraction depends not on new Modifications, but on the original and
8293 unchangeable Dispositions of the Rays, he would have found it as
8294 difficult to explain how those Dispositions which he supposed to be
8295 impress'd on the Rays by the first Crystal, could be in them before
8296 their Incidence on that Crystal, and in general, how all Rays emitted by
8297 shining Bodies, can have those Dispositions in them from the beginning.
8298 To me, at least, this seems inexplicable, if Light be nothing else than
8299 Pression or Motion propagated through _Æther_.
8300
8301 And it is as difficult to explain by these Hypotheses, how Rays can be
8302 alternately in Fits of easy Reflexion and easy Transmission; unless
8303 perhaps one might suppose that there are in all Space two Æthereal
8304 vibrating Mediums, and that the Vibrations of one of them constitute
8305 Light, and the Vibrations of the other are swifter, and as often as they
8306 overtake the Vibrations of the first, put them into those Fits. But how
8307 two _Æthers_ can be diffused through all Space, one of which acts upon
8308 the other, and by consequence is re-acted upon, without retarding,
8309 shattering, dispersing and confounding one anothers Motions, is
8310 inconceivable. And against filling the Heavens with fluid Mediums,
8311 unless they be exceeding rare, a great Objection arises from the regular
8312 and very lasting Motions of the Planets and Comets in all manner of
8313 Courses through the Heavens. For thence it is manifest, that the Heavens
8314 are void of all sensible Resistance, and by consequence of all sensible
8315 Matter.
8316
8317 For the resisting Power of fluid Mediums arises partly from the
8318 Attrition of the Parts of the Medium, and partly from the _Vis inertiæ_
8319 of the Matter. That part of the Resistance of a spherical Body which
8320 arises from the Attrition of the Parts of the Medium is very nearly as
8321 the Diameter, or, at the most, as the _Factum_ of the Diameter, and the
8322 Velocity of the spherical Body together. And that part of the Resistance
8323 which arises from the _Vis inertiæ_ of the Matter, is as the Square of
8324 that _Factum_. And by this difference the two sorts of Resistance may be
8325 distinguish'd from one another in any Medium; and these being
8326 distinguish'd, it will be found that almost all the Resistance of Bodies
8327 of a competent Magnitude moving in Air, Water, Quick-silver, and such
8328 like Fluids with a competent Velocity, arises from the _Vis inertiæ_ of
8329 the Parts of the Fluid.
8330
8331 Now that part of the resisting Power of any Medium which arises from the
8332 Tenacity, Friction or Attrition of the Parts of the Medium, may be
8333 diminish'd by dividing the Matter into smaller Parts, and making the
8334 Parts more smooth and slippery: But that part of the Resistance which
8335 arises from the _Vis inertiæ_, is proportional to the Density of the
8336 Matter, and cannot be diminish'd by dividing the Matter into smaller
8337 Parts, nor by any other means than by decreasing the Density of the
8338 Medium. And for these Reasons the Density of fluid Mediums is very
8339 nearly proportional to their Resistance. Liquors which differ not much
8340 in Density, as Water, Spirit of Wine, Spirit of Turpentine, hot Oil,
8341 differ not much in Resistance. Water is thirteen or fourteen times
8342 lighter than Quick-silver and by consequence thirteen or fourteen times
8343 rarer, and its Resistance is less than that of Quick-silver in the same
8344 Proportion, or thereabouts, as I have found by Experiments made with
8345 Pendulums. The open Air in which we breathe is eight or nine hundred
8346 times lighter than Water, and by consequence eight or nine hundred times
8347 rarer, and accordingly its Resistance is less than that of Water in the
8348 same Proportion, or thereabouts; as I have also found by Experiments
8349 made with Pendulums. And in thinner Air the Resistance is still less,
8350 and at length, by ratifying the Air, becomes insensible. For small
8351 Feathers falling in the open Air meet with great Resistance, but in a
8352 tall Glass well emptied of Air, they fall as fast as Lead or Gold, as I
8353 have seen tried several times. Whence the Resistance seems still to
8354 decrease in proportion to the Density of the Fluid. For I do not find by
8355 any Experiments, that Bodies moving in Quick-silver, Water or Air, meet
8356 with any other sensible Resistance than what arises from the Density and
8357 Tenacity of those sensible Fluids, as they would do if the Pores of
8358 those Fluids, and all other Spaces, were filled with a dense and
8359 subtile Fluid. Now if the Resistance in a Vessel well emptied of Air,
8360 was but an hundred times less than in the open Air, it would be about a
8361 million of times less than in Quick-silver. But it seems to be much less
8362 in such a Vessel, and still much less in the Heavens, at the height of
8363 three or four hundred Miles from the Earth, or above. For Mr. _Boyle_
8364 has shew'd that Air may be rarified above ten thousand times in Vessels
8365 of Glass; and the Heavens are much emptier of Air than any _Vacuum_ we
8366 can make below. For since the Air is compress'd by the Weight of the
8367 incumbent Atmosphere, and the Density of Air is proportional to the
8368 Force compressing it, it follows by Computation, that at the height of
8369 about seven and a half _English_ Miles from the Earth, the Air is four
8370 times rarer than at the Surface of the Earth; and at the height of 15
8371 Miles it is sixteen times rarer than that at the Surface of the Earth;
8372 and at the height of 22-1/2, 30, or 38 Miles, it is respectively 64,
8373 256, or 1024 times rarer, or thereabouts; and at the height of 76, 152,
8374 228 Miles, it is about 1000000, 1000000000000, or 1000000000000000000
8375 times rarer; and so on.
8376
8377 Heat promotes Fluidity very much by diminishing the Tenacity of Bodies.
8378 It makes many Bodies fluid which are not fluid in cold, and increases
8379 the Fluidity of tenacious Liquids, as of Oil, Balsam, and Honey, and
8380 thereby decreases their Resistance. But it decreases not the Resistance
8381 of Water considerably, as it would do if any considerable part of the
8382 Resistance of Water arose from the Attrition or Tenacity of its Parts.
8383 And therefore the Resistance of Water arises principally and almost
8384 entirely from the _Vis inertiæ_ of its Matter; and by consequence, if
8385 the Heavens were as dense as Water, they would not have much less
8386 Resistance than Water; if as dense as Quick-silver, they would not have
8387 much less Resistance than Quick-silver; if absolutely dense, or full of
8388 Matter without any _Vacuum_, let the Matter be never so subtil and
8389 fluid, they would have a greater Resistance than Quick-silver. A solid
8390 Globe in such a Medium would lose above half its Motion in moving three
8391 times the length of its Diameter, and a Globe not solid (such as are the
8392 Planets,) would be retarded sooner. And therefore to make way for the
8393 regular and lasting Motions of the Planets and Comets, it's necessary to
8394 empty the Heavens of all Matter, except perhaps some very thin Vapours,
8395 Steams, or Effluvia, arising from the Atmospheres of the Earth, Planets,
8396 and Comets, and from such an exceedingly rare Æthereal Medium as we
8397 described above. A dense Fluid can be of no use for explaining the
8398 Phænomena of Nature, the Motions of the Planets and Comets being better
8399 explain'd without it. It serves only to disturb and retard the Motions
8400 of those great Bodies, and make the Frame of Nature languish: And in the
8401 Pores of Bodies, it serves only to stop the vibrating Motions of their
8402 Parts, wherein their Heat and Activity consists. And as it is of no use,
8403 and hinders the Operations of Nature, and makes her languish, so there
8404 is no evidence for its Existence, and therefore it ought to be rejected.
8405 And if it be rejected, the Hypotheses that Light consists in Pression
8406 or Motion, propagated through such a Medium, are rejected with it.
8407
8408 And for rejecting such a Medium, we have the Authority of those the
8409 oldest and most celebrated Philosophers of _Greece_ and _Phoenicia_,
8410 who made a _Vacuum_, and Atoms, and the Gravity of Atoms, the first
8411 Principles of their Philosophy; tacitly attributing Gravity to some
8412 other Cause than dense Matter. Later Philosophers banish the
8413 Consideration of such a Cause out of natural Philosophy, feigning
8414 Hypotheses for explaining all things mechanically, and referring other
8415 Causes to Metaphysicks: Whereas the main Business of natural Philosophy
8416 is to argue from Phænomena without feigning Hypotheses, and to deduce
8417 Causes from Effects, till we come to the very first Cause, which
8418 certainly is not mechanical; and not only to unfold the Mechanism of the
8419 World, but chiefly to resolve these and such like Questions. What is
8420 there in places almost empty of Matter, and whence is it that the Sun
8421 and Planets gravitate towards one another, without dense Matter between
8422 them? Whence is it that Nature doth nothing in vain; and whence arises
8423 all that Order and Beauty which we see in the World? To what end are
8424 Comets, and whence is it that Planets move all one and the same way in
8425 Orbs concentrick, while Comets move all manner of ways in Orbs very
8426 excentrick; and what hinders the fix'd Stars from falling upon one
8427 another? How came the Bodies of Animals to be contrived with so much
8428 Art, and for what ends were their several Parts? Was the Eye contrived
8429 without Skill in Opticks, and the Ear without Knowledge of Sounds? How
8430 do the Motions of the Body follow from the Will, and whence is the
8431 Instinct in Animals? Is not the Sensory of Animals that place to which
8432 the sensitive Substance is present, and into which the sensible Species
8433 of Things are carried through the Nerves and Brain, that there they may
8434 be perceived by their immediate presence to that Substance? And these
8435 things being rightly dispatch'd, does it not appear from Phænomena that
8436 there is a Being incorporeal, living, intelligent, omnipresent, who in
8437 infinite Space, as it were in his Sensory, sees the things themselves
8438 intimately, and throughly perceives them, and comprehends them wholly by
8439 their immediate presence to himself: Of which things the Images only
8440 carried through the Organs of Sense into our little Sensoriums, are
8441 there seen and beheld by that which in us perceives and thinks. And
8442 though every true Step made in this Philosophy brings us not immediately
8443 to the Knowledge of the first Cause, yet it brings us nearer to it, and
8444 on that account is to be highly valued.
8445
8446 _Qu._ 29. Are not the Rays of Light very small Bodies emitted from
8447 shining Substances? For such Bodies will pass through uniform Mediums in
8448 right Lines without bending into the Shadow, which is the Nature of the
8449 Rays of Light. They will also be capable of several Properties, and be
8450 able to conserve their Properties unchanged in passing through several
8451 Mediums, which is another Condition of the Rays of Light. Pellucid
8452 Substances act upon the Rays of Light at a distance in refracting,
8453 reflecting, and inflecting them, and the Rays mutually agitate the Parts
8454 of those Substances at a distance for heating them; and this Action and
8455 Re-action at a distance very much resembles an attractive Force between
8456 Bodies. If Refraction be perform'd by Attraction of the Rays, the Sines
8457 of Incidence must be to the Sines of Refraction in a given Proportion,
8458 as we shew'd in our Principles of Philosophy: And this Rule is true by
8459 Experience. The Rays of Light in going out of Glass into a _Vacuum_, are
8460 bent towards the Glass; and if they fall too obliquely on the _Vacuum_,
8461 they are bent backwards into the Glass, and totally reflected; and this
8462 Reflexion cannot be ascribed to the Resistance of an absolute _Vacuum_,
8463 but must be caused by the Power of the Glass attracting the Rays at
8464 their going out of it into the _Vacuum_, and bringing them back. For if
8465 the farther Surface of the Glass be moisten'd with Water or clear Oil,
8466 or liquid and clear Honey, the Rays which would otherwise be reflected
8467 will go into the Water, Oil, or Honey; and therefore are not reflected
8468 before they arrive at the farther Surface of the Glass, and begin to go
8469 out of it. If they go out of it into the Water, Oil, or Honey, they go
8470 on, because the Attraction of the Glass is almost balanced and rendered
8471 ineffectual by the contrary Attraction of the Liquor. But if they go out
8472 of it into a _Vacuum_ which has no Attraction to balance that of the
8473 Glass, the Attraction of the Glass either bends and refracts them, or
8474 brings them back and reflects them. And this is still more evident by
8475 laying together two Prisms of Glass, or two Object-glasses of very long
8476 Telescopes, the one plane, the other a little convex, and so compressing
8477 them that they do not fully touch, nor are too far asunder. For the
8478 Light which falls upon the farther Surface of the first Glass where the
8479 Interval between the Glasses is not above the ten hundred thousandth
8480 Part of an Inch, will go through that Surface, and through the Air or
8481 _Vacuum_ between the Glasses, and enter into the second Glass, as was
8482 explain'd in the first, fourth, and eighth Observations of the first
8483 Part of the second Book. But, if the second Glass be taken away, the
8484 Light which goes out of the second Surface of the first Glass into the
8485 Air or _Vacuum_, will not go on forwards, but turns back into the first
8486 Glass, and is reflected; and therefore it is drawn back by the Power of
8487 the first Glass, there being nothing else to turn it back. Nothing more
8488 is requisite for producing all the variety of Colours, and degrees of
8489 Refrangibility, than that the Rays of Light be Bodies of different
8490 Sizes, the least of which may take violet the weakest and darkest of the
8491 Colours, and be more easily diverted by refracting Surfaces from the
8492 right Course; and the rest as they are bigger and bigger, may make the
8493 stronger and more lucid Colours, blue, green, yellow, and red, and be
8494 more and more difficultly diverted. Nothing more is requisite for
8495 putting the Rays of Light into Fits of easy Reflexion and easy
8496 Transmission, than that they be small Bodies which by their attractive
8497 Powers, or some other Force, stir up Vibrations in what they act upon,
8498 which Vibrations being swifter than the Rays, overtake them
8499 successively, and agitate them so as by turns to increase and decrease
8500 their Velocities, and thereby put them into those Fits. And lastly, the
8501 unusual Refraction of Island-Crystal looks very much as if it were
8502 perform'd by some kind of attractive virtue lodged in certain Sides both
8503 of the Rays, and of the Particles of the Crystal. For were it not for
8504 some kind of Disposition or Virtue lodged in some Sides of the Particles
8505 of the Crystal, and not in their other Sides, and which inclines and
8506 bends the Rays towards the Coast of unusual Refraction, the Rays which
8507 fall perpendicularly on the Crystal, would not be refracted towards that
8508 Coast rather than towards any other Coast, both at their Incidence and
8509 at their Emergence, so as to emerge perpendicularly by a contrary
8510 Situation of the Coast of unusual Refraction at the second Surface; the
8511 Crystal acting upon the Rays after they have pass'd through it, and are
8512 emerging into the Air; or, if you please, into a _Vacuum_. And since the
8513 Crystal by this Disposition or Virtue does not act upon the Rays, unless
8514 when one of their Sides of unusual Refraction looks towards that Coast,
8515 this argues a Virtue or Disposition in those Sides of the Rays, which
8516 answers to, and sympathizes with that Virtue or Disposition of the
8517 Crystal, as the Poles of two Magnets answer to one another. And as
8518 Magnetism may be intended and remitted, and is found only in the Magnet
8519 and in Iron: So this Virtue of refracting the perpendicular Rays is
8520 greater in Island-Crystal, less in Crystal of the Rock, and is not yet
8521 found in other Bodies. I do not say that this Virtue is magnetical: It
8522 seems to be of another kind. I only say, that whatever it be, it's
8523 difficult to conceive how the Rays of Light, unless they be Bodies, can
8524 have a permanent Virtue in two of their Sides which is not in their
8525 other Sides, and this without any regard to their Position to the Space
8526 or Medium through which they pass.
8527
8528 What I mean in this Question by a _Vacuum_, and by the Attractions of
8529 the Rays of Light towards Glass or Crystal, may be understood by what
8530 was said in the 18th, 19th, and 20th Questions.
8531
8532 _Quest._ 30. Are not gross Bodies and Light convertible into one
8533 another, and may not Bodies receive much of their Activity from the
8534 Particles of Light which enter their Composition? For all fix'd Bodies
8535 being heated emit Light so long as they continue sufficiently hot, and
8536 Light mutually stops in Bodies as often as its Rays strike upon their
8537 Parts, as we shew'd above. I know no Body less apt to shine than Water;
8538 and yet Water by frequent Distillations changes into fix'd Earth, as Mr.
8539 _Boyle_ has try'd; and then this Earth being enabled to endure a
8540 sufficient Heat, shines by Heat like other Bodies.
8541
8542 The changing of Bodies into Light, and Light into Bodies, is very
8543 conformable to the Course of Nature, which seems delighted with
8544 Transmutations. Water, which is a very fluid tasteless Salt, she changes
8545 by Heat into Vapour, which is a sort of Air, and by Cold into Ice, which
8546 is a hard, pellucid, brittle, fusible Stone; and this Stone returns into
8547 Water by Heat, and Vapour returns into Water by Cold. Earth by Heat
8548 becomes Fire, and by Cold returns into Earth. Dense Bodies by
8549 Fermentation rarify into several sorts of Air, and this Air by
8550 Fermentation, and sometimes without it, returns into dense Bodies.
8551 Mercury appears sometimes in the form of a fluid Metal, sometimes in the
8552 form of a hard brittle Metal, sometimes in the form of a corrosive
8553 pellucid Salt call'd Sublimate, sometimes in the form of a tasteless,
8554 pellucid, volatile white Earth, call'd _Mercurius Dulcis_; or in that of
8555 a red opake volatile Earth, call'd Cinnaber; or in that of a red or
8556 white Precipitate, or in that of a fluid Salt; and in Distillation it
8557 turns into Vapour, and being agitated _in Vacuo_, it shines like Fire.
8558 And after all these Changes it returns again into its first form of
8559 Mercury. Eggs grow from insensible Magnitudes, and change into Animals;
8560 Tadpoles into Frogs; and Worms into Flies. All Birds, Beasts and Fishes,
8561 Insects, Trees, and other Vegetables, with their several Parts, grow out
8562 of Water and watry Tinctures and Salts, and by Putrefaction return again
8563 into watry Substances. And Water standing a few Days in the open Air,
8564 yields a Tincture, which (like that of Malt) by standing longer yields a
8565 Sediment and a Spirit, but before Putrefaction is fit Nourishment for
8566 Animals and Vegetables. And among such various and strange
8567 Transmutations, why may not Nature change Bodies into Light, and Light
8568 into Bodies?
8569
8570 _Quest._ 31. Have not the small Particles of Bodies certain Powers,
8571 Virtues, or Forces, by which they act at a distance, not only upon the
8572 Rays of Light for reflecting, refracting, and inflecting them, but also
8573 upon one another for producing a great Part of the Phænomena of Nature?
8574 For it's well known, that Bodies act one upon another by the Attractions
8575 of Gravity, Magnetism, and Electricity; and these Instances shew the
8576 Tenor and Course of Nature, and make it not improbable but that there
8577 may be more attractive Powers than these. For Nature is very consonant
8578 and conformable to her self. How these Attractions may be perform'd, I
8579 do not here consider. What I call Attraction may be perform'd by
8580 impulse, or by some other means unknown to me. I use that Word here to
8581 signify only in general any Force by which Bodies tend towards one
8582 another, whatsoever be the Cause. For we must learn from the Phænomena
8583 of Nature what Bodies attract one another, and what are the Laws and
8584 Properties of the Attraction, before we enquire the Cause by which the
8585 Attraction is perform'd. The Attractions of Gravity, Magnetism, and
8586 Electricity, reach to very sensible distances, and so have been observed
8587 by vulgar Eyes, and there may be others which reach to so small
8588 distances as hitherto escape Observation; and perhaps electrical
8589 Attraction may reach to such small distances, even without being excited
8590 by Friction.
8591
8592 For when Salt of Tartar runs _per Deliquium_, is not this done by an
8593 Attraction between the Particles of the Salt of Tartar, and the
8594 Particles of the Water which float in the Air in the form of Vapours?
8595 And why does not common Salt, or Salt-petre, or Vitriol, run _per
8596 Deliquium_, but for want of such an Attraction? Or why does not Salt of
8597 Tartar draw more Water out of the Air than in a certain Proportion to
8598 its quantity, but for want of an attractive Force after it is satiated
8599 with Water? And whence is it but from this attractive Power that Water
8600 which alone distils with a gentle luke-warm Heat, will not distil from
8601 Salt of Tartar without a great Heat? And is it not from the like
8602 attractive Power between the Particles of Oil of Vitriol and the
8603 Particles of Water, that Oil of Vitriol draws to it a good quantity of
8604 Water out of the Air, and after it is satiated draws no more, and in
8605 Distillation lets go the Water very difficultly? And when Water and Oil
8606 of Vitriol poured successively into the same Vessel grow very hot in the
8607 mixing, does not this Heat argue a great Motion in the Parts of the
8608 Liquors? And does not this Motion argue, that the Parts of the two
8609 Liquors in mixing coalesce with Violence, and by consequence rush
8610 towards one another with an accelerated Motion? And when _Aqua fortis_,
8611 or Spirit of Vitriol poured upon Filings of Iron dissolves the Filings
8612 with a great Heat and Ebullition, is not this Heat and Ebullition
8613 effected by a violent Motion of the Parts, and does not that Motion
8614 argue that the acid Parts of the Liquor rush towards the Parts of the
8615 Metal with violence, and run forcibly into its Pores till they get
8616 between its outmost Particles, and the main Mass of the Metal, and
8617 surrounding those Particles loosen them from the main Mass, and set them
8618 at liberty to float off into the Water? And when the acid Particles,
8619 which alone would distil with an easy Heat, will not separate from the
8620 Particles of the Metal without a very violent Heat, does not this
8621 confirm the Attraction between them?
8622
8623 When Spirit of Vitriol poured upon common Salt or Salt-petre makes an
8624 Ebullition with the Salt, and unites with it, and in Distillation the
8625 Spirit of the common Salt or Salt-petre comes over much easier than it
8626 would do before, and the acid part of the Spirit of Vitriol stays
8627 behind; does not this argue that the fix'd Alcaly of the Salt attracts
8628 the acid Spirit of the Vitriol more strongly than its own Spirit, and
8629 not being able to hold them both, lets go its own? And when Oil of
8630 Vitriol is drawn off from its weight of Nitre, and from both the
8631 Ingredients a compound Spirit of Nitre is distilled, and two parts of
8632 this Spirit are poured on one part of Oil of Cloves or Carraway Seeds,
8633 or of any ponderous Oil of vegetable or animal Substances, or Oil of
8634 Turpentine thicken'd with a little Balsam of Sulphur, and the Liquors
8635 grow so very hot in mixing, as presently to send up a burning Flame;
8636 does not this very great and sudden Heat argue that the two Liquors mix
8637 with violence, and that their Parts in mixing run towards one another
8638 with an accelerated Motion, and clash with the greatest Force? And is it
8639 not for the same reason that well rectified Spirit of Wine poured on the
8640 same compound Spirit flashes; and that the _Pulvis fulminans_, composed
8641 of Sulphur, Nitre, and Salt of Tartar, goes off with a more sudden and
8642 violent Explosion than Gun-powder, the acid Spirits of the Sulphur and
8643 Nitre rushing towards one another, and towards the Salt of Tartar, with
8644 so great a violence, as by the shock to turn the whole at once into
8645 Vapour and Flame? Where the Dissolution is slow, it makes a slow
8646 Ebullition and a gentle Heat; and where it is quicker, it makes a
8647 greater Ebullition with more heat; and where it is done at once, the
8648 Ebullition is contracted into a sudden Blast or violent Explosion, with
8649 a heat equal to that of Fire and Flame. So when a Drachm of the
8650 above-mention'd compound Spirit of Nitre was poured upon half a Drachm
8651 of Oil of Carraway Seeds _in vacuo_, the Mixture immediately made a
8652 flash like Gun-powder, and burst the exhausted Receiver, which was a
8653 Glass six Inches wide, and eight Inches deep. And even the gross Body of
8654 Sulphur powder'd, and with an equal weight of Iron Filings and a little
8655 Water made into Paste, acts upon the Iron, and in five or six hours
8656 grows too hot to be touch'd, and emits a Flame. And by these Experiments
8657 compared with the great quantity of Sulphur with which the Earth
8658 abounds, and the warmth of the interior Parts of the Earth, and hot
8659 Springs, and burning Mountains, and with Damps, mineral Coruscations,
8660 Earthquakes, hot suffocating Exhalations, Hurricanes, and Spouts; we may
8661 learn that sulphureous Steams abound in the Bowels of the Earth and
8662 ferment with Minerals, and sometimes take fire with a sudden Coruscation
8663 and Explosion; and if pent up in subterraneous Caverns, burst the
8664 Caverns with a great shaking of the Earth, as in springing of a Mine.
8665 And then the Vapour generated by the Explosion, expiring through the
8666 Pores of the Earth, feels hot and suffocates, and makes Tempests and
8667 Hurricanes, and sometimes causes the Land to slide, or the Sea to boil,
8668 and carries up the Water thereof in Drops, which by their weight fall
8669 down again in Spouts. Also some sulphureous Steams, at all times when
8670 the Earth is dry, ascending into the Air, ferment there with nitrous
8671 Acids, and sometimes taking fire cause Lightning and Thunder, and fiery
8672 Meteors. For the Air abounds with acid Vapours fit to promote
8673 Fermentations, as appears by the rusting of Iron and Copper in it, the
8674 kindling of Fire by blowing, and the beating of the Heart by means of
8675 Respiration. Now the above-mention'd Motions are so great and violent as
8676 to shew that in Fermentations the Particles of Bodies which almost rest,
8677 are put into new Motions by a very potent Principle, which acts upon
8678 them only when they approach one another, and causes them to meet and
8679 clash with great violence, and grow hot with the motion, and dash one
8680 another into pieces, and vanish into Air, and Vapour, and Flame.
8681
8682 When Salt of Tartar _per deliquium_, being poured into the Solution of
8683 any Metal, precipitates the Metal and makes it fall down to the bottom
8684 of the Liquor in the form of Mud: Does not this argue that the acid
8685 Particles are attracted more strongly by the Salt of Tartar than by the
8686 Metal, and by the stronger Attraction go from the Metal to the Salt of
8687 Tartar? And so when a Solution of Iron in _Aqua fortis_ dissolves the
8688 _Lapis Calaminaris_, and lets go the Iron, or a Solution of Copper
8689 dissolves Iron immersed in it and lets go the Copper, or a Solution of
8690 Silver dissolves Copper and lets go the Silver, or a Solution of Mercury
8691 in _Aqua fortis_ being poured upon Iron, Copper, Tin, or Lead, dissolves
8692 the Metal and lets go the Mercury; does not this argue that the acid
8693 Particles of the _Aqua fortis_ are attracted more strongly by the _Lapis
8694 Calaminaris_ than by Iron, and more strongly by Iron than by Copper, and
8695 more strongly by Copper than by Silver, and more strongly by Iron,
8696 Copper, Tin, and Lead, than by Mercury? And is it not for the same
8697 reason that Iron requires more _Aqua fortis_ to dissolve it than Copper,
8698 and Copper more than the other Metals; and that of all Metals, Iron is
8699 dissolved most easily, and is most apt to rust; and next after Iron,
8700 Copper?
8701
8702 When Oil of Vitriol is mix'd with a little Water, or is run _per
8703 deliquium_, and in Distillation the Water ascends difficultly, and
8704 brings over with it some part of the Oil of Vitriol in the form of
8705 Spirit of Vitriol, and this Spirit being poured upon Iron, Copper, or
8706 Salt of Tartar, unites with the Body and lets go the Water; doth not
8707 this shew that the acid Spirit is attracted by the Water, and more
8708 attracted by the fix'd Body than by the Water, and therefore lets go the
8709 Water to close with the fix'd Body? And is it not for the same reason
8710 that the Water and acid Spirits which are mix'd together in Vinegar,
8711 _Aqua fortis_, and Spirit of Salt, cohere and rise together in
8712 Distillation; but if the _Menstruum_ be poured on Salt of Tartar, or on
8713 Lead, or Iron, or any fix'd Body which it can dissolve, the Acid by a
8714 stronger Attraction adheres to the Body, and lets go the Water? And is
8715 it not also from a mutual Attraction that the Spirits of Soot and
8716 Sea-Salt unite and compose the Particles of Sal-armoniac, which are less
8717 volatile than before, because grosser and freer from Water; and that the
8718 Particles of Sal-armoniac in Sublimation carry up the Particles of
8719 Antimony, which will not sublime alone; and that the Particles of
8720 Mercury uniting with the acid Particles of Spirit of Salt compose
8721 Mercury sublimate, and with the Particles of Sulphur, compose Cinnaber;
8722 and that the Particles of Spirit of Wine and Spirit of Urine well
8723 rectified unite, and letting go the Water which dissolved them, compose
8724 a consistent Body; and that in subliming Cinnaber from Salt of Tartar,
8725 or from quick Lime, the Sulphur by a stronger Attraction of the Salt or
8726 Lime lets go the Mercury, and stays with the fix'd Body; and that when
8727 Mercury sublimate is sublimed from Antimony, or from Regulus of
8728 Antimony, the Spirit of Salt lets go the Mercury, and unites with the
8729 antimonial metal which attracts it more strongly, and stays with it till
8730 the Heat be great enough to make them both ascend together, and then
8731 carries up the Metal with it in the form of a very fusible Salt, called
8732 Butter of Antimony, although the Spirit of Salt alone be almost as
8733 volatile as Water, and the Antimony alone as fix'd as Lead?
8734
8735 When _Aqua fortis_ dissolves Silver and not Gold, and _Aqua regia_
8736 dissolves Gold and not Silver, may it not be said that _Aqua fortis_ is
8737 subtil enough to penetrate Gold as well as Silver, but wants the
8738 attractive Force to give it Entrance; and that _Aqua regia_ is subtil
8739 enough to penetrate Silver as well as Gold, but wants the attractive
8740 Force to give it Entrance? For _Aqua regia_ is nothing else than _Aqua
8741 fortis_ mix'd with some Spirit of Salt, or with Sal-armoniac; and even
8742 common Salt dissolved in _Aqua fortis_, enables the _Menstruum_ to
8743 dissolve Gold, though the Salt be a gross Body. When therefore Spirit of
8744 Salt precipitates Silver out of _Aqua fortis_, is it not done by
8745 attracting and mixing with the _Aqua fortis_, and not attracting, or
8746 perhaps repelling Silver? And when Water precipitates Antimony out of
8747 the Sublimate of Antimony and Sal-armoniac, or out of Butter of
8748 Antimony, is it not done by its dissolving, mixing with, and weakening
8749 the Sal-armoniac or Spirit of Salt, and its not attracting, or perhaps
8750 repelling the Antimony? And is it not for want of an attractive virtue
8751 between the Parts of Water and Oil, of Quick-silver and Antimony, of
8752 Lead and Iron, that these Substances do not mix; and by a weak
8753 Attraction, that Quick-silver and Copper mix difficultly; and from a
8754 strong one, that Quick-silver and Tin, Antimony and Iron, Water and
8755 Salts, mix readily? And in general, is it not from the same Principle
8756 that Heat congregates homogeneal Bodies, and separates heterogeneal
8757 ones?
8758
8759 When Arsenick with Soap gives a Regulus, and with Mercury sublimate a
8760 volatile fusible Salt, like Butter of Antimony, doth not this shew that
8761 Arsenick, which is a Substance totally volatile, is compounded of fix'd
8762 and volatile Parts, strongly cohering by a mutual Attraction, so that
8763 the volatile will not ascend without carrying up the fixed? And so, when
8764 an equal weight of Spirit of Wine and Oil of Vitriol are digested
8765 together, and in Distillation yield two fragrant and volatile Spirits
8766 which will not mix with one another, and a fix'd black Earth remains
8767 behind; doth not this shew that Oil of Vitriol is composed of volatile
8768 and fix'd Parts strongly united by Attraction, so as to ascend together
8769 in form of a volatile, acid, fluid Salt, until the Spirit of Wine
8770 attracts and separates the volatile Parts from the fixed? And therefore,
8771 since Oil of Sulphur _per Campanam_ is of the same Nature with Oil of
8772 Vitriol, may it not be inferred, that Sulphur is also a mixture of
8773 volatile and fix'd Parts so strongly cohering by Attraction, as to
8774 ascend together in Sublimation. By dissolving Flowers of Sulphur in Oil
8775 of Turpentine, and distilling the Solution, it is found that Sulphur is
8776 composed of an inflamable thick Oil or fat Bitumen, an acid Salt, a very
8777 fix'd Earth, and a little Metal. The three first were found not much
8778 unequal to one another, the fourth in so small a quantity as scarce to
8779 be worth considering. The acid Salt dissolved in Water, is the same with
8780 Oil of Sulphur _per Campanam_, and abounding much in the Bowels of the
8781 Earth, and particularly in Markasites, unites it self to the other
8782 Ingredients of the Markasite, which are, Bitumen, Iron, Copper, and
8783 Earth, and with them compounds Allum, Vitriol, and Sulphur. With the
8784 Earth alone it compounds Allum; with the Metal alone, or Metal and
8785 Earth together, it compounds Vitriol; and with the Bitumen and Earth it
8786 compounds Sulphur. Whence it comes to pass that Markasites abound with
8787 those three Minerals. And is it not from the mutual Attraction of the
8788 Ingredients that they stick together for compounding these Minerals, and
8789 that the Bitumen carries up the other Ingredients of the Sulphur, which
8790 without it would not sublime? And the same Question may be put
8791 concerning all, or almost all the gross Bodies in Nature. For all the
8792 Parts of Animals and Vegetables are composed of Substances volatile and
8793 fix'd, fluid and solid, as appears by their Analysis; and so are Salts
8794 and Minerals, so far as Chymists have been hitherto able to examine
8795 their Composition.
8796
8797 When Mercury sublimate is re-sublimed with fresh Mercury, and becomes
8798 _Mercurius Dulcis_, which is a white tasteless Earth scarce dissolvable
8799 in Water, and _Mercurius Dulcis_ re-sublimed with Spirit of Salt returns
8800 into Mercury sublimate; and when Metals corroded with a little acid turn
8801 into rust, which is an Earth tasteless and indissolvable in Water, and
8802 this Earth imbibed with more acid becomes a metallick Salt; and when
8803 some Stones, as Spar of Lead, dissolved in proper _Menstruums_ become
8804 Salts; do not these things shew that Salts are dry Earth and watry Acid
8805 united by Attraction, and that the Earth will not become a Salt without
8806 so much acid as makes it dissolvable in Water? Do not the sharp and
8807 pungent Tastes of Acids arise from the strong Attraction whereby the
8808 acid Particles rush upon and agitate the Particles of the Tongue? And
8809 when Metals are dissolved in acid _Menstruums_, and the Acids in
8810 conjunction with the Metal act after a different manner, so that the
8811 Compound has a different Taste much milder than before, and sometimes a
8812 sweet one; is it not because the Acids adhere to the metallick
8813 Particles, and thereby lose much of their Activity? And if the Acid be
8814 in too small a Proportion to make the Compound dissolvable in Water,
8815 will it not by adhering strongly to the Metal become unactive and lose
8816 its Taste, and the Compound be a tasteless Earth? For such things as are
8817 not dissolvable by the Moisture of the Tongue, act not upon the Taste.
8818
8819 As Gravity makes the Sea flow round the denser and weightier Parts of
8820 the Globe of the Earth, so the Attraction may make the watry Acid flow
8821 round the denser and compacter Particles of Earth for composing the
8822 Particles of Salt. For otherwise the Acid would not do the Office of a
8823 Medium between the Earth and common Water, for making Salts dissolvable
8824 in the Water; nor would Salt of Tartar readily draw off the Acid from
8825 dissolved Metals, nor Metals the Acid from Mercury. Now, as in the great
8826 Globe of the Earth and Sea, the densest Bodies by their Gravity sink
8827 down in Water, and always endeavour to go towards the Center of the
8828 Globe; so in Particles of Salt, the densest Matter may always endeavour
8829 to approach the Center of the Particle: So that a Particle of Salt may
8830 be compared to a Chaos; being dense, hard, dry, and earthy in the
8831 Center; and rare, soft, moist, and watry in the Circumference. And
8832 hence it seems to be that Salts are of a lasting Nature, being scarce
8833 destroy'd, unless by drawing away their watry Parts by violence, or by
8834 letting them soak into the Pores of the central Earth by a gentle Heat
8835 in Putrefaction, until the Earth be dissolved by the Water, and
8836 separated into smaller Particles, which by reason of their Smallness
8837 make the rotten Compound appear of a black Colour. Hence also it may be,
8838 that the Parts of Animals and Vegetables preserve their several Forms,
8839 and assimilate their Nourishment; the soft and moist Nourishment easily
8840 changing its Texture by a gentle Heat and Motion, till it becomes like
8841 the dense, hard, dry, and durable Earth in the Center of each Particle.
8842 But when the Nourishment grows unfit to be assimilated, or the central
8843 Earth grows too feeble to assimilate it, the Motion ends in Confusion,
8844 Putrefaction, and Death.
8845
8846 If a very small quantity of any Salt or Vitriol be dissolved in a great
8847 quantity of Water, the Particles of the Salt or Vitriol will not sink to
8848 the bottom, though they be heavier in Specie than the Water, but will
8849 evenly diffuse themselves into all the Water, so as to make it as saline
8850 at the top as at the bottom. And does not this imply that the Parts of
8851 the Salt or Vitriol recede from one another, and endeavour to expand
8852 themselves, and get as far asunder as the quantity of Water in which
8853 they float, will allow? And does not this Endeavour imply that they have
8854 a repulsive Force by which they fly from one another, or at least, that
8855 they attract the Water more strongly than they do one another? For as
8856 all things ascend in Water which are less attracted than Water, by the
8857 gravitating Power of the Earth; so all the Particles of Salt which float
8858 in Water, and are less attracted than Water by any one Particle of Salt,
8859 must recede from that Particle, and give way to the more attracted
8860 Water.
8861
8862 When any saline Liquor is evaporated to a Cuticle and let cool, the Salt
8863 concretes in regular Figures; which argues, that the Particles of the
8864 Salt before they concreted, floated in the Liquor at equal distances in
8865 rank and file, and by consequence that they acted upon one another by
8866 some Power which at equal distances is equal, at unequal distances
8867 unequal. For by such a Power they will range themselves uniformly, and
8868 without it they will float irregularly, and come together as
8869 irregularly. And since the Particles of Island-Crystal act all the same
8870 way upon the Rays of Light for causing the unusual Refraction, may it
8871 not be supposed that in the Formation of this Crystal, the Particles not
8872 only ranged themselves in rank and file for concreting in regular
8873 Figures, but also by some kind of polar Virtue turned their homogeneal
8874 Sides the same way.
8875
8876 The Parts of all homogeneal hard Bodies which fully touch one another,
8877 stick together very strongly. And for explaining how this may be, some
8878 have invented hooked Atoms, which is begging the Question; and others
8879 tell us that Bodies are glued together by rest, that is, by an occult
8880 Quality, or rather by nothing; and others, that they stick together by
8881 conspiring Motions, that is, by relative rest amongst themselves. I had
8882 rather infer from their Cohesion, that their Particles attract one
8883 another by some Force, which in immediate Contact is exceeding strong,
8884 at small distances performs the chymical Operations above-mention'd, and
8885 reaches not far from the Particles with any sensible Effect.
8886
8887 All Bodies seem to be composed of hard Particles: For otherwise Fluids
8888 would not congeal; as Water, Oils, Vinegar, and Spirit or Oil of Vitriol
8889 do by freezing; Mercury by Fumes of Lead; Spirit of Nitre and Mercury,
8890 by dissolving the Mercury and evaporating the Flegm; Spirit of Wine and
8891 Spirit of Urine, by deflegming and mixing them; and Spirit of Urine and
8892 Spirit of Salt, by subliming them together to make Sal-armoniac. Even
8893 the Rays of Light seem to be hard Bodies; for otherwise they would not
8894 retain different Properties in their different Sides. And therefore
8895 Hardness may be reckon'd the Property of all uncompounded Matter. At
8896 least, this seems to be as evident as the universal Impenetrability of
8897 Matter. For all Bodies, so far as Experience reaches, are either hard,
8898 or may be harden'd; and we have no other Evidence of universal
8899 Impenetrability, besides a large Experience without an experimental
8900 Exception. Now if compound Bodies are so very hard as we find some of
8901 them to be, and yet are very porous, and consist of Parts which are only
8902 laid together; the simple Particles which are void of Pores, and were
8903 never yet divided, must be much harder. For such hard Particles being
8904 heaped up together, can scarce touch one another in more than a few
8905 Points, and therefore must be separable by much less Force than is
8906 requisite to break a solid Particle, whose Parts touch in all the Space
8907 between them, without any Pores or Interstices to weaken their Cohesion.
8908 And how such very hard Particles which are only laid together and touch
8909 only in a few Points, can stick together, and that so firmly as they do,
8910 without the assistance of something which causes them to be attracted or
8911 press'd towards one another, is very difficult to conceive.
8912
8913 The same thing I infer also from the cohering of two polish'd Marbles
8914 _in vacuo_, and from the standing of Quick-silver in the Barometer at
8915 the height of 50, 60 or 70 Inches, or above, when ever it is well-purged
8916 of Air and carefully poured in, so that its Parts be every where
8917 contiguous both to one another and to the Glass. The Atmosphere by its
8918 weight presses the Quick-silver into the Glass, to the height of 29 or
8919 30 Inches. And some other Agent raises it higher, not by pressing it
8920 into the Glass, but by making its Parts stick to the Glass, and to one
8921 another. For upon any discontinuation of Parts, made either by Bubbles
8922 or by shaking the Glass, the whole Mercury falls down to the height of
8923 29 or 30 Inches.
8924
8925 And of the same kind with these Experiments are those that follow. If
8926 two plane polish'd Plates of Glass (suppose two pieces of a polish'd
8927 Looking-glass) be laid together, so that their sides be parallel and at
8928 a very small distance from one another, and then their lower edges be
8929 dipped into Water, the Water will rise up between them. And the less
8930 the distance of the Glasses is, the greater will be the height to which
8931 the Water will rise. If the distance be about the hundredth part of an
8932 Inch, the Water will rise to the height of about an Inch; and if the
8933 distance be greater or less in any Proportion, the height will be
8934 reciprocally proportional to the distance very nearly. For the
8935 attractive Force of the Glasses is the same, whether the distance
8936 between them be greater or less; and the weight of the Water drawn up is
8937 the same, if the height of it be reciprocally proportional to the
8938 distance of the Glasses. And in like manner, Water ascends between two
8939 Marbles polish'd plane, when their polish'd sides are parallel, and at a
8940 very little distance from one another, And if slender Pipes of Glass be
8941 dipped at one end into stagnating Water, the Water will rise up within
8942 the Pipe, and the height to which it rises will be reciprocally
8943 proportional to the Diameter of the Cavity of the Pipe, and will equal
8944 the height to which it rises between two Planes of Glass, if the
8945 Semi-diameter of the Cavity of the Pipe be equal to the distance between
8946 the Planes, or thereabouts. And these Experiments succeed after the same
8947 manner _in vacuo_ as in the open Air, (as hath been tried before the
8948 Royal Society,) and therefore are not influenced by the Weight or
8949 Pressure of the Atmosphere.
8950
8951 And if a large Pipe of Glass be filled with sifted Ashes well pressed
8952 together in the Glass, and one end of the Pipe be dipped into stagnating
8953 Water, the Water will rise up slowly in the Ashes, so as in the space
8954 of a Week or Fortnight to reach up within the Glass, to the height of 30
8955 or 40 Inches above the stagnating Water. And the Water rises up to this
8956 height by the Action only of those Particles of the Ashes which are upon
8957 the Surface of the elevated Water; the Particles which are within the
8958 Water, attracting or repelling it as much downwards as upwards. And
8959 therefore the Action of the Particles is very strong. But the Particles
8960 of the Ashes being not so dense and close together as those of Glass,
8961 their Action is not so strong as that of Glass, which keeps Quick-silver
8962 suspended to the height of 60 or 70 Inches, and therefore acts with a
8963 Force which would keep Water suspended to the height of above 60 Feet.
8964
8965 By the same Principle, a Sponge sucks in Water, and the Glands in the
8966 Bodies of Animals, according to their several Natures and Dispositions,
8967 suck in various Juices from the Blood.
8968
8969 If two plane polish'd Plates of Glass three or four Inches broad, and
8970 twenty or twenty five long, be laid one of them parallel to the Horizon,
8971 the other upon the first, so as at one of their ends to touch one
8972 another, and contain an Angle of about 10 or 15 Minutes, and the same be
8973 first moisten'd on their inward sides with a clean Cloth dipp'd into Oil
8974 of Oranges or Spirit of Turpentine, and a Drop or two of the Oil or
8975 Spirit be let fall upon the lower Glass at the other; so soon as the
8976 upper Glass is laid down upon the lower, so as to touch it at one end as
8977 above, and to touch the Drop at the other end, making with the lower
8978 Glass an Angle of about 10 or 15 Minutes; the Drop will begin to move
8979 towards the Concourse of the Glasses, and will continue to move with an
8980 accelerated Motion, till it arrives at that Concourse of the Glasses.
8981 For the two Glasses attract the Drop, and make it run that way towards
8982 which the Attractions incline. And if when the Drop is in motion you
8983 lift up that end of the Glasses where they meet, and towards which the
8984 Drop moves, the Drop will ascend between the Glasses, and therefore is
8985 attracted. And as you lift up the Glasses more and more, the Drop will
8986 ascend slower and slower, and at length rest, being then carried
8987 downward by its Weight, as much as upwards by the Attraction. And by
8988 this means you may know the Force by which the Drop is attracted at all
8989 distances from the Concourse of the Glasses.
8990
8991 Now by some Experiments of this kind, (made by Mr. _Hauksbee_) it has
8992 been found that the Attraction is almost reciprocally in a duplicate
8993 Proportion of the distance of the middle of the Drop from the Concourse
8994 of the Glasses, _viz._ reciprocally in a simple Proportion, by reason of
8995 the spreading of the Drop, and its touching each Glass in a larger
8996 Surface; and again reciprocally in a simple Proportion, by reason of the
8997 Attractions growing stronger within the same quantity of attracting
8998 Surface. The Attraction therefore within the same quantity of attracting
8999 Surface, is reciprocally as the distance between the Glasses. And
9000 therefore where the distance is exceeding small, the Attraction must be
9001 exceeding great. By the Table in the second Part of the second Book,
9002 wherein the thicknesses of colour'd Plates of Water between two Glasses
9003 are set down, the thickness of the Plate where it appears very black, is
9004 three eighths of the ten hundred thousandth part of an Inch. And where
9005 the Oil of Oranges between the Glasses is of this thickness, the
9006 Attraction collected by the foregoing Rule, seems to be so strong, as
9007 within a Circle of an Inch in diameter, to suffice to hold up a Weight
9008 equal to that of a Cylinder of Water of an Inch in diameter, and two or
9009 three Furlongs in length. And where it is of a less thickness the
9010 Attraction may be proportionally greater, and continue to increase,
9011 until the thickness do not exceed that of a single Particle of the Oil.
9012 There are therefore Agents in Nature able to make the Particles of
9013 Bodies stick together by very strong Attractions. And it is the Business
9014 of experimental Philosophy to find them out.
9015
9016 Now the smallest Particles of Matter may cohere by the strongest
9017 Attractions, and compose bigger Particles of weaker Virtue; and many of
9018 these may cohere and compose bigger Particles whose Virtue is still
9019 weaker, and so on for divers Successions, until the Progression end in
9020 the biggest Particles on which the Operations in Chymistry, and the
9021 Colours of natural Bodies depend, and which by cohering compose Bodies
9022 of a sensible Magnitude. If the Body is compact, and bends or yields
9023 inward to Pression without any sliding of its Parts, it is hard and
9024 elastick, returning to its Figure with a Force rising from the mutual
9025 Attraction of its Parts. If the Parts slide upon one another, the Body
9026 is malleable or soft. If they slip easily, and are of a fit Size to be
9027 agitated by Heat, and the Heat is big enough to keep them in Agitation,
9028 the Body is fluid; and if it be apt to stick to things, it is humid; and
9029 the Drops of every fluid affect a round Figure by the mutual Attraction
9030 of their Parts, as the Globe of the Earth and Sea affects a round Figure
9031 by the mutual Attraction of its Parts by Gravity.
9032
9033 Since Metals dissolved in Acids attract but a small quantity of the
9034 Acid, their attractive Force can reach but to a small distance from
9035 them. And as in Algebra, where affirmative Quantities vanish and cease,
9036 there negative ones begin; so in Mechanicks, where Attraction ceases,
9037 there a repulsive Virtue ought to succeed. And that there is such a
9038 Virtue, seems to follow from the Reflexions and Inflexions of the Rays
9039 of Light. For the Rays are repelled by Bodies in both these Cases,
9040 without the immediate Contact of the reflecting or inflecting Body. It
9041 seems also to follow from the Emission of Light; the Ray so soon as it
9042 is shaken off from a shining Body by the vibrating Motion of the Parts
9043 of the Body, and gets beyond the reach of Attraction, being driven away
9044 with exceeding great Velocity. For that Force which is sufficient to
9045 turn it back in Reflexion, may be sufficient to emit it. It seems also
9046 to follow from the Production of Air and Vapour. The Particles when they
9047 are shaken off from Bodies by Heat or Fermentation, so soon as they are
9048 beyond the reach of the Attraction of the Body, receding from it, and
9049 also from one another with great Strength, and keeping at a distance,
9050 so as sometimes to take up above a Million of Times more space than they
9051 did before in the form of a dense Body. Which vast Contraction and
9052 Expansion seems unintelligible, by feigning the Particles of Air to be
9053 springy and ramous, or rolled up like Hoops, or by any other means than
9054 a repulsive Power. The Particles of Fluids which do not cohere too
9055 strongly, and are of such a Smallness as renders them most susceptible
9056 of those Agitations which keep Liquors in a Fluor, are most easily
9057 separated and rarified into Vapour, and in the Language of the Chymists,
9058 they are volatile, rarifying with an easy Heat, and condensing with
9059 Cold. But those which are grosser, and so less susceptible of Agitation,
9060 or cohere by a stronger Attraction, are not separated without a stronger
9061 Heat, or perhaps not without Fermentation. And these last are the Bodies
9062 which Chymists call fix'd, and being rarified by Fermentation, become
9063 true permanent Air; those Particles receding from one another with the
9064 greatest Force, and being most difficultly brought together, which upon
9065 Contact cohere most strongly. And because the Particles of permanent Air
9066 are grosser, and arise from denser Substances than those of Vapours,
9067 thence it is that true Air is more ponderous than Vapour, and that a
9068 moist Atmosphere is lighter than a dry one, quantity for quantity. From
9069 the same repelling Power it seems to be that Flies walk upon the Water
9070 without wetting their Feet; and that the Object-glasses of long
9071 Telescopes lie upon one another without touching; and that dry Powders
9072 are difficultly made to touch one another so as to stick together,
9073 unless by melting them, or wetting them with Water, which by exhaling
9074 may bring them together; and that two polish'd Marbles, which by
9075 immediate Contact stick together, are difficultly brought so close
9076 together as to stick.
9077
9078 And thus Nature will be very conformable to her self and very simple,
9079 performing all the great Motions of the heavenly Bodies by the
9080 Attraction of Gravity which intercedes those Bodies, and almost all the
9081 small ones of their Particles by some other attractive and repelling
9082 Powers which intercede the Particles. The _Vis inertiæ_ is a passive
9083 Principle by which Bodies persist in their Motion or Rest, receive
9084 Motion in proportion to the Force impressing it, and resist as much as
9085 they are resisted. By this Principle alone there never could have been
9086 any Motion in the World. Some other Principle was necessary for putting
9087 Bodies into Motion; and now they are in Motion, some other Principle is
9088 necessary for conserving the Motion. For from the various Composition of
9089 two Motions, 'tis very certain that there is not always the same
9090 quantity of Motion in the World. For if two Globes joined by a slender
9091 Rod, revolve about their common Center of Gravity with an uniform
9092 Motion, while that Center moves on uniformly in a right Line drawn in
9093 the Plane of their circular Motion; the Sum of the Motions of the two
9094 Globes, as often as the Globes are in the right Line described by their
9095 common Center of Gravity, will be bigger than the Sum of their Motions,
9096 when they are in a Line perpendicular to that right Line. By this
9097 Instance it appears that Motion may be got or lost. But by reason of the
9098 Tenacity of Fluids, and Attrition of their Parts, and the Weakness of
9099 Elasticity in Solids, Motion is much more apt to be lost than got, and
9100 is always upon the Decay. For Bodies which are either absolutely hard,
9101 or so soft as to be void of Elasticity, will not rebound from one
9102 another. Impenetrability makes them only stop. If two equal Bodies meet
9103 directly _in vacuo_, they will by the Laws of Motion stop where they
9104 meet, and lose all their Motion, and remain in rest, unless they be
9105 elastick, and receive new Motion from their Spring. If they have so much
9106 Elasticity as suffices to make them re-bound with a quarter, or half, or
9107 three quarters of the Force with which they come together, they will
9108 lose three quarters, or half, or a quarter of their Motion. And this may
9109 be try'd, by letting two equal Pendulums fall against one another from
9110 equal heights. If the Pendulums be of Lead or soft Clay, they will lose
9111 all or almost all their Motions: If of elastick Bodies they will lose
9112 all but what they recover from their Elasticity. If it be said, that
9113 they can lose no Motion but what they communicate to other Bodies, the
9114 consequence is, that _in vacuo_ they can lose no Motion, but when they
9115 meet they must go on and penetrate one another's Dimensions. If three
9116 equal round Vessels be filled, the one with Water, the other with Oil,
9117 the third with molten Pitch, and the Liquors be stirred about alike to
9118 give them a vortical Motion; the Pitch by its Tenacity will lose its
9119 Motion quickly, the Oil being less tenacious will keep it longer, and
9120 the Water being less tenacious will keep it longest, but yet will lose
9121 it in a short time. Whence it is easy to understand, that if many
9122 contiguous Vortices of molten Pitch were each of them as large as those
9123 which some suppose to revolve about the Sun and fix'd Stars, yet these
9124 and all their Parts would, by their Tenacity and Stiffness, communicate
9125 their Motion to one another till they all rested among themselves.
9126 Vortices of Oil or Water, or some fluider Matter, might continue longer
9127 in Motion; but unless the Matter were void of all Tenacity and Attrition
9128 of Parts, and Communication of Motion, (which is not to be supposed,)
9129 the Motion would constantly decay. Seeing therefore the variety of
9130 Motion which we find in the World is always decreasing, there is a
9131 necessity of conserving and recruiting it by active Principles, such as
9132 are the cause of Gravity, by which Planets and Comets keep their Motions
9133 in their Orbs, and Bodies acquire great Motion in falling; and the cause
9134 of Fermentation, by which the Heart and Blood of Animals are kept in
9135 perpetual Motion and Heat; the inward Parts of the Earth are constantly
9136 warm'd, and in some places grow very hot; Bodies burn and shine,
9137 Mountains take fire, the Caverns of the Earth are blown up, and the Sun
9138 continues violently hot and lucid, and warms all things by his Light.
9139 For we meet with very little Motion in the World, besides what is owing
9140 to these active Principles. And if it were not for these Principles, the
9141 Bodies of the Earth, Planets, Comets, Sun, and all things in them,
9142 would grow cold and freeze, and become inactive Masses; and all
9143 Putrefaction, Generation, Vegetation and Life would cease, and the
9144 Planets and Comets would not remain in their Orbs.
9145
9146 All these things being consider'd, it seems probable to me, that God in
9147 the Beginning form'd Matter in solid, massy, hard, impenetrable,
9148 moveable Particles, of such Sizes and Figures, and with such other
9149 Properties, and in such Proportion to Space, as most conduced to the End
9150 for which he form'd them; and that these primitive Particles being
9151 Solids, are incomparably harder than any porous Bodies compounded of
9152 them; even so very hard, as never to wear or break in pieces; no
9153 ordinary Power being able to divide what God himself made one in the
9154 first Creation. While the Particles continue entire, they may compose
9155 Bodies of one and the same Nature and Texture in all Ages: But should
9156 they wear away, or break in pieces, the Nature of Things depending on
9157 them, would be changed. Water and Earth, composed of old worn Particles
9158 and Fragments of Particles, would not be of the same Nature and Texture
9159 now, with Water and Earth composed of entire Particles in the Beginning.
9160 And therefore, that Nature may be lasting, the Changes of corporeal
9161 Things are to be placed only in the various Separations and new
9162 Associations and Motions of these permanent Particles; compound Bodies
9163 being apt to break, not in the midst of solid Particles, but where those
9164 Particles are laid together, and only touch in a few Points.
9165
9166 It seems to me farther, that these Particles have not only a _Vis
9167 inertiæ_, accompanied with such passive Laws of Motion as naturally
9168 result from that Force, but also that they are moved by certain active
9169 Principles, such as is that of Gravity, and that which causes
9170 Fermentation, and the Cohesion of Bodies. These Principles I consider,
9171 not as occult Qualities, supposed to result from the specifick Forms of
9172 Things, but as general Laws of Nature, by which the Things themselves
9173 are form'd; their Truth appearing to us by Phænomena, though their
9174 Causes be not yet discover'd. For these are manifest Qualities, and
9175 their Causes only are occult. And the _Aristotelians_ gave the Name of
9176 occult Qualities, not to manifest Qualities, but to such Qualities only
9177 as they supposed to lie hid in Bodies, and to be the unknown Causes of
9178 manifest Effects: Such as would be the Causes of Gravity, and of
9179 magnetick and electrick Attractions, and of Fermentations, if we should
9180 suppose that these Forces or Actions arose from Qualities unknown to us,
9181 and uncapable of being discovered and made manifest. Such occult
9182 Qualities put a stop to the Improvement of natural Philosophy, and
9183 therefore of late Years have been rejected. To tell us that every
9184 Species of Things is endow'd with an occult specifick Quality by which
9185 it acts and produces manifest Effects, is to tell us nothing: But to
9186 derive two or three general Principles of Motion from Phænomena, and
9187 afterwards to tell us how the Properties and Actions of all corporeal
9188 Things follow from those manifest Principles, would be a very great step
9189 in Philosophy, though the Causes of those Principles were not yet
9190 discover'd: And therefore I scruple not to propose the Principles of
9191 Motion above-mention'd, they being of very general Extent, and leave
9192 their Causes to be found out.
9193
9194 Now by the help of these Principles, all material Things seem to have
9195 been composed of the hard and solid Particles above-mention'd, variously
9196 associated in the first Creation by the Counsel of an intelligent Agent.
9197 For it became him who created them to set them in order. And if he did
9198 so, it's unphilosophical to seek for any other Origin of the World, or
9199 to pretend that it might arise out of a Chaos by the mere Laws of
9200 Nature; though being once form'd, it may continue by those Laws for many
9201 Ages. For while Comets move in very excentrick Orbs in all manner of
9202 Positions, blind Fate could never make all the Planets move one and the
9203 same way in Orbs concentrick, some inconsiderable Irregularities
9204 excepted, which may have risen from the mutual Actions of Comets and
9205 Planets upon one another, and which will be apt to increase, till this
9206 System wants a Reformation. Such a wonderful Uniformity in the Planetary
9207 System must be allowed the Effect of Choice. And so must the Uniformity
9208 in the Bodies of Animals, they having generally a right and a left side
9209 shaped alike, and on either side of their Bodies two Legs behind, and
9210 either two Arms, or two Legs, or two Wings before upon their Shoulders,
9211 and between their Shoulders a Neck running down into a Back-bone, and a
9212 Head upon it; and in the Head two Ears, two Eyes, a Nose, a Mouth, and
9213 a Tongue, alike situated. Also the first Contrivance of those very
9214 artificial Parts of Animals, the Eyes, Ears, Brain, Muscles, Heart,
9215 Lungs, Midriff, Glands, Larynx, Hands, Wings, swimming Bladders, natural
9216 Spectacles, and other Organs of Sense and Motion; and the Instinct of
9217 Brutes and Insects, can be the effect of nothing else than the Wisdom
9218 and Skill of a powerful ever-living Agent, who being in all Places, is
9219 more able by his Will to move the Bodies within his boundless uniform
9220 Sensorium, and thereby to form and reform the Parts of the Universe,
9221 than we are by our Will to move the Parts of our own Bodies. And yet we
9222 are not to consider the World as the Body of God, or the several Parts
9223 thereof, as the Parts of God. He is an uniform Being, void of Organs,
9224 Members or Parts, and they are his Creatures subordinate to him, and
9225 subservient to his Will; and he is no more the Soul of them, than the
9226 Soul of Man is the Soul of the Species of Things carried through the
9227 Organs of Sense into the place of its Sensation, where it perceives them
9228 by means of its immediate Presence, without the Intervention of any
9229 third thing. The Organs of Sense are not for enabling the Soul to
9230 perceive the Species of Things in its Sensorium, but only for conveying
9231 them thither; and God has no need of such Organs, he being every where
9232 present to the Things themselves. And since Space is divisible _in
9233 infinitum_, and Matter is not necessarily in all places, it may be also
9234 allow'd that God is able to create Particles of Matter of several Sizes
9235 and Figures, and in several Proportions to Space, and perhaps of
9236 different Densities and Forces, and thereby to vary the Laws of Nature,
9237 and make Worlds of several sorts in several Parts of the Universe. At
9238 least, I see nothing of Contradiction in all this.
9239
9240 As in Mathematicks, so in Natural Philosophy, the Investigation of
9241 difficult Things by the Method of Analysis, ought ever to precede the
9242 Method of Composition. This Analysis consists in making Experiments and
9243 Observations, and in drawing general Conclusions from them by Induction,
9244 and admitting of no Objections against the Conclusions, but such as are
9245 taken from Experiments, or other certain Truths. For Hypotheses are not
9246 to be regarded in experimental Philosophy. And although the arguing from
9247 Experiments and Observations by Induction be no Demonstration of general
9248 Conclusions; yet it is the best way of arguing which the Nature of
9249 Things admits of, and may be looked upon as so much the stronger, by how
9250 much the Induction is more general. And if no Exception occur from
9251 Phænomena, the Conclusion may be pronounced generally. But if at any
9252 time afterwards any Exception shall occur from Experiments, it may then
9253 begin to be pronounced with such Exceptions as occur. By this way of
9254 Analysis we may proceed from Compounds to Ingredients, and from Motions
9255 to the Forces producing them; and in general, from Effects to their
9256 Causes, and from particular Causes to more general ones, till the
9257 Argument end in the most general. This is the Method of Analysis: And
9258 the Synthesis consists in assuming the Causes discover'd, and
9259 establish'd as Principles, and by them explaining the Phænomena
9260 proceeding from them, and proving the Explanations.
9261
9262 In the two first Books of these Opticks, I proceeded by this Analysis to
9263 discover and prove the original Differences of the Rays of Light in
9264 respect of Refrangibility, Reflexibility, and Colour, and their
9265 alternate Fits of easy Reflexion and easy Transmission, and the
9266 Properties of Bodies, both opake and pellucid, on which their Reflexions
9267 and Colours depend. And these Discoveries being proved, may be assumed
9268 in the Method of Composition for explaining the Phænomena arising from
9269 them: An Instance of which Method I gave in the End of the first Book.
9270 In this third Book I have only begun the Analysis of what remains to be
9271 discover'd about Light and its Effects upon the Frame of Nature, hinting
9272 several things about it, and leaving the Hints to be examin'd and
9273 improv'd by the farther Experiments and Observations of such as are
9274 inquisitive. And if natural Philosophy in all its Parts, by pursuing
9275 this Method, shall at length be perfected, the Bounds of Moral
9276 Philosophy will be also enlarged. For so far as we can know by natural
9277 Philosophy what is the first Cause, what Power he has over us, and what
9278 Benefits we receive from him, so far our Duty towards him, as well as
9279 that towards one another, will appear to us by the Light of Nature. And
9280 no doubt, if the Worship of false Gods had not blinded the Heathen,
9281 their moral Philosophy would have gone farther than to the four
9282 Cardinal Virtues; and instead of teaching the Transmigration of Souls,
9283 and to worship the Sun and Moon, and dead Heroes, they would have taught
9284 us to worship our true Author and Benefactor, as their Ancestors did
9285 under the Government of _Noah_ and his Sons before they corrupted
9286 themselves.
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