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src/testdata/Isaac.Newton-Opticks.txt
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4
5
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9
10OPTICKS:
11
12OR, A
13
14TREATISE
15
16OF THE
17
18_Reflections_, _Refractions_,
19_Inflections_ and _Colours_
20
21OF
22
23LIGHT.
24
25_The_ FOURTH EDITION, _corrected_.
26
27By Sir _ISAAC NEWTON_, Knt.
28
29LONDON:
30
31Printed for WILLIAM INNYS at the West-End of St. _Paul's_. MDCCXXX.
32
33TITLE PAGE OF THE 1730 EDITION
34
35
36
37
38SIR ISAAC NEWTON'S ADVERTISEMENTS
39
40
41
42
43Advertisement I
44
45
46_Part of the ensuing Discourse about Light was written at the Desire of
47some Gentlemen of the_ Royal-Society, _in the Year 1675, and then sent
48to their Secretary, and read at their Meetings, and the rest was added
49about twelve Years after to complete the Theory; except the third Book,
50and the last Proposition of the Second, which were since put together
51out of scatter'd Papers. To avoid being engaged in Disputes about these
52Matters, I have hitherto delayed the printing, and should still have
53delayed it, had not the Importunity of Friends prevailed upon me. If any
54other Papers writ on this Subject are got out of my Hands they are
55imperfect, and were perhaps written before I had tried all the
56Experiments here set down, and fully satisfied my self about the Laws of
57Refractions and Composition of Colours. I have here publish'd what I
58think proper to come abroad, wishing that it may not be translated into
59another Language without my Consent._
60
61_The Crowns of Colours, which sometimes appear about the Sun and Moon, I
62have endeavoured to give an Account of; but for want of sufficient
63Observations leave that Matter to be farther examined. The Subject of
64the Third Book I have also left imperfect, not having tried all the
65Experiments which I intended when I was about these Matters, nor
66repeated some of those which I did try, until I had satisfied my self
67about all their Circumstances. To communicate what I have tried, and
68leave the rest to others for farther Enquiry, is all my Design in
69publishing these Papers._
70
71_In a Letter written to Mr._ Leibnitz _in the year 1679, and published
72by Dr._ Wallis, _I mention'd a Method by which I had found some general
73Theorems about squaring Curvilinear Figures, or comparing them with the
74Conic Sections, or other the simplest Figures with which they may be
75compared. And some Years ago I lent out a Manuscript containing such
76Theorems, and having since met with some Things copied out of it, I have
77on this Occasion made it publick, prefixing to it an_ Introduction, _and
78subjoining a_ Scholium _concerning that Method. And I have joined with
79it another small Tract concerning the Curvilinear Figures of the Second
80Kind, which was also written many Years ago, and made known to some
81Friends, who have solicited the making it publick._
82
83 _I. N._
84
85April 1, 1704.
86
87
88Advertisement II
89
90_In this Second Edition of these Opticks I have omitted the Mathematical
91Tracts publish'd at the End of the former Edition, as not belonging to
92the Subject. And at the End of the Third Book I have added some
93Questions. And to shew that I do not take Gravity for an essential
94Property of Bodies, I have added one Question concerning its Cause,
95chusing to propose it by way of a Question, because I am not yet
96satisfied about it for want of Experiments._
97
98 _I. N._
99
100July 16, 1717.
101
102
103Advertisement to this Fourth Edition
104
105_This new Edition of Sir_ Isaac Newton's Opticks _is carefully printed
106from the Third Edition, as it was corrected by the Author's own Hand,
107and left before his Death with the Bookseller. Since Sir_ Isaac's
108Lectiones Opticæ, _which he publickly read in the University of_
109Cambridge _in the Years 1669, 1670, and 1671, are lately printed, it has
110been thought proper to make at the bottom of the Pages several Citations
111from thence, where may be found the Demonstrations, which the Author
112omitted in these_ Opticks.
113
114 * * * * *
115
116Transcriber's Note: There are several greek letters used in the
117descriptions of the illustrations. They are signified by [Greek:
118letter]. Square roots are noted by the letters sqrt before the equation.
119
120 * * * * *
121
122THE FIRST BOOK OF OPTICKS
123
124
125
126
127_PART I._
128
129
130My Design in this Book is not to explain the Properties of Light by
131Hypotheses, but to propose and prove them by Reason and Experiments: In
132order to which I shall premise the following Definitions and Axioms.
133
134
135
136
137_DEFINITIONS_
138
139
140DEFIN. I.
141
142_By the Rays of Light I understand its least Parts, and those as well
143Successive in the same Lines, as Contemporary in several Lines._ For it
144is manifest that Light consists of Parts, both Successive and
145Contemporary; because in the same place you may stop that which comes
146one moment, and let pass that which comes presently after; and in the
147same time you may stop it in any one place, and let it pass in any
148other. For that part of Light which is stopp'd cannot be the same with
149that which is let pass. The least Light or part of Light, which may be
150stopp'd alone without the rest of the Light, or propagated alone, or do
151or suffer any thing alone, which the rest of the Light doth not or
152suffers not, I call a Ray of Light.
153
154
155DEFIN. II.
156
157_Refrangibility of the Rays of Light, is their Disposition to be
158refracted or turned out of their Way in passing out of one transparent
159Body or Medium into another. And a greater or less Refrangibility of
160Rays, is their Disposition to be turned more or less out of their Way in
161like Incidences on the same Medium._ Mathematicians usually consider the
162Rays of Light to be Lines reaching from the luminous Body to the Body
163illuminated, and the refraction of those Rays to be the bending or
164breaking of those lines in their passing out of one Medium into another.
165And thus may Rays and Refractions be considered, if Light be propagated
166in an instant. But by an Argument taken from the Æquations of the times
167of the Eclipses of _Jupiter's Satellites_, it seems that Light is
168propagated in time, spending in its passage from the Sun to us about
169seven Minutes of time: And therefore I have chosen to define Rays and
170Refractions in such general terms as may agree to Light in both cases.
171
172
173DEFIN. III.
174
175_Reflexibility of Rays, is their Disposition to be reflected or turned
176back into the same Medium from any other Medium upon whose Surface they
177fall. And Rays are more or less reflexible, which are turned back more
178or less easily._ As if Light pass out of a Glass into Air, and by being
179inclined more and more to the common Surface of the Glass and Air,
180begins at length to be totally reflected by that Surface; those sorts of
181Rays which at like Incidences are reflected most copiously, or by
182inclining the Rays begin soonest to be totally reflected, are most
183reflexible.
184
185
186DEFIN. IV.
187
188_The Angle of Incidence is that Angle, which the Line described by the
189incident Ray contains with the Perpendicular to the reflecting or
190refracting Surface at the Point of Incidence._
191
192
193DEFIN. V.
194
195_The Angle of Reflexion or Refraction, is the Angle which the line
196described by the reflected or refracted Ray containeth with the
197Perpendicular to the reflecting or refracting Surface at the Point of
198Incidence._
199
200
201DEFIN. VI.
202
203_The Sines of Incidence, Reflexion, and Refraction, are the Sines of the
204Angles of Incidence, Reflexion, and Refraction._
205
206
207DEFIN. VII
208
209_The Light whose Rays are all alike Refrangible, I call Simple,
210Homogeneal and Similar; and that whose Rays are some more Refrangible
211than others, I call Compound, Heterogeneal and Dissimilar._ The former
212Light I call Homogeneal, not because I would affirm it so in all
213respects, but because the Rays which agree in Refrangibility, agree at
214least in all those their other Properties which I consider in the
215following Discourse.
216
217
218DEFIN. VIII.
219
220_The Colours of Homogeneal Lights, I call Primary, Homogeneal and
221Simple; and those of Heterogeneal Lights, Heterogeneal and Compound._
222For these are always compounded of the colours of Homogeneal Lights; as
223will appear in the following Discourse.
224
225
226
227
228_AXIOMS._
229
230
231AX. I.
232
233_The Angles of Reflexion and Refraction, lie in one and the same Plane
234with the Angle of Incidence._
235
236
237AX. II.
238
239_The Angle of Reflexion is equal to the Angle of Incidence._
240
241
242AX. III.
243
244_If the refracted Ray be returned directly back to the Point of
245Incidence, it shall be refracted into the Line before described by the
246incident Ray._
247
248
249AX. IV.
250
251_Refraction out of the rarer Medium into the denser, is made towards the
252Perpendicular; that is, so that the Angle of Refraction be less than the
253Angle of Incidence._
254
255
256AX. V.
257
258_The Sine of Incidence is either accurately or very nearly in a given
259Ratio to the Sine of Refraction._
260
261Whence if that Proportion be known in any one Inclination of the
262incident Ray, 'tis known in all the Inclinations, and thereby the
263Refraction in all cases of Incidence on the same refracting Body may be
264determined. Thus if the Refraction be made out of Air into Water, the
265Sine of Incidence of the red Light is to the Sine of its Refraction as 4
266to 3. If out of Air into Glass, the Sines are as 17 to 11. In Light of
267other Colours the Sines have other Proportions: but the difference is so
268little that it need seldom be considered.
269
270[Illustration: FIG. 1]
271
272Suppose therefore, that RS [in _Fig._ 1.] represents the Surface of
273stagnating Water, and that C is the point of Incidence in which any Ray
274coming in the Air from A in the Line AC is reflected or refracted, and I
275would know whither this Ray shall go after Reflexion or Refraction: I
276erect upon the Surface of the Water from the point of Incidence the
277Perpendicular CP and produce it downwards to Q, and conclude by the
278first Axiom, that the Ray after Reflexion and Refraction, shall be
279found somewhere in the Plane of the Angle of Incidence ACP produced. I
280let fall therefore upon the Perpendicular CP the Sine of Incidence AD;
281and if the reflected Ray be desired, I produce AD to B so that DB be
282equal to AD, and draw CB. For this Line CB shall be the reflected Ray;
283the Angle of Reflexion BCP and its Sine BD being equal to the Angle and
284Sine of Incidence, as they ought to be by the second Axiom, But if the
285refracted Ray be desired, I produce AD to H, so that DH may be to AD as
286the Sine of Refraction to the Sine of Incidence, that is, (if the Light
287be red) as 3 to 4; and about the Center C and in the Plane ACP with the
288Radius CA describing a Circle ABE, I draw a parallel to the
289Perpendicular CPQ, the Line HE cutting the Circumference in E, and
290joining CE, this Line CE shall be the Line of the refracted Ray. For if
291EF be let fall perpendicularly on the Line PQ, this Line EF shall be the
292Sine of Refraction of the Ray CE, the Angle of Refraction being ECQ; and
293this Sine EF is equal to DH, and consequently in Proportion to the Sine
294of Incidence AD as 3 to 4.
295
296In like manner, if there be a Prism of Glass (that is, a Glass bounded
297with two Equal and Parallel Triangular ends, and three plain and well
298polished Sides, which meet in three Parallel Lines running from the
299three Angles of one end to the three Angles of the other end) and if the
300Refraction 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
302three Parallel lines or edges there where the Light passeth through it,
303and let DE be the Ray incident upon the first side of the Prism AC where
304the Light goes into the Glass; and by putting the Proportion of the Sine
305of Incidence to the Sine of Refraction as 17 to 11 find EF the first
306refracted Ray. Then taking this Ray for the Incident Ray upon the second
307side of the Glass BC where the Light goes out, find the next refracted
308Ray FG by putting the Proportion of the Sine of Incidence to the Sine of
309Refraction as 11 to 17. For if the Sine of Incidence out of Air into
310Glass be to the Sine of Refraction as 17 to 11, the Sine of Incidence
311out of Glass into Air must on the contrary be to the Sine of Refraction
312as 11 to 17, by the third Axiom.
313
314[Illustration: FIG. 2.]
315
316Much after the same manner, if ACBD [in _Fig._ 3.] represent a Glass
317spherically convex on both sides (usually called a _Lens_, such as is a
318Burning-glass, or Spectacle-glass, or an Object-glass of a Telescope)
319and it be required to know how Light falling upon it from any lucid
320point Q shall be refracted, let QM represent a Ray falling upon any
321point M of its first spherical Surface ACB, and by erecting a
322Perpendicular to the Glass at the point M, find the first refracted Ray
323MN by the Proportion of the Sines 17 to 11. Let that Ray in going out of
324the Glass be incident upon N, and then find the second refracted Ray
325N_q_ by the Proportion of the Sines 11 to 17. And after the same manner
326may the Refraction be found when the Lens is convex on one side and
327plane or concave on the other, or concave on both sides.
328
329[Illustration: FIG. 3.]
330
331
332AX. VI.
333
334_Homogeneal Rays which flow from several Points of any Object, and fall
335perpendicularly or almost perpendicularly on any reflecting or
336refracting Plane or spherical Surface, shall afterwards diverge from so
337many other Points, or be parallel to so many other Lines, or converge to
338so many other Points, either accurately or without any sensible Error.
339And the same thing will happen, if the Rays be reflected or refracted
340successively by two or three or more Plane or Spherical Surfaces._
341
342The Point from which Rays diverge or to which they converge may be
343called their _Focus_. And the Focus of the incident Rays being given,
344that of the reflected or refracted ones may be found by finding the
345Refraction 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,
348and Q the Focus of the incident Rays, and Q_q_C a Perpendicular to that
349Plane. And if this Perpendicular be produced to _q_, so that _q_C be
350equal to QC, the Point _q_ shall be the Focus of the reflected Rays: Or
351if _q_C be taken on the same side of the Plane with QC, and in
352proportion to QC as the Sine of Incidence to the Sine of Refraction, the
353Point _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
358whose Centre is E. Bisect any Radius thereof, (suppose EC) in T, and if
359in 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
361Q be the Focus of the incident Rays, the Point _q_ shall be the Focus of
362the reflected ones.
363
364[Illustration: FIG. 5.]
365
366_Cas._ 3. Let ACB [in _Fig._ 6.] be the refracting Surface of any Sphere
367whose Centre is E. In any Radius thereof EC produced both ways take ET
368and C_t_ equal to one another and severally in such Proportion to that
369Radius as the lesser of the Sines of Incidence and Refraction hath to
370the difference of those Sines. And then if in the same Line you find any
371two Points Q and _q_, so that TQ be to ET as E_t_ to _tq_, taking _tq_
372the contrary way from _t_ which TQ lieth from T, and if the Point Q be
373the Focus of any incident Rays, the Point _q_ shall be the Focus of the
374refracted ones.
375
376[Illustration: FIG. 6.]
377
378And by the same means the Focus of the Rays after two or more Reflexions
379or Refractions may be found.
380
381[Illustration: FIG. 7.]
382
383_Cas._ 4. Let ACBD [in _Fig._ 7.] be any refracting Lens, spherically
384Convex or Concave or Plane on either side, and let CD be its Axis (that
385is, the Line which cuts both its Surfaces perpendicularly, and passes
386through 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
388Rays on both sides the Lens are parallel to the same Axis; and upon the
389Diameter F_f_ bisected in E, describe a Circle. Suppose now that any
390Point Q be the Focus of any incident Rays. Draw QE cutting the said
391Circle 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
393doth from T, and _q_ shall be the Focus of the refracted Rays without
394any sensible Error, provided the Point Q be not so remote from the Axis,
395nor the Lens so broad as to make any of the Rays fall too obliquely on
396the refracting Surfaces.[A]
397
398And by the like Operations may the reflecting or refracting Surfaces be
399found when the two Foci are given, and thereby a Lens be formed, which
400shall make the Rays flow towards or from what Place you please.[B]
401
402So then the Meaning of this Axiom is, that if Rays fall upon any Plane
403or Spherical Surface or Lens, and before their Incidence flow from or
404towards any Point Q, they shall after Reflexion or Refraction flow from
405or towards the Point _q_ found by the foregoing Rules. And if the
406incident Rays flow from or towards several points Q, the reflected or
407refracted Rays shall flow from or towards so many other Points _q_
408found by the same Rules. Whether the reflected and refracted Rays flow
409from or towards the Point _q_ is easily known by the situation of that
410Point. For if that Point be on the same side of the reflecting or
411refracting Surface or Lens with the Point Q, and the incident Rays flow
412from the Point Q, the reflected flow towards the Point _q_ and the
413refracted from it; and if the incident Rays flow towards Q, the
414reflected flow from _q_, and the refracted towards it. And the contrary
415happens when _q_ is on the other side of the Surface.
416
417
418AX. VII.
419
420_Wherever the Rays which come from all the Points of any Object meet
421again in so many Points after they have been made to converge by
422Reflection or Refraction, there they will make a Picture of the Object
423upon any white Body on which they fall._
424
425So if PR [in _Fig._ 3.] represent any Object without Doors, and AB be a
426Lens placed at a hole in the Window-shut of a dark Chamber, whereby the
427Rays that come from any Point Q of that Object are made to converge and
428meet 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
430will appear upon the Paper in its proper shape and Colours. For as the
431Light which comes from the Point Q goes to the Point _q_, so the Light
432which comes from other Points P and R of the Object, will go to so many
433other correspondent Points _p_ and _r_ (as is manifest by the sixth
434Axiom;) so that every Point of the Object shall illuminate a
435correspondent Point of the Picture, and thereby make a Picture like the
436Object in Shape and Colour, this only excepted, that the Picture shall
437be inverted. And this is the Reason of that vulgar Experiment of casting
438the Species of Objects from abroad upon a Wall or Sheet of white Paper
439in a dark Room.
440
441In like manner, when a Man views any Object PQR, [in _Fig._ 8.] the
442Light which comes from the several Points of the Object is so refracted
443by the transparent skins and humours of the Eye, (that is, by the
444outward coat EFG, called the _Tunica Cornea_, and by the crystalline
445humour AB which is beyond the Pupil _mk_) as to converge and meet again
446in so many Points in the bottom of the Eye, and there to paint the
447Picture of the Object upon that skin (called the _Tunica Retina_) with
448which the bottom of the Eye is covered. For Anatomists, when they have
449taken off from the bottom of the Eye that outward and most thick Coat
450called the _Dura Mater_, can then see through the thinner Coats, the
451Pictures of Objects lively painted thereon. And these Pictures,
452propagated by Motion along the Fibres of the Optick Nerves into the
453Brain, are the cause of Vision. For accordingly as these Pictures are
454perfect or imperfect, the Object is seen perfectly or imperfectly. If
455the Eye be tinged with any colour (as in the Disease of the _Jaundice_)
456so as to tinge the Pictures in the bottom of the Eye with that Colour,
457then all Objects appear tinged with the same Colour. If the Humours of
458the Eye by old Age decay, so as by shrinking to make the _Cornea_ and
459Coat of the _Crystalline Humour_ grow flatter than before, the Light
460will not be refracted enough, and for want of a sufficient Refraction
461will not converge to the bottom of the Eye but to some place beyond it,
462and by consequence paint in the bottom of the Eye a confused Picture,
463and according to the Indistinctness of this Picture the Object will
464appear confused. This is the reason of the decay of sight in old Men,
465and shews why their Sight is mended by Spectacles. For those Convex
466glasses supply the defect of plumpness in the Eye, and by increasing the
467Refraction make the Rays converge sooner, so as to convene distinctly at
468the bottom of the Eye if the Glass have a due degree of convexity. And
469the contrary happens in short-sighted Men whose Eyes are too plump. For
470the Refraction being now too great, the Rays converge and convene in the
471Eyes before they come at the bottom; and therefore the Picture made in
472the bottom and the Vision caused thereby will not be distinct, unless
473the Object be brought so near the Eye as that the place where the
474converging Rays convene may be removed to the bottom, or that the
475plumpness of the Eye be taken off and the Refractions diminished by a
476Concave-glass of a due degree of Concavity, or lastly that by Age the
477Eye grow flatter till it come to a due Figure: For short-sighted Men see
478remote Objects best in Old Age, and therefore they are accounted to have
479the most lasting Eyes.
480
481[Illustration: FIG. 8.]
482
483
484AX. VIII.
485
486_An Object seen by Reflexion or Refraction, appears in that place from
487whence the Rays after their last Reflexion or Refraction diverge in
488falling on the Spectator's Eye._
489
490[Illustration: FIG. 9.]
491
492If 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
494at _a_, from whence any Rays AB, AC, AD, which flow from one and the
495same Point of the Object, do after their Reflexion made in the Points B,
496C, D, diverge in going from the Glass to E, F, G, where they are
497incident on the Spectator's Eyes. For these Rays do make the same
498Picture in the bottom of the Eyes as if they had come from the Object
499really placed at _a_ without the Interposition of the Looking-glass; and
500all Vision is made according to the place and shape of that Picture.
501
502In like manner the Object D [in FIG. 2.] seen through a Prism, appears
503not 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
508And so the Object Q [in FIG. 10.] seen through the Lens AB, appears at
509the place _q_ from whence the Rays diverge in passing from the Lens to
510the Eye. Now it is to be noted, that the Image of the Object at _q_ is
511so much bigger or lesser than the Object it self at Q, as the distance
512of the Image at _q_ from the Lens AB is bigger or less than the distance
513of the Object at Q from the same Lens. And if the Object be seen through
514two or more such Convex or Concave-glasses, every Glass shall make a new
515Image, and the Object shall appear in the place of the bigness of the
516last Image. Which consideration unfolds the Theory of Microscopes and
517Telescopes. For that Theory consists in almost nothing else than the
518describing such Glasses as shall make the last Image of any Object as
519distinct and large and luminous as it can conveniently be made.
520
521I have now given in Axioms and their Explications the sum of what hath
522hitherto been treated of in Opticks. For what hath been generally
523agreed on I content my self to assume under the notion of Principles, in
524order to what I have farther to write. And this may suffice for an
525Introduction to Readers of quick Wit and good Understanding not yet
526versed in Opticks: Although those who are already acquainted with this
527Science, and have handled Glasses, will more readily apprehend what
528followeth.
529
530FOOTNOTES:
531
532[A] In our Author's _Lectiones Opticæ_, Part I. Sect. IV. Prop 29, 30,
533there is an elegant Method of determining these _Foci_; not only in
534spherical Surfaces, but likewise in any other curved Figure whatever:
535And in Prop. 32, 33, the same thing is done for any Ray lying out of the
536Axis.
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
550Refrangibility._
551
552The PROOF by Experiments.
553
554_Exper._ 1.
555
556I took a black oblong stiff Paper terminated by Parallel Sides, and with
557a Perpendicular right Line drawn cross from one Side to the other,
558distinguished it into two equal Parts. One of these parts I painted with
559a red colour and the other with a blue. The Paper was very black, and
560the Colours intense and thickly laid on, that the Phænomenon might be
561more conspicuous. This Paper I view'd through a Prism of solid Glass,
562whose two Sides through which the Light passed to the Eye were plane and
563well polished, and contained an Angle of about sixty degrees; which
564Angle I call the refracting Angle of the Prism. And whilst I view'd it,
565I held it and the Prism before a Window in such manner that the Sides of
566the Paper were parallel to the Prism, and both those Sides and the Prism
567were parallel to the Horizon, and the cross Line was also parallel to
568it: and that the Light which fell from the Window upon the Paper made an
569Angle with the Paper, equal to that Angle which was made with the same
570Paper by the Light reflected from it to the Eye. Beyond the Prism was
571the Wall of the Chamber under the Window covered over with black Cloth,
572and the Cloth was involved in Darkness that no Light might be reflected
573from thence, which in passing by the Edges of the Paper to the Eye,
574might mingle itself with the Light of the Paper, and obscure the
575Phænomenon thereof. These things being thus ordered, I found that if the
576refracting Angle of the Prism be turned upwards, so that the Paper may
577seem to be lifted upwards by the Refraction, its blue half will be
578lifted higher by the Refraction than its red half. But if the refracting
579Angle of the Prism be turned downward, so that the Paper may seem to be
580carried lower by the Refraction, its blue half will be carried something
581lower thereby than its red half. Wherefore in both Cases the Light which
582comes from the blue half of the Paper through the Prism to the Eye, does
583in like Circumstances suffer a greater Refraction than the Light which
584comes from the red half, and by consequence is more refrangible.
585
586_Illustration._ In the eleventh Figure, MN represents the Window, and DE
587the Paper terminated with parallel Sides DJ and HE, and by the
588transverse Line FG distinguished into two halfs, the one DG of an
589intensely blue Colour, the other FE of an intensely red. And BAC_cab_
590represents the Prism whose refracting Planes AB_ba_ and AC_ca_ meet in
591the Edge of the refracting Angle A_a_. This Edge A_a_ being upward, is
592parallel both to the Horizon, and to the Parallel-Edges of the Paper DJ
593and HE, and the transverse Line FG is perpendicular to the Plane of the
594Window. And _de_ represents the Image of the Paper seen by Refraction
595upwards in such manner, that the blue half DG is carried higher to _dg_
596than the red half FE is to _fe_, and therefore suffers a greater
597Refraction. If the Edge of the refracting Angle be turned downward, the
598Image of the Paper will be refracted downward; suppose to [Greek: de],
599and the blue half will be refracted lower to [Greek: dg] than the red
600half is to [Greek: pe].
601
602[Illustration: FIG. 11.]
603
604_Exper._ 2. About the aforesaid Paper, whose two halfs were painted over
605with red and blue, and which was stiff like thin Pasteboard, I lapped
606several times a slender Thred of very black Silk, in such manner that
607the several parts of the Thred might appear upon the Colours like so
608many black Lines drawn over them, or like long and slender dark Shadows
609cast upon them. I might have drawn black Lines with a Pen, but the
610Threds were smaller and better defined. This Paper thus coloured and
611lined I set against a Wall perpendicularly to the Horizon, so that one
612of the Colours might stand to the Right Hand, and the other to the Left.
613Close before the Paper, at the Confine of the Colours below, I placed a
614Candle to illuminate the Paper strongly: For the Experiment was tried in
615the Night. The Flame of the Candle reached up to the lower edge of the
616Paper, or a very little higher. Then at the distance of six Feet, and
617one or two Inches from the Paper upon the Floor I erected a Glass Lens
618four Inches and a quarter broad, which might collect the Rays coming
619from the several Points of the Paper, and make them converge towards so
620many other Points at the same distance of six Feet, and one or two
621Inches on the other side of the Lens, and so form the Image of the
622coloured Paper upon a white Paper placed there, after the same manner
623that a Lens at a Hole in a Window casts the Images of Objects abroad
624upon a Sheet of white Paper in a dark Room. The aforesaid white Paper,
625erected perpendicular to the Horizon, and to the Rays which fell upon it
626from the Lens, I moved sometimes towards the Lens, sometimes from it, to
627find the Places where the Images of the blue and red Parts of the
628coloured Paper appeared most distinct. Those Places I easily knew by the
629Images of the black Lines which I had made by winding the Silk about the
630Paper. For the Images of those fine and slender Lines (which by reason
631of their Blackness were like Shadows on the Colours) were confused and
632scarce visible, unless when the Colours on either side of each Line were
633terminated most distinctly, Noting therefore, as diligently as I could,
634the Places where the Images of the red and blue halfs of the coloured
635Paper appeared most distinct, I found that where the red half of the
636Paper appeared distinct, the blue half appeared confused, so that the
637black Lines drawn upon it could scarce be seen; and on the contrary,
638where the blue half appeared most distinct, the red half appeared
639confused, so that the black Lines upon it were scarce visible. And
640between the two Places where these Images appeared distinct there was
641the distance of an Inch and a half; the distance of the white Paper from
642the Lens, when the Image of the red half of the coloured Paper appeared
643most distinct, being greater by an Inch and an half than the distance of
644the same white Paper from the Lens, when the Image of the blue half
645appeared most distinct. In like Incidences therefore of the blue and red
646upon the Lens, the blue was refracted more by the Lens than the red, so
647as to converge sooner by an Inch and a half, and therefore is more
648refrangible.
649
650_Illustration._ In the twelfth Figure (p. 27), DE signifies the coloured
651Paper, DG the blue half, FE the red half, MN the Lens, HJ the white
652Paper in that Place where the red half with its black Lines appeared
653distinct, and _hi_ the same Paper in that Place where the blue half
654appeared distinct. The Place _hi_ was nearer to the Lens MN than the
655Place HJ by an Inch and an half.
656
657_Scholium._ The same Things succeed, notwithstanding that some of the
658Circumstances be varied; as in the first Experiment when the Prism and
659Paper are any ways inclined to the Horizon, and in both when coloured
660Lines are drawn upon very black Paper. But in the Description of these
661Experiments, I have set down such Circumstances, by which either the
662Phænomenon might be render'd more conspicuous, or a Novice might more
663easily try them, or by which I did try them only. The same Thing, I have
664often done in the following Experiments: Concerning all which, this one
665Admonition may suffice. Now from these Experiments it follows not, that
666all the Light of the blue is more refrangible than all the Light of the
667red: For both Lights are mixed of Rays differently refrangible, so that
668in the red there are some Rays not less refrangible than those of the
669blue, and in the blue there are some Rays not more refrangible than
670those of the red: But these Rays, in proportion to the whole Light, are
671but few, and serve to diminish the Event of the Experiment, but are not
672able to destroy it. For, if the red and blue Colours were more dilute
673and weak, the distance of the Images would be less than an Inch and a
674half; and if they were more intense and full, that distance would be
675greater, as will appear hereafter. These Experiments may suffice for the
676Colours of Natural Bodies. For in the Colours made by the Refraction of
677Prisms, this Proposition will appear by the Experiments which are now to
678follow in the next Proposition.
679
680
681_PROP._ II. THEOR. II.
682
683_The Light of the Sun consists of Rays differently Refrangible._
684
685The PROOF by Experiments.
686
687[Illustration: FIG. 12.]
688
689[Illustration: FIG. 13.]
690
691_Exper._ 3.
692
693In a very dark Chamber, at a round Hole, about one third Part of an Inch
694broad, made in the Shut of a Window, I placed a Glass Prism, whereby the
695Beam of the Sun's Light, which came in at that Hole, might be refracted
696upwards toward the opposite Wall of the Chamber, and there form a
697colour'd Image of the Sun. The Axis of the Prism (that is, the Line
698passing through the middle of the Prism from one end of it to the other
699end parallel to the edge of the Refracting Angle) was in this and the
700following Experiments perpendicular to the incident Rays. About this
701Axis I turned the Prism slowly, and saw the refracted Light on the Wall,
702or coloured Image of the Sun, first to descend, and then to ascend.
703Between the Descent and Ascent, when the Image seemed Stationary, I
704stopp'd the Prism, and fix'd it in that Posture, that it should be moved
705no more. For in that Posture the Refractions of the Light at the two
706Sides of the refracting Angle, that is, at the Entrance of the Rays into
707the Prism, and at their going out of it, were equal to one another.[C]
708So also in other Experiments, as often as I would have the Refractions
709on both sides the Prism to be equal to one another, I noted the Place
710where the Image of the Sun formed by the refracted Light stood still
711between its two contrary Motions, in the common Period of its Progress
712and Regress; and when the Image fell upon that Place, I made fast the
713Prism. And in this Posture, as the most convenient, it is to be
714understood that all the Prisms are placed in the following Experiments,
715unless where some other Posture is described. The Prism therefore being
716placed in this Posture, I let the refracted Light fall perpendicularly
717upon a Sheet of white Paper at the opposite Wall of the Chamber, and
718observed the Figure and Dimensions of the Solar Image formed on the
719Paper by that Light. This Image was Oblong and not Oval, but terminated
720with two Rectilinear and Parallel Sides, and two Semicircular Ends. On
721its Sides it was bounded pretty distinctly, but on its Ends very
722confusedly and indistinctly, the Light there decaying and vanishing by
723degrees. The Breadth of this Image answered to the Sun's Diameter, and
724was about two Inches and the eighth Part of an Inch, including the
725Penumbra. For the Image was eighteen Feet and an half distant from the
726Prism, and at this distance that Breadth, if diminished by the Diameter
727of the Hole in the Window-shut, that is by a quarter of an Inch,
728subtended an Angle at the Prism of about half a Degree, which is the
729Sun's apparent Diameter. But the Length of the Image was about ten
730Inches and a quarter, and the Length of the Rectilinear Sides about
731eight Inches; and the refracting Angle of the Prism, whereby so great a
732Length was made, was 64 degrees. With a less Angle the Length of the
733Image was less, the Breadth remaining the same. If the Prism was turned
734about its Axis that way which made the Rays emerge more obliquely out of
735the second refracting Surface of the Prism, the Image soon became an
736Inch or two longer, or more; and if the Prism was turned about the
737contrary way, so as to make the Rays fall more obliquely on the first
738refracting Surface, the Image soon became an Inch or two shorter. And
739therefore in trying this Experiment, I was as curious as I could be in
740placing the Prism by the above-mention'd Rule exactly in such a Posture,
741that the Refractions of the Rays at their Emergence out of the Prism
742might be equal to that at their Incidence on it. This Prism had some
743Veins running along within the Glass from one end to the other, which
744scattered some of the Sun's Light irregularly, but had no sensible
745Effect in increasing the Length of the coloured Spectrum. For I tried
746the same Experiment with other Prisms with the same Success. And
747particularly with a Prism which seemed free from such Veins, and whose
748refracting Angle was 62-1/2 Degrees, I found the Length of the Image
7499-3/4 or 10 Inches at the distance of 18-1/2 Feet from the Prism, the
750Breadth of the Hole in the Window-shut being 1/4 of an Inch, as before.
751And because it is easy to commit a Mistake in placing the Prism in its
752due Posture, I repeated the Experiment four or five Times, and always
753found the Length of the Image that which is set down above. With another
754Prism of clearer Glass and better Polish, which seemed free from Veins,
755and whose refracting Angle was 63-1/2 Degrees, the Length of this Image
756at the same distance of 18-1/2 Feet was also about 10 Inches, or 10-1/8.
757Beyond these Measures for about a 1/4 or 1/3 of an Inch at either end of
758the Spectrum the Light of the Clouds seemed to be a little tinged with
759red and violet, but so very faintly, that I suspected that Tincture
760might either wholly, or in great Measure arise from some Rays of the
761Spectrum scattered irregularly by some Inequalities in the Substance and
762Polish of the Glass, and therefore I did not include it in these
763Measures. Now the different Magnitude of the hole in the Window-shut,
764and different thickness of the Prism where the Rays passed through it,
765and different inclinations of the Prism to the Horizon, made no sensible
766changes in the length of the Image. Neither did the different matter of
767the Prisms make any: for in a Vessel made of polished Plates of Glass
768cemented together in the shape of a Prism and filled with Water, there
769is the like Success of the Experiment according to the quantity of the
770Refraction. It is farther to be observed, that the Rays went on in right
771Lines from the Prism to the Image, and therefore at their very going out
772of the Prism had all that Inclination to one another from which the
773length of the Image proceeded, that is, the Inclination of more than two
774degrees and an half. And yet according to the Laws of Opticks vulgarly
775received, they could not possibly be so much inclined to one another.[D]
776For let EG [_Fig._ 13. (p. 27)] represent the Window-shut, F the hole
777made therein through which a beam of the Sun's Light was transmitted
778into the darkened Chamber, and ABC a Triangular Imaginary Plane whereby
779the Prism is feigned to be cut transversely through the middle of the
780Light. Or if you please, let ABC represent the Prism it self, looking
781directly towards the Spectator's Eye with its nearer end: And let XY be
782the Sun, MN the Paper upon which the Solar Image or Spectrum is cast,
783and PT the Image it self whose sides towards _v_ and _w_ are Rectilinear
784and Parallel, and ends towards P and T Semicircular. YKHP and XLJT are
785two Rays, the first of which comes from the lower part of the Sun to the
786higher part of the Image, and is refracted in the Prism at K and H, and
787the latter comes from the higher part of the Sun to the lower part of
788the Image, and is refracted at L and J. Since the Refractions on both
789sides the Prism are equal to one another, that is, the Refraction at K
790equal to the Refraction at J, and the Refraction at L equal to the
791Refraction at H, so that the Refractions of the incident Rays at K and L
792taken together, are equal to the Refractions of the emergent Rays at H
793and J taken together: it follows by adding equal things to equal things,
794that the Refractions at K and H taken together, are equal to the
795Refractions at J and L taken together, and therefore the two Rays being
796equally refracted, have the same Inclination to one another after
797Refraction which they had before; that is, the Inclination of half a
798Degree answering to the Sun's Diameter. For so great was the inclination
799of the Rays to one another before Refraction. So then, the length of the
800Image PT would by the Rules of Vulgar Opticks subtend an Angle of half a
801Degree at the Prism, and by Consequence be equal to the breadth _vw_;
802and therefore the Image would be round. Thus it would be were the two
803Rays XLJT and YKHP, and all the rest which form the Image P_w_T_v_,
804alike refrangible. And therefore seeing by Experience it is found that
805the Image is not round, but about five times longer than broad, the Rays
806which going to the upper end P of the Image suffer the greatest
807Refraction, must be more refrangible than those which go to the lower
808end T, unless the Inequality of Refraction be casual.
809
810This Image or Spectrum PT was coloured, being red at its least refracted
811end T, and violet at its most refracted end P, and yellow green and
812blue in the intermediate Spaces. Which agrees with the first
813Proposition, that Lights which differ in Colour, do also differ in
814Refrangibility. The length of the Image in the foregoing Experiments, I
815measured from the faintest and outmost red at one end, to the faintest
816and outmost blue at the other end, excepting only a little Penumbra,
817whose 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
820the hole in the Window-shut, at the distance of some Feet from the hole,
821I held the Prism in such a Posture, that its Axis might be perpendicular
822to that Beam. Then I looked through the Prism upon the hole, and turning
823the Prism to and fro about its Axis, to make the Image of the Hole
824ascend and descend, when between its two contrary Motions it seemed
825Stationary, I stopp'd the Prism, that the Refractions of both sides of
826the refracting Angle might be equal to each other, as in the former
827Experiment. In this situation of the Prism viewing through it the said
828Hole, I observed the length of its refracted Image to be many times
829greater than its breadth, and that the most refracted part thereof
830appeared violet, the least refracted red, the middle parts blue, green
831and yellow in order. The same thing happen'd when I removed the Prism
832out of the Sun's Light, and looked through it upon the hole shining by
833the Light of the Clouds beyond it. And yet if the Refraction were done
834regularly according to one certain Proportion of the Sines of Incidence
835and Refraction as is vulgarly supposed, the refracted Image ought to
836have appeared round.
837
838So then, by these two Experiments it appears, that in Equal Incidences
839there is a considerable inequality of Refractions. But whence this
840inequality arises, whether it be that some of the incident Rays are
841refracted more, and others less, constantly, or by chance, or that one
842and the same Ray is by Refraction disturbed, shatter'd, dilated, and as
843it were split and spread into many diverging Rays, as _Grimaldo_
844supposes, does not yet appear by these Experiments, but will appear by
845those that follow.
846
847_Exper._ 5. Considering therefore, that if in the third Experiment the
848Image of the Sun should be drawn out into an oblong Form, either by a
849Dilatation of every Ray, or by any other casual inequality of the
850Refractions, the same oblong Image would by a second Refraction made
851sideways be drawn out as much in breadth by the like Dilatation of the
852Rays, or other casual inequality of the Refractions sideways, I tried
853what would be the Effects of such a second Refraction. For this end I
854ordered all things as in the third Experiment, and then placed a second
855Prism immediately after the first in a cross Position to it, that it
856might again refract the beam of the Sun's Light which came to it through
857the first Prism. In the first Prism this beam was refracted upwards, and
858in the second sideways. And I found that by the Refraction of the second
859Prism, the breadth of the Image was not increased, but its superior
860part, which in the first Prism suffered the greater Refraction, and
861appeared violet and blue, did again in the second Prism suffer a greater
862Refraction than its inferior part, which appeared red and yellow, and
863this 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
868the Window, ABC the first Prism, DH the second Prism, Y the round Image
869of the Sun made by a direct beam of Light when the Prisms are taken
870away, PT the oblong Image of the Sun made by that beam passing through
871the first Prism alone, when the second Prism is taken away, and _pt_ the
872Image made by the cross Refractions of both Prisms together. Now if the
873Rays which tend towards the several Points of the round Image Y were
874dilated and spread by the Refraction of the first Prism, so that they
875should not any longer go in single Lines to single Points, but that
876every Ray being split, shattered, and changed from a Linear Ray to a
877Superficies of Rays diverging from the Point of Refraction, and lying in
878the Plane of the Angles of Incidence and Refraction, they should go in
879those Planes to so many Lines reaching almost from one end of the Image
880PT to the other, and if that Image should thence become oblong: those
881Rays and their several parts tending towards the several Points of the
882Image PT ought to be again dilated and spread sideways by the transverse
883Refraction of the second Prism, so as to compose a four square Image,
884such as is represented at [Greek: pt]. For the better understanding of
885which, let the Image PT be distinguished into five equal parts PQK,
886KQRL, LRSM, MSVN, NVT. And by the same irregularity that the orbicular
887Light Y is by the Refraction of the first Prism dilated and drawn out
888into a long Image PT, the Light PQK which takes up a space of the same
889length and breadth with the Light Y ought to be by the Refraction of the
890second Prism dilated and drawn out into the long Image _[Greek: p]qkp_,
891and the Light KQRL into the long Image _kqrl_, and the Lights LRSM,
892MSVN, NVT, into so many other long Images _lrsm_, _msvn_, _nvt[Greek:
893t]_; 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,
895and spread into a triangular Superficies of Rays diverging from the
896Point of Refraction. For the second Refraction would spread the Rays one
897way as much as the first doth another, and so dilate the Image in
898breadth as much as the first doth in length. And the same thing ought to
899happen, were some rays casually refracted more than others. But the
900Event is otherwise. The Image PT was not made broader by the Refraction
901of 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
903distance than its lower end T. So then the Light which went towards the
904upper end P of the Image, was (at equal Incidences) more refracted in
905the second Prism, than the Light which tended towards the lower end T,
906that is the blue and violet, than the red and yellow; and therefore was
907more refrangible. The same Light was by the Refraction of the first
908Prism translated farther from the place Y to which it tended before
909Refraction; and therefore suffered as well in the first Prism as in the
910second a greater Refraction than the rest of the Light, and by
911consequence was more refrangible than the rest, even before its
912incidence on the first Prism.
913
914Sometimes I placed a third Prism after the second, and sometimes also a
915fourth after the third, by all which the Image might be often refracted
916sideways: but the Rays which were more refracted than the rest in the
917first Prism were also more refracted in all the rest, and that without
918any Dilatation of the Image sideways: and therefore those Rays for their
919constancy of a greater Refraction are deservedly reputed more
920refrangible.
921
922[Illustration: FIG. 15]
923
924But that the meaning of this Experiment may more clearly appear, it is
925to be considered that the Rays which are equally refrangible do fall
926upon a Circle answering to the Sun's Disque. For this was proved in the
927third Experiment. By a Circle I understand not here a perfect
928geometrical Circle, but any orbicular Figure whose length is equal to
929its 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
931propagated from the whole Disque of the Sun, would illuminate and paint
932upon the opposite Wall if they were alone; EL the Circle which all the
933least refrangible Rays would in like manner illuminate and paint if they
934were alone; BH, CJ, DK, the Circles which so many intermediate sorts of
935Rays would successively paint upon the Wall, if they were singly
936propagated from the Sun in successive order, the rest being always
937intercepted; and conceive that there are other intermediate Circles
938without Number, which innumerable other intermediate sorts of Rays would
939successively paint upon the Wall if the Sun should successively emit
940every sort apart. And seeing the Sun emits all these sorts at once, they
941must all together illuminate and paint innumerable equal Circles, of all
942which, being according to their degrees of Refrangibility placed in
943order in a continual Series, that oblong Spectrum PT is composed which I
944described 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
946Dilation of the single Rays, or by any other irregularity in the
947Refraction of the first Prism, converted into the oblong Spectrum, PT:
948then ought every Circle AG, BH, CJ, &c. in that Spectrum, by the cross
949Refraction of the second Prism again dilating or otherwise scattering
950the Rays as before, to be in like manner drawn out and transformed into
951an oblong Figure, and thereby the breadth of the Image PT would be now
952as much augmented as the length of the Image Y was before by the
953Refraction of the first Prism; and thus by the Refractions of both
954Prisms together would be formed a four square Figure _p[Greek:
955p]t[Greek: t]_, as I described above. Wherefore since the breadth of the
956Spectrum PT is not increased by the Refraction sideways, it is certain
957that the Rays are not split or dilated, or otherways irregularly
958scatter'd by that Refraction, but that every Circle is by a regular and
959uniform Refraction translated entire into another Place, as the Circle
960AG by the greatest Refraction into the place _ag_, the Circle BH by a
961less Refraction into the place _bh_, the Circle CJ by a Refraction still
962less into the place _ci_, and so of the rest; by which means a new
963Spectrum _pt_ inclined to the former PT is in like manner composed of
964Circles lying in a right Line; and these Circles must be of the same
965bigness with the former, because the breadths of all the Spectrums Y, PT
966and _pt_ at equal distances from the Prisms are equal.
967
968I considered farther, that by the breadth of the hole F through which
969the Light enters into the dark Chamber, there is a Penumbra made in the
970Circuit of the Spectrum Y, and that Penumbra remains in the rectilinear
971Sides of the Spectrums PT and _pt_. I placed therefore at that hole a
972Lens or Object-glass of a Telescope which might cast the Image of the
973Sun distinctly on Y without any Penumbra at all, and found that the
974Penumbra of the rectilinear Sides of the oblong Spectrums PT and _pt_
975was also thereby taken away, so that those Sides appeared as distinctly
976defined as did the Circumference of the first Image Y. Thus it happens
977if the Glass of the Prisms be free from Veins, and their sides be
978accurately plane and well polished without those numberless Waves or
979Curles which usually arise from Sand-holes a little smoothed in
980polishing with Putty. If the Glass be only well polished and free from
981Veins, and the Sides not accurately plane, but a little Convex or
982Concave, 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
984from this want of Penumbras, I knew more certainly that every one of the
985Circles was refracted according to some most regular, uniform and
986constant Law. For if there were any irregularity in the Refraction, the
987right Lines AE and GL, which all the Circles in the Spectrum PT do
988touch, could not by that Refraction be translated into the Lines _ae_
989and _gl_ as distinct and straight as they were before, but there would
990arise in those translated Lines some Penumbra or Crookedness or
991Undulation, or other sensible Perturbation contrary to what is found by
992Experience. Whatsoever Penumbra or Perturbation should be made in the
993Circles by the cross Refraction of the second Prism, all that Penumbra
994or Perturbation would be conspicuous in the right Lines _ae_ and _gl_
995which touch those Circles. And therefore since there is no such Penumbra
996or Perturbation in those right Lines, there must be none in the
997Circles. Since the distance between those Tangents or breadth of the
998Spectrum is not increased by the Refractions, the Diameters of the
999Circles are not increased thereby. Since those Tangents continue to be
1000right Lines, every Circle which in the first Prism is more or less
1001refracted, is exactly in the same proportion more or less refracted in
1002the second. And seeing all these things continue to succeed after the
1003same manner when the Rays are again in a third Prism, and again in a
1004fourth refracted sideways, it is evident that the Rays of one and the
1005same Circle, as to their degree of Refrangibility, continue always
1006uniform and homogeneal to one another, and that those of several Circles
1007do differ in degree of Refrangibility, and that in some certain and
1008constant Proportion. Which is the thing I was to prove.
1009
1010There is yet another Circumstance or two of this Experiment by which it
1011becomes still more plain and convincing. Let the second Prism DH [in
1012_Fig._ 16.] be placed not immediately after the first, but at some
1013distance from it; suppose in the mid-way between it and the Wall on
1014which the oblong Spectrum PT is cast, so that the Light from the first
1015Prism may fall upon it in the form of an oblong Spectrum [Greek: pt]
1016parallel to this second Prism, and be refracted sideways to form the
1017oblong Spectrum _pt_ upon the Wall. And you will find as before, that
1018this Spectrum _pt_ is inclined to that Spectrum PT, which the first
1019Prism forms alone without the second; the blue ends P and _p_ being
1020farther distant from one another than the red ones T and _t_, and by
1021consequence that the Rays which go to the blue end [Greek: p] of the
1022Image [Greek: pt], and which therefore suffer the greatest Refraction in
1023the first Prism, are again in the second Prism more refracted than the
1024rest.
1025
1026[Illustration: FIG. 16.]
1027
1028[Illustration: FIG. 17.]
1029
1030The same thing I try'd also by letting the Sun's Light into a dark Room
1031through two little round holes F and [Greek: ph] [in _Fig._ 17.] made in
1032the Window, and with two parallel Prisms ABC and [Greek: abg] placed at
1033those holes (one at each) refracting those two beams of Light to the
1034opposite Wall of the Chamber, in such manner that the two colour'd
1035Images PT and MN which they there painted were joined end to end and lay
1036in one straight Line, the red end T of the one touching the blue end M
1037of the other. For if these two refracted Beams were again by a third
1038Prism DH placed cross to the two first, refracted sideways, and the
1039Spectrums thereby translated to some other part of the Wall of the
1040Chamber, suppose the Spectrum PT to _pt_ and the Spectrum MN to _mn_,
1041these translated Spectrums _pt_ and _mn_ would not lie in one straight
1042Line with their ends contiguous as before, but be broken off from one
1043another and become parallel, the blue end _m_ of the Image _mn_ being by
1044a greater Refraction translated farther from its former place MT, than
1045the red end _t_ of the other Image _pt_ from the same place MT; which
1046puts the Proposition past Dispute. And this happens whether the third
1047Prism DH be placed immediately after the two first, or at a great
1048distance from them, so that the Light refracted in the two first Prisms
1049be either white and circular, or coloured and oblong when it falls on
1050the third.
1051
1052_Exper._ 6. In the middle of two thin Boards I made round holes a third
1053part of an Inch in diameter, and in the Window-shut a much broader hole
1054being made to let into my darkned Chamber a large Beam of the Sun's
1055Light; I placed a Prism behind the Shut in that beam to refract it
1056towards the opposite Wall, and close behind the Prism I fixed one of the
1057Boards, in such manner that the middle of the refracted Light might pass
1058through the hole made in it, and the rest be intercepted by the Board.
1059Then at the distance of about twelve Feet from the first Board I fixed
1060the other Board in such manner that the middle of the refracted Light
1061which came through the hole in the first Board, and fell upon the
1062opposite Wall, might pass through the hole in this other Board, and the
1063rest being intercepted by the Board might paint upon it the coloured
1064Spectrum of the Sun. And close behind this Board I fixed another Prism
1065to refract the Light which came through the hole. Then I returned
1066speedily to the first Prism, and by turning it slowly to and fro about
1067its Axis, I caused the Image which fell upon the second Board to move up
1068and down upon that Board, that all its parts might successively pass
1069through the hole in that Board and fall upon the Prism behind it. And in
1070the mean time, I noted the places on the opposite Wall to which that
1071Light after its Refraction in the second Prism did pass; and by the
1072difference of the places I found that the Light which being most
1073refracted in the first Prism did go to the blue end of the Image, was
1074again more refracted in the second Prism than the Light which went to
1075the red end of that Image, which proves as well the first Proposition as
1076the second. And this happened whether the Axis of the two Prisms were
1077parallel, or inclined to one another, and to the Horizon in any given
1078Angles.
1079
1080_Illustration._ Let F [in _Fig._ 18.] be the wide hole in the
1081Window-shut, through which the Sun shines upon the first Prism ABC, and
1082let the refracted Light fall upon the middle of the Board DE, and the
1083middle part of that Light upon the hole G made in the middle part of
1084that Board. Let this trajected part of that Light fall again upon the
1085middle of the second Board _de_, and there paint such an oblong coloured
1086Image of the Sun as was described in the third Experiment. By turning
1087the Prism ABC slowly to and fro about its Axis, this Image will be made
1088to move up and down the Board _de_, and by this means all its parts from
1089one 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
1091Prism _abc_ is to be fixed next after that hole _g_, to refract the
1092trajected Light a second time. And these things being thus ordered, I
1093marked the places M and N of the opposite Wall upon which the refracted
1094Light fell, and found that whilst the two Boards and second Prism
1095remained unmoved, those places by turning the first Prism about its Axis
1096were changed perpetually. For when the lower part of the Light which
1097fell upon the second Board _de_ was cast through the hole _g_, it went
1098to a lower place M on the Wall and when the higher part of that Light
1099was cast through the same hole _g_, it went to a higher place N on the
1100Wall, and when any intermediate part of the Light was cast through that
1101hole, it went to some place on the Wall between M and N. The unchanged
1102Position of the holes in the Boards, made the Incidence of the Rays upon
1103the second Prism to be the same in all cases. And yet in that common
1104Incidence some of the Rays were more refracted, and others less. And
1105those were more refracted in this Prism, which by a greater Refraction
1106in the first Prism were more turned out of the way, and therefore for
1107their Constancy of being more refracted are deservedly called more
1108refrangible.
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
1115placed 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
1117the Sun. And at a little distance from the Wall I placed a long slender
1118Paper with straight and parallel edges, and ordered the Prisms and Paper
1119so, that the red Colour of one Image might fall directly upon one half
1120of the Paper, and the violet Colour of the other Image upon the other
1121half of the same Paper; so that the Paper appeared of two Colours, red
1122and violet, much after the manner of the painted Paper in the first and
1123second Experiments. Then with a black Cloth I covered the Wall behind
1124the Paper, that no Light might be reflected from it to disturb the
1125Experiment, and viewing the Paper through a third Prism held parallel
1126to it, I saw that half of it which was illuminated by the violet Light
1127to be divided from the other half by a greater Refraction, especially
1128when I went a good way off from the Paper. For when I viewed it too near
1129at hand, the two halfs of the Paper did not appear fully divided from
1130one another, but seemed contiguous at one of their Angles like the
1131painted Paper in the first Experiment. Which also happened when the
1132Paper was too broad.
1133
1134[Illustration: FIG. 19.]
1135
1136Sometimes instead of the Paper I used a white Thred, and this appeared
1137through the Prism divided into two parallel Threds as is represented in
1138the nineteenth Figure, where DG denotes the Thred illuminated with
1139violet Light from D to E and with red Light from F to G, and _defg_ are
1140the parts of the Thred seen by Refraction. If one half of the Thred be
1141constantly illuminated with red, and the other half be illuminated with
1142all the Colours successively, (which may be done by causing one of the
1143Prisms to be turned about its Axis whilst the other remains unmoved)
1144this other half in viewing the Thred through the Prism, will appear in
1145a continual right Line with the first half when illuminated with red,
1146and begin to be a little divided from it when illuminated with Orange,
1147and remove farther from it when illuminated with yellow, and still
1148farther when with green, and farther when with blue, and go yet farther
1149off when illuminated with Indigo, and farthest when with deep violet.
1150Which plainly shews, that the Lights of several Colours are more and
1151more refrangible one than another, in this Order of their Colours, red,
1152orange, yellow, green, blue, indigo, deep violet; and so proves as well
1153the first Proposition as the second.
1154
1155I caused also the coloured Spectrums PT [in _Fig._ 17.] and MN made in a
1156dark Chamber by the Refractions of two Prisms to lie in a Right Line end
1157to end, as was described above in the fifth Experiment, and viewing them
1158through a third Prism held parallel to their Length, they appeared no
1159longer in a Right Line, but became broken from one another, as they are
1160represented at _pt_ and _mn_, the violet end _m_ of the Spectrum _mn_
1161being by a greater Refraction translated farther from its former Place
1162MT than the red end _t_ of the other Spectrum _pt_.
1163
1164I farther caused those two Spectrums PT [in _Fig._ 20.] and MN to become
1165co-incident in an inverted Order of their Colours, the red end of each
1166falling on the violet end of the other, as they are represented in the
1167oblong Figure PTMN; and then viewing them through a Prism DH held
1168parallel to their Length, they appeared not co-incident, as when view'd
1169with 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
1171X. Which shews that the red of the one Spectrum and violet of the other,
1172which were co-incident at PN and MT, being parted from one another by a
1173greater Refraction of the violet to _p_ and _m_ than of the red to _n_
1174and _t_, do differ in degrees of Refrangibility.
1175
1176I illuminated also a little Circular Piece of white Paper all over with
1177the Lights of both Prisms intermixed, and when it was illuminated with
1178the red of one Spectrum, and deep violet of the other, so as by the
1179Mixture of those Colours to appear all over purple, I viewed the Paper,
1180first at a less distance, and then at a greater, through a third Prism;
1181and as I went from the Paper, the refracted Image thereof became more
1182and more divided by the unequal Refraction of the two mixed Colours, and
1183at length parted into two distinct Images, a red one and a violet one,
1184whereof the violet was farthest from the Paper, and therefore suffered
1185the greatest Refraction. And when that Prism at the Window, which cast
1186the violet on the Paper was taken away, the violet Image disappeared;
1187but when the other Prism was taken away the red vanished; which shews,
1188that these two Images were nothing else than the Lights of the two
1189Prisms, which had been intermixed on the purple Paper, but were parted
1190again by their unequal Refractions made in the third Prism, through
1191which the Paper was view'd. This also was observable, that if one of the
1192Prisms at the Window, suppose that which cast the violet on the Paper,
1193was turned about its Axis to make all the Colours in this order,
1194violet, indigo, blue, green, yellow, orange, red, fall successively on
1195the Paper from that Prism, the violet Image changed Colour accordingly,
1196turning successively to indigo, blue, green, yellow and red, and in
1197changing Colour came nearer and nearer to the red Image made by the
1198other Prism, until when it was also red both Images became fully
1199co-incident.
1200
1201I placed also two Paper Circles very near one another, the one in the
1202red Light of one Prism, and the other in the violet Light of the other.
1203The Circles were each of them an Inch in diameter, and behind them the
1204Wall was dark, that the Experiment might not be disturbed by any Light
1205coming from thence. These Circles thus illuminated, I viewed through a
1206Prism, so held, that the Refraction might be made towards the red
1207Circle, and as I went from them they came nearer and nearer together,
1208and at length became co-incident; and afterwards when I went still
1209farther off, they parted again in a contrary Order, the violet by a
1210greater Refraction being carried beyond the red.
1211
1212_Exper._ 8. In Summer, when the Sun's Light uses to be strongest, I
1213placed a Prism at the Hole of the Window-shut, as in the third
1214Experiment, yet so that its Axis might be parallel to the Axis of the
1215World, and at the opposite Wall in the Sun's refracted Light, I placed
1216an open Book. Then going six Feet and two Inches from the Book, I placed
1217there the above-mentioned Lens, by which the Light reflected from the
1218Book might be made to converge and meet again at the distance of six
1219Feet and two Inches behind the Lens, and there paint the Species of the
1220Book upon a Sheet of white Paper much after the manner of the second
1221Experiment. The Book and Lens being made fast, I noted the Place where
1222the Paper was, when the Letters of the Book, illuminated by the fullest
1223red Light of the Solar Image falling upon it, did cast their Species on
1224that Paper most distinctly: And then I stay'd till by the Motion of the
1225Sun, and consequent Motion of his Image on the Book, all the Colours
1226from that red to the middle of the blue pass'd over those Letters; and
1227when those Letters were illuminated by that blue, I noted again the
1228Place of the Paper when they cast their Species most distinctly upon it:
1229And I found that this last Place of the Paper was nearer to the Lens
1230than its former Place by about two Inches and an half, or two and three
1231quarters. So much sooner therefore did the Light in the violet end of
1232the Image by a greater Refraction converge and meet, than the Light in
1233the red end. But in trying this, the Chamber was as dark as I could make
1234it. For, if these Colours be diluted and weakned by the Mixture of any
1235adventitious Light, the distance between the Places of the Paper will
1236not be so great. This distance in the second Experiment, where the
1237Colours of natural Bodies were made use of, was but an Inch and an half,
1238by reason of the Imperfection of those Colours. Here in the Colours of
1239the Prism, which are manifestly more full, intense, and lively than
1240those of natural Bodies, the distance is two Inches and three quarters.
1241And were the Colours still more full, I question not but that the
1242distance would be considerably greater. For the coloured Light of the
1243Prism, by the interfering of the Circles described in the second Figure
1244of the fifth Experiment, and also by the Light of the very bright Clouds
1245next the Sun's Body intermixing with these Colours, and by the Light
1246scattered by the Inequalities in the Polish of the Prism, was so very
1247much compounded, that the Species which those faint and dark Colours,
1248the indigo and violet, cast upon the Paper were not distinct enough to
1249be well observed.
1250
1251_Exper._ 9. A Prism, whose two Angles at its Base were equal to one
1252another, and half right ones, and the third a right one, I placed in a
1253Beam of the Sun's Light let into a dark Chamber through a Hole in the
1254Window-shut, as in the third Experiment. And turning the Prism slowly
1255about its Axis, until all the Light which went through one of its
1256Angles, and was refracted by it began to be reflected by its Base, at
1257which till then it went out of the Glass, I observed that those Rays
1258which had suffered the greatest Refraction were sooner reflected than
1259the rest. I conceived therefore, that those Rays of the reflected Light,
1260which were most refrangible, did first of all by a total Reflexion
1261become more copious in that Light than the rest, and that afterwards the
1262rest also, by a total Reflexion, became as copious as these. To try
1263this, I made the reflected Light pass through another Prism, and being
1264refracted by it to fall afterwards upon a Sheet of white Paper placed
1265at some distance behind it, and there by that Refraction to paint the
1266usual Colours of the Prism. And then causing the first Prism to be
1267turned about its Axis as above, I observed that when those Rays, which
1268in this Prism had suffered the greatest Refraction, and appeared of a
1269blue and violet Colour began to be totally reflected, the blue and
1270violet Light on the Paper, which was most refracted in the second Prism,
1271received a sensible Increase above that of the red and yellow, which was
1272least refracted; and afterwards, when the rest of the Light which was
1273green, yellow, and red, began to be totally reflected in the first
1274Prism, the Light of those Colours on the Paper received as great an
1275Increase as the violet and blue had done before. Whence 'tis manifest,
1276that the Beam of Light reflected by the Base of the Prism, being
1277augmented first by the more refrangible Rays, and afterwards by the less
1278refrangible ones, is compounded of Rays differently refrangible. And
1279that all such reflected Light is of the same Nature with the Sun's Light
1280before its Incidence on the Base of the Prism, no Man ever doubted; it
1281being generally allowed, that Light by such Reflexions suffers no
1282Alteration in its Modifications and Properties. I do not here take
1283Notice of any Refractions made in the sides of the first Prism, because
1284the Light enters it perpendicularly at the first side, and goes out
1285perpendicularly at the second side, and therefore suffers none. So then,
1286the Sun's incident Light being of the same Temper and Constitution with
1287his emergent Light, and the last being compounded of Rays differently
1288refrangible, 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
1293its Base, B and C its equal Angles at the Base, each of 45 Degrees, A
1294its rectangular Vertex, FM a beam of the Sun's Light let into a dark
1295Room through a hole F one third part of an Inch broad, M its Incidence
1296on the Base of the Prism, MG a less refracted Ray, MH a more refracted
1297Ray, MN the beam of Light reflected from the Base, VXY the second Prism
1298by which this beam in passing through it is refracted, N_t_ the less
1299refracted Light of this beam, and N_p_ the more refracted part thereof.
1300When the first Prism ABC is turned about its Axis according to the order
1301of the Letters ABC, the Rays MH emerge more and more obliquely out of
1302that Prism, and at length after their most oblique Emergence are
1303reflected towards N, and going on to _p_ do increase the Number of the
1304Rays N_p_. Afterwards by continuing the Motion of the first Prism, the
1305Rays MG are also reflected to N and increase the number of the Rays
1306N_t_. And therefore the Light MN admits into its Composition, first the
1307more refrangible Rays, and then the less refrangible Rays, and yet after
1308this Composition is of the same Nature with the Sun's immediate Light
1309FM, 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,
1312that their Axis and opposite Sides being parallel, they composed a
1313Parallelopiped. And, the Sun shining into my dark Chamber through a
1314little hole in the Window-shut, I placed that Parallelopiped in his beam
1315at some distance from the hole, in such a Posture, that the Axes of the
1316Prisms might be perpendicular to the incident Rays, and that those Rays
1317being incident upon the first Side of one Prism, might go on through the
1318two contiguous Sides of both Prisms, and emerge out of the last Side of
1319the second Prism. This Side being parallel to the first Side of the
1320first Prism, caused the emerging Light to be parallel to the incident.
1321Then, beyond these two Prisms I placed a third, which might refract that
1322emergent Light, and by that Refraction cast the usual Colours of the
1323Prism upon the opposite Wall, or upon a sheet of white Paper held at a
1324convenient Distance behind the Prism for that refracted Light to fall
1325upon it. After this I turned the Parallelopiped about its Axis, and
1326found that when the contiguous Sides of the two Prisms became so oblique
1327to the incident Rays, that those Rays began all of them to be
1328reflected, those Rays which in the third Prism had suffered the greatest
1329Refraction, and painted the Paper with violet and blue, were first of
1330all by a total Reflexion taken out of the transmitted Light, the rest
1331remaining and on the Paper painting their Colours of green, yellow,
1332orange and red, as before; and afterwards by continuing the Motion of
1333the two Prisms, the rest of the Rays also by a total Reflexion vanished
1334in order, according to their degrees of Refrangibility. The Light
1335therefore which emerged out of the two Prisms is compounded of Rays
1336differently refrangible, seeing the more refrangible Rays may be taken
1337out of it, while the less refrangible remain. But this Light being
1338trajected only through the parallel Superficies of the two Prisms, if it
1339suffer'd any change by the Refraction of one Superficies it lost that
1340Impression by the contrary Refraction of the other Superficies, and so
1341being restor'd to its pristine Constitution, became of the same Nature
1342and Condition as at first before its Incidence on those Prisms; and
1343therefore, before its Incidence, was as much compounded of Rays
1344differently refrangible, as afterwards.
1345
1346[Illustration: FIG. 22.]
1347
1348_Illustration._ In the twenty second Figure ABC and BCD are the two
1349Prisms tied together in the form of a Parallelopiped, their Sides BC and
1350CB being contiguous, and their Sides AB and CD parallel. And HJK is the
1351third Prism, by which the Sun's Light propagated through the hole F into
1352the dark Chamber, and there passing through those sides of the Prisms
1353AB, BC, CB and CD, is refracted at O to the white Paper PT, falling
1354there partly upon P by a greater Refraction, partly upon T by a less
1355Refraction, and partly upon R and other intermediate places by
1356intermediate Refractions. By turning the Parallelopiped ACBD about its
1357Axis, according to the order of the Letters A, C, D, B, at length when
1358the contiguous Planes BC and CB become sufficiently oblique to the Rays
1359FM, which are incident upon them at M, there will vanish totally out of
1360the refracted Light OPT, first of all the most refracted Rays OP, (the
1361rest OR and OT remaining as before) then the Rays OR and other
1362intermediate ones, and lastly, the least refracted Rays OT. For when
1363the Plane BC becomes sufficiently oblique to the Rays incident upon it,
1364those Rays will begin to be totally reflected by it towards N; and first
1365the most refrangible Rays will be totally reflected (as was explained in
1366the preceding Experiment) and by Consequence must first disappear at P,
1367and afterwards the rest as they are in order totally reflected to N,
1368they must disappear in the same order at R and T. So then the Rays which
1369at O suffer the greatest Refraction, may be taken out of the Light MO
1370whilst the rest of the Rays remain in it, and therefore that Light MO is
1371compounded of Rays differently refrangible. And because the Planes AB
1372and CD are parallel, and therefore by equal and contrary Refractions
1373destroy one anothers Effects, the incident Light FM must be of the same
1374Kind and Nature with the emergent Light MO, and therefore doth also
1375consist of Rays differently refrangible. These two Lights FM and MO,
1376before the most refrangible Rays are separated out of the emergent Light
1377MO, agree in Colour, and in all other Properties so far as my
1378Observation reaches, and therefore are deservedly reputed of the same
1379Nature and Constitution, and by Consequence the one is compounded as
1380well as the other. But after the most refrangible Rays begin to be
1381totally reflected, and thereby separated out of the emergent Light MO,
1382that Light changes its Colour from white to a dilute and faint yellow, a
1383pretty good orange, a very full red successively, and then totally
1384vanishes. For after the most refrangible Rays which paint the Paper at
1385P with a purple Colour, are by a total Reflexion taken out of the beam
1386of Light MO, the rest of the Colours which appear on the Paper at R and
1387T being mix'd in the Light MO compound there a faint yellow, and after
1388the blue and part of the green which appear on the Paper between P and R
1389are taken away, the rest which appear between R and T (that is the
1390yellow, orange, red and a little green) being mixed in the beam MO
1391compound there an orange; and when all the Rays are by Reflexion taken
1392out of the beam MO, except the least refrangible, which at T appear of a
1393full red, their Colour is the same in that beam MO as afterwards at T,
1394the Refraction of the Prism HJK serving only to separate the differently
1395refrangible Rays, without making any Alteration in their Colours, as
1396shall be more fully proved hereafter. All which confirms as well the
1397first Proposition as the second.
1398
1399_Scholium._ If this Experiment and the former be conjoined and made one
1400by applying a fourth Prism VXY [in _Fig._ 22.] to refract the reflected
1401beam MN towards _tp_, the Conclusion will be clearer. For then the Light
1402N_p_ which in the fourth Prism is more refracted, will become fuller and
1403stronger when the Light OP, which in the third Prism HJK is more
1404refracted, vanishes at P; and afterwards when the less refracted Light
1405OT vanishes at T, the less refracted Light N_t_ will become increased
1406whilst the more refracted Light at _p_ receives no farther increase. And
1407as the trajected beam MO in vanishing is always of such a Colour as
1408ought to result from the mixture of the Colours which fall upon the
1409Paper PT, so is the reflected beam MN always of such a Colour as ought
1410to 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
1412out of the beam MO, and leave that beam of an orange Colour, the Excess
1413of those Rays in the reflected Light, does not only make the violet,
1414indigo and blue at _p_ more full, but also makes the beam MN change from
1415the yellowish Colour of the Sun's Light, to a pale white inclining to
1416blue, and afterward recover its yellowish Colour again, so soon as all
1417the rest of the transmitted Light MOT is reflected.
1418
1419Now seeing that in all this variety of Experiments, whether the Trial be
1420made in Light reflected, and that either from natural Bodies, as in the
1421first and second Experiment, or specular, as in the ninth; or in Light
1422refracted, and that either before the unequally refracted Rays are by
1423diverging separated from one another, and losing their whiteness which
1424they have altogether, appear severally of several Colours, as in the
1425fifth Experiment; or after they are separated from one another, and
1426appear colour'd as in the sixth, seventh, and eighth Experiments; or in
1427Light trajected through parallel Superficies, destroying each others
1428Effects, as in the tenth Experiment; there are always found Rays, which
1429at equal Incidences on the same Medium suffer unequal Refractions, and
1430that without any splitting or dilating of single Rays, or contingence in
1431the inequality of the Refractions, as is proved in the fifth and sixth
1432Experiments. And seeing the Rays which differ in Refrangibility may be
1433parted and sorted from one another, and that either by Refraction as in
1434the third Experiment, or by Reflexion as in the tenth, and then the
1435several sorts apart at equal Incidences suffer unequal Refractions, and
1436those sorts are more refracted than others after Separation, which were
1437more refracted before it, as in the sixth and following Experiments, and
1438if the Sun's Light be trajected through three or more cross Prisms
1439successively, those Rays which in the first Prism are refracted more
1440than others, are in all the following Prisms refracted more than others
1441in the same Rate and Proportion, as appears by the fifth Experiment;
1442it's manifest that the Sun's Light is an heterogeneous Mixture of Rays,
1443some of which are constantly more refrangible than others, as was
1444proposed.
1445
1446
1447_PROP._ III. THEOR. III.
1448
1449_The Sun's Light consists of Rays differing in Reflexibility, and those
1450Rays are more reflexible than others which are more refrangible._
1451
1452This is manifest by the ninth and tenth Experiments: For in the ninth
1453Experiment, by turning the Prism about its Axis, until the Rays within
1454it which in going out into the Air were refracted by its Base, became so
1455oblique to that Base, as to begin to be totally reflected thereby; those
1456Rays became first of all totally reflected, which before at equal
1457Incidences with the rest had suffered the greatest Refraction. And the
1458same thing happens in the Reflexion made by the common Base of the two
1459Prisms 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
1468The heterogeneous Rays are in some measure separated from one another by
1469the Refraction of the Prism in the third Experiment, and in the fifth
1470Experiment, by taking away the Penumbra from the rectilinear sides of
1471the coloured Image, that Separation in those very rectilinear sides or
1472straight edges of the Image becomes perfect. But in all places between
1473those rectilinear edges, those innumerable Circles there described,
1474which are severally illuminated by homogeneal Rays, by interfering with
1475one another, and being every where commix'd, do render the Light
1476sufficiently compound. But if these Circles, whilst their Centers keep
1477their Distances and Positions, could be made less in Diameter, their
1478interfering one with another, and by Consequence the Mixture of the
1479heterogeneous Rays would be proportionally diminish'd. In the twenty
1480third Figure let AG, BH, CJ, DK, EL, FM be the Circles which so many
1481sorts of Rays flowing from the same disque of the Sun, do in the third
1482Experiment illuminate; of all which and innumerable other intermediate
1483ones lying in a continual Series between the two rectilinear and
1484parallel edges of the Sun's oblong Image PT, that Image is compos'd, as
1485was 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
1487between two parallel right Lines _af_ and _gm_ with the same distances
1488between their Centers, and illuminated by the same sorts of Rays, that
1489is the Circle _ag_ with the same sort by which the corresponding Circle
1490AG was illuminated, and the Circle _bh_ with the same sort by which the
1491corresponding Circle BH was illuminated, and the rest of the Circles
1492_ci_, _dk_, _el_, _fm_ respectively, with the same sorts of Rays by
1493which the several corresponding Circles CJ, DK, EL, FM were illuminated.
1494In the Figure PT composed of the greater Circles, three of those Circles
1495AG, BH, CJ, are so expanded into one another, that the three sorts of
1496Rays by which those Circles are illuminated, together with other
1497innumerable sorts of intermediate Rays, are mixed at QR in the middle
1498of the Circle BH. And the like Mixture happens throughout almost the
1499whole length of the Figure PT. But in the Figure _pt_ composed of the
1500less Circles, the three less Circles _ag_, _bh_, _ci_, which answer to
1501those three greater, do not extend into one another; nor are there any
1502where mingled so much as any two of the three sorts of Rays by which
1503those Circles are illuminated, and which in the Figure PT are all of
1504them intermingled at BH.
1505
1506Now he that shall thus consider it, will easily understand that the
1507Mixture is diminished in the same Proportion with the Diameters of the
1508Circles. If the Diameters of the Circles whilst their Centers remain the
1509same, be made three times less than before, the Mixture will be also
1510three times less; if ten times less, the Mixture will be ten times less,
1511and so of other Proportions. That is, the Mixture of the Rays in the
1512greater Figure PT will be to their Mixture in the less _pt_, as the
1513Latitude of the greater Figure is to the Latitude of the less. For the
1514Latitudes of these Figures are equal to the Diameters of their Circles.
1515And hence it easily follows, that the Mixture of the Rays in the
1516refracted Spectrum _pt_ is to the Mixture of the Rays in the direct and
1517immediate Light of the Sun, as the breadth of that Spectrum is to the
1518difference between the length and breadth of the same Spectrum.
1519
1520So then, if we would diminish the Mixture of the Rays, we are to
1521diminish the Diameters of the Circles. Now these would be diminished if
1522the Sun's Diameter to which they answer could be made less than it is,
1523or (which comes to the same Purpose) if without Doors, at a great
1524distance from the Prism towards the Sun, some opake Body were placed,
1525with a round hole in the middle of it, to intercept all the Sun's Light,
1526excepting so much as coming from the middle of his Body could pass
1527through that Hole to the Prism. For so the Circles AG, BH, and the rest,
1528would not any longer answer to the whole Disque of the Sun, but only to
1529that Part of it which could be seen from the Prism through that Hole,
1530that it is to the apparent Magnitude of that Hole view'd from the Prism.
1531But that these Circles may answer more distinctly to that Hole, a Lens
1532is to be placed by the Prism to cast the Image of the Hole, (that is,
1533every one of the Circles AG, BH, &c.) distinctly upon the Paper at PT,
1534after such a manner, as by a Lens placed at a Window, the Species of
1535Objects abroad are cast distinctly upon a Paper within the Room, and the
1536rectilinear Sides of the oblong Solar Image in the fifth Experiment
1537became distinct without any Penumbra. If this be done, it will not be
1538necessary to place that Hole very far off, no not beyond the Window. And
1539therefore instead of that Hole, I used the Hole in the Window-shut, as
1540follows.
1541
1542_Exper._ 11. In the Sun's Light let into my darken'd Chamber through a
1543small round Hole in my Window-shut, at about ten or twelve Feet from the
1544Window, I placed a Lens, by which the Image of the Hole might be
1545distinctly cast upon a Sheet of white Paper, placed at the distance of
1546six, eight, ten, or twelve Feet from the Lens. For, according to the
1547difference of the Lenses I used various distances, which I think not
1548worth the while to describe. Then immediately after the Lens I placed a
1549Prism, by which the trajected Light might be refracted either upwards or
1550sideways, and thereby the round Image, which the Lens alone did cast
1551upon the Paper might be drawn out into a long one with Parallel Sides,
1552as in the third Experiment. This oblong Image I let fall upon another
1553Paper at about the same distance from the Prism as before, moving the
1554Paper either towards the Prism or from it, until I found the just
1555distance where the Rectilinear Sides of the Image became most distinct.
1556For in this Case, the Circular Images of the Hole, which compose that
1557Image after the same manner that the Circles _ag_, _bh_, _ci_, &c. do
1558the Figure _pt_ [in _Fig._ 23.] were terminated most distinctly without
1559any Penumbra, and therefore extended into one another the least that
1560they could, and by consequence the Mixture of the heterogeneous Rays was
1561now the least of all. By this means I used to form an oblong Image (such
1562as 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
1564in the Window-shut, I made the Circular Images _ag_, _bh_, _ci_, &c. of
1565which it was formed, to become greater or less at pleasure, and thereby
1566the Mixture of the Rays in the Image _pt_ to be as much, or as little as
1567I desired.
1568
1569[Illustration: FIG. 24.]
1570
1571_Illustration._ In the twenty-fourth Figure, F represents the Circular
1572Hole in the Window-shut, MN the Lens, whereby the Image or Species of
1573that Hole is cast distinctly upon a Paper at J, ABC the Prism, whereby
1574the Rays are at their emerging out of the Lens refracted from J towards
1575another Paper at _pt_, and the round Image at J is turned into an oblong
1576Image _pt_ falling on that other Paper. This Image _pt_ consists of
1577Circles placed one after another in a Rectilinear Order, as was
1578sufficiently explained in the fifth Experiment; and these Circles are
1579equal to the Circle J, and consequently answer in magnitude to the Hole
1580F; and therefore by diminishing that Hole they may be at pleasure
1581diminished, whilst their Centers remain in their Places. By this means I
1582made the Breadth of the Image _pt_ to be forty times, and sometimes
1583sixty or seventy times less than its Length. As for instance, if the
1584Breadth of the Hole F be one tenth of an Inch, and MF the distance of
1585the Lens from the Hole be 12 Feet; and if _p_B or _p_M the distance of
1586the Image _pt_ from the Prism or Lens be 10 Feet, and the refracting
1587Angle of the Prism be 62 Degrees, the Breadth of the Image _pt_ will be
1588one twelfth of an Inch, and the Length about six Inches, and therefore
1589the Length to the Breadth as 72 to 1, and by consequence the Light of
1590this Image 71 times less compound than the Sun's direct Light. And Light
1591thus far simple and homogeneal, is sufficient for trying all the
1592Experiments in this Book about simple Light. For the Composition of
1593heterogeneal Rays is in this Light so little, that it is scarce to be
1594discovered and perceiv'd by Sense, except perhaps in the indigo and
1595violet. For these being dark Colours do easily suffer a sensible Allay
1596by that little scattering Light which uses to be refracted irregularly
1597by the Inequalities of the Prism.
1598
1599Yet instead of the Circular Hole F, 'tis better to substitute an oblong
1600Hole shaped like a long Parallelogram with its Length parallel to the
1601Prism ABC. For if this Hole be an Inch or two long, and but a tenth or
1602twentieth 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
1604much broader, and therefore more fit to have Experiments try'd in its
1605Light than before.
1606
1607Instead of this Parallelogram Hole may be substituted a triangular one
1608of equal Sides, whose Base, for instance, is about the tenth Part of an
1609Inch, and its Height an Inch or more. For by this means, if the Axis of
1610the 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
1613ones answering to the triangular Hole in Shape and Bigness, and lying
1614one after another in a continual Series between two Parallel Lines _af_
1615and _gm_. These Triangles are a little intermingled at their Bases, but
1616not at their Vertices; and therefore the Light on the brighter Side _af_
1617of the Image, where the Bases of the Triangles are, is a little
1618compounded, but on the darker Side _gm_ is altogether uncompounded, and
1619in all Places between the Sides the Composition is proportional to the
1620distances of the Places from that obscurer Side _gm_. And having a
1621Spectrum _pt_ of such a Composition, we may try Experiments either in
1622its stronger and less simple Light near the Side _af_, or in its weaker
1623and simpler Light near the other Side _gm_, as it shall seem most
1624convenient.
1625
1626[Illustration: FIG. 25.]
1627
1628But in making Experiments of this kind, the Chamber ought to be made as
1629dark as can be, lest any Foreign Light mingle it self with the Light of
1630the Spectrum _pt_, and render it compound; especially if we would try
1631Experiments in the more simple Light next the Side _gm_ of the Spectrum;
1632which being fainter, will have a less proportion to the Foreign Light;
1633and so by the mixture of that Light be more troubled, and made more
1634compound. The Lens also ought to be good, such as may serve for optical
1635Uses, and the Prism ought to have a large Angle, suppose of 65 or 70
1636Degrees, and to be well wrought, being made of Glass free from Bubbles
1637and Veins, with its Sides not a little convex or concave, as usually
1638happens, but truly plane, and its Polish elaborate, as in working
1639Optick-glasses, and not such as is usually wrought with Putty, whereby
1640the edges of the Sand-holes being worn away, there are left all over the
1641Glass a numberless Company of very little convex polite Risings like
1642Waves. The edges also of the Prism and Lens, so far as they may make any
1643irregular Refraction, must be covered with a black Paper glewed on. And
1644all the Light of the Sun's Beam let into the Chamber, which is useless
1645and unprofitable to the Experiment, ought to be intercepted with black
1646Paper, or other black Obstacles. For otherwise the useless Light being
1647reflected every way in the Chamber, will mix with the oblong Spectrum,
1648and help to disturb it. In trying these Things, so much diligence is not
1649altogether necessary, but it will promote the Success of the
1650Experiments, and by a very scrupulous Examiner of Things deserves to be
1651apply'd. It's difficult to get Glass Prisms fit for this Purpose, and
1652therefore I used sometimes prismatick Vessels made with pieces of broken
1653Looking-glasses, and filled with Rain Water. And to increase the
1654Refraction, I sometimes impregnated the Water strongly with _Saccharum
1655Saturni_.
1656
1657
1658_PROP._ V. THEOR. IV.
1659
1660_Homogeneal Light is refracted regularly without any Dilatation
1661splitting or shattering of the Rays, and the confused Vision of Objects
1662seen through refracting Bodies by heterogeneal Light arises from the
1663different Refrangibility of several sorts of Rays._
1664
1665The first Part of this Proposition has been already sufficiently proved
1666in the fifth Experiment, and will farther appear by the Experiments
1667which follow.
1668
1669_Exper._ 12. In the middle of a black Paper I made a round Hole about a
1670fifth or sixth Part of an Inch in diameter. Upon this Paper I caused the
1671Spectrum of homogeneal Light described in the former Proposition, so to
1672fall, that some part of the Light might pass through the Hole of the
1673Paper. This transmitted part of the Light I refracted with a Prism
1674placed behind the Paper, and letting this refracted Light fall
1675perpendicularly upon a white Paper two or three Feet distant from the
1676Prism, I found that the Spectrum formed on the Paper by this Light was
1677not oblong, as when 'tis made (in the third Experiment) by refracting
1678the Sun's compound Light, but was (so far as I could judge by my Eye)
1679perfectly circular, the Length being no greater than the Breadth. Which
1680shews, that this Light is refracted regularly without any Dilatation of
1681the Rays.
1682
1683_Exper._ 13. In the homogeneal Light I placed a Paper Circle of a
1684quarter of an Inch in diameter, and in the Sun's unrefracted
1685heterogeneal white Light I placed another Paper Circle of the same
1686Bigness. And going from the Papers to the distance of some Feet, I
1687viewed both Circles through a Prism. The Circle illuminated by the Sun's
1688heterogeneal Light appeared very oblong, as in the fourth Experiment,
1689the Length being many times greater than the Breadth; but the other
1690Circle, illuminated with homogeneal Light, appeared circular and
1691distinctly defined, as when 'tis view'd with the naked Eye. Which proves
1692the whole Proposition.
1693
1694_Exper._ 14. In the homogeneal Light I placed Flies, and such-like
1695minute Objects, and viewing them through a Prism, I saw their Parts as
1696distinctly defined, as if I had viewed them with the naked Eye. The same
1697Objects placed in the Sun's unrefracted heterogeneal Light, which was
1698white, I viewed also through a Prism, and saw them most confusedly
1699defined, so that I could not distinguish their smaller Parts from one
1700another. I placed also the Letters of a small print, one while in the
1701homogeneal Light, and then in the heterogeneal, and viewing them through
1702a Prism, they appeared in the latter Case so confused and indistinct,
1703that I could not read them; but in the former they appeared so distinct,
1704that I could read readily, and thought I saw them as distinct, as when I
1705view'd them with my naked Eye. In both Cases I view'd the same Objects,
1706through the same Prism at the same distance from me, and in the same
1707Situation. There was no difference, but in the Light by which the
1708Objects were illuminated, and which in one Case was simple, and in the
1709other compound; and therefore, the distinct Vision in the former Case,
1710and confused in the latter, could arise from nothing else than from that
1711difference of the Lights. Which proves the whole Proposition.
1712
1713And in these three Experiments it is farther very remarkable, that the
1714Colour 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
1720Refraction in a given Ratio._
1721
1722That every Ray consider'd apart, is constant to it self in some degree
1723of Refrangibility, is sufficiently manifest out of what has been said.
1724Those Rays, which in the first Refraction, are at equal Incidences most
1725refracted, are also in the following Refractions at equal Incidences
1726most refracted; and so of the least refrangible, and the rest which have
1727any mean Degree of Refrangibility, as is manifest by the fifth, sixth,
1728seventh, eighth, and ninth Experiments. And those which the first Time
1729at like Incidences are equally refracted, are again at like Incidences
1730equally and uniformly refracted, and that whether they be refracted
1731before they be separated from one another, as in the fifth Experiment,
1732or whether they be refracted apart, as in the twelfth, thirteenth and
1733fourteenth Experiments. The Refraction therefore of every Ray apart is
1734regular, and what Rule that Refraction observes we are now to shew.[E]
1735
1736The late Writers in Opticks teach, that the Sines of Incidence are in a
1737given Proportion to the Sines of Refraction, as was explained in the
1738fifth Axiom, and some by Instruments fitted for measuring of
1739Refractions, or otherwise experimentally examining this Proportion, do
1740acquaint us that they have found it accurate. But whilst they, not
1741understanding the different Refrangibility of several Rays, conceived
1742them all to be refracted according to one and the same Proportion, 'tis
1743to be presumed that they adapted their Measures only to the middle of
1744the refracted Light; so that from their Measures we may conclude only
1745that the Rays which have a mean Degree of Refrangibility, that is, those
1746which when separated from the rest appear green, are refracted according
1747to a given Proportion of their Sines. And therefore we are now to shew,
1748that the like given Proportions obtain in all the rest. That it should
1749be so is very reasonable, Nature being ever conformable to her self; but
1750an experimental Proof is desired. And such a Proof will be had, if we
1751can shew that the Sines of Refraction of Rays differently refrangible
1752are one to another in a given Proportion when their Sines of Incidence
1753are equal. For, if the Sines of Refraction of all the Rays are in given
1754Proportions to the Sine of Refractions of a Ray which has a mean Degree
1755of Refrangibility, and this Sine is in a given Proportion to the equal
1756Sines of Incidence, those other Sines of Refraction will also be in
1757given Proportions to the equal Sines of Incidence. Now, when the Sines
1758of Incidence are equal, it will appear by the following Experiment, that
1759the 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
1764Hole in the Window-shut, let S [in _Fig._ 26.] represent his round white
1765Image painted on the opposite Wall by his direct Light, PT his oblong
1766coloured Image made by refracting that Light with a Prism placed at the
1767Window; and _pt_, or _2p 2t_, _3p 3t_, his oblong colour'd Image made by
1768refracting again the same Light sideways with a second Prism placed
1769immediately after the first in a cross Position to it, as was explained
1770in the fifth Experiment; that is to say, _pt_ when the Refraction of the
1771second Prism is small, _2p 2t_ when its Refraction is greater, and _3p
17723t_ when it is greatest. For such will be the diversity of the
1773Refractions, if the refracting Angle of the second Prism be of various
1774Magnitudes; suppose of fifteen or twenty Degrees to make the Image _pt_,
1775of thirty or forty to make the Image _2p 2t_, and of sixty to make the
1776Image _3p 3t_. But for want of solid Glass Prisms with Angles of
1777convenient Bignesses, there may be Vessels made of polished Plates of
1778Glass cemented together in the form of Prisms and filled with Water.
1779These things being thus ordered, I observed that all the solar Images or
1780coloured Spectrums PT, _pt_, _2p 2t_, _3p 3t_ did very nearly converge
1781to the place S on which the direct Light of the Sun fell and painted his
1782white round Image when the Prisms were taken away. The Axis of the
1783Spectrum PT, that is the Line drawn through the middle of it parallel to
1784its rectilinear Sides, did when produced pass exactly through the middle
1785of that white round Image S. And when the Refraction of the second Prism
1786was equal to the Refraction of the first, the refracting Angles of them
1787both being about 60 Degrees, the Axis of the Spectrum _3p 3t_ made by
1788that Refraction, did when produced pass also through the middle of the
1789same white round Image S. But when the Refraction of the second Prism
1790was less than that of the first, the produced Axes of the Spectrums _tp_
1791or _2t 2p_ made by that Refraction did cut the produced Axis of the
1792Spectrum TP in the points _m_ and _n_, a little beyond the Center of
1793that white round Image S. Whence the proportion of the Line 3_t_T to the
1794Line 3_p_P was a little greater than the Proportion of 2_t_T or 2_p_P,
1795and this Proportion a little greater than that of _t_T to _p_P. Now when
1796the Light of the Spectrum PT falls perpendicularly upon the Wall, those
1797Lines 3_t_T, 3_p_P, and 2_t_T, and 2_p_P, and _t_T, _p_P, are the
1798Tangents of the Refractions, and therefore by this Experiment the
1799Proportions of the Tangents of the Refractions are obtained, from whence
1800the Proportions of the Sines being derived, they come out equal, so far
1801as by viewing the Spectrums, and using some mathematical Reasoning I
1802could estimate. For I did not make an accurate Computation. So then the
1803Proposition holds true in every Ray apart, so far as appears by
1804Experiment. And that it is accurately true, may be demonstrated upon
1805this Supposition. _That Bodies refract Light by acting upon its Rays in
1806Lines perpendicular to their Surfaces._ But in order to this
1807Demonstration, I must distinguish the Motion of every Ray into two
1808Motions, the one perpendicular to the refracting Surface, the other
1809parallel to it, and concerning the perpendicular Motion lay down the
1810following Proposition.
1811
1812If any Motion or moving thing whatsoever be incident with any Velocity
1813on any broad and thin space terminated on both sides by two parallel
1814Planes, and in its Passage through that space be urged perpendicularly
1815towards the farther Plane by any force which at given distances from the
1816Plane is of given Quantities; the perpendicular velocity of that Motion
1817or Thing, at its emerging out of that space, shall be always equal to
1818the square Root of the sum of the square of the perpendicular velocity
1819of that Motion or Thing at its Incidence on that space; and of the
1820square of the perpendicular velocity which that Motion or Thing would
1821have at its Emergence, if at its Incidence its perpendicular velocity
1822was infinitely little.
1823
1824And the same Proposition holds true of any Motion or Thing
1825perpendicularly retarded in its passage through that space, if instead
1826of the sum of the two Squares you take their difference. The
1827Demonstration Mathematicians will easily find out, and therefore I shall
1828not trouble the Reader with it.
1829
1830Suppose now that a Ray coming most obliquely in the Line MC [in _Fig._
18311.] be refracted at C by the Plane RS into the Line CN, and if it be
1832required to find the Line CE, into which any other Ray AC shall be
1833refracted; let MC, AD, be the Sines of Incidence of the two Rays, and
1834NG, EF, their Sines of Refraction, and let the equal Motions of the
1835incident Rays be represented by the equal Lines MC and AC, and the
1836Motion MC being considered as parallel to the refracting Plane, let the
1837other Motion AC be distinguished into two Motions AD and DC, one of
1838which AD is parallel, and the other DC perpendicular to the refracting
1839Surface. In like manner, let the Motions of the emerging Rays be
1840distinguish'd into two, whereof the perpendicular ones are MC/NG × CG
1841and AD/EF × CF. And if the force of the refracting Plane begins to act
1842upon the Rays either in that Plane or at a certain distance from it on
1843the one side, and ends at a certain distance from it on the other side,
1844and in all places between those two limits acts upon the Rays in Lines
1845perpendicular to that refracting Plane, and the Actions upon the Rays at
1846equal distances from the refracting Plane be equal, and at unequal ones
1847either equal or unequal according to any rate whatever; that Motion of
1848the Ray which is parallel to the refracting Plane, will suffer no
1849Alteration by that Force; and that Motion which is perpendicular to it
1850will be altered according to the rule of the foregoing Proposition. If
1851therefore for the perpendicular velocity of the emerging Ray CN you
1852write MC/NG × CG as above, then the perpendicular velocity of any other
1853emerging Ray CE which was AD/EF × CF, will be equal to the square Root
1854of CD_q_ + (_MCq/NGq_ × CG_q_). And by squaring these Equals, and adding
1855to them the Equals AD_q_ and MC_q_ - CD_q_, and dividing the Sums by the
1856Equals 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
1858Refraction, as MC to NG, that is, in a given _ratio_. And this
1859Demonstration being general, without determining what Light is, or by
1860what kind of Force it is refracted, or assuming any thing farther than
1861that the refracting Body acts upon the Rays in Lines perpendicular to
1862its Surface; I take it to be a very convincing Argument of the full
1863truth of this Proposition.
1864
1865So then, if the _ratio_ of the Sines of Incidence and Refraction of any
1866sort of Rays be found in any one case, 'tis given in all cases; and this
1867may 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
1873of the Rays of Light._
1874
1875The Imperfection of Telescopes is vulgarly attributed to the spherical
1876Figures of the Glasses, and therefore Mathematicians have propounded to
1877figure them by the conical Sections. To shew that they are mistaken, I
1878have inserted this Proposition; the truth of which will appear by the
1879measure of the Refractions of the several sorts of Rays; and these
1880measures I thus determine.
1881
1882In the third Experiment of this first Part, where the refracting Angle
1883of the Prism was 62-1/2 Degrees, the half of that Angle 31 deg. 15 min.
1884is the Angle of Incidence of the Rays at their going out of the Glass
1885into the Air[F]; and the Sine of this Angle is 5188, the Radius being
188610000. When the Axis of this Prism was parallel to the Horizon, and the
1887Refraction of the Rays at their Incidence on this Prism equal to that at
1888their Emergence out of it, I observed with a Quadrant the Angle which
1889the mean refrangible Rays, (that is those which went to the middle of
1890the Sun's coloured Image) made with the Horizon, and by this Angle and
1891the Sun's altitude observed at the same time, I found the Angle which
1892the emergent Rays contained with the incident to be 44 deg. and 40 min.
1893and the half of this Angle added to the Angle of Incidence 31 deg. 15
1894min. makes the Angle of Refraction, which is therefore 53 deg. 35 min.
1895and its Sine 8047. These are the Sines of Incidence and Refraction of
1896the mean refrangible Rays, and their Proportion in round Numbers is 20
1897to 31. This Glass was of a Colour inclining to green. The last of the
1898Prisms mentioned in the third Experiment was of clear white Glass. Its
1899refracting Angle 63-1/2 Degrees. The Angle which the emergent Rays
1900contained, with the incident 45 deg. 50 min. The Sine of half the first
1901Angle 5262. The Sine of half the Sum of the Angles 8157. And their
1902Proportion in round Numbers 20 to 31, as before.
1903
1904From the Length of the Image, which was about 9-3/4 or 10 Inches,
1905subduct its Breadth, which was 2-1/8 Inches, and the Remainder 7-3/4
1906Inches would be the Length of the Image were the Sun but a Point, and
1907therefore subtends the Angle which the most and least refrangible Rays,
1908when incident on the Prism in the same Lines, do contain with one
1909another after their Emergence. Whence this Angle is 2 deg. 0´. 7´´. For
1910the distance between the Image and the Prism where this Angle is made,
1911was 18-1/2 Feet, and at that distance the Chord 7-3/4 Inches subtends an
1912Angle of 2 deg. 0´. 7´´. Now half this Angle is the Angle which these
1913emergent Rays contain with the emergent mean refrangible Rays, and a
1914quarter thereof, that is 30´. 2´´. may be accounted the Angle which they
1915would contain with the same emergent mean refrangible Rays, were they
1916co-incident to them within the Glass, and suffered no other Refraction
1917than that at their Emergence. For, if two equal Refractions, the one at
1918the Incidence of the Rays on the Prism, the other at their Emergence,
1919make half the Angle 2 deg. 0´. 7´´. then one of those Refractions will
1920make about a quarter of that Angle, and this quarter added to, and
1921subducted from the Angle of Refraction of the mean refrangible Rays,
1922which was 53 deg. 35´, gives the Angles of Refraction of the most and
1923least refrangible Rays 54 deg. 5´ 2´´, and 53 deg. 4´ 58´´, whose Sines
1924are 8099 and 7995, the common Angle of Incidence being 31 deg. 15´, and
1925its Sine 5188; and these Sines in the least round Numbers are in
1926proportion to one another, as 78 and 77 to 50.
1927
1928Now, if you subduct the common Sine of Incidence 50 from the Sines of
1929Refraction 77 and 78, the Remainders 27 and 28 shew, that in small
1930Refractions the Refraction of the least refrangible Rays is to the
1931Refraction of the most refrangible ones, as 27 to 28 very nearly, and
1932that the difference of the Refractions of the least refrangible and most
1933refrangible Rays is about the 27-1/2th Part of the whole Refraction of
1934the mean refrangible Rays.
1935
1936Whence they that are skilled in Opticks will easily understand,[G] that
1937the Breadth of the least circular Space, into which Object-glasses of
1938Telescopes can collect all sorts of Parallel Rays, is about the 27-1/2th
1939Part of half the Aperture of the Glass, or 55th Part of the whole
1940Aperture; and that the Focus of the most refrangible Rays is nearer to
1941the Object-glass than the Focus of the least refrangible ones, by about
1942the 27-1/2th Part of the distance between the Object-glass and the Focus
1943of the mean refrangible ones.
1944
1945And if Rays of all sorts, flowing from any one lucid Point in the Axis
1946of any convex Lens, be made by the Refraction of the Lens to converge to
1947Points not too remote from the Lens, the Focus of the most refrangible
1948Rays shall be nearer to the Lens than the Focus of the least refrangible
1949ones, by a distance which is to the 27-1/2th Part of the distance of the
1950Focus of the mean refrangible Rays from the Lens, as the distance
1951between that Focus and the lucid Point, from whence the Rays flow, is to
1952the distance between that lucid Point and the Lens very nearly.
1953
1954Now to examine whether the Difference between the Refractions, which the
1955most refrangible and the least refrangible Rays flowing from the same
1956Point suffer in the Object-glasses of Telescopes and such-like Glasses,
1957be 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,
1960being placed six Feet and an Inch distant from any Object, collected the
1961Species of that Object by the mean refrangible Rays at the distance of
1962six Feet and an Inch from the Lens on the other side. And therefore by
1963the foregoing Rule, it ought to collect the Species of that Object by
1964the least refrangible Rays at the distance of six Feet and 3-2/3 Inches
1965from the Lens, and by the most refrangible ones at the distance of five
1966Feet and 10-1/3 Inches from it: So that between the two Places, where
1967these least and most refrangible Rays collect the Species, there may be
1968the distance of about 5-1/3 Inches. For by that Rule, as six Feet and an
1969Inch (the distance of the Lens from the lucid Object) is to twelve Feet
1970and two Inches (the distance of the lucid Object from the Focus of the
1971mean refrangible Rays) that is, as One is to Two; so is the 27-1/2th
1972Part of six Feet and an Inch (the distance between the Lens and the same
1973Focus) to the distance between the Focus of the most refrangible Rays
1974and the Focus of the least refrangible ones, which is therefore 5-17/55
1975Inches, that is very nearly 5-1/3 Inches. Now to know whether this
1976Measure was true, I repeated the second and eighth Experiment with
1977coloured Light, which was less compounded than that I there made use of:
1978For I now separated the heterogeneous Rays from one another by the
1979Method I described in the eleventh Experiment, so as to make a coloured
1980Spectrum about twelve or fifteen Times longer than broad. This Spectrum
1981I cast on a printed Book, and placing the above-mentioned Lens at the
1982distance of six Feet and an Inch from this Spectrum to collect the
1983Species of the illuminated Letters at the same distance on the other
1984side, I found that the Species of the Letters illuminated with blue were
1985nearer to the Lens than those illuminated with deep red by about three
1986Inches, or three and a quarter; but the Species of the Letters
1987illuminated with indigo and violet appeared so confused and indistinct,
1988that I could not read them: Whereupon viewing the Prism, I found it was
1989full of Veins running from one end of the Glass to the other; so that
1990the Refraction could not be regular. I took another Prism therefore
1991which was free from Veins, and instead of the Letters I used two or
1992three Parallel black Lines a little broader than the Strokes of the
1993Letters, and casting the Colours upon these Lines in such manner, that
1994the Lines ran along the Colours from one end of the Spectrum to the
1995other, I found that the Focus where the indigo, or confine of this
1996Colour and violet cast the Species of the black Lines most distinctly,
1997to be about four Inches, or 4-1/4 nearer to the Lens than the Focus,
1998where the deepest red cast the Species of the same black Lines most
1999distinctly. The violet was so faint and dark, that I could not discern
2000the Species of the Lines distinctly by that Colour; and therefore
2001considering that the Prism was made of a dark coloured Glass inclining
2002to green, I took another Prism of clear white Glass; but the Spectrum of
2003Colours which this Prism made had long white Streams of faint Light
2004shooting out from both ends of the Colours, which made me conclude that
2005something was amiss; and viewing the Prism, I found two or three little
2006Bubbles in the Glass, which refracted the Light irregularly. Wherefore I
2007covered that Part of the Glass with black Paper, and letting the Light
2008pass through another Part of it which was free from such Bubbles, the
2009Spectrum of Colours became free from those irregular Streams of Light,
2010and was now such as I desired. But still I found the violet so dark and
2011faint, that I could scarce see the Species of the Lines by the violet,
2012and not at all by the deepest Part of it, which was next the end of the
2013Spectrum. I suspected therefore, that this faint and dark Colour might
2014be allayed by that scattering Light which was refracted, and reflected
2015irregularly, partly by some very small Bubbles in the Glasses, and
2016partly by the Inequalities of their Polish; which Light, tho' it was but
2017little, yet it being of a white Colour, might suffice to affect the
2018Sense so strongly as to disturb the Phænomena of that weak and dark
2019Colour the violet, and therefore I tried, as in the 12th, 13th, and 14th
2020Experiments, whether the Light of this Colour did not consist of a
2021sensible Mixture of heterogeneous Rays, but found it did not. Nor did
2022the Refractions cause any other sensible Colour than violet to emerge
2023out of this Light, as they would have done out of white Light, and by
2024consequence out of this violet Light had it been sensibly compounded
2025with white Light. And therefore I concluded, that the reason why I could
2026not see the Species of the Lines distinctly by this Colour, was only
2027the Darkness of this Colour, and Thinness of its Light, and its distance
2028from the Axis of the Lens; I divided therefore those Parallel black
2029Lines into equal Parts, by which I might readily know the distances of
2030the Colours in the Spectrum from one another, and noted the distances of
2031the Lens from the Foci of such Colours, as cast the Species of the Lines
2032distinctly, and then considered whether the difference of those
2033distances bear such proportion to 5-1/3 Inches, the greatest Difference
2034of the distances, which the Foci of the deepest red and violet ought to
2035have from the Lens, as the distance of the observed Colours from one
2036another in the Spectrum bear to the greatest distance of the deepest red
2037and violet measured in the Rectilinear Sides of the Spectrum, that is,
2038to the Length of those Sides, or Excess of the Length of the Spectrum
2039above its Breadth. And my Observations were as follows.
2040
2041When I observed and compared the deepest sensible red, and the Colour in
2042the Confine of green and blue, which at the Rectilinear Sides of the
2043Spectrum was distant from it half the Length of those Sides, the Focus
2044where the Confine of green and blue cast the Species of the Lines
2045distinctly on the Paper, was nearer to the Lens than the Focus, where
2046the red cast those Lines distinctly on it by about 2-1/2 or 2-3/4
2047Inches. For sometimes the Measures were a little greater, sometimes a
2048little less, but seldom varied from one another above 1/3 of an Inch.
2049For it was very difficult to define the Places of the Foci, without some
2050little Errors. Now, if the Colours distant half the Length of the
2051Image, (measured at its Rectilinear Sides) give 2-1/2 or 2-3/4
2052Difference of the distances of their Foci from the Lens, then the
2053Colours distant the whole Length ought to give 5 or 5-1/2 Inches
2054difference of those distances.
2055
2056But here it's to be noted, that I could not see the red to the full end
2057of the Spectrum, but only to the Center of the Semicircle which bounded
2058that end, or a little farther; and therefore I compared this red not
2059with that Colour which was exactly in the middle of the Spectrum, or
2060Confine of green and blue, but with that which verged a little more to
2061the blue than to the green: And as I reckoned the whole Length of the
2062Colours not to be the whole Length of the Spectrum, but the Length of
2063its Rectilinear Sides, so compleating the semicircular Ends into
2064Circles, when either of the observed Colours fell within those Circles,
2065I measured the distance of that Colour from the semicircular End of the
2066Spectrum, and subducting half this distance from the measured distance
2067of the two Colours, I took the Remainder for their corrected distance;
2068and in these Observations set down this corrected distance for the
2069difference of the distances of their Foci from the Lens. For, as the
2070Length of the Rectilinear Sides of the Spectrum would be the whole
2071Length of all the Colours, were the Circles of which (as we shewed) that
2072Spectrum consists contracted and reduced to Physical Points, so in that
2073Case this corrected distance would be the real distance of the two
2074observed Colours.
2075
2076When therefore I farther observed the deepest sensible red, and that
2077blue whose corrected distance from it was 7/12 Parts of the Length of
2078the Rectilinear Sides of the Spectrum, the difference of the distances
2079of their Foci from the Lens was about 3-1/4 Inches, and as 7 to 12, so
2080is 3-1/4 to 5-4/7.
2081
2082When I observed the deepest sensible red, and that indigo whose
2083corrected distance was 8/12 or 2/3 of the Length of the Rectilinear
2084Sides of the Spectrum, the difference of the distances of their Foci
2085from the Lens, was about 3-2/3 Inches, and as 2 to 3, so is 3-2/3 to
20865-1/2.
2087
2088When I observed the deepest sensible red, and that deep indigo whose
2089corrected distance from one another was 9/12 or 3/4 of the Length of the
2090Rectilinear Sides of the Spectrum, the difference of the distances of
2091their Foci from the Lens was about 4 Inches; and as 3 to 4, so is 4 to
20925-1/3.
2093
2094When I observed the deepest sensible red, and that Part of the violet
2095next the indigo, whose corrected distance from the red was 10/12 or 5/6
2096of the Length of the Rectilinear Sides of the Spectrum, the difference
2097of the distances of their Foci from the Lens was about 4-1/2 Inches, and
2098as 5 to 6, so is 4-1/2 to 5-2/5. For sometimes, when the Lens was
2099advantageously placed, so that its Axis respected the blue, and all
2100Things else were well ordered, and the Sun shone clear, and I held my
2101Eye very near to the Paper on which the Lens cast the Species of the
2102Lines, I could see pretty distinctly the Species of those Lines by that
2103Part of the violet which was next the indigo; and sometimes I could see
2104them by above half the violet, For in making these Experiments I had
2105observed, that the Species of those Colours only appear distinct, which
2106were in or near the Axis of the Lens: So that if the blue or indigo were
2107in the Axis, I could see their Species distinctly; and then the red
2108appeared much less distinct than before. Wherefore I contrived to make
2109the Spectrum of Colours shorter than before, so that both its Ends might
2110be nearer to the Axis of the Lens. And now its Length was about 2-1/2
2111Inches, and Breadth about 1/5 or 1/6 of an Inch. Also instead of the
2112black Lines on which the Spectrum was cast, I made one black Line
2113broader than those, that I might see its Species more easily; and this
2114Line I divided by short cross Lines into equal Parts, for measuring the
2115distances of the observed Colours. And now I could sometimes see the
2116Species of this Line with its Divisions almost as far as the Center of
2117the semicircular violet End of the Spectrum, and made these farther
2118Observations.
2119
2120When I observed the deepest sensible red, and that Part of the violet,
2121whose corrected distance from it was about 8/9 Parts of the Rectilinear
2122Sides of the Spectrum, the Difference of the distances of the Foci of
2123those Colours from the Lens, was one time 4-2/3, another time 4-3/4,
2124another time 4-7/8 Inches; and as 8 to 9, so are 4-2/3, 4-3/4, 4-7/8, to
21255-1/4, 5-11/32, 5-31/64 respectively.
2126
2127When I observed the deepest sensible red, and deepest sensible violet,
2128(the corrected distance of which Colours, when all Things were ordered
2129to the best Advantage, and the Sun shone very clear, was about 11/12 or
213015/16 Parts of the Length of the Rectilinear Sides of the coloured
2131Spectrum) I found the Difference of the distances of their Foci from the
2132Lens sometimes 4-3/4 sometimes 5-1/4, and for the most part 5 Inches or
2133thereabouts; and as 11 to 12, or 15 to 16, so is five Inches to 5-2/2 or
21345-1/3 Inches.
2135
2136And by this Progression of Experiments I satisfied my self, that had the
2137Light at the very Ends of the Spectrum been strong enough to make the
2138Species of the black Lines appear plainly on the Paper, the Focus of the
2139deepest violet would have been found nearer to the Lens, than the Focus
2140of the deepest red, by about 5-1/3 Inches at least. And this is a
2141farther Evidence, that the Sines of Incidence and Refraction of the
2142several sorts of Rays, hold the same Proportion to one another in the
2143smallest Refractions which they do in the greatest.
2144
2145My Progress in making this nice and troublesome Experiment I have set
2146down more at large, that they that shall try it after me may be aware of
2147the Circumspection requisite to make it succeed well. And if they cannot
2148make it succeed so well as I did, they may notwithstanding collect by
2149the Proportion of the distance of the Colours of the Spectrum, to the
2150Difference of the distances of their Foci from the Lens, what would be
2151the Success in the more distant Colours by a better trial. And yet, if
2152they use a broader Lens than I did, and fix it to a long strait Staff,
2153by means of which it may be readily and truly directed to the Colour
2154whose Focus is desired, I question not but the Experiment will succeed
2155better with them than it did with me. For I directed the Axis as nearly
2156as I could to the middle of the Colours, and then the faint Ends of the
2157Spectrum being remote from the Axis, cast their Species less distinctly
2158on the Paper than they would have done, had the Axis been successively
2159directed to them.
2160
2161Now by what has been said, it's certain that the Rays which differ in
2162Refrangibility do not converge to the same Focus; but if they flow from
2163a lucid Point, as far from the Lens on one side as their Foci are on the
2164other, the Focus of the most refrangible Rays shall be nearer to the
2165Lens than that of the least refrangible, by above the fourteenth Part of
2166the whole distance; and if they flow from a lucid Point, so very remote
2167from the Lens, that before their Incidence they may be accounted
2168parallel, the Focus of the most refrangible Rays shall be nearer to the
2169Lens than the Focus of the least refrangible, by about the 27th or 28th
2170Part of their whole distance from it. And the Diameter of the Circle in
2171the middle Space between those two Foci which they illuminate, when they
2172fall there on any Plane, perpendicular to the Axis (which Circle is the
2173least into which they can all be gathered) is about the 55th Part of the
2174Diameter of the Aperture of the Glass. So that 'tis a wonder, that
2175Telescopes represent Objects so distinct as they do. But were all the
2176Rays of Light equally refrangible, the Error arising only from the
2177Sphericalness of the Figures of Glasses would be many hundred times
2178less. For, if the Object-glass of a Telescope be Plano-convex, and the
2179Plane side be turned towards the Object, and the Diameter of the
2180Sphere, whereof this Glass is a Segment, be called D, and the
2181Semi-diameter of the Aperture of the Glass be called S, and the Sine of
2182Incidence out of Glass into Air, be to the Sine of Refraction as I to R;
2183the Rays which come parallel to the Axis of the Glass, shall in the
2184Place where the Image of the Object is most distinctly made, be
2185scattered all over a little Circle, whose Diameter is _(Rq/Iq) × (S
2186cub./D quad.)_ very nearly,[H] as I gather by computing the Errors of
2187the Rays by the Method of infinite Series, and rejecting the Terms,
2188whose Quantities are inconsiderable. As for instance, if the Sine of
2189Incidence I, be to the Sine of Refraction R, as 20 to 31, and if D the
2190Diameter of the Sphere, to which the Convex-side of the Glass is ground,
2191be 100 Feet or 1200 Inches, and S the Semi-diameter of the Aperture be
2192two Inches, the Diameter of the little Circle, (that is (_Rq × S
2193cub.)/(Iq × D quad._)) will be (31 × 31 × 8)/(20 × 20 × 1200 × 1200) (or
2194961/72000000) Parts of an Inch. But the Diameter of the little Circle,
2195through which these Rays are scattered by unequal Refrangibility, will
2196be about the 55th Part of the Aperture of the Object-glass, which here
2197is four Inches. And therefore, the Error arising from the Spherical
2198Figure of the Glass, is to the Error arising from the different
2199Refrangibility of the Rays, as 961/72000000 to 4/55, that is as 1 to
22005449; and therefore being in comparison so very little, deserves not to
2201be considered.
2202
2203[Illustration: FIG. 27.]
2204
2205But you will say, if the Errors caused by the different Refrangibility
2206be so very great, how comes it to pass, that Objects appear through
2207Telescopes so distinct as they do? I answer, 'tis because the erring
2208Rays are not scattered uniformly over all that Circular Space, but
2209collected infinitely more densely in the Center than in any other Part
2210of the Circle, and in the Way from the Center to the Circumference, grow
2211continually rarer and rarer, so as at the Circumference to become
2212infinitely rare; and by reason of their Rarity are not strong enough to
2213be visible, unless in the Center and very near it. Let ADE [in _Fig._
221427.] represent one of those Circles described with the Center C, and
2215Semi-diameter AC, and let BFG be a smaller Circle concentrick to the
2216former, cutting with its Circumference the Diameter AC in B, and bisect
2217AC in N; and by my reckoning, the Density of the Light in any Place B,
2218will be to its Density in N, as AB to BC; and the whole Light within the
2219lesser Circle BFG, will be to the whole Light within the greater AED, as
2220the Excess of the Square of AC above the Square of AB, is to the Square
2221of AC. As if BC be the fifth Part of AC, the Light will be four times
2222denser in B than in N, and the whole Light within the less Circle, will
2223be to the whole Light within the greater, as nine to twenty-five. Whence
2224it's evident, that the Light within the less Circle, must strike the
2225Sense much more strongly, than that faint and dilated Light round about
2226between it and the Circumference of the greater.
2227
2228But it's farther to be noted, that the most luminous of the Prismatick
2229Colours are the yellow and orange. These affect the Senses more strongly
2230than all the rest together, and next to these in strength are the red
2231and green. The blue compared with these is a faint and dark Colour, and
2232the indigo and violet are much darker and fainter, so that these
2233compared with the stronger Colours are little to be regarded. The Images
2234of Objects are therefore to be placed, not in the Focus of the mean
2235refrangible Rays, which are in the Confine of green and blue, but in the
2236Focus of those Rays which are in the middle of the orange and yellow;
2237there where the Colour is most luminous and fulgent, that is in the
2238brightest yellow, that yellow which inclines more to orange than to
2239green. And by the Refraction of these Rays (whose Sines of Incidence and
2240Refraction in Glass are as 17 and 11) the Refraction of Glass and
2241Crystal for Optical Uses is to be measured. Let us therefore place the
2242Image of the Object in the Focus of these Rays, and all the yellow and
2243orange will fall within a Circle, whose Diameter is about the 250th
2244Part of the Diameter of the Aperture of the Glass. And if you add the
2245brighter half of the red, (that half which is next the orange) and the
2246brighter half of the green, (that half which is next the yellow) about
2247three fifth Parts of the Light of these two Colours will fall within the
2248same Circle, and two fifth Parts will fall without it round about; and
2249that which falls without will be spread through almost as much more
2250space as that which falls within, and so in the gross be almost three
2251times rarer. Of the other half of the red and green, (that is of the
2252deep dark red and willow green) about one quarter will fall within this
2253Circle, and three quarters without, and that which falls without will be
2254spread through about four or five times more space than that which falls
2255within; and so in the gross be rarer, and if compared with the whole
2256Light within it, will be about 25 times rarer than all that taken in the
2257gross; or rather more than 30 or 40 times rarer, because the deep red in
2258the end of the Spectrum of Colours made by a Prism is very thin and
2259rare, and the willow green is something rarer than the orange and
2260yellow. The Light of these Colours therefore being so very much rarer
2261than that within the Circle, will scarce affect the Sense, especially
2262since the deep red and willow green of this Light, are much darker
2263Colours than the rest. And for the same reason the blue and violet being
2264much darker Colours than these, and much more rarified, may be
2265neglected. For the dense and bright Light of the Circle, will obscure
2266the rare and weak Light of these dark Colours round about it, and
2267render them almost insensible. The sensible Image of a lucid Point is
2268therefore scarce broader than a Circle, whose Diameter is the 250th Part
2269of the Diameter of the Aperture of the Object-glass of a good Telescope,
2270or not much broader, if you except a faint and dark misty Light round
2271about it, which a Spectator will scarce regard. And therefore in a
2272Telescope, whose Aperture is four Inches, and Length an hundred Feet, it
2273exceeds not 2´´ 45´´´, or 3´´. And in a Telescope whose Aperture is two
2274Inches, and Length 20 or 30 Feet, it may be 5´´ or 6´´, and scarce
2275above. And this answers well to Experience: For some Astronomers have
2276found the Diameters of the fix'd Stars, in Telescopes of between 20 and
227760 Feet in length, to be about 5´´ or 6´´, or at most 8´´ or 10´´ in
2278diameter. But if the Eye-Glass be tincted faintly with the Smoak of a
2279Lamp or Torch, to obscure the Light of the Star, the fainter Light in
2280the Circumference of the Star ceases to be visible, and the Star (if the
2281Glass be sufficiently soiled with Smoak) appears something more like a
2282mathematical Point. And for the same Reason, the enormous Part of the
2283Light in the Circumference of every lucid Point ought to be less
2284discernible in shorter Telescopes than in longer, because the shorter
2285transmit less Light to the Eye.
2286
2287Now, that the fix'd Stars, by reason of their immense Distance, appear
2288like Points, unless so far as their Light is dilated by Refraction, may
2289appear from hence; that when the Moon passes over them and eclipses
2290them, their Light vanishes, not gradually like that of the Planets, but
2291all at once; and in the end of the Eclipse it returns into Sight all at
2292once, or certainly in less time than the second of a Minute; the
2293Refraction of the Moon's Atmosphere a little protracting the time in
2294which the Light of the Star first vanishes, and afterwards returns into
2295Sight.
2296
2297Now, if we suppose the sensible Image of a lucid Point, to be even 250
2298times narrower than the Aperture of the Glass; yet this Image would be
2299still much greater than if it were only from the spherical Figure of the
2300Glass. For were it not for the different Refrangibility of the Rays, its
2301breadth in an 100 Foot Telescope whose aperture is 4 Inches, would be
2302but 961/72000000 parts of an Inch, as is manifest by the foregoing
2303Computation. And therefore in this case the greatest Errors arising from
2304the spherical Figure of the Glass, would be to the greatest sensible
2305Errors arising from the different Refrangibility of the Rays as
2306961/72000000 to 4/250 at most, that is only as 1 to 1200. And this
2307sufficiently shews that it is not the spherical Figures of Glasses, but
2308the different Refrangibility of the Rays which hinders the perfection of
2309Telescopes.
2310
2311There is another Argument by which it may appear that the different
2312Refrangibility of Rays, is the true cause of the imperfection of
2313Telescopes. For the Errors of the Rays arising from the spherical
2314Figures of Object-glasses, are as the Cubes of the Apertures of the
2315Object Glasses; and thence to make Telescopes of various Lengths magnify
2316with equal distinctness, the Apertures of the Object-glasses, and the
2317Charges or magnifying Powers ought to be as the Cubes of the square
2318Roots of their lengths; which doth not answer to Experience. But the
2319Errors of the Rays arising from the different Refrangibility, are as the
2320Apertures of the Object-glasses; and thence to make Telescopes of
2321various lengths, magnify with equal distinctness, their Apertures and
2322Charges ought to be as the square Roots of their lengths; and this
2323answers to Experience, as is well known. For Instance, a Telescope of 64
2324Feet in length, with an Aperture of 2-2/3 Inches, magnifies about 120
2325times, with as much distinctness as one of a Foot in length, with 1/3 of
2326an Inch aperture, magnifies 15 times.
2327
2328[Illustration: FIG. 28.]
2329
2330Now were it not for this different Refrangibility of Rays, Telescopes
2331might be brought to a greater perfection than we have yet describ'd, by
2332composing the Object-glass of two Glasses with Water between them. Let
2333ADFC [in _Fig._ 28.] represent the Object-glass composed of two Glasses
2334ABED and BEFC, alike convex on the outsides AGD and CHF, and alike
2335concave on the insides BME, BNE, with Water in the concavity BMEN. Let
2336the Sine of Incidence out of Glass into Air be as I to R, and out of
2337Water into Air, as K to R, and by consequence out of Glass into Water,
2338as I to K: and let the Diameter of the Sphere to which the convex sides
2339AGD and CHF are ground be D, and the Diameter of the Sphere to which the
2340concave sides BME and BNE, are ground be to D, as the Cube Root of
2341KK--KI to the Cube Root of RK--RI: and the Refractions on the concave
2342sides of the Glasses, will very much correct the Errors of the
2343Refractions on the convex sides, so far as they arise from the
2344sphericalness of the Figure. And by this means might Telescopes be
2345brought to sufficient perfection, were it not for the different
2346Refrangibility of several sorts of Rays. But by reason of this different
2347Refrangibility, I do not yet see any other means of improving Telescopes
2348by Refractions alone, than that of increasing their lengths, for which
2349end the late Contrivance of _Hugenius_ seems well accommodated. For very
2350long Tubes are cumbersome, and scarce to be readily managed, and by
2351reason of their length are very apt to bend, and shake by bending, so as
2352to cause a continual trembling in the Objects, whereby it becomes
2353difficult to see them distinctly: whereas by his Contrivance the Glasses
2354are readily manageable, and the Object-glass being fix'd upon a strong
2355upright Pole becomes more steady.
2356
2357Seeing therefore the Improvement of Telescopes of given lengths by
2358Refractions is desperate; I contrived heretofore a Perspective by
2359Reflexion, using instead of an Object-glass a concave Metal. The
2360diameter of the Sphere to which the Metal was ground concave was about
236125 _English_ Inches, and by consequence the length of the Instrument
2362about six Inches and a quarter. The Eye-glass was Plano-convex, and the
2363diameter of the Sphere to which the convex side was ground was about 1/5
2364of an Inch, or a little less, and by consequence it magnified between 30
2365and 40 times. By another way of measuring I found that it magnified
2366about 35 times. The concave Metal bore an Aperture of an Inch and a
2367third part; but the Aperture was limited not by an opake Circle,
2368covering the Limb of the Metal round about, but by an opake Circle
2369placed between the Eyeglass and the Eye, and perforated in the middle
2370with a little round hole for the Rays to pass through to the Eye. For
2371this Circle by being placed here, stopp'd much of the erroneous Light,
2372which otherwise would have disturbed the Vision. By comparing it with a
2373pretty good Perspective of four Feet in length, made with a concave
2374Eye-glass, I could read at a greater distance with my own Instrument
2375than with the Glass. Yet Objects appeared much darker in it than in the
2376Glass, and that partly because more Light was lost by Reflexion in the
2377Metal, than by Refraction in the Glass, and partly because my Instrument
2378was overcharged. Had it magnified but 30 or 25 times, it would have made
2379the Object appear more brisk and pleasant. Two of these I made about 16
2380Years ago, and have one of them still by me, by which I can prove the
2381truth of what I write. Yet it is not so good as at the first. For the
2382concave has been divers times tarnished and cleared again, by rubbing
2383it with very soft Leather. When I made these an Artist in _London_
2384undertook to imitate it; but using another way of polishing them than I
2385did, he fell much short of what I had attained to, as I afterwards
2386understood by discoursing the Under-workman he had employed. The Polish
2387I used was in this manner. I had two round Copper Plates, each six
2388Inches in Diameter, the one convex, the other concave, ground very true
2389to one another. On the convex I ground the Object-Metal or Concave which
2390was to be polish'd, 'till it had taken the Figure of the Convex and was
2391ready for a Polish. Then I pitched over the convex very thinly, by
2392dropping melted Pitch upon it, and warming it to keep the Pitch soft,
2393whilst I ground it with the concave Copper wetted to make it spread
2394eavenly all over the convex. Thus by working it well I made it as thin
2395as a Groat, and after the convex was cold I ground it again to give it
2396as true a Figure as I could. Then I took Putty which I had made very
2397fine by washing it from all its grosser Particles, and laying a little
2398of this upon the Pitch, I ground it upon the Pitch with the concave
2399Copper, till it had done making a Noise; and then upon the Pitch I
2400ground the Object-Metal with a brisk motion, for about two or three
2401Minutes of time, leaning hard upon it. Then I put fresh Putty upon the
2402Pitch, and ground it again till it had done making a noise, and
2403afterwards ground the Object-Metal upon it as before. And this Work I
2404repeated till the Metal was polished, grinding it the last time with all
2405my strength for a good while together, and frequently breathing upon
2406the Pitch, to keep it moist without laying on any more fresh Putty. The
2407Object-Metal was two Inches broad, and about one third part of an Inch
2408thick, to keep it from bending. I had two of these Metals, and when I
2409had polished them both, I tried which was best, and ground the other
2410again, to see if I could make it better than that which I kept. And thus
2411by many Trials I learn'd the way of polishing, till I made those two
2412reflecting Perspectives I spake of above. For this Art of polishing will
2413be better learn'd by repeated Practice than by my Description. Before I
2414ground the Object-Metal on the Pitch, I always ground the Putty on it
2415with the concave Copper, till it had done making a noise, because if the
2416Particles of the Putty were not by this means made to stick fast in the
2417Pitch, they would by rolling up and down grate and fret the Object-Metal
2418and fill it full of little holes.
2419
2420But because Metal is more difficult to polish than Glass, and is
2421afterwards very apt to be spoiled by tarnishing, and reflects not so
2422much Light as Glass quick-silver'd over does: I would propound to use
2423instead of the Metal, a Glass ground concave on the foreside, and as
2424much convex on the backside, and quick-silver'd over on the convex side.
2425The Glass must be every where of the same thickness exactly. Otherwise
2426it will make Objects look colour'd and indistinct. By such a Glass I
2427tried about five or six Years ago to make a reflecting Telescope of four
2428Feet in length to magnify about 150 times, and I satisfied my self that
2429there wants nothing but a good Artist to bring the Design to
2430perfection. For the Glass being wrought by one of our _London_ Artists
2431after such a manner as they grind Glasses for Telescopes, though it
2432seemed as well wrought as the Object-glasses use to be, yet when it was
2433quick-silver'd, the Reflexion discovered innumerable Inequalities all
2434over the Glass. And by reason of these Inequalities, Objects appeared
2435indistinct in this Instrument. For the Errors of reflected Rays caused
2436by any Inequality of the Glass, are about six times greater than the
2437Errors of refracted Rays caused by the like Inequalities. Yet by this
2438Experiment I satisfied my self that the Reflexion on the concave side of
2439the Glass, which I feared would disturb the Vision, did no sensible
2440prejudice to it, and by consequence that nothing is wanting to perfect
2441these Telescopes, but good Workmen who can grind and polish Glasses
2442truly spherical. An Object-glass of a fourteen Foot Telescope, made by
2443an Artificer at _London_, I once mended considerably, by grinding it on
2444Pitch with Putty, and leaning very easily on it in the grinding, lest
2445the Putty should scratch it. Whether this way may not do well enough for
2446polishing these reflecting Glasses, I have not yet tried. But he that
2447shall try either this or any other way of polishing which he may think
2448better, may do well to make his Glasses ready for polishing, by grinding
2449them without that Violence, wherewith our _London_ Workmen press their
2450Glasses in grinding. For by such violent pressure, Glasses are apt to
2451bend a little in the grinding, and such bending will certainly spoil
2452their Figure. To recommend therefore the consideration of these
2453reflecting Glasses to such Artists as are curious in figuring Glasses, I
2454shall describe this optical Instrument in the following Proposition.
2455
2456
2457_PROP._ VIII. PROB. II.
2458
2459_To shorten Telescopes._
2460
2461Let ABCD [in _Fig._ 29.] represent a Glass spherically concave on the
2462foreside AB, and as much convex on the backside CD, so that it be every
2463where of an equal thickness. Let it not be thicker on one side than on
2464the other, lest it make Objects appear colour'd and indistinct, and let
2465it be very truly wrought and quick-silver'd over on the backside; and
2466set in the Tube VXYZ which must be very black within. Let EFG represent
2467a Prism of Glass or Crystal placed near the other end of the Tube, in
2468the middle of it, by means of a handle of Brass or Iron FGK, to the end
2469of which made flat it is cemented. Let this Prism be rectangular at E,
2470and let the other two Angles at F and G be accurately equal to each
2471other, and by consequence equal to half right ones, and let the plane
2472sides FE and GE be square, and by consequence the third side FG a
2473rectangular Parallelogram, whose length is to its breadth in a
2474subduplicate proportion of two to one. Let it be so placed in the Tube,
2475that the Axis of the Speculum may pass through the middle of the square
2476side EF perpendicularly and by consequence through the middle of the
2477side FG at an Angle of 45 Degrees, and let the side EF be turned towards
2478the Speculum, and the distance of this Prism from the Speculum be such
2479that the Rays of the Light PQ, RS, &c. which are incident upon the
2480Speculum in Lines parallel to the Axis thereof, may enter the Prism at
2481the side EF, and be reflected by the side FG, and thence go out of it
2482through the side GE, to the Point T, which must be the common Focus of
2483the Speculum ABDC, and of a Plano-convex Eye-glass H, through which
2484those Rays must pass to the Eye. And let the Rays at their coming out of
2485the Glass pass through a small round hole, or aperture made in a little
2486plate of Lead, Brass, or Silver, wherewith the Glass is to be covered,
2487which hole must be no bigger than is necessary for Light enough to pass
2488through. 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
2490from the verges of the Speculum AB. Such an Instrument well made, if it
2491be six Foot long, (reckoning the length from the Speculum to the Prism,
2492and thence to the Focus T) will bear an aperture of six Inches at the
2493Speculum, and magnify between two and three hundred times. But the hole
2494H here limits the aperture with more advantage, than if the aperture was
2495placed at the Speculum. If the Instrument be made longer or shorter, the
2496aperture must be in proportion as the Cube of the square-square Root of
2497the length, and the magnifying as the aperture. But it's convenient that
2498the Speculum be an Inch or two broader than the aperture at the least,
2499and that the Glass of the Speculum be thick, that it bend not in the
2500working. The Prism EFG must be no bigger than is necessary, and its back
2501side FG must not be quick-silver'd over. For without quicksilver it will
2502reflect all the Light incident on it from the Speculum.
2503
2504[Illustration: FIG. 29.]
2505
2506In this Instrument the Object will be inverted, but may be erected by
2507making the square sides FF and EG of the Prism EFG not plane but
2508spherically convex, that the Rays may cross as well before they come at
2509it as afterwards between it and the Eye-glass. If it be desired that the
2510Instrument bear a larger aperture, that may be also done by composing
2511the Speculum of two Glasses with Water between them.
2512
2513If the Theory of making Telescopes could at length be fully brought into
2514Practice, yet there would be certain Bounds beyond which Telescopes
2515could not perform. For the Air through which we look upon the Stars, is
2516in a perpetual Tremor; as may be seen by the tremulous Motion of Shadows
2517cast from high Towers, and by the twinkling of the fix'd Stars. But
2518these Stars do not twinkle when viewed through Telescopes which have
2519large apertures. For the Rays of Light which pass through divers parts
2520of the aperture, tremble each of them apart, and by means of their
2521various and sometimes contrary Tremors, fall at one and the same time
2522upon different points in the bottom of the Eye, and their trembling
2523Motions are too quick and confused to be perceived severally. And all
2524these illuminated Points constitute one broad lucid Point, composed of
2525those many trembling Points confusedly and insensibly mixed with one
2526another by very short and swift Tremors, and thereby cause the Star to
2527appear broader than it is, and without any trembling of the whole. Long
2528Telescopes may cause Objects to appear brighter and larger than short
2529ones can do, but they cannot be so formed as to take away that confusion
2530of the Rays which arises from the Tremors of the Atmosphere. The only
2531Remedy is a most serene and quiet Air, such as may perhaps be found on
2532the tops of the highest Mountains above the grosser Clouds.
2533
2534FOOTNOTES:
2535
2536[C] _See our_ Author's Lectiones Opticæ § 10. _Sect. II. § 29. and Sect.
2537III. 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_
2542I. _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
2555THE 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
2566by new Modifications of the Light variously impress'd, according to the
2567various Terminations of the Light and Shadow_.
2568
2569The PROOF by Experiments.
2570
2571_Exper._ 1. For if the Sun shine into a very dark Chamber through an
2572oblong hole F, [in _Fig._ 1.] whose breadth is the sixth or eighth part
2573of an Inch, or something less; and his beam FH do afterwards pass first
2574through a very large Prism ABC, distant about 20 Feet from the hole, and
2575parallel to it, and then (with its white part) through an oblong hole H,
2576whose breadth is about the fortieth or sixtieth part of an Inch, and
2577which is made in a black opake Body GI, and placed at the distance of
2578two or three Feet from the Prism, in a parallel Situation both to the
2579Prism and to the former hole, and if this white Light thus transmitted
2580through the hole H, fall afterwards upon a white Paper _pt_, placed
2581after that hole H, at the distance of three or four Feet from it, and
2582there paint the usual Colours of the Prism, suppose red at _t_, yellow
2583at _s_, green at _r_, blue at _q_, and violet at _p_; you may with an
2584Iron Wire, or any such like slender opake Body, whose breadth is about
2585the 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
2588an Obstacle something bigger you may take away any two, or three, or
2589four Colours together, the rest remaining: So that any one of the
2590Colours as well as violet may become outmost in the Confine of the
2591Shadow towards _p_, and any one of them as well as red may become
2592outmost in the Confine of the Shadow towards _t_, and any one of them
2593may also border upon the Shadow made within the Colours by the Obstacle
2594R intercepting some intermediate part of the Light; and, lastly, any one
2595of them by being left alone, may border upon the Shadow on either hand.
2596All the Colours have themselves indifferently to any Confines of Shadow,
2597and therefore the differences of these Colours from one another, do not
2598arise from the different Confines of Shadow, whereby Light is variously
2599modified, as has hitherto been the Opinion of Philosophers. In trying
2600these things 'tis to be observed, that by how much the holes F and H are
2601narrower, and the Intervals between them and the Prism greater, and the
2602Chamber darker, by so much the better doth the Experiment succeed;
2603provided 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
2605enough for this Experiment will be difficult, and therefore a prismatick
2606Vessel must be made of polish'd Glass Plates cemented together, and
2607filled 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
2612hole F, [in _Fig._ 2.] half an Inch wide, passed first through the Prism
2613ABC placed at the hole, and then through a Lens PT something more than
2614four Inches broad, and about eight Feet distant from the Prism, and
2615thence converged to O the Focus of the Lens distant from it about three
2616Feet, and there fell upon a white Paper DE. If that Paper was
2617perpendicular to that Light incident upon it, as 'tis represented in the
2618posture DE, all the Colours upon it at O appeared white. But if the
2619Paper being turned about an Axis parallel to the Prism, became very much
2620inclined 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,
2622in the other blue. Here one and the same part of the Light in one and
2623the same place, according to the various Inclinations of the Paper,
2624appeared in one case white, in another yellow or red, in a third blue,
2625whilst the Confine of Light and shadow, and the Refractions of the Prism
2626in 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.
2633Let a broad beam of the Sun's Light coming into a dark Chamber through a
2634hole in the Window-shut be refracted by a large Prism ABC, [in _Fig._
26353.] whose refracting Angle C is more than 60 Degrees, and so soon as it
2636comes out of the Prism, let it fall upon the white Paper DE glewed upon
2637a 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
2639when the Paper is very much inclin'd to it in such a manner as to keep
2640always parallel to the Axis of the Prism, the whiteness of the whole
2641Light upon the Paper will according to the inclination of the Paper this
2642way 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
2644Light before it fall upon the Paper be twice refracted the same way by
2645two parallel Prisms, these Colours will become the more conspicuous.
2646Here all the middle parts of the broad beam of white Light which fell
2647upon the Paper, did without any Confine of Shadow to modify it, become
2648colour'd all over with one uniform Colour, the Colour being always the
2649same in the middle of the Paper as at the edges, and this Colour changed
2650according to the various Obliquity of the reflecting Paper, without any
2651change in the Refractions or Shadow, or in the Light which fell upon the
2652Paper. And therefore these Colours are to be derived from some other
2653Cause than the new Modifications of Light by Refractions and Shadows.
2654
2655If it be asked, what then is their Cause? I answer, That the Paper in
2656the posture _de_, being more oblique to the more refrangible Rays than
2657to the less refrangible ones, is more strongly illuminated by the latter
2658than by the former, and therefore the less refrangible Rays are
2659predominant in the reflected Light. And where-ever they are predominant
2660in any Light, they tinge it with red or yellow, as may in some measure
2661appear by the first Proposition of the first Part of this Book, and will
2662more fully appear hereafter. And the contrary happens in the posture of
2663the Paper [Greek: de], the more refrangible Rays being then predominant
2664which always tinge Light with blues and violets.
2665
2666_Exper._ 4. The Colours of Bubbles with which Children play are various,
2667and change their Situation variously, without any respect to any Confine
2668or Shadow. If such a Bubble be cover'd with a concave Glass, to keep it
2669from being agitated by any Wind or Motion of the Air, the Colours will
2670slowly and regularly change their situation, even whilst the Eye and the
2671Bubble, and all Bodies which emit any Light, or cast any Shadow, remain
2672unmoved. And therefore their Colours arise from some regular Cause which
2673depends not on any Confine of Shadow. What this Cause is will be shewed
2674in the next Book.
2675
2676To these Experiments may be added the tenth Experiment of the first Part
2677of this first Book, where the Sun's Light in a dark Room being
2678trajected through the parallel Superficies of two Prisms tied together
2679in the form of a Parallelopipede, became totally of one uniform yellow
2680or red Colour, at its emerging out of the Prisms. Here, in the
2681production of these Colours, the Confine of Shadow can have nothing to
2682do. For the Light changes from white to yellow, orange and red
2683successively, without any alteration of the Confine of Shadow: And at
2684both edges of the emerging Light where the contrary Confines of Shadow
2685ought to produce different Effects, the Colour is one and the same,
2686whether it be white, yellow, orange or red: And in the middle of the
2687emerging Light, where there is no Confine of Shadow at all, the Colour
2688is the very same as at the edges, the whole Light at its very first
2689Emergence being of one uniform Colour, whether white, yellow, orange or
2690red, and going on thence perpetually without any change of Colour, such
2691as the Confine of Shadow is vulgarly supposed to work in refracted Light
2692after its Emergence. Neither can these Colours arise from any new
2693Modifications of the Light by Refractions, because they change
2694successively from white to yellow, orange and red, while the Refractions
2695remain the same, and also because the Refractions are made contrary ways
2696by parallel Superficies which destroy one another's Effects. They arise
2697not therefore from any Modifications of Light made by Refractions and
2698Shadows, but have some other Cause. What that Cause is we shewed above
2699in this tenth Experiment, and need not here repeat it.
2700
2701There is yet another material Circumstance of this Experiment. For this
2702emerging Light being by a third Prism HIK [in _Fig._ 22. _Part_ I.][I]
2703refracted towards the Paper PT, and there painting the usual Colours of
2704the Prism, red, yellow, green, blue, violet: If these Colours arose from
2705the Refractions of that Prism modifying the Light, they would not be in
2706the Light before its Incidence on that Prism. And yet in that Experiment
2707we found, that when by turning the two first Prisms about their common
2708Axis all the Colours were made to vanish but the red; the Light which
2709makes that red being left alone, appeared of the very same red Colour
2710before its Incidence on the third Prism. And in general we find by other
2711Experiments, that when the Rays which differ in Refrangibility are
2712separated from one another, and any one Sort of them is considered
2713apart, the Colour of the Light which they compose cannot be changed by
2714any Refraction or Reflexion whatever, as it ought to be were Colours
2715nothing else than Modifications of Light caused by Refractions, and
2716Reflexions, and Shadows. This Unchangeableness of Colour I am now to
2717describe 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
2723Refrangibility, and that Colour cannot be changed by Reflexions and
2724Refractions._
2725
2726In the Experiments of the fourth Proposition of the first Part of this
2727first Book, when I had separated the heterogeneous Rays from one
2728another, the Spectrum _pt_ formed by the separated Rays, did in the
2729Progress from its End _p_, on which the most refrangible Rays fell, unto
2730its other End _t_, on which the least refrangible Rays fell, appear
2731tinged with this Series of Colours, violet, indigo, blue, green, yellow,
2732orange, red, together with all their intermediate Degrees in a continual
2733Succession perpetually varying. So that there appeared as many Degrees
2734of Colours, as there were sorts of Rays differing in Refrangibility.
2735
2736_Exper._ 5. Now, that these Colours could not be changed by Refraction,
2737I knew by refracting with a Prism sometimes one very little Part of this
2738Light, sometimes another very little Part, as is described in the
2739twelfth Experiment of the first Part of this Book. For by this
2740Refraction the Colour of the Light was never changed in the least. If
2741any Part of the red Light was refracted, it remained totally of the same
2742red Colour as before. No orange, no yellow, no green or blue, no other
2743new Colour was produced by that Refraction. Neither did the Colour any
2744ways change by repeated Refractions, but continued always the same red
2745entirely as at first. The like Constancy and Immutability I found also
2746in the blue, green, and other Colours. So also, if I looked through a
2747Prism upon any Body illuminated with any part of this homogeneal Light,
2748as in the fourteenth Experiment of the first Part of this Book is
2749described; I could not perceive any new Colour generated this way. All
2750Bodies illuminated with compound Light appear through Prisms confused,
2751(as was said above) and tinged with various new Colours, but those
2752illuminated with homogeneal Light appeared through Prisms neither less
2753distinct, nor otherwise colour'd, than when viewed with the naked Eyes.
2754Their Colours were not in the least changed by the Refraction of the
2755interposed Prism. I speak here of a sensible Change of Colour: For the
2756Light which I here call homogeneal, being not absolutely homogeneal,
2757there ought to arise some little Change of Colour from its
2758Heterogeneity. But, if that Heterogeneity was so little as it might be
2759made by the said Experiments of the fourth Proposition, that Change was
2760not sensible, and therefore in Experiments, where Sense is Judge, ought
2761to be accounted none at all.
2762
2763_Exper._ 6. And as these Colours were not changeable by Refractions, so
2764neither were they by Reflexions. For all white, grey, red, yellow,
2765green, blue, violet Bodies, as Paper, Ashes, red Lead, Orpiment, Indico
2766Bise, Gold, Silver, Copper, Grass, blue Flowers, Violets, Bubbles of
2767Water tinged with various Colours, Peacock's Feathers, the Tincture of
2768_Lignum Nephriticum_, and such-like, in red homogeneal Light appeared
2769totally red, in blue Light totally blue, in green Light totally green,
2770and so of other Colours. In the homogeneal Light of any Colour they all
2771appeared totally of that same Colour, with this only Difference, that
2772some of them reflected that Light more strongly, others more faintly. I
2773never yet found any Body, which by reflecting homogeneal Light could
2774sensibly change its Colour.
2775
2776From all which it is manifest, that if the Sun's Light consisted of but
2777one sort of Rays, there would be but one Colour in the whole World, nor
2778would it be possible to produce any new Colour by Reflexions and
2779Refractions, and by consequence that the variety of Colours depends upon
2780the Composition of Light.
2781
2782
2783_DEFINITION._
2784
2785The homogeneal Light and Rays which appear red, or rather make Objects
2786appear so, I call Rubrifick or Red-making; those which make Objects
2787appear yellow, green, blue, and violet, I call Yellow-making,
2788Green-making, Blue-making, Violet-making, and so of the rest. And if at
2789any time I speak of Light and Rays as coloured or endued with Colours, I
2790would be understood to speak not philosophically and properly, but
2791grossly, and accordingly to such Conceptions as vulgar People in seeing
2792all these Experiments would be apt to frame. For the Rays to speak
2793properly are not coloured. In them there is nothing else than a certain
2794Power and Disposition to stir up a Sensation of this or that Colour.
2795For as Sound in a Bell or musical String, or other sounding Body, is
2796nothing but a trembling Motion, and in the Air nothing but that Motion
2797propagated from the Object, and in the Sensorium 'tis a Sense of that
2798Motion under the Form of Sound; so Colours in the Object are nothing but
2799a Disposition to reflect this or that sort of Rays more copiously than
2800the rest; in the Rays they are nothing but their Dispositions to
2801propagate this or that Motion into the Sensorium, and in the Sensorium
2802they 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
2808answering to the several Colours._
2809
2810For determining this Problem I made the following Experiment.[J]
2811
2812_Exper._ 7. When I had caused the Rectilinear Sides AF, GM, [in _Fig._
28134.] of the Spectrum of Colours made by the Prism to be distinctly
2814defined, as in the fifth Experiment of the first Part of this Book is
2815described, there were found in it all the homogeneal Colours in the same
2816Order and Situation one among another as in the Spectrum of simple
2817Light, described in the fourth Proposition of that Part. For the Circles
2818of which the Spectrum of compound Light PT is composed, and which in
2819the middle Parts of the Spectrum interfere, and are intermix'd with one
2820another, are not intermix'd in their outmost Parts where they touch
2821those Rectilinear Sides AF and GM. And therefore, in those Rectilinear
2822Sides when distinctly defined, there is no new Colour generated by
2823Refraction. I observed also, that if any where between the two outmost
2824Circles TMF and PGA a Right Line, as [Greek: gd], was cross to the
2825Spectrum, so as both Ends to fall perpendicularly upon its Rectilinear
2826Sides, there appeared one and the same Colour, and degree of Colour from
2827one End of this Line to the other. I delineated therefore in a Paper the
2828Perimeter of the Spectrum FAP GMT, and in trying the third Experiment of
2829the first Part of this Book, I held the Paper so that the Spectrum might
2830fall upon this delineated Figure, and agree with it exactly, whilst an
2831Assistant, whose Eyes for distinguishing Colours were more critical than
2832mine, did by Right Lines [Greek: ab, gd, ez,] &c. drawn cross the
2833Spectrum, note the Confines of the Colours, that is of the red M[Greek:
2834ab]F, of the orange [Greek: agdb], of the yellow [Greek: gezd], of the
2835green [Greek: eêthz], of the blue [Greek: êikth], of the indico [Greek:
2836ilmk], and of the violet [Greek: l]GA[Greek: m]. And this Operation
2837being divers times repeated both in the same, and in several Papers, I
2838found that the Observations agreed well enough with one another, and
2839that the Rectilinear Sides MG and FA were by the said cross Lines
2840divided after the manner of a Musical Chord. Let GM be produced to X,
2841that 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
2843proportion to one another, as the Numbers, 1, 8/9, 5/6, 3/4, 2/3, 3/5,
28449/16, 1/2, and so to represent the Chords of the Key, and of a Tone, a
2845third Minor, a fourth, a fifth, a sixth Major, a seventh and an eighth
2846above 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
2848Spaces which the several Colours (red, orange, yellow, green, blue,
2849indigo, violet) take up.
2850
2851[Illustration: FIG. 4.]
2852
2853[Illustration: FIG. 5.]
2854
2855Now these Intervals or Spaces subtending the Differences of the
2856Refractions of the Rays going to the Limits of those Colours, that is,
2857to the Points M, [Greek: a], [Greek: g], [Greek: e], [Greek: ê], [Greek:
2858i], [Greek: l], G, may without any sensible Error be accounted
2859proportional to the Differences of the Sines of Refraction of those Rays
2860having one common Sine of Incidence, and therefore since the common Sine
2861of Incidence of the most and least refrangible Rays out of Glass into
2862Air was (by a Method described above) found in proportion to their Sines
2863of Refraction, as 50 to 77 and 78, divide the Difference between the
2864Sines of Refraction 77 and 78, as the Line GM is divided by those
2865Intervals, and you will have 77, 77-1/8, 77-1/5, 77-1/3, 77-1/2, 77-2/3,
286677-7/9, 78, the Sines of Refraction of those Rays out of Glass into Air,
2867their common Sine of Incidence being 50. So then the Sines of the
2868Incidences of all the red-making Rays out of Glass into Air, were to the
2869Sines of their Refractions, not greater than 50 to 77, nor less than 50
2870to 77-1/8, but they varied from one another according to all
2871intermediate Proportions. And the Sines of the Incidences of the
2872green-making Rays were to the Sines of their Refractions in all
2873Proportions from that of 50 to 77-1/3, unto that of 50 to 77-1/2. And
2874by the like Limits above-mentioned were the Refractions of the Rays
2875belonging to the rest of the Colours defined, the Sines of the
2876red-making Rays extending from 77 to 77-1/8, those of the orange-making
2877from 77-1/8 to 77-1/5, those of the yellow-making from 77-1/5 to 77-1/3,
2878those of the green-making from 77-1/3 to 77-1/2, those of the
2879blue-making from 77-1/2 to 77-2/3, those of the indigo-making from
288077-2/3 to 77-7/9, and those of the violet from 77-7/9, to 78.
2881
2882These are the Laws of the Refractions made out of Glass into Air, and
2883thence by the third Axiom of the first Part of this Book, the Laws of
2884the 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
2887several contiguous refracting Mediums as through Water and Glass, and
2888thence goes out again into Air, whether the refracting Superficies be
2889parallel or inclin'd to one another, that Light as often as by contrary
2890Refractions 'tis so corrected, that it emergeth in Lines parallel to
2891those in which it was incident, continues ever after to be white. But if
2892the emergent Rays be inclined to the incident, the Whiteness of the
2893emerging Light will by degrees in passing on from the Place of
2894Emergence, become tinged in its Edges with Colours. This I try'd by
2895refracting Light with Prisms of Glass placed within a Prismatick Vessel
2896of Water. Now those Colours argue a diverging and separation of the
2897heterogeneous Rays from one another by means of their unequal
2898Refractions, as in what follows will more fully appear. And, on the
2899contrary, the permanent whiteness argues, that in like Incidences of the
2900Rays there is no such separation of the emerging Rays, and by
2901consequence no inequality of their whole Refractions. Whence I seem to
2902gather the two following Theorems.
2903
29041. The Excesses of the Sines of Refraction of several sorts of Rays
2905above their common Sine of Incidence when the Refractions are made out
2906of divers denser Mediums immediately into one and the same rarer Medium,
2907suppose of Air, are to one another in a given Proportion.
2908
29092. The Proportion of the Sine of Incidence to the Sine of Refraction of
2910one and the same sort of Rays out of one Medium into another, is
2911composed of the Proportion of the Sine of Incidence to the Sine of
2912Refraction out of the first Medium into any third Medium, and of the
2913Proportion of the Sine of Incidence to the Sine of Refraction out of
2914that third Medium into the second Medium.
2915
2916By the first Theorem the Refractions of the Rays of every sort made out
2917of any Medium into Air are known by having the Refraction of the Rays of
2918any one sort. As for instance, if the Refractions of the Rays of every
2919sort out of Rain-water into Air be desired, let the common Sine of
2920Incidence out of Glass into Air be subducted from the Sines of
2921Refraction, and the Excesses will be 27, 27-1/8, 27-1/5, 27-1/3, 27-1/2,
292227-2/3, 27-7/9, 28. Suppose now that the Sine of Incidence of the least
2923refrangible Rays be to their Sine of Refraction out of Rain-water into
2924Air as 3 to 4, and say as 1 the difference of those Sines is to 3 the
2925Sine of Incidence, so is 27 the least of the Excesses above-mentioned to
2926a fourth Number 81; and 81 will be the common Sine of Incidence out of
2927Rain-water into Air, to which Sine if you add all the above-mentioned
2928Excesses, you will have the desired Sines of the Refractions 108,
2929108-1/8, 108-1/5, 108-1/3, 108-1/2, 108-2/3, 108-7/9, 109.
2930
2931By the latter Theorem the Refraction out of one Medium into another is
2932gathered as often as you have the Refractions out of them both into any
2933third Medium. As if the Sine of Incidence of any Ray out of Glass into
2934Air be to its Sine of Refraction, as 20 to 31, and the Sine of Incidence
2935of the same Ray out of Air into Water, be to its Sine of Refraction as 4
2936to 3; the Sine of Incidence of that Ray out of Glass into Water will be
2937to its Sine of Refraction as 20 to 31 and 4 to 3 jointly, that is, as
2938the Factum of 20 and 4 to the Factum of 31 and 3, or as 80 to 93.
2939
2940And these Theorems being admitted into Opticks, there would be scope
2941enough of handling that Science voluminously after a new manner,[K] not
2942only by teaching those things which tend to the perfection of Vision,
2943but also by determining mathematically all kinds of Phænomena of Colours
2944which could be produced by Refractions. For to do this, there is nothing
2945else requisite than to find out the Separations of heterogeneous Rays,
2946and their various Mixtures and Proportions in every Mixture. By this
2947way of arguing I invented almost all the Phænomena described in these
2948Books, beside some others less necessary to the Argument; and by the
2949successes I met with in the Trials, I dare promise, that to him who
2950shall argue truly, and then try all things with good Glasses and
2951sufficient Circumspection, the expected Event will not be wanting. But
2952he is first to know what Colours will arise from any others mix'd in any
2953assigned Proportion.
2954
2955
2956_PROP._ IV. THEOR. III.
2957
2958_Colours may be produced by Composition which shall be like to the
2959Colours of homogeneal Light as to the Appearance of Colour, but not as
2960to the Immutability of Colour and Constitution of Light. And those
2961Colours by how much they are more compounded by so much are they less
2962full and intense, and by too much Composition they maybe diluted and
2963weaken'd till they cease, and the Mixture becomes white or grey. There
2964may be also Colours produced by Composition, which are not fully like
2965any of the Colours of homogeneal Light._
2966
2967For a Mixture of homogeneal red and yellow compounds an Orange, like in
2968appearance of Colour to that orange which in the series of unmixed
2969prismatick Colours lies between them; but the Light of one orange is
2970homogeneal as to Refrangibility, and that of the other is heterogeneal,
2971and the Colour of the one, if viewed through a Prism, remains unchanged,
2972that of the other is changed and resolved into its component Colours red
2973and yellow. And after the same manner other neighbouring homogeneal
2974Colours may compound new Colours, like the intermediate homogeneal ones,
2975as yellow and green, the Colour between them both, and afterwards, if
2976blue be added, there will be made a green the middle Colour of the three
2977which enter the Composition. For the yellow and blue on either hand, if
2978they are equal in quantity they draw the intermediate green equally
2979towards themselves in Composition, and so keep it as it were in
2980Æquilibrion, that it verge not more to the yellow on the one hand, and
2981to the blue on the other, but by their mix'd Actions remain still a
2982middle Colour. To this mix'd green there may be farther added some red
2983and violet, and yet the green will not presently cease, but only grow
2984less full and vivid, and by increasing the red and violet, it will grow
2985more and more dilute, until by the prevalence of the added Colours it be
2986overcome and turned into whiteness, or some other Colour. So if to the
2987Colour of any homogeneal Light, the Sun's white Light composed of all
2988sorts of Rays be added, that Colour will not vanish or change its
2989Species, but be diluted, and by adding more and more white it will be
2990diluted more and more perpetually. Lastly, If red and violet be mingled,
2991there will be generated according to their various Proportions various
2992Purples, such as are not like in appearance to the Colour of any
2993homogeneal Light, and of these Purples mix'd with yellow and blue may be
2994made other new Colours.
2995
2996
2997_PROP._ V. THEOR. IV.
2998
2999_Whiteness and all grey Colours between white and black, may be
3000compounded of Colours, and the whiteness of the Sun's Light is
3001compounded of all the primary Colours mix'd in a due Proportion._
3002
3003The PROOF by Experiments.
3004
3005_Exper._ 9. The Sun shining into a dark Chamber through a little round
3006hole in the Window-shut, and his Light being there refracted by a Prism
3007to cast his coloured Image PT [in _Fig._ 5.] upon the opposite Wall: I
3008held a white Paper V to that image in such manner that it might be
3009illuminated by the colour'd Light reflected from thence, and yet not
3010intercept any part of that Light in its passage from the Prism to the
3011Spectrum. And I found that when the Paper was held nearer to any Colour
3012than to the rest, it appeared of that Colour to which it approached
3013nearest; but when it was equally or almost equally distant from all the
3014Colours, so that it might be equally illuminated by them all it appeared
3015white. And in this last situation of the Paper, if some Colours were
3016intercepted, the Paper lost its white Colour, and appeared of the Colour
3017of the rest of the Light which was not intercepted. So then the Paper
3018was illuminated with Lights of various Colours, namely, red, yellow,
3019green, blue and violet, and every part of the Light retained its proper
3020Colour, until it was incident on the Paper, and became reflected thence
3021to the Eye; so that if it had been either alone (the rest of the Light
3022being intercepted) or if it had abounded most, and been predominant in
3023the Light reflected from the Paper, it would have tinged the Paper with
3024its own Colour; and yet being mixed with the rest of the Colours in a
3025due proportion, it made the Paper look white, and therefore by a
3026Composition with the rest produced that Colour. The several parts of the
3027coloured Light reflected from the Spectrum, whilst they are propagated
3028from thence through the Air, do perpetually retain their proper Colours,
3029because wherever they fall upon the Eyes of any Spectator, they make the
3030several parts of the Spectrum to appear under their proper Colours. They
3031retain therefore their proper Colours when they fall upon the Paper V,
3032and so by the confusion and perfect mixture of those Colours compound
3033the whiteness of the Light reflected from thence.
3034
3035_Exper._ 10. Let that Spectrum or solar Image PT [in _Fig._ 6.] fall now
3036upon the Lens MN above four Inches broad, and about six Feet distant
3037from the Prism ABC and so figured that it may cause the coloured Light
3038which divergeth from the Prism to converge and meet again at its Focus
3039G, about six or eight Feet distant from the Lens, and there to fall
3040perpendicularly upon a white Paper DE. And if you move this Paper to and
3041fro, you will perceive that near the Lens, as at _de_, the whole solar
3042Image (suppose at _pt_) will appear upon it intensely coloured after the
3043manner above-explained, and that by receding from the Lens those Colours
3044will perpetually come towards one another, and by mixing more and more
3045dilute one another continually, until at length the Paper come to the
3046Focus G, where by a perfect mixture they will wholly vanish and be
3047converted into whiteness, the whole Light appearing now upon the Paper
3048like a little white Circle. And afterwards by receding farther from the
3049Lens, the Rays which before converged will now cross one another in the
3050Focus G, and diverge from thence, and thereby make the Colours to appear
3051again, but yet in a contrary order; suppose at [Greek: de], where the
3052red _t_ is now above which before was below, and the violet _p_ is below
3053which before was above.
3054
3055Let us now stop the Paper at the Focus G, where the Light appears
3056totally white and circular, and let us consider its whiteness. I say,
3057that this is composed of the converging Colours. For if any of those
3058Colours be intercepted at the Lens, the whiteness will cease and
3059degenerate into that Colour which ariseth from the composition of the
3060other Colours which are not intercepted. And then if the intercepted
3061Colours be let pass and fall upon that compound Colour, they mix with
3062it, and by their mixture restore the whiteness. So if the violet, blue
3063and green be intercepted, the remaining yellow, orange and red will
3064compound upon the Paper an orange, and then if the intercepted Colours
3065be let pass, they will fall upon this compounded orange, and together
3066with it decompound a white. So also if the red and violet be
3067intercepted, the remaining yellow, green and blue, will compound a green
3068upon the Paper, and then the red and violet being let pass will fall
3069upon this green, and together with it decompound a white. And that in
3070this Composition of white the several Rays do not suffer any Change in
3071their colorific Qualities by acting upon one another, but are only
3072mixed, and by a mixture of their Colours produce white, may farther
3073appear by these Arguments.
3074
3075[Illustration: FIG. 6.]
3076
3077If the Paper be placed beyond the Focus G, suppose at [Greek: de], and
3078then the red Colour at the Lens be alternately intercepted, and let pass
3079again, the violet Colour on the Paper will not suffer any Change
3080thereby, as it ought to do if the several sorts of Rays acted upon one
3081another in the Focus G, where they cross. Neither will the red upon the
3082Paper be changed by any alternate stopping, and letting pass the violet
3083which crosseth it.
3084
3085And if the Paper be placed at the Focus G, and the white round Image at
3086G be viewed through the Prism HIK, and by the Refraction of that Prism
3087be translated to the place _rv_, and there appear tinged with various
3088Colours, namely, the violet at _v_ and red at _r_, and others between,
3089and then the red Colours at the Lens be often stopp'd and let pass by
3090turns, the red at _r_ will accordingly disappear, and return as often,
3091but the violet at _v_ will not thereby suffer any Change. And so by
3092stopping and letting pass alternately the blue at the Lens, the blue at
3093_v_ will accordingly disappear and return, without any Change made in
3094the red at _r_. The red therefore depends on one sort of Rays, and the
3095blue on another sort, which in the Focus G where they are commix'd, do
3096not act on one another. And there is the same Reason of the other
3097Colours.
3098
3099I considered farther, that when the most refrangible Rays P_p_, and the
3100least refrangible ones T_t_, are by converging inclined to one another,
3101the Paper, if held very oblique to those Rays in the Focus G, might
3102reflect one sort of them more copiously than the other sort, and by that
3103Means the reflected Light would be tinged in that Focus with the Colour
3104of the predominant Rays, provided those Rays severally retained their
3105Colours, or colorific Qualities in the Composition of White made by them
3106in that Focus. But if they did not retain them in that White, but became
3107all of them severally endued there with a Disposition to strike the
3108Sense with the Perception of White, then they could never lose their
3109Whiteness by such Reflexions. I inclined therefore the Paper to the Rays
3110very obliquely, as in the second Experiment of this second Part of the
3111first Book, that the most refrangible Rays, might be more copiously
3112reflected than the rest, and the Whiteness at Length changed
3113successively into blue, indigo, and violet. Then I inclined it the
3114contrary Way, that the least refrangible Rays might be more copious in
3115the reflected Light than the rest, and the Whiteness turned successively
3116to yellow, orange, and red.
3117
3118Lastly, I made an Instrument XY in fashion of a Comb, whose Teeth being
3119in number sixteen, were about an Inch and a half broad, and the
3120Intervals of the Teeth about two Inches wide. Then by interposing
3121successively the Teeth of this Instrument near the Lens, I intercepted
3122Part of the Colours by the interposed Tooth, whilst the rest of them
3123went on through the Interval of the Teeth to the Paper DE, and there
3124painted a round Solar Image. But the Paper I had first placed so, that
3125the Image might appear white as often as the Comb was taken away; and
3126then the Comb being as was said interposed, that Whiteness by reason of
3127the intercepted Part of the Colours at the Lens did always change into
3128the Colour compounded of those Colours which were not intercepted, and
3129that Colour was by the Motion of the Comb perpetually varied so, that in
3130the passing of every Tooth over the Lens all these Colours, red, yellow,
3131green, blue, and purple, did always succeed one another. I caused
3132therefore all the Teeth to pass successively over the Lens, and when the
3133Motion was slow, there appeared a perpetual Succession of the Colours
3134upon the Paper: But if I so much accelerated the Motion, that the
3135Colours by reason of their quick Succession could not be distinguished
3136from one another, the Appearance of the single Colours ceased. There was
3137no red, no yellow, no green, no blue, nor purple to be seen any longer,
3138but from a Confusion of them all there arose one uniform white Colour.
3139Of the Light which now by the Mixture of all the Colours appeared white,
3140there was no Part really white. One Part was red, another yellow, a
3141third green, a fourth blue, a fifth purple, and every Part retains its
3142proper Colour till it strike the Sensorium. If the Impressions follow
3143one another slowly, so that they may be severally perceived, there is
3144made a distinct Sensation of all the Colours one after another in a
3145continual Succession. But if the Impressions follow one another so
3146quickly, that they cannot be severally perceived, there ariseth out of
3147them all one common Sensation, which is neither of this Colour alone nor
3148of that alone, but hath it self indifferently to 'em all, and this is a
3149Sensation of Whiteness. By the Quickness of the Successions, the
3150Impressions of the several Colours are confounded in the Sensorium, and
3151out of that Confusion ariseth a mix'd Sensation. If a burning Coal be
3152nimbly moved round in a Circle with Gyrations continually repeated, the
3153whole Circle will appear like Fire; the reason of which is, that the
3154Sensation of the Coal in the several Places of that Circle remains
3155impress'd on the Sensorium, until the Coal return again to the same
3156Place. And so in a quick Consecution of the Colours the Impression of
3157every Colour remains in the Sensorium, until a Revolution of all the
3158Colours be compleated, and that first Colour return again. The
3159Impressions therefore of all the successive Colours are at once in the
3160Sensorium, and jointly stir up a Sensation of them all; and so it is
3161manifest by this Experiment, that the commix'd Impressions of all the
3162Colours do stir up and beget a Sensation of white, that is, that
3163Whiteness is compounded of all the Colours.
3164
3165And if the Comb be now taken away, that all the Colours may at once pass
3166from the Lens to the Paper, and be there intermixed, and together
3167reflected thence to the Spectator's Eyes; their Impressions on the
3168Sensorium being now more subtilly and perfectly commixed there, ought
3169much more to stir up a Sensation of Whiteness.
3170
3171You may instead of the Lens use two Prisms HIK and LMN, which by
3172refracting the coloured Light the contrary Way to that of the first
3173Refraction, may make the diverging Rays converge and meet again in G, as
3174you see represented in the seventh Figure. For where they meet and mix,
3175they 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
3178the Wall of a dark Chamber, as in the third Experiment of the first
3179Book, and let the same be viewed through a Prism _abc_, held parallel to
3180the Prism ABC, by whose Refraction that Image was made, and let it now
3181appear lower than before, suppose in the Place S over-against the red
3182Colour T. And if you go near to the Image PT, the Spectrum S will appear
3183oblong and coloured like the Image PT; but if you recede from it, the
3184Colours of the spectrum S will be contracted more and more, and at
3185length vanish, that Spectrum S becoming perfectly round and white; and
3186if you recede yet farther, the Colours will emerge again, but in a
3187contrary Order. Now that Spectrum S appears white in that Case, when the
3188Rays of several sorts which converge from the several Parts of the Image
3189PT, to the Prism _abc_, are so refracted unequally by it, that in their
3190Passage from the Prism to the Eye they may diverge from one and the same
3191Point of the Spectrum S, and so fall afterwards upon one and the same
3192Point in the bottom of the Eye, and there be mingled.
3193
3194[Illustration: FIG. 7.]
3195
3196[Illustration: FIG. 8.]
3197
3198And farther, if the Comb be here made use of, by whose Teeth the Colours
3199at the Image PT may be successively intercepted; the Spectrum S, when
3200the Comb is moved slowly, will be perpetually tinged with successive
3201Colours: But when by accelerating the Motion of the Comb, the Succession
3202of the Colours is so quick that they cannot be severally seen, that
3203Spectrum S, by a confused and mix'd Sensation of them all, will appear
3204white.
3205
3206_Exper._ 12. The Sun shining through a large Prism ABC [in _Fig._ 9.]
3207upon a Comb XY, placed immediately behind the Prism, his Light which
3208passed through the Interstices of the Teeth fell upon a white Paper DE.
3209The Breadths of the Teeth were equal to their Interstices, and seven
3210Teeth together with their Interstices took up an Inch in Breadth. Now,
3211when the Paper was about two or three Inches distant from the Comb, the
3212Light which passed through its several Interstices painted so many
3213Ranges of Colours, _kl_, _mn_, _op_, _qr_, &c. which were parallel to
3214one another, and contiguous, and without any Mixture of white. And these
3215Ranges of Colours, if the Comb was moved continually up and down with a
3216reciprocal Motion, ascended and descended in the Paper, and when the
3217Motion of the Comb was so quick, that the Colours could not be
3218distinguished from one another, the whole Paper by their Confusion and
3219Mixture in the Sensorium appeared white.
3220
3221[Illustration: FIG. 9.]
3222
3223Let the Comb now rest, and let the Paper be removed farther from the
3224Prism, and the several Ranges of Colours will be dilated and expanded
3225into one another more and more, and by mixing their Colours will dilute
3226one another, and at length, when the distance of the Paper from the Comb
3227is about a Foot, or a little more (suppose in the Place 2D 2E) they will
3228so far dilute one another, as to become white.
3229
3230With any Obstacle, let all the Light be now stopp'd which passes through
3231any one Interval of the Teeth, so that the Range of Colours which comes
3232from thence may be taken away, and you will see the Light of the rest of
3233the Ranges to be expanded into the Place of the Range taken away, and
3234there to be coloured. Let the intercepted Range pass on as before, and
3235its Colours falling upon the Colours of the other Ranges, and mixing
3236with them, will restore the Whiteness.
3237
3238Let the Paper 2D 2E be now very much inclined to the Rays, so that the
3239most refrangible Rays may be more copiously reflected than the rest, and
3240the white Colour of the Paper through the Excess of those Rays will be
3241changed into blue and violet. Let the Paper be as much inclined the
3242contrary way, that the least refrangible Rays may be now more copiously
3243reflected than the rest, and by their Excess the Whiteness will be
3244changed into yellow and red. The several Rays therefore in that white
3245Light do retain their colorific Qualities, by which those of any sort,
3246whenever they become more copious than the rest, do by their Excess and
3247Predominance cause their proper Colour to appear.
3248
3249And by the same way of arguing, applied to the third Experiment of this
3250second Part of the first Book, it may be concluded, that the white
3251Colour of all refracted Light at its very first Emergence, where it
3252appears as white as before its Incidence, is compounded of various
3253Colours.
3254
3255[Illustration: FIG. 10.]
3256
3257_Exper._ 13. In the foregoing Experiment the several Intervals of the
3258Teeth of the Comb do the Office of so many Prisms, every Interval
3259producing the Phænomenon of one Prism. Whence instead of those Intervals
3260using several Prisms, I try'd to compound Whiteness by mixing their
3261Colours, and did it by using only three Prisms, as also by using only
3262two as follows. Let two Prisms ABC and _abc_, [in _Fig._ 10.] whose
3263refracting Angles B and _b_ are equal, be so placed parallel to one
3264another, that the refracting Angle B of the one may touch the Angle _c_
3265at the Base of the other, and their Planes CB and _cb_, at which the
3266Rays emerge, may lie in Directum. Then let the Light trajected through
3267them fall upon the Paper MN, distant about 8 or 12 Inches from the
3268Prisms. And the Colours generated by the interior Limits B and _c_ of
3269the two Prisms, will be mingled at PT, and there compound white. For if
3270either Prism be taken away, the Colours made by the other will appear in
3271that Place PT, and when the Prism is restored to its Place again, so
3272that its Colours may there fall upon the Colours of the other, the
3273Mixture of them both will restore the Whiteness.
3274
3275This Experiment succeeds also, as I have tried, when the Angle _b_ of
3276the lower Prism, is a little greater than the Angle B of the upper, and
3277between the interior Angles B and _c_, there intercedes some Space B_c_,
3278as is represented in the Figure, and the refracting Planes BC and _bc_,
3279are neither in Directum, nor parallel to one another. For there is
3280nothing more requisite to the Success of this Experiment, than that the
3281Rays of all sorts may be uniformly mixed upon the Paper in the Place PT.
3282If the most refrangible Rays coming from the superior Prism take up all
3283the Space from M to P, the Rays of the same sort which come from the
3284inferior Prism ought to begin at P, and take up all the rest of the
3285Space from thence towards N. If the least refrangible Rays coming from
3286the superior Prism take up the Space MT, the Rays of the same kind which
3287come from the other Prism ought to begin at T, and take up the
3288remaining Space TN. If one sort of the Rays which have intermediate
3289Degrees of Refrangibility, and come from the superior Prism be extended
3290through the Space MQ, and another sort of those Rays through the Space
3291MR, and a third sort of them through the Space MS, the same sorts of
3292Rays coming from the lower Prism, ought to illuminate the remaining
3293Spaces QN, RN, SN, respectively. And the same is to be understood of all
3294the other sorts of Rays. For thus the Rays of every sort will be
3295scattered uniformly and evenly through the whole Space MN, and so being
3296every where mix'd in the same Proportion, they must every where produce
3297the same Colour. And therefore, since by this Mixture they produce white
3298in the Exterior Spaces MP and TN, they must also produce white in the
3299Interior Space PT. This is the reason of the Composition by which
3300Whiteness was produced in this Experiment, and by what other way soever
3301I made the like Composition, the Result was Whiteness.
3302
3303Lastly, If with the Teeth of a Comb of a due Size, the coloured Lights
3304of the two Prisms which fall upon the Space PT be alternately
3305intercepted, that Space PT, when the Motion of the Comb is slow, will
3306always appear coloured, but by accelerating the Motion of the Comb so
3307much that the successive Colours cannot be distinguished from one
3308another, it will appear white.
3309
3310_Exper._ 14. Hitherto I have produced Whiteness by mixing the Colours of
3311Prisms. If now the Colours of natural Bodies are to be mingled, let
3312Water a little thicken'd with Soap be agitated to raise a Froth, and
3313after that Froth has stood a little, there will appear to one that shall
3314view it intently various Colours every where in the Surfaces of the
3315several Bubbles; but to one that shall go so far off, that he cannot
3316distinguish the Colours from one another, the whole Froth will grow
3317white with a perfect Whiteness.
3318
3319_Exper._ 15. Lastly, In attempting to compound a white, by mixing the
3320coloured Powders which Painters use, I consider'd that all colour'd
3321Powders do suppress and stop in them a very considerable Part of the
3322Light by which they are illuminated. For they become colour'd by
3323reflecting the Light of their own Colours more copiously, and that of
3324all other Colours more sparingly, and yet they do not reflect the Light
3325of their own Colours so copiously as white Bodies do. If red Lead, for
3326instance, and a white Paper, be placed in the red Light of the colour'd
3327Spectrum made in a dark Chamber by the Refraction of a Prism, as is
3328described in the third Experiment of the first Part of this Book; the
3329Paper will appear more lucid than the red Lead, and therefore reflects
3330the red-making Rays more copiously than red Lead doth. And if they be
3331held in the Light of any other Colour, the Light reflected by the Paper
3332will exceed the Light reflected by the red Lead in a much greater
3333Proportion. And the like happens in Powders of other Colours. And
3334therefore by mixing such Powders, we are not to expect a strong and
3335full White, such as is that of Paper, but some dusky obscure one, such
3336as might arise from a Mixture of Light and Darkness, or from white and
3337black, that is, a grey, or dun, or russet brown, such as are the Colours
3338of a Man's Nail, of a Mouse, of Ashes, of ordinary Stones, of Mortar, of
3339Dust and Dirt in High-ways, and the like. And such a dark white I have
3340often produced by mixing colour'd Powders. For thus one Part of red
3341Lead, and five Parts of _Viride Æris_, composed a dun Colour like that
3342of a Mouse. For these two Colours were severally so compounded of
3343others, that in both together were a Mixture of all Colours; and there
3344was less red Lead used than _Viride Æris_, because of the Fulness of its
3345Colour. Again, one Part of red Lead, and four Parts of blue Bise,
3346composed a dun Colour verging a little to purple, and by adding to this
3347a certain Mixture of Orpiment and _Viride Æris_ in a due Proportion, the
3348Mixture lost its purple Tincture, and became perfectly dun. But the
3349Experiment succeeded best without Minium thus. To Orpiment I added by
3350little and little a certain full bright purple, which Painters use,
3351until the Orpiment ceased to be yellow, and became of a pale red. Then I
3352diluted that red by adding a little _Viride Æris_, and a little more
3353blue Bise than _Viride Æris_, until it became of such a grey or pale
3354white, as verged to no one of the Colours more than to another. For thus
3355it became of a Colour equal in Whiteness to that of Ashes, or of Wood
3356newly cut, or of a Man's Skin. The Orpiment reflected more Light than
3357did any other of the Powders, and therefore conduced more to the
3358Whiteness of the compounded Colour than they. To assign the Proportions
3359accurately may be difficult, by reason of the different Goodness of
3360Powders of the same kind. Accordingly, as the Colour of any Powder is
3361more or less full and luminous, it ought to be used in a less or greater
3362Proportion.
3363
3364Now, considering that these grey and dun Colours may be also produced by
3365mixing Whites and Blacks, and by consequence differ from perfect Whites,
3366not in Species of Colours, but only in degree of Luminousness, it is
3367manifest that there is nothing more requisite to make them perfectly
3368white than to increase their Light sufficiently; and, on the contrary,
3369if by increasing their Light they can be brought to perfect Whiteness,
3370it will thence also follow, that they are of the same Species of Colour
3371with the best Whites, and differ from them only in the Quantity of
3372Light. And this I tried as follows. I took the third of the
3373above-mention'd grey Mixtures, (that which was compounded of Orpiment,
3374Purple, Bise, and _Viride Æris_) and rubbed it thickly upon the Floor of
3375my Chamber, where the Sun shone upon it through the opened Casement; and
3376by it, in the shadow, I laid a Piece of white Paper of the same Bigness.
3377Then going from them to the distance of 12 or 18 Feet, so that I could
3378not discern the Unevenness of the Surface of the Powder, nor the little
3379Shadows let fall from the gritty Particles thereof; the Powder appeared
3380intensely white, so as to transcend even the Paper it self in Whiteness,
3381especially if the Paper were a little shaded from the Light of the
3382Clouds, and then the Paper compared with the Powder appeared of such a
3383grey Colour as the Powder had done before. But by laying the Paper where
3384the Sun shines through the Glass of the Window, or by shutting the
3385Window that the Sun might shine through the Glass upon the Powder, and
3386by such other fit Means of increasing or decreasing the Lights wherewith
3387the Powder and Paper were illuminated, the Light wherewith the Powder is
3388illuminated may be made stronger in such a due Proportion than the Light
3389wherewith the Paper is illuminated, that they shall both appear exactly
3390alike in Whiteness. For when I was trying this, a Friend coming to visit
3391me, I stopp'd him at the Door, and before I told him what the Colours
3392were, or what I was doing; I asked him, Which of the two Whites were the
3393best, and wherein they differed? And after he had at that distance
3394viewed them well, he answer'd, that they were both good Whites, and that
3395he could not say which was best, nor wherein their Colours differed.
3396Now, if you consider, that this White of the Powder in the Sun-shine was
3397compounded of the Colours which the component Powders (Orpiment, Purple,
3398Bise, and _Viride Æris_) have in the same Sun-shine, you must
3399acknowledge by this Experiment, as well as by the former, that perfect
3400Whiteness may be compounded of Colours.
3401
3402From what has been said it is also evident, that the Whiteness of the
3403Sun's Light is compounded of all the Colours wherewith the several sorts
3404of Rays whereof that Light consists, when by their several
3405Refrangibilities they are separated from one another, do tinge Paper or
3406any other white Body whereon they fall. For those Colours (by _Prop._
3407II. _Part_ 2.) are unchangeable, and whenever all those Rays with those
3408their Colours are mix'd again, they reproduce the same white Light as
3409before.
3410
3411
3412_PROP._ VI. PROB. II.
3413
3414_In a mixture of Primary Colours, the Quantity and Quality of each being
3415given, to know the Colour of the Compound._
3416
3417[Illustration: FIG. 11.]
3418
3419With the Center O [in _Fig._ 11.] and Radius OD describe a Circle ADF,
3420and distinguish its Circumference into seven Parts DE, EF, FG, GA, AB,
3421BC, CD, proportional to the seven Musical Tones or Intervals of the
3422eight Sounds, _Sol_, _la_, _fa_, _sol_, _la_, _mi_, _fa_, _sol_,
3423contained in an eight, that is, proportional to the Number 1/9, 1/16,
34241/10, 1/9, 1/16, 1/16, 1/9. Let the first Part DE represent a red
3425Colour, the second EF orange, the third FG yellow, the fourth CA green,
3426the fifth AB blue, the sixth BC indigo, and the seventh CD violet. And
3427conceive that these are all the Colours of uncompounded Light gradually
3428passing into one another, as they do when made by Prisms; the
3429Circumference DEFGABCD, representing the whole Series of Colours from
3430one end of the Sun's colour'd Image to the other, so that from D to E be
3431all degrees of red, at E the mean Colour between red and orange, from E
3432to F all degrees of orange, at F the mean between orange and yellow,
3433from F to G all degrees of yellow, and so on. Let _p_ be the Center of
3434Gravity of the Arch DE, and _q_, _r_, _s_, _t_, _u_, _x_, the Centers of
3435Gravity of the Arches EF, FG, GA, AB, BC, and CD respectively, and about
3436those Centers of Gravity let Circles proportional to the Number of Rays
3437of 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,
3439the Circle _q_ proportional to the Number of the orange-making Rays in
3440the Mixture, and so of the rest. Find the common Center of Gravity of
3441all those Circles, _p_, _q_, _r_, _s_, _t_, _u_, _x_. Let that Center be
3442Z; and from the Center of the Circle ADF, through Z to the
3443Circumference, drawing the Right Line OY, the Place of the Point Y in
3444the Circumference shall shew the Colour arising from the Composition of
3445all the Colours in the given Mixture, and the Line OZ shall be
3446proportional to the Fulness or Intenseness of the Colour, that is, to
3447its distance from Whiteness. As if Y fall in the middle between F and G,
3448the compounded Colour shall be the best yellow; if Y verge from the
3449middle towards F or G, the compound Colour shall accordingly be a
3450yellow, verging towards orange or green. If Z fall upon the
3451Circumference, the Colour shall be intense and florid in the highest
3452Degree; if it fall in the mid-way between the Circumference and Center,
3453it shall be but half so intense, that is, it shall be such a Colour as
3454would be made by diluting the intensest yellow with an equal quantity of
3455whiteness; and if it fall upon the center O, the Colour shall have lost
3456all its intenseness, and become a white. But it is to be noted, That if
3457the point Z fall in or near the line OD, the main ingredients being the
3458red and violet, the Colour compounded shall not be any of the prismatick
3459Colours, but a purple, inclining to red or violet, accordingly as the
3460point Z lieth on the side of the line DO towards E or towards C, and in
3461general the compounded violet is more bright and more fiery than the
3462uncompounded. Also if only two of the primary Colours which in the
3463circle are opposite to one another be mixed in an equal proportion, the
3464point Z shall fall upon the center O, and yet the Colour compounded of
3465those two shall not be perfectly white, but some faint anonymous Colour.
3466For I could never yet by mixing only two primary Colours produce a
3467perfect white. Whether it may be compounded of a mixture of three taken
3468at equal distances in the circumference I do not know, but of four or
3469five I do not much question but it may. But these are Curiosities of
3470little or no moment to the understanding the Phænomena of Nature. For in
3471all whites produced by Nature, there uses to be a mixture of all sorts
3472of Rays, and by consequence a composition of all Colours.
3473
3474To give an instance of this Rule; suppose a Colour is compounded of
3475these homogeneal Colours, of violet one part, of indigo one part, of
3476blue two parts, of green three parts, of yellow five parts, of orange
3477six parts, and of red ten parts. Proportional to these parts describe
3478the Circles _x_, _v_, _t_, _s_, _r_, _q_, _p_, respectively, that is, so
3479that if the Circle _x_ be one, the Circle _v_ may be one, the Circle _t_
3480two, the Circle _s_ three, and the Circles _r_, _q_ and _p_, five, six
3481and ten. Then I find Z the common center of gravity of these Circles,
3482and through Z drawing the Line OY, the Point Y falls upon the
3483circumference between E and F, something nearer to E than to F, and
3484thence I conclude, that the Colour compounded of these Ingredients will
3485be an orange, verging a little more to red than to yellow. Also I find
3486that OZ is a little less than one half of OY, and thence I conclude,
3487that this orange hath a little less than half the fulness or intenseness
3488of an uncompounded orange; that is to say, that it is such an orange as
3489may be made by mixing an homogeneal orange with a good white in the
3490proportion of the Line OZ to the Line ZY, this Proportion being not of
3491the quantities of mixed orange and white Powders, but of the quantities
3492of the Lights reflected from them.
3493
3494This Rule I conceive accurate enough for practice, though not
3495mathematically accurate; and the truth of it may be sufficiently proved
3496to Sense, by stopping any of the Colours at the Lens in the tenth
3497Experiment of this Book. For the rest of the Colours which are not
3498stopp'd, but pass on to the Focus of the Lens, will there compound
3499either accurately or very nearly such a Colour, as by this Rule ought to
3500result 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
3506on the Power of Imagination, are either the Colours of homogeneal
3507Lights, or compounded of these, and that either accurately or very
3508nearly, according to the Rule of the foregoing Problem._
3509
3510For it has been proved (in _Prop. 1. Part 2._) that the changes of
3511Colours made by Refractions do not arise from any new Modifications of
3512the Rays impress'd by those Refractions, and by the various Terminations
3513of Light and Shadow, as has been the constant and general Opinion of
3514Philosophers. It has also been proved that the several Colours of the
3515homogeneal Rays do constantly answer to their degrees of Refrangibility,
3516(_Prop._ 1. _Part_ 1. and _Prop._ 2. _Part_ 2.) and that their degrees
3517of Refrangibility cannot be changed by Refractions and Reflexions
3518(_Prop._ 2. _Part_ 1.) and by consequence that those their Colours are
3519likewise immutable. It has also been proved directly by refracting and
3520reflecting homogeneal Lights apart, that their Colours cannot be
3521changed, (_Prop._ 2. _Part_ 2.) It has been proved also, that when the
3522several sorts of Rays are mixed, and in crossing pass through the same
3523space, they do not act on one another so as to change each others
3524colorific qualities. (_Exper._ 10. _Part_ 2.) but by mixing their
3525Actions in the Sensorium beget a Sensation differing from what either
3526would do apart, that is a Sensation of a mean Colour between their
3527proper Colours; and particularly when by the concourse and mixtures of
3528all sorts of Rays, a white Colour is produced, the white is a mixture of
3529all the Colours which the Rays would have apart, (_Prop._ 5. _Part_ 2.)
3530The Rays in that mixture do not lose or alter their several colorific
3531qualities, but by all their various kinds of Actions mix'd in the
3532Sensorium, beget a Sensation of a middling Colour between all their
3533Colours, which is whiteness. For whiteness is a mean between all
3534Colours, having it self indifferently to them all, so as with equal
3535facility to be tinged with any of them. A red Powder mixed with a little
3536blue, or a blue with a little red, doth not presently lose its Colour,
3537but a white Powder mix'd with any Colour is presently tinged with that
3538Colour, and is equally capable of being tinged with any Colour whatever.
3539It has been shewed also, that as the Sun's Light is mix'd of all sorts
3540of Rays, so its whiteness is a mixture of the Colours of all sorts of
3541Rays; those Rays having from the beginning their several colorific
3542qualities as well as their several Refrangibilities, and retaining them
3543perpetually unchanged notwithstanding any Refractions or Reflexions they
3544may at any time suffer, and that whenever any sort of the Sun's Rays is
3545by any means (as by Reflexion in _Exper._ 9, and 10. _Part_ 1. or by
3546Refraction as happens in all Refractions) separated from the rest, they
3547then manifest their proper Colours. These things have been prov'd, and
3548the sum of all this amounts to the Proposition here to be proved. For if
3549the Sun's Light is mix'd of several sorts of Rays, each of which have
3550originally their several Refrangibilities and colorific Qualities, and
3551notwithstanding their Refractions and Reflexions, and their various
3552Separations or Mixtures, keep those their original Properties
3553perpetually the same without alteration; then all the Colours in the
3554World must be such as constantly ought to arise from the original
3555colorific qualities of the Rays whereof the Lights consist by which
3556those Colours are seen. And therefore if the reason of any Colour
3557whatever be required, we have nothing else to do than to consider how
3558the Rays in the Sun's Light have by Reflexions or Refractions, or other
3559causes, been parted from one another, or mixed together; or otherwise to
3560find out what sorts of Rays are in the Light by which that Colour is
3561made, and in what Proportion; and then by the last Problem to learn the
3562Colour which ought to arise by mixing those Rays (or their Colours) in
3563that proportion. I speak here of Colours so far as they arise from
3564Light. For they appear sometimes by other Causes, as when by the power
3565of Phantasy we see Colours in a Dream, or a Mad-man sees things before
3566him which are not there; or when we see Fire by striking the Eye, or see
3567Colours like the Eye of a Peacock's Feather, by pressing our Eyes in
3568either corner whilst we look the other way. Where these and such like
3569Causes interpose not, the Colour always answers to the sort or sorts of
3570the Rays whereof the Light consists, as I have constantly found in
3571whatever Phænomena of Colours I have hitherto been able to examine. I
3572shall in the following Propositions give instances of this in the
3573Phænomena of chiefest note.
3574
3575
3576_PROP._ VIII. PROB. III.
3577
3578_By the discovered Properties of Light to explain the Colours made by
3579Prisms._
3580
3581Let ABC [in _Fig._ 12.] represent a Prism refracting the Light of the
3582Sun, which comes into a dark Chamber through a hole F[Greek: ph] almost
3583as broad as the Prism, and let MN represent a white Paper on which the
3584refracted Light is cast, and suppose the most refrangible or deepest
3585violet-making Rays fall upon the Space P[Greek: p], the least
3586refrangible or deepest red-making Rays upon the Space T[Greek: t], the
3587middle sort between the indigo-making and blue-making Rays upon the
3588Space Q[Greek: ch], the middle sort of the green-making Rays upon the
3589Space R, the middle sort between the yellow-making and orange-making
3590Rays upon the Space S[Greek: s], and other intermediate sorts upon
3591intermediate Spaces. For so the Spaces upon which the several sorts
3592adequately fall will by reason of the different Refrangibility of those
3593sorts be one lower than another. Now if the Paper MN be so near the
3594Prism that the Spaces PT and [Greek: pt] do not interfere with one
3595another, the distance between them T[Greek: p] will be illuminated by
3596all the sorts of Rays in that proportion to one another which they have
3597at their very first coming out of the Prism, and consequently be white.
3598But the Spaces PT and [Greek: pt] on either hand, will not be
3599illuminated by them all, and therefore will appear coloured. And
3600particularly at P, where the outmost violet-making Rays fall alone, the
3601Colour must be the deepest violet. At Q where the violet-making and
3602indigo-making Rays are mixed, it must be a violet inclining much to
3603indigo. At R where the violet-making, indigo-making, blue-making, and
3604one half of the green-making Rays are mixed, their Colours must (by the
3605construction of the second Problem) compound a middle Colour between
3606indigo and blue. At S where all the Rays are mixed, except the
3607red-making and orange-making, their Colours ought by the same Rule to
3608compound a faint blue, verging more to green than indigo. And in the
3609progress from S to T, this blue will grow more and more faint and
3610dilute, till at T, where all the Colours begin to be mixed, it ends in
3611whiteness.
3612
3613[Illustration: FIG. 12.]
3614
3615So again, on the other side of the white at [Greek: t], where the least
3616refrangible or utmost red-making Rays are alone, the Colour must be the
3617deepest red. At [Greek: s] the mixture of red and orange will compound a
3618red inclining to orange. At [Greek: r] the mixture of red, orange,
3619yellow, and one half of the green must compound a middle Colour between
3620orange and yellow. At [Greek: ch] the mixture of all Colours but violet
3621and indigo will compound a faint yellow, verging more to green than to
3622orange. And this yellow will grow more faint and dilute continually in
3623its progress from [Greek: ch] to [Greek: p], where by a mixture of all
3624sorts of Rays it will become white.
3625
3626These Colours ought to appear were the Sun's Light perfectly white: But
3627because it inclines to yellow, the Excess of the yellow-making Rays
3628whereby 'tis tinged with that Colour, being mixed with the faint blue
3629between S and T, will draw it to a faint green. And so the Colours in
3630order from P to [Greek: t] ought to be violet, indigo, blue, very faint
3631green, white, faint yellow, orange, red. Thus it is by the computation:
3632And they that please to view the Colours made by a Prism will find it so
3633in Nature.
3634
3635These are the Colours on both sides the white when the Paper is held
3636between the Prism and the Point X where the Colours meet, and the
3637interjacent white vanishes. For if the Paper be held still farther off
3638from the Prism, the most refrangible and least refrangible Rays will be
3639wanting in the middle of the Light, and the rest of the Rays which are
3640found there, will by mixture produce a fuller green than before. Also
3641the yellow and blue will now become less compounded, and by consequence
3642more intense than before. And this also agrees with experience.
3643
3644And if one look through a Prism upon a white Object encompassed with
3645blackness or darkness, the reason of the Colours arising on the edges is
3646much the same, as will appear to one that shall a little consider it. If
3647a black Object be encompassed with a white one, the Colours which appear
3648through the Prism are to be derived from the Light of the white one,
3649spreading into the Regions of the black, and therefore they appear in a
3650contrary order to that, when a white Object is surrounded with black.
3651And the same is to be understood when an Object is viewed, whose parts
3652are some of them less luminous than others. For in the borders of the
3653more and less luminous Parts, Colours ought always by the same
3654Principles to arise from the Excess of the Light of the more luminous,
3655and to be of the same kind as if the darker parts were black, but yet to
3656be more faint and dilute.
3657
3658What is said of Colours made by Prisms may be easily applied to Colours
3659made by the Glasses of Telescopes or Microscopes, or by the Humours of
3660the Eye. For if the Object-glass of a Telescope be thicker on one side
3661than on the other, or if one half of the Glass, or one half of the Pupil
3662of the Eye be cover'd with any opake substance; the Object-glass, or
3663that part of it or of the Eye which is not cover'd, may be consider'd as
3664a Wedge with crooked Sides, and every Wedge of Glass or other pellucid
3665Substance has the effect of a Prism in refracting the Light which passes
3666through it.[L]
3667
3668How the Colours in the ninth and tenth Experiments of the first Part
3669arise from the different Reflexibility of Light, is evident by what was
3670there said. But it is observable in the ninth Experiment, that whilst
3671the Sun's direct Light is yellow, the Excess of the blue-making Rays in
3672the reflected beam of Light MN, suffices only to bring that yellow to a
3673pale white inclining to blue, and not to tinge it with a manifestly blue
3674Colour. To obtain therefore a better blue, I used instead of the yellow
3675Light of the Sun the white Light of the Clouds, by varying a little the
3676Experiment, as follows.
3677
3678[Illustration: FIG. 13.]
3679
3680_Exper._ 16 Let HFG [in _Fig._ 13.] represent a Prism in the open Air,
3681and S the Eye of the Spectator, viewing the Clouds by their Light coming
3682into the Prism at the Plane Side FIGK, and reflected in it by its Base
3683HEIG, and thence going out through its Plane Side HEFK to the Eye. And
3684when the Prism and Eye are conveniently placed, so that the Angles of
3685Incidence and Reflexion at the Base may be about 40 Degrees, the
3686Spectator will see a Bow MN of a blue Colour, running from one End of
3687the Base to the other, with the Concave Side towards him, and the Part
3688of the Base IMNG beyond this Bow will be brighter than the other Part
3689EMNH on the other Side of it. This blue Colour MN being made by nothing
3690else than by Reflexion of a specular Superficies, seems so odd a
3691Phænomenon, and so difficult to be explained by the vulgar Hypothesis of
3692Philosophers, that I could not but think it deserved to be taken Notice
3693of. Now for understanding the Reason of it, suppose the Plane ABC to cut
3694the Plane Sides and Base of the Prism perpendicularly. From the Eye to
3695the Line BC, wherein that Plane cuts the Base, draw the Lines S_p_ and
3696S_t_, in the Angles S_pc_ 50 degr. 1/9, and S_tc_ 49 degr. 1/28, and the
3697Point _p_ will be the Limit beyond which none of the most refrangible
3698Rays can pass through the Base of the Prism, and be refracted, whose
3699Incidence 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,
3701beyond which none of them can pass through the Base, whose Incidence is
3702such that by Reflexion they may come to the Eye. And the Point _r_ taken
3703in the middle Way between _p_ and _t_, will be the like Limit for the
3704meanly refrangible Rays. And therefore all the least refrangible Rays
3705which fall upon the Base beyond _t_, that is, between _t_ and B, and can
3706come 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
3708transmitted through the Base. And all the most refrangible Rays which
3709fall upon the Base beyond _p_, that is, between, _p_ and B, and can by
3710Reflexion come from thence to the Eye, will be reflected thither, but
3711every where between _p_ and _c_, many of these Rays will get through the
3712Base, and be refracted; and the same is to be understood of the meanly
3713refrangible Rays on either side of the Point _r_. Whence it follows,
3714that the Base of the Prism must every where between _t_ and B, by a
3715total Reflexion of all sorts of Rays to the Eye, look white and bright.
3716And every where between _p_ and C, by reason of the Transmission of many
3717Rays of every sort, look more pale, obscure, and dark. But at _r_, and
3718in other Places between _p_ and _t_, where all the more refrangible Rays
3719are reflected to the Eye, and many of the less refrangible are
3720transmitted, the Excess of the most refrangible in the reflected Light
3721will tinge that Light with their Colour, which is violet and blue. And
3722this happens by taking the Line C _prt_ B any where between the Ends of
3723the 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
3729Rain-bow._
3730
3731[Illustration: FIG. 14.]
3732
3733This Bow never appears, but where it rains in the Sun-shine, and may be
3734made artificially by spouting up Water which may break aloft, and
3735scatter into Drops, and fall down like Rain. For the Sun shining upon
3736these Drops certainly causes the Bow to appear to a Spectator standing
3737in a due Position to the Rain and Sun. And hence it is now agreed upon,
3738that this Bow is made by Refraction of the Sun's Light in drops of
3739falling Rain. This was understood by some of the Antients, and of late
3740more fully discover'd and explain'd by the famous _Antonius de Dominis_
3741Archbishop of _Spalato_, in his book _De Radiis Visûs & Lucis_,
3742published by his Friend _Bartolus_ at _Venice_, in the Year 1611, and
3743written above 20 Years before. For he teaches there how the interior Bow
3744is made in round Drops of Rain by two Refractions of the Sun's Light,
3745and one Reflexion between them, and the exterior by two Refractions, and
3746two sorts of Reflexions between them in each Drop of Water, and proves
3747his Explications by Experiments made with a Phial full of Water, and
3748with Globes of Glass filled with Water, and placed in the Sun to make
3749the Colours of the two Bows appear in them. The same Explication
3750_Des-Cartes_ hath pursued in his Meteors, and mended that of the
3751exterior Bow. But whilst they understood not the true Origin of Colours,
3752it's necessary to pursue it here a little farther. For understanding
3753therefore how the Bow is made, let a Drop of Rain, or any other
3754spherical transparent Body be represented by the Sphere BNFG, [in _Fig._
375514.] described with the Center C, and Semi-diameter CN. And let AN be
3756one of the Sun's Rays incident upon it at N, and thence refracted to F,
3757where let it either go out of the Sphere by Refraction towards V, or be
3758reflected to G; and at G let it either go out by Refraction to R, or be
3759reflected to H; and at H let it go out by Refraction towards S, cutting
3760the incident Ray in Y. Produce AN and RG, till they meet in X, and upon
3761AX and NF, let fall the Perpendiculars CD and CE, and produce CD till it
3762fall upon the Circumference at L. Parallel to the incident Ray AN draw
3763the Diameter BQ, and let the Sine of Incidence out of Air into Water be
3764to the Sine of Refraction as I to R. Now, if you suppose the Point of
3765Incidence N to move from the Point B, continually till it come to L, the
3766Arch QF will first increase and then decrease, and so will the Angle AXR
3767which the Rays AN and GR contain; and the Arch QF and Angle AXR will be
3768biggest when ND is to CN as sqrt(II - RR) to sqrt(3)RR, in which
3769case NE will be to ND as 2R to I. Also the Angle AYS, which the Rays AN
3770and HS contain will first decrease, and then increase and grow least
3771when ND is to CN as sqrt(II - RR) to sqrt(8)RR, in which case NE
3772will 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
3774incident Ray AN will come to its Limit when ND is to CN as sqrt(II -
3775RR) to sqrt(15)RR, in which case NE will be to ND as 4R to I. And the
3776Angle which the Ray next after that Emergent, that is, the Ray emergent
3777after four Reflexions, contains with the Incident, will come to its
3778Limit, when ND is to CN as sqrt(II - RR) to sqrt(24)RR, in which
3779case NE will be to ND as 5R to I; and so on infinitely, the Numbers 3,
37808, 15, 24, &c. being gather'd by continual Addition of the Terms of the
3781arithmetical Progression 3, 5, 7, 9, &c. The Truth of all this
3782Mathematicians will easily examine.[M]
3783
3784Now it is to be observed, that as when the Sun comes to his Tropicks,
3785Days increase and decrease but a very little for a great while together;
3786so when by increasing the distance CD, these Angles come to their
3787Limits, they vary their quantity but very little for some time together,
3788and therefore a far greater number of the Rays which fall upon all the
3789Points N in the Quadrant BL, shall emerge in the Limits of these Angles,
3790than in any other Inclinations. And farther it is to be observed, that
3791the Rays which differ in Refrangibility will have different Limits of
3792their Angles of Emergence, and by consequence according to their
3793different Degrees of Refrangibility emerge most copiously in different
3794Angles, and being separated from one another appear each in their proper
3795Colours. And what those Angles are may be easily gather'd from the
3796foregoing Theorem by Computation.
3797
3798For in the least refrangible Rays the Sines I and R (as was found above)
3799are 108 and 81, and thence by Computation the greatest Angle AXR will be
3800found 42 Degrees and 2 Minutes, and the least Angle AYS, 50 Degrees and
380157 Minutes. And in the most refrangible Rays the Sines I and R are 109
3802and 81, and thence by Computation the greatest Angle AXR will be found
380340 Degrees and 17 Minutes, and the least Angle AYS 54 Degrees and 7
3804Minutes.
3805
3806Suppose now that O [in _Fig._ 15.] is the Spectator's Eye, and OP a Line
3807drawn parallel to the Sun's Rays and let POE, POF, POG, POH, be Angles
3808of 40 Degr. 17 Min. 42 Degr. 2 Min. 50 Degr. 57 Min. and 54 Degr. 7 Min.
3809respectively, and these Angles turned about their common Side OP, shall
3810with their other Sides OE, OF; OG, OH, describe the Verges of two
3811Rain-bows AF, BE and CHDG. For if E, F, G, H, be drops placed any where
3812in the conical Superficies described by OE, OF, OG, OH, and be
3813illuminated by the Sun's Rays SE, SF, SG, SH; the Angle SEO being equal
3814to the Angle POE, or 40 Degr. 17 Min. shall be the greatest Angle in
3815which the most refrangible Rays can after one Reflexion be refracted to
3816the Eye, and therefore all the Drops in the Line OE shall send the most
3817refrangible Rays most copiously to the Eye, and thereby strike the
3818Senses with the deepest violet Colour in that Region. And in like
3819manner the Angle SFO being equal to the Angle POF, or 42 Degr. 2 Min.
3820shall be the greatest in which the least refrangible Rays after one
3821Reflexion can emerge out of the Drops, and therefore those Rays shall
3822come most copiously to the Eye from the Drops in the Line OF, and strike
3823the Senses with the deepest red Colour in that Region. And by the same
3824Argument, the Rays which have intermediate Degrees of Refrangibility
3825shall come most copiously from Drops between E and F, and strike the
3826Senses with the intermediate Colours, in the Order which their Degrees
3827of Refrangibility require, that is in the Progress from E to F, or from
3828the inside of the Bow to the outside in this order, violet, indigo,
3829blue, green, yellow, orange, red. But the violet, by the mixture of the
3830white Light of the Clouds, will appear faint and incline to purple.
3831
3832[Illustration: FIG. 15.]
3833
3834Again, the Angle SGO being equal to the Angle POG, or 50 Gr. 51 Min.
3835shall be the least Angle in which the least refrangible Rays can after
3836two Reflexions emerge out of the Drops, and therefore the least
3837refrangible Rays shall come most copiously to the Eye from the Drops in
3838the Line OG, and strike the Sense with the deepest red in that Region.
3839And the Angle SHO being equal to the Angle POH, or 54 Gr. 7 Min. shall
3840be the least Angle, in which the most refrangible Rays after two
3841Reflexions can emerge out of the Drops; and therefore those Rays shall
3842come most copiously to the Eye from the Drops in the Line OH, and strike
3843the Senses with the deepest violet in that Region. And by the same
3844Argument, the Drops in the Regions between G and H shall strike the
3845Sense with the intermediate Colours in the Order which their Degrees of
3846Refrangibility require, that is, in the Progress from G to H, or from
3847the inside of the Bow to the outside in this order, red, orange, yellow,
3848green, blue, indigo, violet. And since these four Lines OE, OF, OG, OH,
3849may be situated any where in the above-mention'd conical Superficies;
3850what is said of the Drops and Colours in these Lines is to be understood
3851of the Drops and Colours every where in those Superficies.
3852
3853Thus shall there be made two Bows of Colours, an interior and stronger,
3854by one Reflexion in the Drops, and an exterior and fainter by two; for
3855the Light becomes fainter by every Reflexion. And their Colours shall
3856lie in a contrary Order to one another, the red of both Bows bordering
3857upon the Space GF, which is between the Bows. The Breadth of the
3858interior Bow EOF measured cross the Colours shall be 1 Degr. 45 Min. and
3859the Breadth of the exterior GOH shall be 3 Degr. 10 Min. and the
3860distance between them GOF shall be 8 Gr. 15 Min. the greatest
3861Semi-diameter of the innermost, that is, the Angle POF being 42 Gr. 2
3862Min. and the least Semi-diameter of the outermost POG, being 50 Gr. 57
3863Min. These are the Measures of the Bows, as they would be were the Sun
3864but a Point; for by the Breadth of his Body, the Breadth of the Bows
3865will be increased, and their Distance decreased by half a Degree, and so
3866the breadth of the interior Iris will be 2 Degr. 15 Min. that of the
3867exterior 3 Degr. 40 Min. their distance 8 Degr. 25 Min. the greatest
3868Semi-diameter of the interior Bow 42 Degr. 17 Min. and the least of the
3869exterior 50 Degr. 42 Min. And such are the Dimensions of the Bows in the
3870Heavens found to be very nearly, when their Colours appear strong and
3871perfect. For once, by such means as I then had, I measured the greatest
3872Semi-diameter of the interior Iris about 42 Degrees, and the breadth of
3873the red, yellow and green in that Iris 63 or 64 Minutes, besides the
3874outmost faint red obscured by the brightness of the Clouds, for which we
3875may allow 3 or 4 Minutes more. The breadth of the blue was about 40
3876Minutes more besides the violet, which was so much obscured by the
3877brightness of the Clouds, that I could not measure its breadth. But
3878supposing the breadth of the blue and violet together to equal that of
3879the red, yellow and green together, the whole breadth of this Iris will
3880be about 2-1/4 Degrees, as above. The least distance between this Iris
3881and the exterior Iris was about 8 Degrees and 30 Minutes. The exterior
3882Iris was broader than the interior, but so faint, especially on the blue
3883side, that I could not measure its breadth distinctly. At another time
3884when both Bows appeared more distinct, I measured the breadth of the
3885interior Iris 2 Gr. 10´, and the breadth of the red, yellow and green in
3886the exterior Iris, was to the breadth of the same Colours in the
3887interior as 3 to 2.
3888
3889This Explication of the Rain-bow is yet farther confirmed by the known
3890Experiment (made by _Antonius de Dominis_ and _Des-Cartes_) of hanging
3891up any where in the Sun-shine a Glass Globe filled with Water, and
3892viewing it in such a posture, that the Rays which come from the Globe to
3893the Eye may contain with the Sun's Rays an Angle of either 42 or 50
3894Degrees. 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
3896opposed to the Sun as 'tis represented at F, and if that Angle become
3897less (suppose by depressing the Globe to E) there will appear other
3898Colours, yellow, green and blue successive in the same side of the
3899Globe. But if the Angle be made about 50 Degrees (suppose by lifting up
3900the Globe to G) there will appear a red Colour in that side of the Globe
3901towards the Sun, and if the Angle be made greater (suppose by lifting
3902up the Globe to H) the red will turn successively to the other Colours,
3903yellow, green and blue. The same thing I have tried, by letting a Globe
3904rest, and raising or depressing the Eye, or otherwise moving it to make
3905the Angle of a just magnitude.
3906
3907I have heard it represented, that if the Light of a Candle be refracted
3908by a Prism to the Eye; when the blue Colour falls upon the Eye, the
3909Spectator shall see red in the Prism, and when the red falls upon the
3910Eye he shall see blue; and if this were certain, the Colours of the
3911Globe and Rain-bow ought to appear in a contrary order to what we find.
3912But the Colours of the Candle being very faint, the mistake seems to
3913arise from the difficulty of discerning what Colours fall on the Eye.
3914For, on the contrary, I have sometimes had occasion to observe in the
3915Sun's Light refracted by a Prism, that the Spectator always sees that
3916Colour in the Prism which falls upon his Eye. And the same I have found
3917true also in Candle-light. For when the Prism is moved slowly from the
3918Line which is drawn directly from the Candle to the Eye, the red appears
3919first in the Prism and then the blue, and therefore each of them is seen
3920when it falls upon the Eye. For the red passes over the Eye first, and
3921then the blue.
3922
3923The Light which comes through drops of Rain by two Refractions without
3924any Reflexion, ought to appear strongest at the distance of about 26
3925Degrees from the Sun, and to decay gradually both ways as the distance
3926from him increases and decreases. And the same is to be understood of
3927Light transmitted through spherical Hail-stones. And if the Hail be a
3928little flatted, as it often is, the Light transmitted may grow so strong
3929at a little less distance than that of 26 Degrees, as to form a Halo
3930about the Sun or Moon; which Halo, as often as the Hail-stones are duly
3931figured may be colour'd, and then it must be red within by the least
3932refrangible Rays, and blue without by the most refrangible ones,
3933especially if the Hail-stones have opake Globules of Snow in their
3934center to intercept the Light within the Halo (as _Hugenius_ has
3935observ'd) and make the inside thereof more distinctly defined than it
3936would otherwise be. For such Hail-stones, though spherical, by
3937terminating the Light by the Snow, may make a Halo red within and
3938colourless without, and darker in the red than without, as Halos used to
3939be. For of those Rays which pass close by the Snow the Rubriform will be
3940least refracted, and so come to the Eye in the directest Lines.
3941
3942The Light which passes through a drop of Rain after two Refractions, and
3943three or more Reflexions, is scarce strong enough to cause a sensible
3944Bow; 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
3951of Natural Bodies._
3952
3953These Colours arise from hence, that some natural Bodies reflect some
3954sorts of Rays, others other sorts more copiously than the rest. Minium
3955reflects the least refrangible or red-making Rays most copiously, and
3956thence appears red. Violets reflect the most refrangible most copiously,
3957and thence have their Colour, and so of other Bodies. Every Body
3958reflects the Rays of its own Colour more copiously than the rest, and
3959from their excess and predominance in the reflected Light has its
3960Colour.
3961
3962_Exper._ 17. For if in the homogeneal Lights obtained by the solution of
3963the Problem proposed in the fourth Proposition of the first Part of this
3964Book, you place Bodies of several Colours, you will find, as I have
3965done, that every Body looks most splendid and luminous in the Light of
3966its own Colour. Cinnaber in the homogeneal red Light is most
3967resplendent, in the green Light it is manifestly less resplendent, and
3968in the blue Light still less. Indigo in the violet blue Light is most
3969resplendent, and its splendor is gradually diminish'd, as it is removed
3970thence by degrees through the green and yellow Light to the red. By a
3971Leek the green Light, and next that the blue and yellow which compound
3972green, are more strongly reflected than the other Colours red and
3973violet, and so of the rest. But to make these Experiments the more
3974manifest, such Bodies ought to be chosen as have the fullest and most
3975vivid Colours, and two of those Bodies are to be compared together.
3976Thus, for instance, if Cinnaber and _ultra_-marine blue, or some other
3977full blue be held together in the red homogeneal Light, they will both
3978appear red, but the Cinnaber will appear of a strongly luminous and
3979resplendent red, and the _ultra_-marine blue of a faint obscure and dark
3980red; and if they be held together in the blue homogeneal Light, they
3981will both appear blue, but the _ultra_-marine will appear of a strongly
3982luminous and resplendent blue, and the Cinnaber of a faint and dark
3983blue. Which puts it out of dispute that the Cinnaber reflects the red
3984Light much more copiously than the _ultra_-marine doth, and the
3985_ultra_-marine reflects the blue Light much more copiously than the
3986Cinnaber doth. The same Experiment may be tried successfully with red
3987Lead and Indigo, or with any other two colour'd Bodies, if due allowance
3988be made for the different strength or weakness of their Colour and
3989Light.
3990
3991And as the reason of the Colours of natural Bodies is evident by these
3992Experiments, so it is farther confirmed and put past dispute by the two
3993first Experiments of the first Part, whereby 'twas proved in such Bodies
3994that the reflected Lights which differ in Colours do differ also in
3995degrees of Refrangibility. For thence it's certain, that some Bodies
3996reflect the more refrangible, others the less refrangible Rays more
3997copiously.
3998
3999And that this is not only a true reason of these Colours, but even the
4000only reason, may appear farther from this Consideration, that the Colour
4001of homogeneal Light cannot be changed by the Reflexion of natural
4002Bodies.
4003
4004For if Bodies by Reflexion cannot in the least change the Colour of any
4005one sort of Rays, they cannot appear colour'd by any other means than by
4006reflecting those which either are of their own Colour, or which by
4007mixture must produce it.
4008
4009But in trying Experiments of this kind care must be had that the Light
4010be sufficiently homogeneal. For if Bodies be illuminated by the ordinary
4011prismatick Colours, they will appear neither of their own Day-light
4012Colours, nor of the Colour of the Light cast on them, but of some middle
4013Colour between both, as I have found by Experience. Thus red Lead (for
4014instance) illuminated with the ordinary prismatick green will not appear
4015either red or green, but orange or yellow, or between yellow and green,
4016accordingly as the green Light by which 'tis illuminated is more or less
4017compounded. For because red Lead appears red when illuminated with white
4018Light, wherein all sorts of Rays are equally mix'd, and in the green
4019Light all sorts of Rays are not equally mix'd, the Excess of the
4020yellow-making, green-making and blue-making Rays in the incident green
4021Light, will cause those Rays to abound so much in the reflected Light,
4022as to draw the Colour from red towards their Colour. And because the red
4023Lead reflects the red-making Rays most copiously in proportion to their
4024number, and next after them the orange-making and yellow-making Rays;
4025these Rays in the reflected Light will be more in proportion to the
4026Light than they were in the incident green Light, and thereby will draw
4027the reflected Light from green towards their Colour. And therefore the
4028red Lead will appear neither red nor green, but of a Colour between
4029both.
4030
4031In transparently colour'd Liquors 'tis observable, that their Colour
4032uses to vary with their thickness. Thus, for instance, a red Liquor in a
4033conical Glass held between the Light and the Eye, looks of a pale and
4034dilute 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
4036where 'tis thickest the red is deepest and darkest. For it is to be
4037conceiv'd that such a Liquor stops the indigo-making and violet-making
4038Rays most easily, the blue-making Rays more difficultly, the
4039green-making Rays still more difficultly, and the red-making most
4040difficultly: And that if the thickness of the Liquor be only so much as
4041suffices to stop a competent number of the violet-making and
4042indigo-making Rays, without diminishing much the number of the rest, the
4043rest must (by _Prop._ 6. _Part_ 2.) compound a pale yellow. But if the
4044Liquor be so much thicker as to stop also a great number of the
4045blue-making Rays, and some of the green-making, the rest must compound
4046an orange; and where it is so thick as to stop also a great number of
4047the green-making and a considerable number of the yellow-making, the
4048rest must begin to compound a red, and this red must grow deeper and
4049darker as the yellow-making and orange-making Rays are more and more
4050stopp'd by increasing the thickness of the Liquor, so that few Rays
4051besides the red-making can get through.
4052
4053Of this kind is an Experiment lately related to me by Mr. _Halley_, who,
4054in diving deep into the Sea in a diving Vessel, found in a clear
4055Sun-shine Day, that when he was sunk many Fathoms deep into the Water
4056the upper part of his Hand on which the Sun shone directly through the
4057Water and through a small Glass Window in the Vessel appeared of a red
4058Colour, like that of a Damask Rose, and the Water below and the under
4059part of his Hand illuminated by Light reflected from the Water below
4060look'd green. For thence it may be gather'd, that the Sea-Water reflects
4061back the violet and blue-making Rays most easily, and lets the
4062red-making Rays pass most freely and copiously to great Depths. For
4063thereby the Sun's direct Light at all great Depths, by reason of the
4064predominating red-making Rays, must appear red; and the greater the
4065Depth is, the fuller and intenser must that red be. And at such Depths
4066as the violet-making Rays scarce penetrate unto, the blue-making,
4067green-making, and yellow-making Rays being reflected from below more
4068copiously than the red-making ones, must compound a green.
4069
4070Now, if there be two Liquors of full Colours, suppose a red and blue,
4071and both of them so thick as suffices to make their Colours sufficiently
4072full; though either Liquor be sufficiently transparent apart, yet will
4073you not be able to see through both together. For, if only the
4074red-making Rays pass through one Liquor, and only the blue-making
4075through the other, no Rays can pass through both. This Mr. _Hook_ tried
4076casually with Glass Wedges filled with red and blue Liquors, and was
4077surprized at the unexpected Event, the reason of it being then unknown;
4078which makes me trust the more to his Experiment, though I have not tried
4079it my self. But he that would repeat it, must take care the Liquors be
4080of very good and full Colours.
4081
4082Now, whilst Bodies become coloured by reflecting or transmitting this or
4083that sort of Rays more copiously than the rest, it is to be conceived
4084that they stop and stifle in themselves the Rays which they do not
4085reflect or transmit. For, if Gold be foliated and held between your Eye
4086and the Light, the Light looks of a greenish blue, and therefore massy
4087Gold lets into its Body the blue-making Rays to be reflected to and fro
4088within it till they be stopp'd and stifled, whilst it reflects the
4089yellow-making outwards, and thereby looks yellow. And much after the
4090same manner that Leaf Gold is yellow by reflected, and blue by
4091transmitted Light, and massy Gold is yellow in all Positions of the Eye;
4092there are some Liquors, as the Tincture of _Lignum Nephriticum_, and
4093some sorts of Glass which transmit one sort of Light most copiously, and
4094reflect another sort, and thereby look of several Colours, according to
4095the Position of the Eye to the Light. But, if these Liquors or Glasses
4096were so thick and massy that no Light could get through them, I question
4097not but they would like all other opake Bodies appear of one and the
4098same Colour in all Positions of the Eye, though this I cannot yet affirm
4099by Experience. For all colour'd Bodies, so far as my Observation
4100reaches, may be seen through if made sufficiently thin, and therefore
4101are in some measure transparent, and differ only in degrees of
4102Transparency from tinged transparent Liquors; these Liquors, as well as
4103those Bodies, by a sufficient Thickness becoming opake. A transparent
4104Body which looks of any Colour by transmitted Light, may also look of
4105the same Colour by reflected Light, the Light of that Colour being
4106reflected by the farther Surface of the Body, or by the Air beyond it.
4107And then the reflected Colour will be diminished, and perhaps cease, by
4108making the Body very thick, and pitching it on the backside to diminish
4109the Reflexion of its farther Surface, so that the Light reflected from
4110the tinging Particles may predominate. In such Cases, the Colour of the
4111reflected Light will be apt to vary from that of the Light transmitted.
4112But whence it is that tinged Bodies and Liquors reflect some sort of
4113Rays, and intromit or transmit other sorts, shall be said in the next
4114Book. In this Proposition I content my self to have put it past dispute,
4115that 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
4121Colour and Nature with a beam of the Sun's direct Light, and therein to
4122experience the Truth of the foregoing Propositions._
4123
4124[Illustration: FIG. 16.]
4125
4126Let ABC _abc_ [in _Fig._ 16.] represent a Prism, by which the Sun's
4127Light let into a dark Chamber through the Hole F, may be refracted
4128towards the Lens MN, and paint upon it at _p_, _q_, _r_, _s_, and _t_,
4129the usual Colours violet, blue, green, yellow, and red, and let the
4130diverging Rays by the Refraction of this Lens converge again towards X,
4131and there, by the mixture of all those their Colours, compound a white
4132according to what was shewn above. Then let another Prism DEG _deg_,
4133parallel to the former, be placed at X, to refract that white Light
4134upwards towards Y. Let the refracting Angles of the Prisms, and their
4135distances from the Lens be equal, so that the Rays which converged from
4136the Lens towards X, and without Refraction, would there have crossed and
4137diverged again, may by the Refraction of the second Prism be reduced
4138into Parallelism and diverge no more. For then those Rays will recompose
4139a beam of white Light XY. If the refracting Angle of either Prism be the
4140bigger, that Prism must be so much the nearer to the Lens. You will know
4141when the Prisms and the Lens are well set together, by observing if the
4142beam of Light XY, which comes out of the second Prism be perfectly white
4143to the very edges of the Light, and at all distances from the Prism
4144continue perfectly and totally white like a beam of the Sun's Light. For
4145till this happens, the Position of the Prisms and Lens to one another
4146must be corrected; and then if by the help of a long beam of Wood, as is
4147represented in the Figure, or by a Tube, or some other such Instrument,
4148made for that Purpose, they be made fast in that Situation, you may try
4149all the same Experiments in this compounded beam of Light XY, which have
4150been made in the Sun's direct Light. For this compounded beam of Light
4151has the same appearance, and is endow'd with all the same Properties
4152with a direct beam of the Sun's Light, so far as my Observation reaches.
4153And in trying Experiments in this beam you may by stopping any of the
4154Colours, _p_, _q_, _r_, _s_, and _t_, at the Lens, see how the Colours
4155produced in the Experiments are no other than those which the Rays had
4156at the Lens before they entered the Composition of this Beam: And by
4157consequence, that they arise not from any new Modifications of the Light
4158by Refractions and Reflexions, but from the various Separations and
4159Mixtures of the Rays originally endow'd with their colour-making
4160Qualities.
4161
4162So, for instance, having with a Lens 4-1/4 Inches broad, and two Prisms
4163on either hand 6-1/4 Feet distant from the Lens, made such a beam of
4164compounded Light; to examine the reason of the Colours made by Prisms, I
4165refracted this compounded beam of Light XY with another Prism HIK _kh_,
4166and thereby cast the usual Prismatick Colours PQRST upon the Paper LV
4167placed 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
4169Paper. So if the Purple _p_ was stopp'd at the Lens, the Purple P upon
4170the Paper would vanish, and the rest of the Colours would remain
4171unalter'd, unless perhaps the blue, so far as some purple latent in it
4172at the Lens might be separated from it by the following Refractions. And
4173so by intercepting the green upon the Lens, the green R upon the Paper
4174would vanish, and so of the rest; which plainly shews, that as the white
4175beam of Light XY was compounded of several Lights variously colour'd at
4176the Lens, so the Colours which afterwards emerge out of it by new
4177Refractions are no other than those of which its Whiteness was
4178compounded. The Refraction of the Prism HIK _kh_ generates the Colours
4179PQRST upon the Paper, not by changing the colorific Qualities of the
4180Rays, but by separating the Rays which had the very same colorific
4181Qualities before they enter'd the Composition of the refracted beam of
4182white Light XY. For otherwise the Rays which were of one Colour at the
4183Lens might be of another upon the Paper, contrary to what we find.
4184
4185So again, to examine the reason of the Colours of natural Bodies, I
4186placed such Bodies in the Beam of Light XY, and found that they all
4187appeared there of those their own Colours which they have in Day-light,
4188and that those Colours depend upon the Rays which had the same Colours
4189at the Lens before they enter'd the Composition of that beam. Thus, for
4190instance, Cinnaber illuminated by this beam appears of the same red
4191Colour as in Day-light; and if at the Lens you intercept the
4192green-making and blue-making Rays, its redness will become more full and
4193lively: But if you there intercept the red-making Rays, it will not any
4194longer appear red, but become yellow or green, or of some other Colour,
4195according to the sorts of Rays which you do not intercept. So Gold in
4196this Light XY appears of the same yellow Colour as in Day-light, but by
4197intercepting at the Lens a due Quantity of the yellow-making Rays it
4198will appear white like Silver (as I have tried) which shews that its
4199yellowness arises from the Excess of the intercepted Rays tinging that
4200Whiteness 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
4202Light XY, looks blue by the reflected Part of the Light, and red by the
4203transmitted Part of it, as when 'tis view'd in Day-light; but if you
4204intercept the blue at the Lens the Infusion will lose its reflected blue
4205Colour, whilst its transmitted red remains perfect, and by the loss of
4206some blue-making Rays, wherewith it was allay'd, becomes more intense
4207and full. And, on the contrary, if the red and orange-making Rays be
4208intercepted at the Lens, the Infusion will lose its transmitted red,
4209whilst its blue will remain and become more full and perfect. Which
4210shews, that the Infusion does not tinge the Rays with blue and red, but
4211only transmits those most copiously which were red-making before, and
4212reflects those most copiously which were blue-making before. And after
4213the same manner may the Reasons of other Phænomena be examined, by
4214trying them in this artificial beam of Light XY.
4215
4216FOOTNOTES:
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
4234THE
4235
4236SECOND BOOK
4237
4238OF
4239
4240OPTICKS
4241
4242
4243
4244
4245_PART I._
4246
4247_Observations concerning the Reflexions, Refractions, and Colours of
4248thin transparent Bodies._
4249
4250
4251It has been observed by others, that transparent Substances, as Glass,
4252Water, Air, &c. when made very thin by being blown into Bubbles, or
4253otherwise formed into Plates, do exhibit various Colours according to
4254their various thinness, altho' at a greater thickness they appear very
4255clear and colourless. In the former Book I forbore to treat of these
4256Colours, because they seemed of a more difficult Consideration, and were
4257not necessary for establishing the Properties of Light there discoursed
4258of. But because they may conduce to farther Discoveries for compleating
4259the Theory of Light, especially as to the constitution of the parts of
4260natural Bodies, on which their Colours or Transparency depend; I have
4261here set down an account of them. To render this Discourse short and
4262distinct, I have first described the principal of my Observations, and
4263then consider'd and made use of them. The Observations are these.
4264
4265_Obs._ 1. Compressing two Prisms hard together that their sides (which
4266by chance were a very little convex) might somewhere touch one another:
4267I found the place in which they touched to become absolutely
4268transparent, as if they had there been one continued piece of Glass. For
4269when the Light fell so obliquely on the Air, which in other places was
4270between them, as to be all reflected; it seemed in that place of contact
4271to be wholly transmitted, insomuch that when look'd upon, it appeared
4272like a black or dark spot, by reason that little or no sensible Light
4273was reflected from thence, as from other places; and when looked through
4274it seemed (as it were) a hole in that Air which was formed into a thin
4275Plate, by being compress'd between the Glasses. And through this hole
4276Objects that were beyond might be seen distinctly, which could not at
4277all be seen through other parts of the Glasses where the Air was
4278interjacent. Although the Glasses were a little convex, yet this
4279transparent spot was of a considerable breadth, which breadth seemed
4280principally to proceed from the yielding inwards of the parts of the
4281Glasses, by reason of their mutual pressure. For by pressing them very
4282hard together it would become much broader than otherwise.
4283
4284_Obs._ 2. When the Plate of Air, by turning the Prisms about their
4285common Axis, became so little inclined to the incident Rays, that some
4286of them began to be transmitted, there arose in it many slender Arcs of
4287Colours which at first were shaped almost like the Conchoid, as you see
4288them delineated in the first Figure. And by continuing the Motion of the
4289Prisms, these Arcs increased and bended more and more about the said
4290transparent spot, till they were compleated into Circles or Rings
4291incompassing it, and afterwards continually grew more and more
4292contracted.
4293
4294[Illustration: FIG. 1.]
4295
4296These Arcs at their first appearance were of a violet and blue Colour,
4297and between them were white Arcs of Circles, which presently by
4298continuing the Motion of the Prisms became a little tinged in their
4299inward Limbs with red and yellow, and to their outward Limbs the blue
4300was adjacent. So that the order of these Colours from the central dark
4301spot, was at that time white, blue, violet; black, red, orange, yellow,
4302white, blue, violet, &c. But the yellow and red were much fainter than
4303the blue and violet.
4304
4305The Motion of the Prisms about their Axis being continued, these Colours
4306contracted more and more, shrinking towards the whiteness on either
4307side of it, until they totally vanished into it. And then the Circles in
4308those parts appear'd black and white, without any other Colours
4309intermix'd. But by farther moving the Prisms about, the Colours again
4310emerged out of the whiteness, the violet and blue at its inward Limb,
4311and at its outward Limb the red and yellow. So that now their order from
4312the central Spot was white, yellow, red; black; violet, blue, white,
4313yellow, red, &c. contrary to what it was before.
4314
4315_Obs._ 3. When the Rings or some parts of them appeared only black and
4316white, they were very distinct and well defined, and the blackness
4317seemed as intense as that of the central Spot. Also in the Borders of
4318the Rings, where the Colours began to emerge out of the whiteness, they
4319were pretty distinct, which made them visible to a very great multitude.
4320I have sometimes number'd above thirty Successions (reckoning every
4321black and white Ring for one Succession) and seen more of them, which by
4322reason of their smalness I could not number. But in other Positions of
4323the Prisms, at which the Rings appeared of many Colours, I could not
4324distinguish above eight or nine of them, and the Exterior of those were
4325very confused and dilute.
4326
4327In these two Observations to see the Rings distinct, and without any
4328other Colour than Black and white, I found it necessary to hold my Eye
4329at a good distance from them. For by approaching nearer, although in the
4330same inclination of my Eye to the Plane of the Rings, there emerged a
4331bluish Colour out of the white, which by dilating it self more and more
4332into the black, render'd the Circles less distinct, and left the white a
4333little tinged with red and yellow. I found also by looking through a
4334slit or oblong hole, which was narrower than the pupil of my Eye, and
4335held close to it parallel to the Prisms, I could see the Circles much
4336distincter and visible to a far greater number than otherwise.
4337
4338_Obs._ 4. To observe more nicely the order of the Colours which arose
4339out of the white Circles as the Rays became less and less inclined to
4340the Plate of Air; I took two Object-glasses, the one a Plano-convex for
4341a fourteen Foot Telescope, and the other a large double Convex for one
4342of about fifty Foot; and upon this, laying the other with its plane side
4343downwards, I pressed them slowly together, to make the Colours
4344successively emerge in the middle of the Circles, and then slowly lifted
4345the upper Glass from the lower to make them successively vanish again in
4346the same place. The Colour, which by pressing the Glasses together,
4347emerged last in the middle of the other Colours, would upon its first
4348appearance look like a Circle of a Colour almost uniform from the
4349circumference to the center and by compressing the Glasses still more,
4350grow continually broader until a new Colour emerged in its center, and
4351thereby it became a Ring encompassing that new Colour. And by
4352compressing the Glasses still more, the diameter of this Ring would
4353increase, and the breadth of its Orbit or Perimeter decrease until
4354another new Colour emerged in the center of the last: And so on until a
4355third, a fourth, a fifth, and other following new Colours successively
4356emerged there, and became Rings encompassing the innermost Colour, the
4357last of which was the black Spot. And, on the contrary, by lifting up
4358the upper Glass from the lower, the diameter of the Rings would
4359decrease, and the breadth of their Orbit increase, until their Colours
4360reached successively to the center; and then they being of a
4361considerable breadth, I could more easily discern and distinguish their
4362Species than before. And by this means I observ'd their Succession and
4363Quantity to be as followeth.
4364
4365Next to the pellucid central Spot made by the contact of the Glasses
4366succeeded blue, white, yellow, and red. The blue was so little in
4367quantity, that I could not discern it in the Circles made by the Prisms,
4368nor could I well distinguish any violet in it, but the yellow and red
4369were pretty copious, and seemed about as much in extent as the white,
4370and four or five times more than the blue. The next Circuit in order of
4371Colours immediately encompassing these were violet, blue, green, yellow,
4372and red: and these were all of them copious and vivid, excepting the
4373green, which was very little in quantity, and seemed much more faint and
4374dilute than the other Colours. Of the other four, the violet was the
4375least in extent, and the blue less than the yellow or red. The third
4376Circuit or Order was purple, blue, green, yellow, and red; in which the
4377purple seemed more reddish than the violet in the former Circuit, and
4378the green was much more conspicuous, being as brisk and copious as any
4379of the other Colours, except the yellow, but the red began to be a
4380little faded, inclining very much to purple. After this succeeded the
4381fourth Circuit of green and red. The green was very copious and lively,
4382inclining on the one side to blue, and on the other side to yellow. But
4383in this fourth Circuit there was neither violet, blue, nor yellow, and
4384the red was very imperfect and dirty. Also the succeeding Colours became
4385more and more imperfect and dilute, till after three or four revolutions
4386they ended in perfect whiteness. Their form, when the Glasses were most
4387compress'd so as to make the black Spot appear in the center, is
4388delineated 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,
4391black, blue, white, yellow, red: violet, blue, green, yellow, red:
4392purple, blue, green, yellow, red: green, red: greenish blue, red:
4393greenish 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
4398interjacent Air, by which each Colour was produced, I measured the
4399Diameters of the first six Rings at the most lucid part of their Orbits,
4400and squaring them, I found their Squares to be in the arithmetical
4401Progression of the odd Numbers, 1, 3, 5, 7, 9, 11. And since one of
4402these Glasses was plane, and the other spherical, their Intervals at
4403those Rings must be in the same Progression. I measured also the
4404Diameters of the dark or faint Rings between the more lucid Colours, and
4405found their Squares to be in the arithmetical Progression of the even
4406Numbers, 2, 4, 6, 8, 10, 12. And it being very nice and difficult to
4407take these measures exactly; I repeated them divers times at divers
4408parts of the Glasses, that by their Agreement I might be confirmed in
4409them. And the same method I used in determining some others of the
4410following Observations.
4411
4412_Obs._ 6. The Diameter of the sixth Ring at the most lucid part of its
4413Orbit was 58/100 parts of an Inch, and the Diameter of the Sphere on
4414which the double convex Object-glass was ground was about 102 Feet, and
4415hence I gathered the thickness of the Air or Aereal Interval of the
4416Glasses at that Ring. But some time after, suspecting that in making
4417this Observation I had not determined the Diameter of the Sphere with
4418sufficient accurateness, and being uncertain whether the Plano-convex
4419Glass was truly plane, and not something concave or convex on that side
4420which I accounted plane; and whether I had not pressed the Glasses
4421together, as I often did, to make them touch; (For by pressing such
4422Glasses together their parts easily yield inwards, and the Rings thereby
4423become sensibly broader than they would be, did the Glasses keep their
4424Figures.) I repeated the Experiment, and found the Diameter of the sixth
4425lucid Ring about 55/100 parts of an Inch. I repeated the Experiment also
4426with such an Object-glass of another Telescope as I had at hand. This
4427was a double Convex ground on both sides to one and the same Sphere, and
4428its Focus was distant from it 83-2/5 Inches. And thence, if the Sines of
4429Incidence and Refraction of the bright yellow Light be assumed in
4430proportion as 11 to 17, the Diameter of the Sphere to which the Glass
4431was figured will by computation be found 182 Inches. This Glass I laid
4432upon a flat one, so that the black Spot appeared in the middle of the
4433Rings of Colours without any other Pressure than that of the weight of
4434the Glass. And now measuring the Diameter of the fifth dark Circle as
4435accurately as I could, I found it the fifth part of an Inch precisely.
4436This Measure was taken with the points of a pair of Compasses on the
4437upper Surface on the upper Glass, and my Eye was about eight or nine
4438Inches distance from the Glass, almost perpendicularly over it, and the
4439Glass was 1/6 of an Inch thick, and thence it is easy to collect that
4440the true Diameter of the Ring between the Glasses was greater than its
4441measur'd Diameter above the Glasses in the Proportion of 80 to 79, or
4442thereabouts, and by consequence equal to 16/79 parts of an Inch, and its
4443true Semi-diameter equal to 8/79 parts. Now as the Diameter of the
4444Sphere (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
4446Air at this fifth dark Ring; which is therefore 32/567931 or
4447100/1774784. Parts of an Inch; and the fifth Part thereof, _viz._ the
44481/88739 Part of an Inch, is the Thickness of the Air at the first of
4449these dark Rings.
4450
4451The same Experiment I repeated with another double convex Object-glass
4452ground on both sides to one and the same Sphere. Its Focus was distant
4453from it 168-1/2 Inches, and therefore the Diameter of that Sphere was
4454184 Inches. This Glass being laid upon the same plain Glass, the
4455Diameter of the fifth of the dark Rings, when the black Spot in their
4456Center appear'd plainly without pressing the Glasses, was by the measure
4457of the Compasses upon the upper Glass 121/600 Parts of an Inch, and by
4458consequence between the Glasses it was 1222/6000: For the upper Glass
4459was 1/8 of an Inch thick, and my Eye was distant from it 8 Inches. And a
4460third proportional to half this from the Diameter of the Sphere is
44615/88850 Parts of an Inch. This is therefore the Thickness of the Air at
4462this Ring, and a fifth Part thereof, _viz._ the 1/88850th Part of an
4463Inch is the Thickness thereof at the first of the Rings, as above.
4464
4465I tried the same Thing, by laying these Object-glasses upon flat Pieces
4466of a broken Looking-glass, and found the same Measures of the Rings:
4467Which makes me rely upon them till they can be determin'd more
4468accurately by Glasses ground to larger Spheres, though in such Glasses
4469greater care must be taken of a true Plane.
4470
4471These Dimensions were taken, when my Eye was placed almost
4472perpendicularly over the Glasses, being about an Inch, or an Inch and a
4473quarter, distant from the incident Rays, and eight Inches distant from
4474the Glass; so that the Rays were inclined to the Glass in an Angle of
4475about four Degrees. Whence by the following Observation you will
4476understand, that had the Rays been perpendicular to the Glasses, the
4477Thickness of the Air at these Rings would have been less in the
4478Proportion of the Radius to the Secant of four Degrees, that is, of
447910000 to 10024. Let the Thicknesses found be therefore diminish'd in
4480this Proportion, and they will become 1/88952 and 1/89063, or (to use
4481the nearest round Number) the 1/89000th Part of an Inch. This is the
4482Thickness of the Air at the darkest Part of the first dark Ring made by
4483perpendicular Rays; and half this Thickness multiplied by the
4484Progression, 1, 3, 5, 7, 9, 11, &c. gives the Thicknesses of the Air at
4485the most luminous Parts of all the brightest Rings, _viz._ 1/178000,
44863/178000, 5/178000, 7/178000, &c. their arithmetical Means 2/178000,
44874/178000, 6/178000, &c. being its Thicknesses at the darkest Parts of
4488all the dark ones.
4489
4490_Obs._ 7. The Rings were least, when my Eye was placed perpendicularly
4491over the Glasses in the Axis of the Rings: And when I view'd them
4492obliquely they became bigger, continually swelling as I removed my Eye
4493farther from the Axis. And partly by measuring the Diameter of the same
4494Circle at several Obliquities of my Eye, partly by other Means, as also
4495by making use of the two Prisms for very great Obliquities, I found its
4496Diameter, and consequently the Thickness of the Air at its Perimeter in
4497all those Obliquities to be very nearly in the Proportions express'd in
4498this Table.
4499
4500-------------------+--------------------+----------+----------
4501Angle 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
4534In the two first Columns are express'd the Obliquities of the incident
4535and emergent Rays to the Plate of the Air, that is, their Angles of
4536Incidence and Refraction. In the third Column the Diameter of any
4537colour'd Ring at those Obliquities is expressed in Parts, of which ten
4538constitute that Diameter when the Rays are perpendicular. And in the
4539fourth Column the Thickness of the Air at the Circumference of that Ring
4540is expressed in Parts, of which also ten constitute its Thickness when
4541the Rays are perpendicular.
4542
4543And from these Measures I seem to gather this Rule: That the Thickness
4544of the Air is proportional to the Secant of an Angle, whose Sine is a
4545certain mean Proportional between the Sines of Incidence and Refraction.
4546And that mean Proportional, so far as by these Measures I can determine
4547it, is the first of an hundred and six arithmetical mean Proportionals
4548between those Sines counted from the bigger Sine, that is, from the Sine
4549of Refraction when the Refraction is made out of the Glass into the
4550Plate of Air, or from the Sine of Incidence when the Refraction is made
4551out 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
4554Obliquation of the Eye, although almost insensibly. But, if instead of
4555the Object-glasses the Prisms were made use of, its Increase was more
4556manifest when viewed so obliquely that no Colours appear'd about it. It
4557was least when the Rays were incident most obliquely on the interjacent
4558Air, and as the obliquity decreased it increased more and more until the
4559colour'd Rings appear'd, and then decreased again, but not so much as it
4560increased before. And hence it is evident, that the Transparency was
4561not only at the absolute Contact of the Glasses, but also where they had
4562some little Interval. I have sometimes observed the Diameter of that
4563Spot to be between half and two fifth parts of the Diameter of the
4564exterior Circumference of the red in the first Circuit or Revolution of
4565Colours when view'd almost perpendicularly; whereas when view'd
4566obliquely it hath wholly vanish'd and become opake and white like the
4567other parts of the Glass; whence it may be collected that the Glasses
4568did then scarcely, or not at all, touch one another, and that their
4569Interval at the perimeter of that Spot when view'd perpendicularly was
4570about a fifth or sixth part of their Interval at the circumference of
4571the said red.
4572
4573_Obs._ 9. By looking through the two contiguous Object-glasses, I found
4574that the interjacent Air exhibited Rings of Colours, as well by
4575transmitting Light as by reflecting it. The central Spot was now white,
4576and from it the order of the Colours were yellowish red; black, violet,
4577blue, white, yellow, red; violet, blue, green, yellow, red, &c. But
4578these Colours were very faint and dilute, unless when the Light was
4579trajected very obliquely through the Glasses: For by that means they
4580became pretty vivid. Only the first yellowish red, like the blue in the
4581fourth Observation, was so little and faint as scarcely to be discern'd.
4582Comparing the colour'd Rings made by Reflexion, with these made by
4583transmission of the Light; I found that white was opposite to black, red
4584to blue, yellow to violet, and green to a Compound of red and violet.
4585That is, those parts of the Glass were black when looked through, which
4586when looked upon appeared white, and on the contrary. And so those which
4587in one case exhibited blue, did in the other case exhibit red. And the
4588like of the other Colours. The manner you have represented in the third
4589Figure, where AB, CD, are the Surfaces of the Glasses contiguous at E,
4590and the black Lines between them are their Distances in arithmetical
4591Progression, and the Colours written above are seen by reflected Light,
4592and those below by Light transmitted (p. 209).
4593
4594_Obs._ 10. Wetting the Object-glasses a little at their edges, the Water
4595crept in slowly between them, and the Circles thereby became less and
4596the Colours more faint: Insomuch that as the Water crept along, one half
4597of them at which it first arrived would appear broken off from the other
4598half, and contracted into a less Room. By measuring them I found the
4599Proportions of their Diameters to the Diameters of the like Circles made
4600by Air to be about seven to eight, and consequently the Intervals of the
4601Glasses at like Circles, caused by those two Mediums Water and Air, are
4602as about three to four. Perhaps it may be a general Rule, That if any
4603other Medium more or less dense than Water be compress'd between the
4604Glasses, their Intervals at the Rings caused thereby will be to their
4605Intervals caused by interjacent Air, as the Sines are which measure the
4606Refraction made out of that Medium into Air.
4607
4608_Obs._ 11. When the Water was between the Glasses, if I pressed the
4609upper Glass variously at its edges to make the Rings move nimbly from
4610one place to another, a little white Spot would immediately follow the
4611center of them, which upon creeping in of the ambient Water into that
4612place would presently vanish. Its appearance was such as interjacent Air
4613would have caused, and it exhibited the same Colours. But it was not
4614air, for where any Bubbles of Air were in the Water they would not
4615vanish. The Reflexion must have rather been caused by a subtiler Medium,
4616which 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
4619examine the Effects of colour'd Light falling on the Glasses, I darken'd
4620the Room, and view'd them by Reflexion of the Colours of a Prism cast on
4621a Sheet of white Paper, my Eye being so placed that I could see the
4622colour'd Paper by Reflexion in the Glasses, as in a Looking-glass. And
4623by this means the Rings became distincter and visible to a far greater
4624number than in the open Air. I have sometimes seen more than twenty of
4625them, 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
4630its Axis, that all the Colours might successively fall on that part of
4631the Paper which I saw by Reflexion from that part of the Glasses, where
4632the Circles appear'd, so that all the Colours might be successively
4633reflected from the Circles to my Eye, whilst I held it immovable, I
4634found the Circles which the red Light made to be manifestly bigger than
4635those which were made by the blue and violet. And it was very pleasant
4636to see them gradually swell or contract accordingly as the Colour of the
4637Light was changed. The Interval of the Glasses at any of the Rings when
4638they were made by the utmost red Light, was to their Interval at the
4639same Ring when made by the utmost violet, greater than as 3 to 2, and
4640less than as 13 to 8. By the most of my Observations it was as 14 to 9.
4641And this Proportion seem'd very nearly the same in all Obliquities of my
4642Eye; unless when two Prisms were made use of instead of the
4643Object-glasses. For then at a certain great obliquity of my Eye, the
4644Rings made by the several Colours seem'd equal, and at a greater
4645obliquity those made by the violet would be greater than the same Rings
4646made by the red: the Refraction of the Prism in this case causing the
4647most refrangible Rays to fall more obliquely on that plate of the Air
4648than the least refrangible ones. Thus the Experiment succeeded in the
4649colour'd Light, which was sufficiently strong and copious to make the
4650Rings sensible. And thence it may be gather'd, that if the most
4651refrangible and least refrangible Rays had been copious enough to make
4652the Rings sensible without the mixture of other Rays, the Proportion
4653which here was 14 to 9 would have been a little greater, suppose 14-1/4
4654or 14-1/3 to 9.
4655
4656_Obs._ 14. Whilst the Prism was turn'd about its Axis with an uniform
4657Motion, to make all the several Colours fall successively upon the
4658Object-glasses, and thereby to make the Rings contract and dilate: The
4659Contraction or Dilatation of each Ring thus made by the variation of its
4660Colour was swiftest in the red, and slowest in the violet, and in the
4661intermediate Colours it had intermediate degrees of Celerity. Comparing
4662the quantity of Contraction and Dilatation made by all the degrees of
4663each Colour, I found that it was greatest in the red; less in the
4664yellow, still less in the blue, and least in the violet. And to make as
4665just an Estimation as I could of the Proportions of their Contractions
4666or Dilatations, I observ'd that the whole Contraction or Dilatation of
4667the Diameter of any Ring made by all the degrees of red, was to that of
4668the Diameter of the same Ring made by all the degrees of violet, as
4669about four to three, or five to four, and that when the Light was of the
4670middle Colour between yellow and green, the Diameter of the Ring was
4671very nearly an arithmetical Mean between the greatest Diameter of the
4672same Ring made by the outmost red, and the least Diameter thereof made
4673by the outmost violet: Contrary to what happens in the Colours of the
4674oblong Spectrum made by the Refraction of a Prism, where the red is most
4675contracted, the violet most expanded, and in the midst of all the
4676Colours is the Confine of green and blue. And hence I seem to collect
4677that the thicknesses of the Air between the Glasses there, where the
4678Ring is successively made by the limits of the five principal Colours
4679(red, yellow, green, blue, violet) in order (that is, by the extreme
4680red, by the limit of red and yellow in the middle of the orange, by the
4681limit of yellow and green, by the limit of green and blue, by the limit
4682of blue and violet in the middle of the indigo, and by the extreme
4683violet) are to one another very nearly as the sixth lengths of a Chord
4684which 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
4686the thicknesses of the Air between the Glasses there, where the Rings
4687are successively made by the limits of the seven Colours, red, orange,
4688yellow, green, blue, indigo, violet in order, are to one another as the
4689Cube Roots of the Squares of the eight lengths of a Chord, which found
4690the 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,
46925/6, 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
4695the open Air, but appeared all over of that prismatick Colour only with
4696which they were illuminated. And by projecting the prismatick Colours
4697immediately upon the Glasses, I found that the Light which fell on the
4698dark Spaces which were between the Colour'd Rings was transmitted
4699through the Glasses without any variation of Colour. For on a white
4700Paper placed behind, it would paint Rings of the same Colour with those
4701which were reflected, and of the bigness of their immediate Spaces. And
4702from thence the origin of these Rings is manifest; namely, that the Air
4703between the Glasses, according to its various thickness, is disposed in
4704some places to reflect, and in others to transmit the Light of any one
4705Colour (as you may see represented in the fourth Figure) and in the same
4706place 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
4711prismatick Colour were in arithmetical Progression, as in the fifth
4712Observation. And the Diameter of the sixth Circle, when made by the
4713citrine yellow, and viewed almost perpendicularly was about 58/100 parts
4714of an Inch, or a little less, agreeable to the sixth Observation.
4715
4716The precedent Observations were made with a rarer thin Medium,
4717terminated by a denser, such as was Air or Water compress'd between two
4718Glasses. In those that follow are set down the Appearances of a denser
4719Medium thin'd within a rarer, such as are Plates of Muscovy Glass,
4720Bubbles of Water, and some other thin Substances terminated on all sides
4721with air.
4722
4723_Obs._ 17. If a Bubble be blown with Water first made tenacious by
4724dissolving a little Soap in it, 'tis a common Observation, that after a
4725while it will appear tinged with a great variety of Colours. To defend
4726these Bubbles from being agitated by the external Air (whereby their
4727Colours are irregularly moved one among another, so that no accurate
4728Observation can be made of them,) as soon as I had blown any of them I
4729cover'd it with a clear Glass, and by that means its Colours emerged in
4730a very regular order, like so many concentrick Rings encompassing the
4731top of the Bubble. And as the Bubble grew thinner by the continual
4732subsiding of the Water, these Rings dilated slowly and overspread the
4733whole Bubble, descending in order to the bottom of it, where they
4734vanish'd successively. In the mean while, after all the Colours were
4735emerged at the top, there grew in the center of the Rings a small round
4736black Spot, like that in the first Observation, which continually
4737dilated it self till it became sometimes more than 1/2 or 3/4 of an Inch
4738in breadth before the Bubble broke. At first I thought there had been no
4739Light reflected from the Water in that place, but observing it more
4740curiously, I saw within it several smaller round Spots, which appeared
4741much blacker and darker than the rest, whereby I knew that there was
4742some Reflexion at the other places which were not so dark as those
4743Spots. And by farther Tryal I found that I could see the Images of some
4744things (as of a Candle or the Sun) very faintly reflected, not only from
4745the great black Spot, but also from the little darker Spots which were
4746within it.
4747
4748Besides the aforesaid colour'd Rings there would often appear small
4749Spots of Colours, ascending and descending up and down the sides of the
4750Bubble, by reason of some Inequalities in the subsiding of the Water.
4751And sometimes small black Spots generated at the sides would ascend up
4752to 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
4755lively than those of the Air thinn'd between two Glasses, and so more
4756easy to be distinguish'd, I shall here give you a farther description of
4757their order, as they were observ'd in viewing them by Reflexion of the
4758Skies when of a white Colour, whilst a black substance was placed
4759behind the Bubble. And they were these, red, blue; red, blue; red, blue;
4760red, green; red, yellow, green, blue, purple; red, yellow, green, blue,
4761violet; red, yellow, white, blue, black.
4762
4763The three first Successions of red and blue were very dilute and dirty,
4764especially the first, where the red seem'd in a manner to be white.
4765Among these there was scarce any other Colour sensible besides red and
4766blue, only the blues (and principally the second blue) inclined a little
4767to green.
4768
4769The fourth red was also dilute and dirty, but not so much as the former
4770three; after that succeeded little or no yellow, but a copious green,
4771which at first inclined a little to yellow, and then became a pretty
4772brisk and good willow green, and afterwards changed to a bluish Colour;
4773but there succeeded neither blue nor violet.
4774
4775The fifth red at first inclined very much to purple, and afterwards
4776became more bright and brisk, but yet not very pure. This was succeeded
4777with a very bright and intense yellow, which was but little in quantity,
4778and soon chang'd to green: But that green was copious and something more
4779pure, deep and lively, than the former green. After that follow'd an
4780excellent blue of a bright Sky-colour, and then a purple, which was less
4781in quantity than the blue, and much inclined to red.
4782
4783The sixth red was at first of a very fair and lively scarlet, and soon
4784after of a brighter Colour, being very pure and brisk, and the best of
4785all the reds. Then after a lively orange follow'd an intense bright and
4786copious yellow, which was also the best of all the yellows, and this
4787changed first to a greenish yellow, and then to a greenish blue; but the
4788green between the yellow and the blue, was very little and dilute,
4789seeming rather a greenish white than a green. The blue which succeeded
4790became very good, and of a very bright Sky-colour, but yet something
4791inferior to the former blue; and the violet was intense and deep with
4792little or no redness in it. And less in quantity than the blue.
4793
4794In the last red appeared a tincture of scarlet next to violet, which
4795soon changed to a brighter Colour, inclining to an orange; and the
4796yellow which follow'd was at first pretty good and lively, but
4797afterwards it grew more dilute until by degrees it ended in perfect
4798whiteness. And this whiteness, if the Water was very tenacious and
4799well-temper'd, would slowly spread and dilate it self over the greater
4800part of the Bubble; continually growing paler at the top, where at
4801length it would crack in many places, and those cracks, as they dilated,
4802would appear of a pretty good, but yet obscure and dark Sky-colour; the
4803white between the blue Spots diminishing, until it resembled the Threds
4804of an irregular Net-work, and soon after vanish'd, and left all the
4805upper part of the Bubble of the said dark blue Colour. And this Colour,
4806after the aforesaid manner, dilated it self downwards, until sometimes
4807it hath overspread the whole Bubble. In the mean while at the top, which
4808was of a darker blue than the bottom, and appear'd also full of many
4809round blue Spots, something darker than the rest, there would emerge
4810one or more very black Spots, and within those, other Spots of an
4811intenser blackness, which I mention'd in the former Observation; and
4812these continually dilated themselves until the Bubble broke.
4813
4814If the Water was not very tenacious, the black Spots would break forth
4815in the white, without any sensible intervention of the blue. And
4816sometimes they would break forth within the precedent yellow, or red, or
4817perhaps within the blue of the second order, before the intermediate
4818Colours had time to display themselves.
4819
4820By this description you may perceive how great an affinity these Colours
4821have with those of Air described in the fourth Observation, although set
4822down in a contrary order, by reason that they begin to appear when the
4823Bubble is thickest, and are most conveniently reckon'd from the lowest
4824and thickest part of the Bubble upwards.
4825
4826_Obs._ 19. Viewing in several oblique Positions of my Eye the Rings of
4827Colours emerging on the top of the Bubble, I found that they were
4828sensibly dilated by increasing the obliquity, but yet not so much by far
4829as those made by thinn'd Air in the seventh Observation. For there they
4830were dilated so much as, when view'd most obliquely, to arrive at a part
4831of the Plate more than twelve times thicker than that where they
4832appear'd when viewed perpendicularly; whereas in this case the thickness
4833of the Water, at which they arrived when viewed most obliquely, was to
4834that thickness which exhibited them by perpendicular Rays, something
4835less than as 8 to 5. By the best of my Observations it was between 15
4836and 15-1/2 to 10; an increase about 24 times less than in the other
4837case.
4838
4839Sometimes the Bubble would become of an uniform thickness all over,
4840except at the top of it near the black Spot, as I knew, because it would
4841exhibit the same appearance of Colours in all Positions of the Eye. And
4842then the Colours which were seen at its apparent circumference by the
4843obliquest Rays, would be different from those that were seen in other
4844places, by Rays less oblique to it. And divers Spectators might see the
4845same part of it of differing Colours, by viewing it at very differing
4846Obliquities. Now observing how much the Colours at the same places of
4847the Bubble, or at divers places of equal thickness, were varied by the
4848several Obliquities of the Rays; by the assistance of the 4th, 14th,
484916th and 18th Observations, as they are hereafter explain'd, I collect
4850the thickness of the Water requisite to exhibit any one and the same
4851Colour, at several Obliquities, to be very nearly in the Proportion
4852expressed 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
4875In the two first Columns are express'd the Obliquities of the Rays to
4876the Superficies of the Water, that is, their Angles of Incidence and
4877Refraction. Where I suppose, that the Sines which measure them are in
4878round Numbers, as 3 to 4, though probably the Dissolution of Soap in the
4879Water, may a little alter its refractive Virtue. In the third Column,
4880the Thickness of the Bubble, at which any one Colour is exhibited in
4881those several Obliquities, is express'd in Parts, of which ten
4882constitute its Thickness when the Rays are perpendicular. And the Rule
4883found by the seventh Observation agrees well with these Measures, if
4884duly apply'd; namely, that the Thickness of a Plate of Water requisite
4885to exhibit one and the same Colour at several Obliquities of the Eye, is
4886proportional to the Secant of an Angle, whose Sine is the first of an
4887hundred and six arithmetical mean Proportionals between the Sines of
4888Incidence and Refraction counted from the lesser Sine, that is, from the
4889Sine of Refraction when the Refraction is made out of Air into Water,
4890otherwise from the Sine of Incidence.
4891
4892I have sometimes observ'd, that the Colours which arise on polish'd
4893Steel by heating it, or on Bell-metal, and some other metalline
4894Substances, when melted and pour'd on the Ground, where they may cool in
4895the open Air, have, like the Colours of Water-bubbles, been a little
4896changed by viewing them at divers Obliquities, and particularly that a
4897deep blue, or violet, when view'd very obliquely, hath been changed to a
4898deep red. But the Changes of these Colours are not so great and
4899sensible as of those made by Water. For the Scoria, or vitrified Part of
4900the Metal, which most Metals when heated or melted do continually
4901protrude, and send out to their Surface, and which by covering the
4902Metals in form of a thin glassy Skin, causes these Colours, is much
4903denser than Water; and I find that the Change made by the Obliquation of
4904the Eye is least in Colours of the densest thin Substances.
4905
4906_Obs._ 20. As in the ninth Observation, so here, the Bubble, by
4907transmitted Light, appear'd of a contrary Colour to that, which it
4908exhibited by Reflexion. Thus when the Bubble being look'd on by the
4909Light of the Clouds reflected from it, seemed red at its apparent
4910Circumference, if the Clouds at the same time, or immediately after,
4911were view'd through it, the Colour at its Circumference would be blue.
4912And, on the contrary, when by reflected Light it appeared blue, it would
4913appear red by transmitted Light.
4914
4915_Obs._ 21. By wetting very thin Plates of _Muscovy_ Glass, whose
4916thinness made the like Colours appear, the Colours became more faint and
4917languid, especially by wetting the Plates on that side opposite to the
4918Eye: But I could not perceive any variation of their Species. So then
4919the thickness of a Plate requisite to produce any Colour, depends only
4920on the density of the Plate, and not on that of the ambient Medium. And
4921hence, by the 10th and 16th Observations, may be known the thickness
4922which Bubbles of Water, or Plates of _Muscovy_ Glass, or other
4923Substances, have at any Colour produced by them.
4924
4925_Obs._ 22. A thin transparent Body, which is denser than its ambient
4926Medium, exhibits more brisk and vivid Colours than that which is so much
4927rarer; as I have particularly observed in the Air and Glass. For blowing
4928Glass very thin at a Lamp Furnace, those Plates encompassed with Air did
4929exhibit Colours much more vivid than those of Air made thin between two
4930Glasses.
4931
4932_Obs._ 23. Comparing the quantity of Light reflected from the several
4933Rings, I found that it was most copious from the first or inmost, and in
4934the exterior Rings became gradually less and less. Also the whiteness of
4935the first Ring was stronger than that reflected from those parts of the
4936thin Medium or Plate which were without the Rings; as I could manifestly
4937perceive by viewing at a distance the Rings made by the two
4938Object-glasses; or by comparing two Bubbles of Water blown at distant
4939Times, in the first of which the Whiteness appear'd, which succeeded all
4940the 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
4943as to make the Rings of the Colours appear, though with my naked Eye I
4944could not discern above eight or nine of those Rings, yet by viewing
4945them through a Prism I have seen a far greater Multitude, insomuch that
4946I could number more than forty, besides many others, that were so very
4947small and close together, that I could not keep my Eye steady on them
4948severally so as to number them, but by their Extent I have sometimes
4949estimated them to be more than an hundred. And I believe the Experiment
4950may be improved to the Discovery of far greater Numbers. For they seem
4951to be really unlimited, though visible only so far as they can be
4952separated by the Refraction of the Prism, as I shall hereafter explain.
4953
4954[Illustration: FIG. 5.]
4955
4956But it was but one side of these Rings, namely, that towards which the
4957Refraction was made, which by that Refraction was render'd distinct, and
4958the other side became more confused than when view'd by the naked Eye,
4959insomuch that there I could not discern above one or two, and sometimes
4960none of those Rings, of which I could discern eight or nine with my
4961naked Eye. And their Segments or Arcs, which on the other side appear'd
4962so numerous, for the most part exceeded not the third Part of a Circle.
4963If the Refraction was very great, or the Prism very distant from the
4964Object-glasses, the middle Part of those Arcs became also confused, so
4965as to disappear and constitute an even Whiteness, whilst on either side
4966their Ends, as also the whole Arcs farthest from the Center, became
4967distincter than before, appearing in the Form as you see them design'd
4968in the fifth Figure.
4969
4970The Arcs, where they seem'd distinctest, were only white and black
4971successively, without any other Colours intermix'd. But in other Places
4972there appeared Colours, whose Order was inverted by the refraction in
4973such manner, that if I first held the Prism very near the
4974Object-glasses, and then gradually removed it farther off towards my
4975Eye, the Colours of the 2d, 3d, 4th, and following Rings, shrunk towards
4976the white that emerged between them, until they wholly vanish'd into it
4977at the middle of the Arcs, and afterwards emerged again in a contrary
4978Order. But at the Ends of the Arcs they retain'd their Order unchanged.
4979
4980I have sometimes so lay'd one Object-glass upon the other, that to the
4981naked Eye they have all over seem'd uniformly white, without the least
4982Appearance of any of the colour'd Rings; and yet by viewing them through
4983a Prism, great Multitudes of those Rings have discover'd themselves. And
4984in like manner Plates of _Muscovy_ Glass, and Bubbles of Glass blown at
4985a Lamp-Furnace, which were not so thin as to exhibit any Colours to the
4986naked Eye, have through the Prism exhibited a great Variety of them
4987ranged irregularly up and down in the Form of Waves. And so Bubbles of
4988Water, before they began to exhibit their Colours to the naked Eye of a
4989Bystander, have appeared through a Prism, girded about with many
4990parallel and horizontal Rings; to produce which Effect, it was necessary
4991to hold the Prism parallel, or very nearly parallel to the Horizon, and
4992to dispose it so that the Rays might be refracted upwards.
4993
4994
4995
4996
4997THE
4998
4999SECOND BOOK
5000
5001OF
5002
5003OPTICKS
5004
5005
5006_PART II._
5007
5008_Remarks upon the foregoing Observations._
5009
5010
5011Having given my Observations of these Colours, before I make use of them
5012to unfold the Causes of the Colours of natural Bodies, it is convenient
5013that by the simplest of them, such as are the 2d, 3d, 4th, 9th, 12th,
501418th, 20th, and 24th, I first explain the more compounded. And first to
5015shew how the Colours in the fourth and eighteenth Observations are
5016produced, 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
5018one another, as the Cube-Roots of the Squares of the Numbers, 1/2, 9/16,
50193/5, 2/3, 3/4, 5/6, 8/9, 1, whereby the Lengths of a Musical Chord to
5020sound all the Notes in an eighth are represented; that is, in the
5021Proportion of the Numbers 6300, 6814, 7114, 7631, 8255, 8855, 9243,
502210000. And at the Points A, B, C, D, E, F, G, H, let Perpendiculars
5023A[Greek: a], B[Greek: b], &c. be erected, by whose Intervals the Extent
5024of the several Colours set underneath against them, is to be
5025represented. Then divide the Line _A[Greek: a]_ in such Proportion as
5026the Numbers 1, 2, 3, 5, 6, 7, 9, 10, 11, &c. set at the Points of
5027Division denote. And through those Divisions from Y draw Lines 1I, 2K,
50283L, 5M, 6N, 7O, &c.
5029
5030Now, if A2 be supposed to represent the Thickness of any thin
5031transparent Body, at which the outmost Violet is most copiously
5032reflected in the first Ring, or Series of Colours, then by the 13th
5033Observation, HK will represent its Thickness, at which the utmost Red is
5034most copiously reflected in the same Series. Also by the 5th and 16th
5035Observations, A6 and HN will denote the Thicknesses at which those
5036extreme Colours are most copiously reflected in the second Series, and
5037A10 and HQ the Thicknesses at which they are most copiously reflected in
5038the third Series, and so on. And the Thickness at which any of the
5039intermediate Colours are reflected most copiously, will, according to
5040the 14th Observation, be defined by the distance of the Line AH from the
5041intermediate parts of the Lines 2K, 6N, 10Q, &c. against which the Names
5042of those Colours are written below.
5043
5044[Illustration: FIG. 6.]
5045
5046But farther, to define the Latitude of these Colours in each Ring or
5047Series, let A1 design the least thickness, and A3 the greatest
5048thickness, at which the extreme violet in the first Series is reflected,
5049and let HI, and HL, design the like limits for the extreme red, and let
5050the intermediate Colours be limited by the intermediate parts of the
5051Lines 1I, and 3L, against which the Names of those Colours are written,
5052and so on: But yet with this caution, that the Reflexions be supposed
5053strongest at the intermediate Spaces, 2K, 6N, 10Q, &c. and from thence
5054to decrease gradually towards these limits, 1I, 3L, 5M, 7O, &c. on
5055either side; where you must not conceive them to be precisely limited,
5056but to decay indefinitely. And whereas I have assign'd the same Latitude
5057to every Series, I did it, because although the Colours in the first
5058Series seem to be a little broader than the rest, by reason of a
5059stronger Reflexion there, yet that inequality is so insensible as
5060scarcely to be determin'd by Observation.
5061
5062Now according to this Description, conceiving that the Rays originally
5063of several Colours are by turns reflected at the Spaces 1I, L3, 5M, O7,
50649PR11, &c. and transmitted at the Spaces AHI1, 3LM5, 7OP9, &c. it is
5065easy to know what Colour must in the open Air be exhibited at any
5066thickness of a transparent thin Body. For if a Ruler be applied parallel
5067to AH, at that distance from it by which the thickness of the Body is
5068represented, the alternate Spaces 1IL3, 5MO7, &c. which it crosseth will
5069denote the reflected original Colours, of which the Colour exhibited in
5070the open Air is compounded. Thus if the constitution of the green in the
5071third 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:
5073p] and yellow at [Greek: s], as well as through the green at [Greek: r],
5074you may conclude that the green exhibited at that thickness of the Body
5075is principally constituted of original green, but not without a mixture
5076of some blue and yellow.
5077
5078By this means you may know how the Colours from the center of the Rings
5079outward ought to succeed in order as they were described in the 4th and
508018th Observations. For if you move the Ruler gradually from AH through
5081all distances, having pass'd over the first Space which denotes little
5082or no Reflexion to be made by thinnest Substances, it will first arrive
5083at 1 the violet, and then very quickly at the blue and green, which
5084together with that violet compound blue, and then at the yellow and red,
5085by whose farther addition that blue is converted into whiteness, which
5086whiteness continues during the transit of the edge of the Ruler from I
5087to 3, and after that by the successive deficience of its component
5088Colours, turns first to compound yellow, and then to red, and last of
5089all the red ceaseth at L. Then begin the Colours of the second Series,
5090which succeed in order during the transit of the edge of the Ruler from
50915 to O, and are more lively than before, because more expanded and
5092severed. And for the same reason instead of the former white there
5093intercedes between the blue and yellow a mixture of orange, yellow,
5094green, blue and indigo, all which together ought to exhibit a dilute and
5095imperfect green. So the Colours of the third Series all succeed in
5096order; first, the violet, which a little interferes with the red of the
5097second order, and is thereby inclined to a reddish purple; then the blue
5098and green, which are less mix'd with other Colours, and consequently
5099more lively than before, especially the green: Then follows the yellow,
5100some of which towards the green is distinct and good, but that part of
5101it towards the succeeding red, as also that red is mix'd with the violet
5102and blue of the fourth Series, whereby various degrees of red very much
5103inclining to purple are compounded. This violet and blue, which should
5104succeed this red, being mixed with, and hidden in it, there succeeds a
5105green. And this at first is much inclined to blue, but soon becomes a
5106good green, the only unmix'd and lively Colour in this fourth Series.
5107For as it verges towards the yellow, it begins to interfere with the
5108Colours of the fifth Series, by whose mixture the succeeding yellow and
5109red are very much diluted and made dirty, especially the yellow, which
5110being the weaker Colour is scarce able to shew it self. After this the
5111several Series interfere more and more, and their Colours become more
5112and more intermix'd, till after three or four more revolutions (in which
5113the red and blue predominate by turns) all sorts of Colours are in all
5114places pretty equally blended, and compound an even whiteness.
5115
5116And since by the 15th Observation the Rays endued with one Colour are
5117transmitted, where those of another Colour are reflected, the reason of
5118the Colours made by the transmitted Light in the 9th and 20th
5119Observations is from hence evident.
5120
5121If not only the Order and Species of these Colours, but also the precise
5122thickness of the Plate, or thin Body at which they are exhibited, be
5123desired in parts of an Inch, that may be also obtained by assistance of
5124the 6th or 16th Observations. For according to those Observations the
5125thickness of the thinned Air, which between two Glasses exhibited the
5126most luminous parts of the first six Rings were 1/178000, 3/178000,
51275/178000, 7/178000, 9/178000, 11/178000 parts of an Inch. Suppose the
5128Light reflected most copiously at these thicknesses be the bright
5129citrine yellow, or confine of yellow and orange, and these thicknesses
5130will be F[Greek: l], F[Greek: m], F[Greek: u], F[Greek: x], F[Greek: o],
5131F[Greek: t]. And this being known, it is easy to determine what
5132thickness of Air is represented by G[Greek: ph], or by any other
5133distance of the Ruler from AH.
5134
5135But farther, since by the 10th Observation the thickness of Air was to
5136the thickness of Water, which between the same Glasses exhibited the
5137same Colour, as 4 to 3, and by the 21st Observation the Colours of thin
5138Bodies are not varied by varying the ambient Medium; the thickness of a
5139Bubble of Water, exhibiting any Colour, will be 3/4 of the thickness of
5140Air producing the same Colour. And so according to the same 10th and
514121st Observations, the thickness of a Plate of Glass, whose Refraction
5142of the mean refrangible Ray, is measured by the proportion of the Sines
514331 to 20, may be 20/31 of the thickness of Air producing the same
5144Colours; and the like of other Mediums. I do not affirm, that this
5145proportion of 20 to 31, holds in all the Rays; for the Sines of other
5146sorts of Rays have other Proportions. But the differences of those
5147Proportions are so little that I do not here consider them. On these
5148Grounds I have composed the following Table, wherein the thickness of
5149Air, Water, and Glass, at which each Colour is most intense and
5150specifick, is expressed in parts of an Inch divided into ten hundred
5151thousand equal parts.
5152
5153Now if this Table be compared with the 6th Scheme, you will there see
5154the constitution of each Colour, as to its Ingredients, or the original
5155Colours of which it is compounded, and thence be enabled to judge of its
5156Intenseness or Imperfection; which may suffice in explication of the 4th
5157and 18th Observations, unless it be farther desired to delineate the
5158manner how the Colours appear, when the two Object-glasses are laid upon
5159one another. To do which, let there be described a large Arc of a
5160Circle, and a streight Line which may touch that Arc, and parallel to
5161that Tangent several occult Lines, at such distances from it, as the
5162Numbers set against the several Colours in the Table denote. For the
5163Arc, and its Tangent, will represent the Superficies of the Glasses
5164terminating the interjacent Air; and the places where the occult Lines
5165cut the Arc will show at what distances from the center, or Point of
5166contact, 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 |
5177Their Colours of the {Blue | 2-2/5 | 1-4/5 | 1-11/22 |
5178first 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 |
5187Of 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 |
5195Of 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 |
5202Of 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 |
5206Of the fifth Order, {Red | 52-1/2 | 39-3/8 | 34 |
5207 |---------+----------+----------|
5208 {Greenish blue | 58-3/4 | 44 | 38 |
5209Of the sixth Order, {Red | 65 | 48-3/4 | 42 |
5210 |---------+----------+----------|
5211Of the seventh Order, {Greenish blue | 71 | 53-1/4 | 45-4/5 |
5212 {Ruddy White | 77 | 57-3/4 | 49-2/3 |
5213 |---------+----------+----------|
5214
5215There are also other Uses of this Table: For by its assistance the
5216thickness of the Bubble in the 19th Observation was determin'd by the
5217Colours which it exhibited. And so the bigness of the parts of natural
5218Bodies may be conjectured by their Colours, as shall be hereafter shewn.
5219Also, if two or more very thin Plates be laid one upon another, so as to
5220compose one Plate equalling them all in thickness, the resulting Colour
5221may be hereby determin'd. For instance, Mr. _Hook_ observed, as is
5222mentioned in his _Micrographia_, that a faint yellow Plate of _Muscovy_
5223Glass laid upon a blue one, constituted a very deep purple. The yellow
5224of the first Order is a faint one, and the thickness of the Plate
5225exhibiting it, according to the Table is 4-3/5, to which add 9, the
5226thickness exhibiting blue of the second Order, and the Sum will be
522713-3/5, which is the thickness exhibiting the purple of the third Order.
5228
5229To explain, in the next place, the circumstances of the 2d and 3d
5230Observations; that is, how the Rings of the Colours may (by turning the
5231Prisms about their common Axis the contrary way to that expressed in
5232those Observations) be converted into white and black Rings, and
5233afterwards into Rings of Colours again, the Colours of each Ring lying
5234now in an inverted order; it must be remember'd, that those Rings of
5235Colours are dilated by the obliquation of the Rays to the Air which
5236intercedes the Glasses, and that according to the Table in the 7th
5237Observation, their Dilatation or Increase of their Diameter is most
5238manifest and speedy when they are obliquest. Now the Rays of yellow
5239being more refracted by the first Superficies of the said Air than those
5240of red, are thereby made more oblique to the second Superficies, at
5241which they are reflected to produce the colour'd Rings, and consequently
5242the yellow Circle in each Ring will be more dilated than the red; and
5243the Excess of its Dilatation will be so much the greater, by how much
5244the greater is the obliquity of the Rays, until at last it become of
5245equal extent with the red of the same Ring. And for the same reason the
5246green, blue and violet, will be also so much dilated by the still
5247greater obliquity of their Rays, as to become all very nearly of equal
5248extent with the red, that is, equally distant from the center of the
5249Rings. And then all the Colours of the same Ring must be co-incident,
5250and by their mixture exhibit a white Ring. And these white Rings must
5251have black and dark Rings between them, because they do not spread and
5252interfere with one another, as before. And for that reason also they
5253must become distincter, and visible to far greater numbers. But yet the
5254violet being obliquest will be something more dilated, in proportion to
5255its extent, than the other Colours, and so very apt to appear at the
5256exterior Verges of the white.
5257
5258Afterwards, by a greater obliquity of the Rays, the violet and blue
5259become more sensibly dilated than the red and yellow, and so being
5260farther removed from the center of the Rings, the Colours must emerge
5261out of the white in an order contrary to that which they had before; the
5262violet and blue at the exterior Limbs of each Ring, and the red and
5263yellow at the interior. And the violet, by reason of the greatest
5264obliquity of its Rays, being in proportion most of all expanded, will
5265soonest appear at the exterior Limb of each white Ring, and become more
5266conspicuous than the rest. And the several Series of Colours belonging
5267to the several Rings, will, by their unfolding and spreading, begin
5268again to interfere, and thereby render the Rings less distinct, and not
5269visible to so great numbers.
5270
5271If instead of the Prisms the Object-glasses be made use of, the Rings
5272which they exhibit become not white and distinct by the obliquity of the
5273Eye, by reason that the Rays in their passage through that Air which
5274intercedes the Glasses are very nearly parallel to those Lines in which
5275they were first incident on the Glasses, and consequently the Rays
5276endued with several Colours are not inclined one more than another to
5277that Air, as it happens in the Prisms.
5278
5279There is yet another circumstance of these Experiments to be consider'd,
5280and that is why the black and white Rings which when view'd at a
5281distance appear distinct, should not only become confused by viewing
5282them near at hand, but also yield a violet Colour at both the edges of
5283every white Ring. And the reason is, that the Rays which enter the Eye
5284at several parts of the Pupil, have several Obliquities to the Glasses,
5285and those which are most oblique, if consider'd apart, would represent
5286the Rings bigger than those which are the least oblique. Whence the
5287breadth of the Perimeter of every white Ring is expanded outwards by the
5288obliquest Rays, and inwards by the least oblique. And this Expansion is
5289so much the greater by how much the greater is the difference of the
5290Obliquity; that is, by how much the Pupil is wider, or the Eye nearer to
5291the Glasses. And the breadth of the violet must be most expanded,
5292because the Rays apt to excite a Sensation of that Colour are most
5293oblique to a second or farther Superficies of the thinn'd Air at which
5294they are reflected, and have also the greatest variation of Obliquity,
5295which makes that Colour soonest emerge out of the edges of the white.
5296And as the breadth of every Ring is thus augmented, the dark Intervals
5297must be diminish'd, until the neighbouring Rings become continuous, and
5298are blended, the exterior first, and then those nearer the center; so
5299that they can no longer be distinguish'd apart, but seem to constitute
5300an even and uniform whiteness.
5301
5302Among all the Observations there is none accompanied with so odd
5303circumstances as the twenty-fourth. Of those the principal are, that in
5304thin Plates, which to the naked Eye seem of an even and uniform
5305transparent whiteness, without any terminations of Shadows, the
5306Refraction of a Prism should make Rings of Colours appear, whereas it
5307usually makes Objects appear colour'd only there where they are
5308terminated with Shadows, or have parts unequally luminous; and that it
5309should make those Rings exceedingly distinct and white, although it
5310usually renders Objects confused and coloured. The Cause of these things
5311you will understand by considering, that all the Rings of Colours are
5312really in the Plate, when view'd with the naked Eye, although by reason
5313of the great breadth of their Circumferences they so much interfere and
5314are blended together, that they seem to constitute an uniform whiteness.
5315But when the Rays pass through the Prism to the Eye, the Orbits of the
5316several Colours in every Ring are refracted, some more than others,
5317according to their degrees of Refrangibility: By which means the Colours
5318on one side of the Ring (that is in the circumference on one side of its
5319center), become more unfolded and dilated, and those on the other side
5320more complicated and contracted. And where by a due Refraction they are
5321so much contracted, that the several Rings become narrower than to
5322interfere with one another, they must appear distinct, and also white,
5323if the constituent Colours be so much contracted as to be wholly
5324co-incident. But on the other side, where the Orbit of every Ring is
5325made broader by the farther unfolding of its Colours, it must interfere
5326more with other Rings than before, and so become less distinct.
5327
5328[Illustration: FIG. 7.]
5329
5330To explain this a little farther, suppose the concentrick Circles AV,
5331and BX, [in _Fig._ 7.] represent the red and violet of any Order, which,
5332together with the intermediate Colours, constitute any one of these
5333Rings. Now these being view'd through a Prism, the violet Circle BX,
5334will, by a greater Refraction, be farther translated from its place than
5335the red AV, and so approach nearer to it on that side of the Circles,
5336towards which the Refractions are made. For instance, if the red be
5337translated to _av_, the violet may be translated to _bx_, so as to
5338approach nearer to it at _x_ than before; and if the red be farther
5339translated to av, the violet may be so much farther translated to bx as
5340to 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,
5344but of all the other intermediate Colours, and also of every revolution
5345of those Colours, you will easily perceive how those of the same
5346revolution or order, by their nearness at _xv_ and [Greek: Yx], and
5347their coincidence at xv, _e_ and _f_, ought to constitute pretty
5348distinct Arcs of Circles, especially at xv, or at _e_ and _f_; and that
5349they will appear severally at _x_[Greek: u] and at xv exhibit whiteness
5350by their coincidence, and again appear severally at [Greek: Yx], but yet
5351in a contrary order to that which they had before, and still retain
5352beyond _e_ and _f_. But on the other side, at _ab_, ab, or [Greek: ab],
5353these Colours must become much more confused by being dilated and spread
5354so as to interfere with those of other Orders. And the same confusion
5355will happen at [Greek: Ux] between _e_ and _f_, if the Refraction be
5356very great, or the Prism very distant from the Object-glasses: In which
5357case 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
5359removing the Prism still farther from the Object-glasses: And these
5360little Arcs must be distinctest and whitest at their middle, and at
5361their ends, where they begin to grow confused, they must be colour'd.
5362And the Colours at one end of every Arc must be in a contrary order to
5363those at the other end, by reason that they cross in the intermediate
5364white; namely, their ends, which verge towards [Greek: Ux], will be red
5365and yellow on that side next the center, and blue and violet on the
5366other side. But their other ends which verge from [Greek: Ux], will on
5367the contrary be blue and violet on that side towards the center, and on
5368the other side red and yellow.
5369
5370Now as all these things follow from the properties of Light by a
5371mathematical way of reasoning, so the truth of them may be manifested by
5372Experiments. For in a dark Room, by viewing these Rings through a Prism,
5373by reflexion of the several prismatick Colours, which an assistant
5374causes to move to and fro upon a Wall or Paper from whence they are
5375reflected, whilst the Spectator's Eye, the Prism, and the
5376Object-glasses, (as in the 13th Observation,) are placed steady; the
5377Position of the Circles made successively by the several Colours, will
5378be found such, in respect of one another, as I have described in the
5379Figures _abxv_, or abxv, or _[Greek: abxU]_. And by the same method the
5380truth of the Explications of other Observations may be examined.
5381
5382By what hath been said, the like Phænomena of Water and thin Plates of
5383Glass may be understood. But in small fragments of those Plates there is
5384this farther observable, that where they lie flat upon a Table, and are
5385turned about their centers whilst they are view'd through a Prism, they
5386will in some postures exhibit Waves of various Colours; and some of them
5387exhibit these Waves in one or two Positions only, but the most of them
5388do in all Positions exhibit them, and make them for the most part appear
5389almost all over the Plates. The reason is, that the Superficies of such
5390Plates are not even, but have many Cavities and Swellings, which, how
5391shallow soever, do a little vary the thickness of the Plate. For at the
5392several sides of those Cavities, for the Reasons newly described, there
5393ought to be produced Waves in several postures of the Prism. Now though
5394it be but some very small and narrower parts of the Glass, by which
5395these Waves for the most part are caused, yet they may seem to extend
5396themselves over the whole Glass, because from the narrowest of those
5397parts there are Colours of several Orders, that is, of several Rings,
5398confusedly reflected, which by Refraction of the Prism are unfolded,
5399separated, and, according to their degrees of Refraction, dispersed to
5400several places, so as to constitute so many several Waves, as there were
5401divers orders of Colours promiscuously reflected from that part of the
5402Glass.
5403
5404These are the principal Phænomena of thin Plates or Bubbles, whose
5405Explications depend on the properties of Light, which I have heretofore
5406deliver'd. And these you see do necessarily follow from them, and agree
5407with them, even to their very least circumstances; and not only so, but
5408do very much tend to their proof. Thus, by the 24th Observation it
5409appears, that the Rays of several Colours, made as well by thin Plates
5410or Bubbles, as by Refractions of a Prism, have several degrees of
5411Refrangibility; whereby those of each order, which at the reflexion from
5412the Plate or Bubble are intermix'd with those of other orders, are
5413separated from them by Refraction, and associated together so as to
5414become visible by themselves like Arcs of Circles. For if the Rays were
5415all alike refrangible, 'tis impossible that the whiteness, which to the
5416naked Sense appears uniform, should by Refraction have its parts
5417transposed and ranged into those black and white Arcs.
5418
5419It appears also that the unequal Refractions of difform Rays proceed not
5420from any contingent irregularities; such as are Veins, an uneven Polish,
5421or fortuitous Position of the Pores of Glass; unequal and casual Motions
5422in the Air or Æther, the spreading, breaking, or dividing the same Ray
5423into many diverging parts; or the like. For, admitting any such
5424irregularities, it would be impossible for Refractions to render those
5425Rings so very distinct, and well defined, as they do in the 24th
5426Observation. It is necessary therefore that every Ray have its proper
5427and constant degree of Refrangibility connate with it, according to
5428which its refraction is ever justly and regularly perform'd; and that
5429several Rays have several of those degrees.
5430
5431And what is said of their Refrangibility may be also understood of their
5432Reflexibility, that is, of their Dispositions to be reflected, some at a
5433greater, and others at a less thickness of thin Plates or Bubbles;
5434namely, that those Dispositions are also connate with the Rays, and
5435immutable; as may appear by the 13th, 14th, and 15th Observations,
5436compared with the fourth and eighteenth.
5437
5438By the Precedent Observations it appears also, that whiteness is a
5439dissimilar mixture of all Colours, and that Light is a mixture of Rays
5440endued with all those Colours. For, considering the multitude of the
5441Rings of Colours in the 3d, 12th, and 24th Observations, it is manifest,
5442that although in the 4th and 18th Observations there appear no more than
5443eight or nine of those Rings, yet there are really a far greater number,
5444which so much interfere and mingle with one another, as after those
5445eight or nine revolutions to dilute one another wholly, and constitute
5446an even and sensibly uniform whiteness. And consequently that whiteness
5447must be allow'd a mixture of all Colours, and the Light which conveys it
5448to the Eye must be a mixture of Rays endued with all those Colours.
5449
5450But farther; by the 24th Observation it appears, that there is a
5451constant relation between Colours and Refrangibility; the most
5452refrangible Rays being violet, the least refrangible red, and those of
5453intermediate Colours having proportionably intermediate degrees of
5454Refrangibility. And by the 13th, 14th, and 15th Observations, compared
5455with the 4th or 18th there appears to be the same constant relation
5456between Colour and Reflexibility; the violet being in like circumstances
5457reflected at least thicknesses of any thin Plate or Bubble, the red at
5458greatest thicknesses, and the intermediate Colours at intermediate
5459thicknesses. Whence it follows, that the colorifick Dispositions of
5460Rays are also connate with them, and immutable; and by consequence, that
5461all the Productions and Appearances of Colours in the World are derived,
5462not from any physical Change caused in Light by Refraction or Reflexion,
5463but only from the various Mixtures or Separations of Rays, by virtue of
5464their different Refrangibility or Reflexibility. And in this respect the
5465Science of Colours becomes a Speculation as truly mathematical as any
5466other part of Opticks. I mean, so far as they depend on the Nature of
5467Light, and are not produced or alter'd by the Power of Imagination, or
5468by striking or pressing the Eye.
5469
5470
5471
5472
5473THE
5474
5475SECOND BOOK
5476
5477OF
5478
5479OPTICKS
5480
5481
5482_PART III._
5483
5484_Of the permanent Colours of natural Bodies, and the Analogy between
5485them and the Colours of thin transparent Plates._
5486
5487I am now come to another part of this Design, which is to consider how
5488the Phænomena of thin transparent Plates stand related to those of all
5489other natural Bodies. Of these Bodies I have already told you that they
5490appear of divers Colours, accordingly as they are disposed to reflect
5491most copiously the Rays originally endued with those Colours. But their
5492Constitutions, whereby they reflect some Rays more copiously than
5493others, remain to be discover'd; and these I shall endeavour to manifest
5494in the following Propositions.
5495
5496
5497PROP. I.
5498
5499_Those Superficies of transparent Bodies reflect the greatest quantity
5500of Light, which have the greatest refracting Power; that is, which
5501intercede Mediums that differ most in their refractive Densities. And in
5502the Confines of equally refracting Mediums there is no Reflexion._
5503
5504The Analogy between Reflexion and Refraction will appear by considering,
5505that when Light passeth obliquely out of one Medium into another which
5506refracts from the perpendicular, the greater is the difference of their
5507refractive Density, the less Obliquity of Incidence is requisite to
5508cause a total Reflexion. For as the Sines are which measure the
5509Refraction, so is the Sine of Incidence at which the total Reflexion
5510begins, to the Radius of the Circle; and consequently that Angle of
5511Incidence is least where there is the greatest difference of the Sines.
5512Thus in the passing of Light out of Water into Air, where the Refraction
5513is measured by the Ratio of the Sines 3 to 4, the total Reflexion begins
5514when the Angle of Incidence is about 48 Degrees 35 Minutes. In passing
5515out of Glass into Air, where the Refraction is measured by the Ratio of
5516the Sines 20 to 31, the total Reflexion begins when the Angle of
5517Incidence is 40 Degrees 10 Minutes; and so in passing out of Crystal, or
5518more strongly refracting Mediums into Air, there is still a less
5519obliquity requisite to cause a total reflexion. Superficies therefore
5520which refract most do soonest reflect all the Light which is incident on
5521them, and so must be allowed most strongly reflexive.
5522
5523But the truth of this Proposition will farther appear by observing, that
5524in the Superficies interceding two transparent Mediums, (such as are
5525Air, Water, Oil, common Glass, Crystal, metalline Glasses, Island
5526Glasses, white transparent Arsenick, Diamonds, &c.) the Reflexion is
5527stronger or weaker accordingly, as the Superficies hath a greater or
5528less refracting Power. For in the Confine of Air and Sal-gem 'tis
5529stronger than in the Confine of Air and Water, and still stronger in the
5530Confine of Air and common Glass or Crystal, and stronger in the Confine
5531of Air and a Diamond. If any of these, and such like transparent Solids,
5532be immerged in Water, its Reflexion becomes, much weaker than before;
5533and still weaker if they be immerged in the more strongly refracting
5534Liquors of well rectified Oil of Vitriol or Spirit of Turpentine. If
5535Water be distinguish'd into two parts by any imaginary Surface, the
5536Reflexion in the Confine of those two parts is none at all. In the
5537Confine of Water and Ice 'tis very little; in that of Water and Oil 'tis
5538something greater; in that of Water and Sal-gem still greater; and in
5539that of Water and Glass, or Crystal or other denser Substances still
5540greater, accordingly as those Mediums differ more or less in their
5541refracting Powers. Hence in the Confine of common Glass and Crystal,
5542there ought to be a weak Reflexion, and a stronger Reflexion in the
5543Confine of common and metalline Glass; though I have not yet tried
5544this. But in the Confine of two Glasses of equal density, there is not
5545any sensible Reflexion; as was shewn in the first Observation. And the
5546same may be understood of the Superficies interceding two Crystals, or
5547two Liquors, or any other Substances in which no Refraction is caused.
5548So then the reason why uniform pellucid Mediums (such as Water, Glass,
5549or Crystal,) have no sensible Reflexion but in their external
5550Superficies, where they are adjacent to other Mediums of a different
5551density, is because all their contiguous parts have one and the same
5552degree of density.
5553
5554
5555PROP. II.
5556
5557_The least parts of almost all natural Bodies are in some measure
5558transparent: And the Opacity of those Bodies ariseth from the multitude
5559of Reflexions caused in their internal Parts._
5560
5561That this is so has been observed by others, and will easily be granted
5562by them that have been conversant with Microscopes. And it may be also
5563tried by applying any substance to a hole through which some Light is
5564immitted into a dark Room. For how opake soever that Substance may seem
5565in the open Air, it will by that means appear very manifestly
5566transparent, if it be of a sufficient thinness. Only white metalline
5567Bodies must be excepted, which by reason of their excessive density seem
5568to reflect almost all the Light incident on their first Superficies;
5569unless by solution in Menstruums they be reduced into very small
5570Particles, and then they become transparent.
5571
5572
5573PROP. III.
5574
5575_Between the parts of opake and colour'd Bodies are many Spaces, either
5576empty, or replenish'd with Mediums of other Densities; as Water between
5577the tinging Corpuscles wherewith any Liquor is impregnated, Air between
5578the aqueous Globules that constitute Clouds or Mists; and for the most
5579part Spaces void of both Air and Water, but yet perhaps not wholly void
5580of all Substance, between the parts of hard Bodies._
5581
5582The truth of this is evinced by the two precedent Propositions: For by
5583the second Proposition there are many Reflexions made by the internal
5584parts of Bodies, which, by the first Proposition, would not happen if
5585the parts of those Bodies were continued without any such Interstices
5586between them; because Reflexions are caused only in Superficies, which
5587intercede Mediums of a differing density, by _Prop._ 1.
5588
5589But farther, that this discontinuity of parts is the principal Cause of
5590the opacity of Bodies, will appear by considering, that opake Substances
5591become transparent by filling their Pores with any Substance of equal or
5592almost equal density with their parts. Thus Paper dipped in Water or
5593Oil, the _Oculus Mundi_ Stone steep'd in Water, Linnen Cloth oiled or
5594varnish'd, and many other Substances soaked in such Liquors as will
5595intimately pervade their little Pores, become by that means more
5596transparent than otherwise; so, on the contrary, the most transparent
5597Substances, may, by evacuating their Pores, or separating their parts,
5598be render'd sufficiently opake; as Salts or wet Paper, or the _Oculus
5599Mundi_ Stone by being dried, Horn by being scraped, Glass by being
5600reduced to Powder, or otherwise flawed; Turpentine by being stirred
5601about with Water till they mix imperfectly, and Water by being form'd
5602into many small Bubbles, either alone in the form of Froth, or by
5603shaking it together with Oil of Turpentine, or Oil Olive, or with some
5604other convenient Liquor, with which it will not perfectly incorporate.
5605And to the increase of the opacity of these Bodies, it conduces
5606something, that by the 23d Observation the Reflexions of very thin
5607transparent Substances are considerably stronger than those made by the
5608same Substances of a greater thickness.
5609
5610
5611PROP. IV.
5612
5613_The Parts of Bodies and their Interstices must not be less than of some
5614definite bigness, to render them opake and colour'd._
5615
5616For the opakest Bodies, if their parts be subtilly divided, (as Metals,
5617by being dissolved in acid Menstruums, &c.) become perfectly
5618transparent. And you may also remember, that in the eighth Observation
5619there was no sensible reflexion at the Superficies of the
5620Object-glasses, where they were very near one another, though they did
5621not absolutely touch. And in the 17th Observation the Reflexion of the
5622Water-bubble where it became thinnest was almost insensible, so as to
5623cause very black Spots to appear on the top of the Bubble, by the want
5624of reflected Light.
5625
5626On these grounds I perceive it is that Water, Salt, Glass, Stones, and
5627such like Substances, are transparent. For, upon divers Considerations,
5628they seem to be as full of Pores or Interstices between their parts as
5629other Bodies are, but yet their Parts and Interstices to be too small to
5630cause Reflexions in their common Surfaces.
5631
5632
5633PROP. V.
5634
5635_The transparent parts of Bodies, according to their several sizes,
5636reflect Rays of one Colour, and transmit those of another, on the same
5637grounds that thin Plates or Bubbles do reflect or transmit those Rays.
5638And this I take to be the ground of all their Colours._
5639
5640For if a thinn'd or plated Body, which being of an even thickness,
5641appears all over of one uniform Colour, should be slit into Threads, or
5642broken into Fragments, of the same thickness with the Plate; I see no
5643reason why every Thread or Fragment should not keep its Colour, and by
5644consequence why a heap of those Threads or Fragments should not
5645constitute a Mass or Powder of the same Colour, which the Plate
5646exhibited before it was broken. And the parts of all natural Bodies
5647being like so many Fragments of a Plate, must on the same grounds
5648exhibit the same Colours.
5649
5650Now, that they do so will appear by the affinity of their Properties.
5651The finely colour'd Feathers of some Birds, and particularly those of
5652Peacocks Tails, do, in the very same part of the Feather, appear of
5653several Colours in several Positions of the Eye, after the very same
5654manner that thin Plates were found to do in the 7th and 19th
5655Observations, and therefore their Colours arise from the thinness of the
5656transparent parts of the Feathers; that is, from the slenderness of the
5657very fine Hairs, or _Capillamenta_, which grow out of the sides of the
5658grosser lateral Branches or Fibres of those Feathers. And to the same
5659purpose it is, that the Webs of some Spiders, by being spun very fine,
5660have appeared colour'd, as some have observ'd, and that the colour'd
5661Fibres of some Silks, by varying the Position of the Eye, do vary their
5662Colour. Also the Colours of Silks, Cloths, and other Substances, which
5663Water or Oil can intimately penetrate, become more faint and obscure by
5664being immerged in those Liquors, and recover their Vigor again by being
5665dried; much after the manner declared of thin Bodies in the 10th and
566621st Observations. Leaf-Gold, some sorts of painted Glass, the Infusion
5667of _Lignum Nephriticum_, and some other Substances, reflect one Colour,
5668and transmit another; like thin Bodies in the 9th and 20th Observations.
5669And some of those colour'd Powders which Painters use, may have their
5670Colours a little changed, by being very elaborately and finely ground.
5671Where I see not what can be justly pretended for those changes, besides
5672the breaking of their parts into less parts by that contrition, after
5673the same manner that the Colour of a thin Plate is changed by varying
5674its thickness. For which reason also it is that the colour'd Flowers of
5675Plants and Vegetables, by being bruised, usually become more transparent
5676than before, or at least in some degree or other change their Colours.
5677Nor is it much less to my purpose, that, by mixing divers Liquors, very
5678odd and remarkable Productions and Changes of Colours may be effected,
5679of which no cause can be more obvious and rational than that the saline
5680Corpuscles of one Liquor do variously act upon or unite with the tinging
5681Corpuscles of another, so as to make them swell, or shrink, (whereby not
5682only their bulk but their density also may be changed,) or to divide
5683them into smaller Corpuscles, (whereby a colour'd Liquor may become
5684transparent,) or to make many of them associate into one cluster,
5685whereby two transparent Liquors may compose a colour'd one. For we see
5686how apt those saline Menstruums are to penetrate and dissolve Substances
5687to which they are applied, and some of them to precipitate what others
5688dissolve. In like manner, if we consider the various Phænomena of the
5689Atmosphere, we may observe, that when Vapours are first raised, they
5690hinder not the transparency of the Air, being divided into parts too
5691small to cause any Reflexion in their Superficies. But when in order to
5692compose drops of Rain they begin to coalesce and constitute Globules of
5693all intermediate sizes, those Globules, when they become of convenient
5694size to reflect some Colours and transmit others, may constitute Clouds
5695of various Colours according to their sizes. And I see not what can be
5696rationally conceived in so transparent a Substance as Water for the
5697production of these Colours, besides the various sizes of its fluid and
5698globular Parcels.
5699
5700
5701PROP. VI.
5702
5703_The parts of Bodies on which their Colours depend, are denser than the
5704Medium which pervades their Interstices._
5705
5706This will appear by considering, that the Colour of a Body depends not
5707only on the Rays which are incident perpendicularly on its parts, but on
5708those also which are incident at all other Angles. And that according to
5709the 7th Observation, a very little variation of obliquity will change
5710the reflected Colour, where the thin Body or small Particles is rarer
5711than the ambient Medium, insomuch that such a small Particle will at
5712diversly oblique Incidences reflect all sorts of Colours, in so great a
5713variety that the Colour resulting from them all, confusedly reflected
5714from a heap of such Particles, must rather be a white or grey than any
5715other Colour, or at best it must be but a very imperfect and dirty
5716Colour. Whereas if the thin Body or small Particle be much denser than
5717the ambient Medium, the Colours, according to the 19th Observation, are
5718so little changed by the variation of obliquity, that the Rays which
5719are reflected least obliquely may predominate over the rest, so much as
5720to cause a heap of such Particles to appear very intensely of their
5721Colour.
5722
5723It conduces also something to the confirmation of this Proposition,
5724that, according to the 22d Observation, the Colours exhibited by the
5725denser thin Body within the rarer, are more brisk than those exhibited
5726by the rarer within the denser.
5727
5728
5729PROP. VII.
5730
5731_The bigness of the component parts of natural Bodies may be conjectured
5732by their Colours._
5733
5734For since the parts of these Bodies, by _Prop._ 5. do most probably
5735exhibit the same Colours with a Plate of equal thickness, provided they
5736have the same refractive density; and since their parts seem for the
5737most part to have much the same density with Water or Glass, as by many
5738circumstances is obvious to collect; to determine the sizes of those
5739parts, you need only have recourse to the precedent Tables, in which the
5740thickness of Water or Glass exhibiting any Colour is expressed. Thus if
5741it be desired to know the diameter of a Corpuscle, which being of equal
5742density with Glass shall reflect green of the third Order; the Number
574316-1/4 shews it to be (16-1/4)/10000 parts of an Inch.
5744
5745The greatest difficulty is here to know of what Order the Colour of any
5746Body is. And for this end we must have recourse to the 4th and 18th
5747Observations; from whence may be collected these particulars.
5748
5749_Scarlets_, and other _reds_, _oranges_, and _yellows_, if they be pure
5750and intense, are most probably of the second order. Those of the first
5751and third order also may be pretty good; only the yellow of the first
5752order is faint, and the orange and red of the third Order have a great
5753Mixture of violet and blue.
5754
5755There may be good _Greens_ of the fourth Order, but the purest are of
5756the third. And of this Order the green of all Vegetables seems to be,
5757partly by reason of the Intenseness of their Colours, and partly because
5758when they wither some of them turn to a greenish yellow, and others to a
5759more perfect yellow or orange, or perhaps to red, passing first through
5760all the aforesaid intermediate Colours. Which Changes seem to be
5761effected by the exhaling of the Moisture which may leave the tinging
5762Corpuscles more dense, and something augmented by the Accretion of the
5763oily and earthy Part of that Moisture. Now the green, without doubt, is
5764of the same Order with those Colours into which it changeth, because the
5765Changes are gradual, and those Colours, though usually not very full,
5766yet 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
5769the best are of the third. Thus the Colour of Violets seems to be of
5770that Order, because their Syrup by acid Liquors turns red, and by
5771urinous and alcalizate turns green. For since it is of the Nature of
5772Acids to dissolve or attenuate, and of Alcalies to precipitate or
5773incrassate, if the Purple Colour of the Syrup was of the second Order,
5774an acid Liquor by attenuating its tinging Corpuscles would change it to
5775a red of the first Order, and an Alcali by incrassating them would
5776change it to a green of the second Order; which red and green,
5777especially the green, seem too imperfect to be the Colours produced by
5778these Changes. But if the said Purple be supposed of the third Order,
5779its Change to red of the second, and green of the third, may without any
5780Inconvenience be allow'd.
5781
5782If there be found any Body of a deeper and less reddish Purple than that
5783of the Violets, its Colour most probably is of the second Order. But yet
5784there being no Body commonly known whose Colour is constantly more deep
5785than theirs, I have made use of their Name to denote the deepest and
5786least reddish Purples, such as manifestly transcend their Colour in
5787purity.
5788
5789The _blue_ of the first Order, though very faint and little, may
5790possibly be the Colour of some Substances; and particularly the azure
5791Colour of the Skies seems to be of this Order. For all Vapours when they
5792begin to condense and coalesce into small Parcels, become first of that
5793Bigness, whereby such an Azure must be reflected before they can
5794constitute Clouds of other Colours. And so this being the first Colour
5795which Vapours begin to reflect, it ought to be the Colour of the finest
5796and most transparent Skies, in which Vapours are not arrived to that
5797Grossness requisite to reflect other Colours, as we find it is by
5798Experience.
5799
5800_Whiteness_, if most intense and luminous, is that of the first Order,
5801if less strong and luminous, a Mixture of the Colours of several Orders.
5802Of this last kind is the Whiteness of Froth, Paper, Linnen, and most
5803white Substances; of the former I reckon that of white Metals to be. For
5804whilst the densest of Metals, Gold, if foliated, is transparent, and all
5805Metals become transparent if dissolved in Menstruums or vitrified, the
5806Opacity of white Metals ariseth not from their Density alone. They being
5807less dense than Gold would be more transparent than it, did not some
5808other Cause concur with their Density to make them opake. And this Cause
5809I take to be such a Bigness of their Particles as fits them to reflect
5810the white of the first order. For, if they be of other Thicknesses they
5811may reflect other Colours, as is manifest by the Colours which appear
5812upon hot Steel in tempering it, and sometimes upon the Surface of melted
5813Metals in the Skin or Scoria which arises upon them in their cooling.
5814And as the white of the first order is the strongest which can be made
5815by Plates of transparent Substances, so it ought to be stronger in the
5816denser Substances of Metals than in the rarer of Air, Water, and Glass.
5817Nor do I see but that metallick Substances of such a Thickness as may
5818fit them to reflect the white of the first order, may, by reason of
5819their great Density (according to the Tenor of the first of these
5820Propositions) reflect all the Light incident upon them, and so be as
5821opake and splendent as it's possible for any Body to be. Gold, or Copper
5822mix'd with less than half their Weight of Silver, or Tin, or Regulus of
5823Antimony, in fusion, or amalgamed with a very little Mercury, become
5824white; which shews both that the Particles of white Metals have much
5825more Superficies, and so are smaller, than those of Gold and Copper, and
5826also that they are so opake as not to suffer the Particles of Gold or
5827Copper to shine through them. Now it is scarce to be doubted but that
5828the Colours of Gold and Copper are of the second and third order, and
5829therefore the Particles of white Metals cannot be much bigger than is
5830requisite to make them reflect the white of the first order. The
5831Volatility of Mercury argues that they are not much bigger, nor may they
5832be much less, lest they lose their Opacity, and become either
5833transparent as they do when attenuated by Vitrification, or by Solution
5834in Menstruums, or black as they do when ground smaller, by rubbing
5835Silver, or Tin, or Lead, upon other Substances to draw black Lines. The
5836first and only Colour which white Metals take by grinding their
5837Particles smaller, is black, and therefore their white ought to be that
5838which borders upon the black Spot in the Center of the Rings of Colours,
5839that is, the white of the first order. But, if you would hence gather
5840the Bigness of metallick Particles, you must allow for their Density.
5841For were Mercury transparent, its Density is such that the Sine of
5842Incidence upon it (by my Computation) would be to the Sine of its
5843Refraction, as 71 to 20, or 7 to 2. And therefore the Thickness of its
5844Particles, that they may exhibit the same Colours with those of Bubbles
5845of Water, ought to be less than the Thickness of the Skin of those
5846Bubbles in the Proportion of 2 to 7. Whence it's possible, that the
5847Particles of Mercury may be as little as the Particles of some
5848transparent and volatile Fluids, and yet reflect the white of the first
5849order.
5850
5851Lastly, for the production of _black_, the Corpuscles must be less than
5852any of those which exhibit Colours. For at all greater sizes there is
5853too much Light reflected to constitute this Colour. But if they be
5854supposed a little less than is requisite to reflect the white and very
5855faint blue of the first order, they will, according to the 4th, 8th,
585617th and 18th Observations, reflect so very little Light as to appear
5857intensely black, and yet may perhaps variously refract it to and fro
5858within themselves so long, until it happen to be stifled and lost, by
5859which means they will appear black in all positions of the Eye without
5860any transparency. And from hence may be understood why Fire, and the
5861more subtile dissolver Putrefaction, by dividing the Particles of
5862Substances, turn them to black, why small quantities of black Substances
5863impart their Colour very freely and intensely to other Substances to
5864which they are applied; the minute Particles of these, by reason of
5865their very great number, easily overspreading the gross Particles of
5866others; 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
5868off from the Glass and Copper, become very black: why black Substances
5869do soonest of all others become hot in the Sun's Light and burn, (which
5870Effect may proceed partly from the multitude of Refractions in a little
5871room, and partly from the easy Commotion of so very small Corpuscles;)
5872and why blacks are usually a little inclined to a bluish Colour. For
5873that they are so may be seen by illuminating white Paper by Light
5874reflected from black Substances. For the Paper will usually appear of a
5875bluish white; and the reason is, that black borders in the obscure blue
5876of the order described in the 18th Observation, and therefore reflects
5877more Rays of that Colour than of any other.
5878
5879In these Descriptions I have been the more particular, because it is not
5880impossible but that Microscopes may at length be improved to the
5881discovery of the Particles of Bodies on which their Colours depend, if
5882they are not already in some measure arrived to that degree of
5883perfection. For if those Instruments are or can be so far improved as
5884with sufficient distinctness to represent Objects five or six hundred
5885times bigger than at a Foot distance they appear to our naked Eyes, I
5886should hope that we might be able to discover some of the greatest of
5887those Corpuscles. And by one that would magnify three or four thousand
5888times perhaps they might all be discover'd, but those which produce
5889blackness. In the mean while I see nothing material in this Discourse
5890that may rationally be doubted of, excepting this Position: That
5891transparent Corpuscles of the same thickness and density with a Plate,
5892do exhibit the same Colour. And this I would have understood not without
5893some Latitude, as well because those Corpuscles may be of irregular
5894Figures, and many Rays must be obliquely incident on them, and so have
5895a shorter way through them than the length of their Diameters, as
5896because the straitness of the Medium put in on all sides within such
5897Corpuscles may a little alter its Motions or other qualities on which
5898the Reflexion depends. But yet I cannot much suspect the last, because I
5899have observed of some small Plates of Muscovy Glass which were of an
5900even thickness, that through a Microscope they have appeared of the same
5901Colour at their edges and corners where the included Medium was
5902terminated, which they appeared of in other places. However it will add
5903much to our Satisfaction, if those Corpuscles can be discover'd with
5904Microscopes; which if we shall at length attain to, I fear it will be
5905the utmost improvement of this Sense. For it seems impossible to see the
5906more secret and noble Works of Nature within the Corpuscles by reason of
5907their transparency.
5908
5909
5910PROP. VIII.
5911
5912_The Cause of Reflexion is not the impinging of Light on the solid or
5913impervious parts of Bodies, as is commonly believed._
5914
5915This will appear by the following Considerations. First, That in the
5916passage of Light out of Glass into Air there is a Reflexion as strong as
5917in its passage out of Air into Glass, or rather a little stronger, and
5918by many degrees stronger than in its passage out of Glass into Water.
5919And it seems not probable that Air should have more strongly reflecting
5920parts than Water or Glass. But if that should possibly be supposed, yet
5921it will avail nothing; for the Reflexion is as strong or stronger when
5922the Air is drawn away from the Glass, (suppose by the Air-Pump invented
5923by _Otto Gueriet_, and improved and made useful by Mr. _Boyle_) as when
5924it is adjacent to it. Secondly, If Light in its passage out of Glass
5925into Air be incident more obliquely than at an Angle of 40 or 41 Degrees
5926it is wholly reflected, if less obliquely it is in great measure
5927transmitted. Now it is not to be imagined that Light at one degree of
5928obliquity should meet with Pores enough in the Air to transmit the
5929greater part of it, and at another degree of obliquity should meet with
5930nothing but parts to reflect it wholly, especially considering that in
5931its passage out of Air into Glass, how oblique soever be its Incidence,
5932it finds Pores enough in the Glass to transmit a great part of it. If
5933any Man suppose that it is not reflected by the Air, but by the outmost
5934superficial parts of the Glass, there is still the same difficulty:
5935Besides, that such a Supposition is unintelligible, and will also appear
5936to be false by applying Water behind some part of the Glass instead of
5937Air. For so in a convenient obliquity of the Rays, suppose of 45 or 46
5938Degrees, at which they are all reflected where the Air is adjacent to
5939the Glass, they shall be in great measure transmitted where the Water is
5940adjacent to it; which argues, that their Reflexion or Transmission
5941depends on the constitution of the Air and Water behind the Glass, and
5942not on the striking of the Rays upon the parts of the Glass. Thirdly,
5943If the Colours made by a Prism placed at the entrance of a Beam of Light
5944into a darken'd Room be successively cast on a second Prism placed at a
5945greater distance from the former, in such manner that they are all alike
5946incident upon it, the second Prism may be so inclined to the incident
5947Rays, that those which are of a blue Colour shall be all reflected by
5948it, and yet those of a red Colour pretty copiously transmitted. Now if
5949the Reflexion be caused by the parts of Air or Glass, I would ask, why
5950at the same Obliquity of Incidence the blue should wholly impinge on
5951those parts, so as to be all reflected, and yet the red find Pores
5952enough to be in a great measure transmitted. Fourthly, Where two Glasses
5953touch one another, there is no sensible Reflexion, as was declared in
5954the first Observation; and yet I see no reason why the Rays should not
5955impinge on the parts of Glass, as much when contiguous to other Glass as
5956when contiguous to Air. Fifthly, When the top of a Water-Bubble (in the
595717th Observation,) by the continual subsiding and exhaling of the Water
5958grew very thin, there was such a little and almost insensible quantity
5959of Light reflected from it, that it appeared intensely black; whereas
5960round about that black Spot, where the Water was thicker, the Reflexion
5961was so strong as to make the Water seem very white. Nor is it only at
5962the least thickness of thin Plates or Bubbles, that there is no manifest
5963Reflexion, but at many other thicknesses continually greater and
5964greater. For in the 15th Observation the Rays of the same Colour were by
5965turns transmitted at one thickness, and reflected at another thickness,
5966for an indeterminate number of Successions. And yet in the Superficies
5967of the thinned Body, where it is of any one thickness, there are as many
5968parts for the Rays to impinge on, as where it is of any other thickness.
5969Sixthly, If Reflexion were caused by the parts of reflecting Bodies, it
5970would be impossible for thin Plates or Bubbles, at one and the same
5971place, to reflect the Rays of one Colour, and transmit those of another,
5972as they do according to the 13th and 15th Observations. For it is not to
5973be imagined that at one place the Rays which, for instance, exhibit a
5974blue Colour, should have the fortune to dash upon the parts, and those
5975which exhibit a red to hit upon the Pores of the Body; and then at
5976another place, where the Body is either a little thicker or a little
5977thinner, that on the contrary the blue should hit upon its pores, and
5978the red upon its parts. Lastly, Were the Rays of Light reflected by
5979impinging on the solid parts of Bodies, their Reflexions from polish'd
5980Bodies could not be so regular as they are. For in polishing Glass with
5981Sand, Putty, or Tripoly, it is not to be imagined that those Substances
5982can, by grating and fretting the Glass, bring all its least Particles to
5983an accurate Polish; so that all their Surfaces shall be truly plain or
5984truly spherical, and look all the same way, so as together to compose
5985one even Surface. The smaller the Particles of those Substances are, the
5986smaller will be the Scratches by which they continually fret and wear
5987away the Glass until it be polish'd; but be they never so small they can
5988wear away the Glass no otherwise than by grating and scratching it, and
5989breaking the Protuberances; and therefore polish it no otherwise than by
5990bringing its roughness to a very fine Grain, so that the Scratches and
5991Frettings of the Surface become too small to be visible. And therefore
5992if Light were reflected by impinging upon the solid parts of the Glass,
5993it would be scatter'd as much by the most polish'd Glass as by the
5994roughest. So then it remains a Problem, how Glass polish'd by fretting
5995Substances can reflect Light so regularly as it does. And this Problem
5996is scarce otherwise to be solved, than by saying, that the Reflexion of
5997a Ray is effected, not by a single point of the reflecting Body, but by
5998some power of the Body which is evenly diffused all over its Surface,
5999and by which it acts upon the Ray without immediate Contact. For that
6000the parts of Bodies do act upon Light at a distance shall be shewn
6001hereafter.
6002
6003Now if Light be reflected, not by impinging on the solid parts of
6004Bodies, but by some other principle; it's probable that as many of its
6005Rays as impinge on the solid parts of Bodies are not reflected but
6006stifled and lost in the Bodies. For otherwise we must allow two sorts of
6007Reflexions. Should all the Rays be reflected which impinge on the
6008internal parts of clear Water or Crystal, those Substances would rather
6009have a cloudy Colour than a clear Transparency. To make Bodies look
6010black, it's necessary that many Rays be stopp'd, retained, and lost in
6011them; and it seems not probable that any Rays can be stopp'd and
6012stifled in them which do not impinge on their parts.
6013
6014And hence we may understand that Bodies are much more rare and porous
6015than is commonly believed. Water is nineteen times lighter, and by
6016consequence nineteen times rarer than Gold; and Gold is so rare as very
6017readily and without the least opposition to transmit the magnetick
6018Effluvia, and easily to admit Quicksilver into its Pores, and to let
6019Water pass through it. For a concave Sphere of Gold filled with Water,
6020and solder'd up, has, upon pressing the Sphere with great force, let the
6021Water squeeze through it, and stand all over its outside in multitudes
6022of small Drops, like Dew, without bursting or cracking the Body of the
6023Gold, as I have been inform'd by an Eye witness. From all which we may
6024conclude, that Gold has more Pores than solid parts, and by consequence
6025that Water has above forty times more Pores than Parts. And he that
6026shall find out an Hypothesis, by which Water may be so rare, and yet not
6027be capable of compression by force, may doubtless by the same Hypothesis
6028make Gold, and Water, and all other Bodies, as much rarer as he pleases;
6029so that Light may find a ready passage through transparent Substances.
6030
6031The Magnet acts upon Iron through all dense Bodies not magnetick nor red
6032hot, without any diminution of its Virtue; as for instance, through
6033Gold, Silver, Lead, Glass, Water. The gravitating Power of the Sun is
6034transmitted through the vast Bodies of the Planets without any
6035diminution, so as to act upon all their parts to their very centers
6036with the same Force and according to the same Laws, as if the part upon
6037which it acts were not surrounded with the Body of the Planet, The Rays
6038of Light, whether they be very small Bodies projected, or only Motion or
6039Force propagated, are moved in right Lines; and whenever a Ray of Light
6040is by any Obstacle turned out of its rectilinear way, it will never
6041return into the same rectilinear way, unless perhaps by very great
6042accident. And yet Light is transmitted through pellucid solid Bodies in
6043right Lines to very great distances. How Bodies can have a sufficient
6044quantity of Pores for producing these Effects is very difficult to
6045conceive, but perhaps not altogether impossible. For the Colours of
6046Bodies arise from the Magnitudes of the Particles which reflect them, as
6047was explained above. Now if we conceive these Particles of Bodies to be
6048so disposed amongst themselves, that the Intervals or empty Spaces
6049between them may be equal in magnitude to them all; and that these
6050Particles may be composed of other Particles much smaller, which have as
6051much empty Space between them as equals all the Magnitudes of these
6052smaller Particles: And that in like manner these smaller Particles are
6053again composed of others much smaller, all which together are equal to
6054all the Pores or empty Spaces between them; and so on perpetually till
6055you come to solid Particles, such as have no Pores or empty Spaces
6056within them: And if in any gross Body there be, for instance, three such
6057degrees of Particles, the least of which are solid; this Body will have
6058seven times more Pores than solid Parts. But if there be four such
6059degrees of Particles, the least of which are solid, the Body will have
6060fifteen times more Pores than solid Parts. If there be five degrees, the
6061Body will have one and thirty times more Pores than solid Parts. If six
6062degrees, the Body will have sixty and three times more Pores than solid
6063Parts. And so on perpetually. And there are other ways of conceiving how
6064Bodies may be exceeding porous. But what is really their inward Frame is
6065not yet known to us.
6066
6067
6068PROP. IX.
6069
6070_Bodies reflect and refract Light by one and the same power, variously
6071exercised in various Circumstances._
6072
6073This appears by several Considerations. First, Because when Light goes
6074out of Glass into Air, as obliquely as it can possibly do. If its
6075Incidence be made still more oblique, it becomes totally reflected. For
6076the power of the Glass after it has refracted the Light as obliquely as
6077is possible, if the Incidence be still made more oblique, becomes too
6078strong to let any of its Rays go through, and by consequence causes
6079total Reflexions. Secondly, Because Light is alternately reflected and
6080transmitted by thin Plates of Glass for many Successions, accordingly as
6081the thickness of the Plate increases in an arithmetical Progression. For
6082here the thickness of the Glass determines whether that Power by which
6083Glass acts upon Light shall cause it to be reflected, or suffer it to
6084be transmitted. And, Thirdly, because those Surfaces of transparent
6085Bodies which have the greatest refracting power, reflect the greatest
6086quantity of Light, as was shewn in the first Proposition.
6087
6088
6089PROP. X.
6090
6091_If Light be swifter in Bodies than in Vacuo, in the proportion of the
6092Sines which measure the Refraction of the Bodies, the Forces of the
6093Bodies to reflect and refract Light, are very nearly proportional to the
6094densities of the same Bodies; excepting that unctuous and sulphureous
6095Bodies refract more than others of this same density._
6096
6097[Illustration: FIG. 8.]
6098
6099Let AB represent the refracting plane Surface of any Body, and IC a Ray
6100incident very obliquely upon the Body in C, so that the Angle ACI may be
6101infinitely little, and let CR be the refracted Ray. From a given Point B
6102perpendicular to the refracting Surface erect BR meeting with the
6103refracting Ray CR in R, and if CR represent the Motion of the refracted
6104Ray, and this Motion be distinguish'd into two Motions CB and BR,
6105whereof CB is parallel to the refracting Plane, and BR perpendicular to
6106it: CB shall represent the Motion of the incident Ray, and BR the
6107Motion generated by the Refraction, as Opticians have of late explain'd.
6108
6109Now if any Body or Thing, in moving through any Space of a given breadth
6110terminated on both sides by two parallel Planes, be urged forward in all
6111parts of that Space by Forces tending directly forwards towards the last
6112Plane, and before its Incidence on the first Plane, had no Motion
6113towards it, or but an infinitely little one; and if the Forces in all
6114parts of that Space, between the Planes, be at equal distances from the
6115Planes equal to one another, but at several distances be bigger or less
6116in any given Proportion, the Motion generated by the Forces in the whole
6117passage of the Body or thing through that Space shall be in a
6118subduplicate Proportion of the Forces, as Mathematicians will easily
6119understand. And therefore, if the Space of activity of the refracting
6120Superficies of the Body be consider'd as such a Space, the Motion of the
6121Ray generated by the refracting Force of the Body, during its passage
6122through that Space, that is, the Motion BR, must be in subduplicate
6123Proportion of that refracting Force. I say therefore, that the Square of
6124the Line BR, and by consequence the refracting Force of the Body, is
6125very nearly as the density of the same Body. For this will appear by the
6126following Table, wherein the Proportion of the Sines which measure the
6127Refractions of several Bodies, the Square of BR, supposing CB an unite,
6128the Densities of the Bodies estimated by their Specifick Gravities, and
6129their Refractive Power in respect of their Densities are set down in
6130several 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---------------------+----------------+----------------+----------+-----------
6142A 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. | | | |
6147Air. | 3201 to 3200 | 0'000625 | 0'0012 | 5208
6148Glass of Antimony. | 17 to 9 | 2'568 | 5'28 | 4864
6149A Selenitis. | 61 to 41 | 1'213 | 2'252 | 5386
6150Glass vulgar. | 31 to 20 | 1'4025 | 2'58 | 5436
6151Crystal of the Rock. | 25 to 16 | 1'445 | 2'65 | 5450
6152Island Crystal. | 5 to 3 | 1'778 | 2'72 | 6536
6153Sal Gemmæ. | 17 to 11 | 1'388 | 2'143 | 6477
6154Alume. | 35 to 24 | 1'1267 | 1'714 | 6570
6155Borax. | 22 to 15 | 1'1511 | 1'714 | 6716
6156Niter. | 32 to 21 | 1'345 | 1'9 | 7079
6157Dantzick Vitriol. | 303 to 200 | 1'295 | 1'715 | 7551
6158Oil of Vitriol. | 10 to 7 | 1'041 | 1'7 | 6124
6159Rain Water. | 529 to 396 | 0'7845 | 1' | 7845
6160Gum Arabick. | 31 to 21 | 1'179 | 1'375 | 8574
6161Spirit of Wine well | | | |
6162 rectified. | 100 to 73 | 0'8765 | 0'866 | 10121
6163Camphire. | 3 to 2 | 1'25 | 0'996 | 12551
6164Oil Olive. | 22 to 15 | 1'1511 | 0'913 | 12607
6165Linseed Oil. | 40 to 27 | 1'1948 | 0'932 | 12819
6166Spirit of Turpentine.| 25 to 17 | 1'1626 | 0'874 | 13222
6167Amber. | 14 to 9 | 1'42 | 1'04 | 13654
6168A Diamond. | 100 to 41 | 4'949 | 3'4 | 14556
6169---------------------+----------------+----------------+----------+-----------
6170
6171The Refraction of the Air in this Table is determin'd by that of the
6172Atmosphere observed by Astronomers. For, if Light pass through many
6173refracting Substances or Mediums gradually denser and denser, and
6174terminated with parallel Surfaces, the Sum of all the Refractions will
6175be equal to the single Refraction which it would have suffer'd in
6176passing immediately out of the first Medium into the last. And this
6177holds true, though the Number of the refracting Substances be increased
6178to Infinity, and the Distances from one another as much decreased, so
6179that the Light may be refracted in every Point of its Passage, and by
6180continual Refractions bent into a Curve-Line. And therefore the whole
6181Refraction of Light in passing through the Atmosphere from the highest
6182and rarest Part thereof down to the lowest and densest Part, must be
6183equal to the Refraction which it would suffer in passing at like
6184Obliquity out of a Vacuum immediately into Air of equal Density with
6185that in the lowest Part of the Atmosphere.
6186
6187Now, although a Pseudo-Topaz, a Selenitis, Rock Crystal, Island Crystal,
6188Vulgar Glass (that is, Sand melted together) and Glass of Antimony,
6189which are terrestrial stony alcalizate Concretes, and Air which probably
6190arises from such Substances by Fermentation, be Substances very
6191differing from one another in Density, yet by this Table, they have
6192their refractive Powers almost in the same Proportion to one another as
6193their Densities are, excepting that the Refraction of that strange
6194Substance, Island Crystal is a little bigger than the rest. And
6195particularly Air, which is 3500 Times rarer than the Pseudo-Topaz, and
61964400 Times rarer than Glass of Antimony, and 2000 Times rarer than the
6197Selenitis, Glass vulgar, or Crystal of the Rock, has notwithstanding its
6198rarity the same refractive Power in respect of its Density which those
6199very dense Substances have in respect of theirs, excepting so far as
6200those differ from one another.
6201
6202Again, the Refraction of Camphire, Oil Olive, Linseed Oil, Spirit of
6203Turpentine and Amber, which are fat sulphureous unctuous Bodies, and a
6204Diamond, which probably is an unctuous Substance coagulated, have their
6205refractive Powers in Proportion to one another as their Densities
6206without any considerable Variation. But the refractive Powers of these
6207unctuous Substances are two or three Times greater in respect of their
6208Densities than the refractive Powers of the former Substances in respect
6209of theirs.
6210
6211Water has a refractive Power in a middle degree between those two sorts
6212of Substances, and probably is of a middle nature. For out of it grow
6213all vegetable and animal Substances, which consist as well of
6214sulphureous fat and inflamable Parts, as of earthy lean and alcalizate
6215ones.
6216
6217Salts and Vitriols have refractive Powers in a middle degree between
6218those of earthy Substances and Water, and accordingly are composed of
6219those two sorts of Substances. For by distillation and rectification of
6220their Spirits a great Part of them goes into Water, and a great Part
6221remains behind in the form of a dry fix'd Earth capable of
6222Vitrification.
6223
6224Spirit of Wine has a refractive Power in a middle degree between those
6225of Water and oily Substances, and accordingly seems to be composed of
6226both, united by Fermentation; the Water, by means of some saline Spirits
6227with which 'tis impregnated, dissolving the Oil, and volatizing it by
6228the Action. For Spirit of Wine is inflamable by means of its oily Parts,
6229and being distilled often from Salt of Tartar, grow by every
6230distillation more and more aqueous and phlegmatick. And Chymists
6231observe, that Vegetables (as Lavender, Rue, Marjoram, &c.) distilled
6232_per se_, before fermentation yield Oils without any burning Spirits,
6233but after fermentation yield ardent Spirits without Oils: Which shews,
6234that their Oil is by fermentation converted into Spirit. They find also,
6235that if Oils be poured in a small quantity upon fermentating Vegetables,
6236they distil over after fermentation in the form of Spirits.
6237
6238So then, by the foregoing Table, all Bodies seem to have their
6239refractive Powers proportional to their Densities, (or very nearly;)
6240excepting so far as they partake more or less of sulphureous oily
6241Particles, and thereby have their refractive Power made greater or less.
6242Whence it seems rational to attribute the refractive Power of all Bodies
6243chiefly, if not wholly, to the sulphureous Parts with which they abound.
6244For it's probable that all Bodies abound more or less with Sulphurs. And
6245as Light congregated by a Burning-glass acts most upon sulphureous
6246Bodies, to turn them into Fire and Flame; so, since all Action is
6247mutual, Sulphurs ought to act most upon Light. For that the action
6248between Light and Bodies is mutual, may appear from this Consideration;
6249That the densest Bodies which refract and reflect Light most strongly,
6250grow hottest in the Summer Sun, by the action of the refracted or
6251reflected Light.
6252
6253I have hitherto explain'd the power of Bodies to reflect and refract,
6254and shew'd, that thin transparent Plates, Fibres, and Particles, do,
6255according to their several thicknesses and densities, reflect several
6256sorts of Rays, and thereby appear of several Colours; and by consequence
6257that nothing more is requisite for producing all the Colours of natural
6258Bodies, than the several sizes and densities of their transparent
6259Particles. But whence it is that these Plates, Fibres, and Particles,
6260do, according to their several thicknesses and densities, reflect
6261several sorts of Rays, I have not yet explain'd. To give some insight
6262into this matter, and make way for understanding the next part of this
6263Book, I shall conclude this part with a few more Propositions. Those
6264which preceded respect the nature of Bodies, these the nature of Light:
6265For both must be understood, before the reason of their Actions upon one
6266another can be known. And because the last Proposition depended upon the
6267velocity of Light, I will begin with a Proposition of that kind.
6268
6269
6270PROP. XI.
6271
6272_Light is propagated from luminous Bodies in time, and spends about
6273seven or eight Minutes of an Hour in passing from the Sun to the Earth._
6274
6275This was observed first by _Roemer_, and then by others, by means of the
6276Eclipses of the Satellites of _Jupiter_. For these Eclipses, when the
6277Earth is between the Sun and _Jupiter_, happen about seven or eight
6278Minutes sooner than they ought to do by the Tables, and when the Earth
6279is beyond the Sun they happen about seven or eight Minutes later than
6280they ought to do; the reason being, that the Light of the Satellites has
6281farther to go in the latter case than in the former by the Diameter of
6282the Earth's Orbit. Some inequalities of time may arise from the
6283Excentricities of the Orbs of the Satellites; but those cannot answer in
6284all the Satellites, and at all times to the Position and Distance of the
6285Earth from the Sun. The mean motions of _Jupiter_'s Satellites is also
6286swifter in his descent from his Aphelium to his Perihelium, than in his
6287ascent in the other half of his Orb. But this inequality has no respect
6288to the position of the Earth, and in the three interior Satellites is
6289insensible, as I find by computation from the Theory of their Gravity.
6290
6291
6292PROP. XII.
6293
6294_Every Ray of Light in its passage through any refracting Surface is put
6295into a certain transient Constitution or State, which in the progress of
6296the Ray returns at equal Intervals, and disposes the Ray at every return
6297to be easily transmitted through the next refracting Surface, and
6298between the returns to be easily reflected by it._
6299
6300This is manifest by the 5th, 9th, 12th, and 15th Observations. For by
6301those Observations it appears, that one and the same sort of Rays at
6302equal Angles of Incidence on any thin transparent Plate, is alternately
6303reflected and transmitted for many Successions accordingly as the
6304thickness of the Plate increases in arithmetical Progression of the
6305Numbers, 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
6307described) be made at the thickness 1, the Rays shall be transmitted at
6308the thicknesses 0, 2, 4, 6, 8, 10, 12, &c. and thereby make the central
6309Spot and Rings of Light, which appear by transmission, and be reflected
6310at the thickness 1, 3, 5, 7, 9, 11, &c. and thereby make the Rings which
6311appear by Reflexion. And this alternate Reflexion and Transmission, as I
6312gather by the 24th Observation, continues for above an hundred
6313vicissitudes, and by the Observations in the next part of this Book, for
6314many thousands, being propagated from one Surface of a Glass Plate to
6315the other, though the thickness of the Plate be a quarter of an Inch or
6316above: So that this alternation seems to be propagated from every
6317refracting Surface to all distances without end or limitation.
6318
6319This alternate Reflexion and Refraction depends on both the Surfaces of
6320every thin Plate, because it depends on their distance. By the 21st
6321Observation, if either Surface of a thin Plate of _Muscovy_ Glass be
6322wetted, the Colours caused by the alternate Reflexion and Refraction
6323grow faint, and therefore it depends on them both.
6324
6325It is therefore perform'd at the second Surface; for if it were
6326perform'd at the first, before the Rays arrive at the second, it would
6327not depend on the second.
6328
6329It is also influenced by some action or disposition, propagated from the
6330first to the second, because otherwise at the second it would not depend
6331on the first. And this action or disposition, in its propagation,
6332intermits and returns by equal Intervals, because in all its progress it
6333inclines the Ray at one distance from the first Surface to be reflected
6334by the second, at another to be transmitted by it, and that by equal
6335Intervals for innumerable vicissitudes. And because the Ray is disposed
6336to Reflexion at the distances 1, 3, 5, 7, 9, &c. and to Transmission at
6337the distances 0, 2, 4, 6, 8, 10, &c. (for its transmission through the
6338first Surface, is at the distance 0, and it is transmitted through both
6339together, if their distance be infinitely little or much less than 1)
6340the disposition to be transmitted at the distances 2, 4, 6, 8, 10, &c.
6341is to be accounted a return of the same disposition which the Ray first
6342had at the distance 0, that is at its transmission through the first
6343refracting Surface. All which is the thing I would prove.
6344
6345What kind of action or disposition this is; Whether it consists in a
6346circulating or a vibrating motion of the Ray, or of the Medium, or
6347something else, I do not here enquire. Those that are averse from
6348assenting to any new Discoveries, but such as they can explain by an
6349Hypothesis, may for the present suppose, that as Stones by falling upon
6350Water put the Water into an undulating Motion, and all Bodies by
6351percussion excite vibrations in the Air; so the Rays of Light, by
6352impinging on any refracting or reflecting Surface, excite vibrations in
6353the refracting or reflecting Medium or Substance, and by exciting them
6354agitate the solid parts of the refracting or reflecting Body, and by
6355agitating them cause the Body to grow warm or hot; that the vibrations
6356thus excited are propagated in the refracting or reflecting Medium or
6357Substance, much after the manner that vibrations are propagated in the
6358Air for causing Sound, and move faster than the Rays so as to overtake
6359them; and that when any Ray is in that part of the vibration which
6360conspires with its Motion, it easily breaks through a refracting
6361Surface, but when it is in the contrary part of the vibration which
6362impedes its Motion, it is easily reflected; and, by consequence, that
6363every Ray is successively disposed to be easily reflected, or easily
6364transmitted, by every vibration which overtakes it. But whether this
6365Hypothesis be true or false I do not here consider. I content my self
6366with the bare Discovery, that the Rays of Light are by some cause or
6367other alternately disposed to be reflected or refracted for many
6368vicissitudes.
6369
6370
6371DEFINITION.
6372
6373_The returns of the disposition of any Ray to be reflected I will call
6374its_ Fits of easy Reflexion, _and those of its disposition to be
6375transmitted its_ Fits of easy Transmission, _and the space it passes
6376between every return and the next return, the_ Interval of its Fits.
6377
6378
6379PROP. XIII.
6380
6381_The reason why the Surfaces of all thick transparent Bodies reflect
6382part of the Light incident on them, and refract the rest, is, that some
6383Rays at their Incidence are in Fits of easy Reflexion, and others in
6384Fits of easy Transmission._
6385
6386This may be gather'd from the 24th Observation, where the Light
6387reflected by thin Plates of Air and Glass, which to the naked Eye
6388appear'd evenly white all over the Plate, did through a Prism appear
6389waved with many Successions of Light and Darkness made by alternate Fits
6390of easy Reflexion and easy Transmission, the Prism severing and
6391distinguishing the Waves of which the white reflected Light was
6392composed, as was explain'd above.
6393
6394And hence Light is in Fits of easy Reflexion and easy Transmission,
6395before its Incidence on transparent Bodies. And probably it is put into
6396such fits at its first emission from luminous Bodies, and continues in
6397them during all its progress. For these Fits are of a lasting nature, as
6398will appear by the next part of this Book.
6399
6400In this Proposition I suppose the transparent Bodies to be thick;
6401because if the thickness of the Body be much less than the Interval of
6402the Fits of easy Reflexion and Transmission of the Rays, the Body loseth
6403its reflecting power. For if the Rays, which at their entering into the
6404Body are put into Fits of easy Transmission, arrive at the farthest
6405Surface of the Body before they be out of those Fits, they must be
6406transmitted. And this is the reason why Bubbles of Water lose their
6407reflecting power when they grow very thin; and why all opake Bodies,
6408when reduced into very small parts, become transparent.
6409
6410
6411PROP. XIV.
6412
6413_Those Surfaces of transparent Bodies, which if the Ray be in a Fit of
6414Refraction do refract it most strongly, if the Ray be in a Fit of
6415Reflexion do reflect it most easily._
6416
6417For we shewed above, in _Prop._ 8. that the cause of Reflexion is not
6418the impinging of Light on the solid impervious parts of Bodies, but some
6419other power by which those solid parts act on Light at a distance. We
6420shewed also in _Prop._ 9. that Bodies reflect and refract Light by one
6421and the same power, variously exercised in various circumstances; and in
6422_Prop._ 1. that the most strongly refracting Surfaces reflect the most
6423Light: All which compared together evince and rarify both this and the
6424last Proposition.
6425
6426
6427PROP. XV.
6428
6429_In any one and the same sort of Rays, emerging in any Angle out of any
6430refracting Surface into one and the same Medium, the Interval of the
6431following Fits of easy Reflexion and Transmission are either accurately
6432or very nearly, as the Rectangle of the Secant of the Angle of
6433Refraction, and of the Secant of another Angle, whose Sine is the first
6434of 106 arithmetical mean Proportionals, between the Sines of Incidence
6435and Refraction, counted from the Sine of Refraction._
6436
6437This is manifest by the 7th and 19th Observations.
6438
6439
6440PROP. XVI.
6441
6442_In several sorts of Rays emerging in equal Angles out of any refracting
6443Surface into the same Medium, the Intervals of the following Fits of
6444easy Reflexion and easy Transmission are either accurately, or very
6445nearly, as the Cube-Roots of the Squares of the lengths of a Chord,
6446which 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
6448Rays, according to the Analogy described in the seventh Experiment of
6449the second Part of the first Book._
6450
6451This is manifest by the 13th and 14th Observations.
6452
6453
6454PROP. XVII.
6455
6456_If Rays of any sort pass perpendicularly into several Mediums, the
6457Intervals of the Fits of easy Reflexion and Transmission in any one
6458Medium, are to those Intervals in any other, as the Sine of Incidence to
6459the Sine of Refraction, when the Rays pass out of the first of those two
6460Mediums into the second._
6461
6462This is manifest by the 10th Observation.
6463
6464
6465PROP. XVIII.
6466
6467_If the Rays which paint the Colour in the Confine of yellow and orange
6468pass perpendicularly out of any Medium into Air, the Intervals of their
6469Fits of easy Reflexion are the 1/89000th part of an Inch. And of the
6470same length are the Intervals of their Fits of easy Transmission._
6471
6472This is manifest by the 6th Observation. From these Propositions it is
6473easy to collect the Intervals of the Fits of easy Reflexion and easy
6474Transmission of any sort of Rays refracted in any angle into any Medium;
6475and thence to know, whether the Rays shall be reflected or transmitted
6476at their subsequent Incidence upon any other pellucid Medium. Which
6477thing, being useful for understanding the next part of this Book, was
6478here to be set down. And for the same reason I add the two following
6479Propositions.
6480
6481
6482PROP. XIX.
6483
6484_If any sort of Rays falling on the polite Surface of any pellucid
6485Medium be reflected back, the Fits of easy Reflexion, which they have at
6486the point of Reflexion, shall still continue to return; and the Returns
6487shall be at distances from the point of Reflexion in the arithmetical
6488progression of the Numbers 2, 4, 6, 8, 10, 12, &c. and between these
6489Fits the Rays shall be in Fits of easy Transmission._
6490
6491For since the Fits of easy Reflexion and easy Transmission are of a
6492returning nature, there is no reason why these Fits, which continued
6493till the Ray arrived at the reflecting Medium, and there inclined the
6494Ray to Reflexion, should there cease. And if the Ray at the point of
6495Reflexion was in a Fit of easy Reflexion, the progression of the
6496distances of these Fits from that point must begin from 0, and so be of
6497the Numbers 0, 2, 4, 6, 8, &c. And therefore the progression of the
6498distances of the intermediate Fits of easy Transmission, reckon'd from
6499the same point, must be in the progression of the odd Numbers 1, 3, 5,
65007, 9, &c. contrary to what happens when the Fits are propagated from
6501points of Refraction.
6502
6503
6504PROP. XX.
6505
6506_The Intervals of the Fits of easy Reflexion and easy Transmission,
6507propagated from points of Reflexion into any Medium, are equal to the
6508Intervals of the like Fits, which the same Rays would have, if refracted
6509into the same Medium in Angles of Refraction equal to their Angles of
6510Reflexion._
6511
6512For when Light is reflected by the second Surface of thin Plates, it
6513goes out afterwards freely at the first Surface to make the Rings of
6514Colours which appear by Reflexion; and, by the freedom of its egress,
6515makes the Colours of these Rings more vivid and strong than those which
6516appear on the other side of the Plates by the transmitted Light. The
6517reflected Rays are therefore in Fits of easy Transmission at their
6518egress; which would not always happen, if the Intervals of the Fits
6519within the Plate after Reflexion were not equal, both in length and
6520number, to their Intervals before it. And this confirms also the
6521proportions set down in the former Proposition. For if the Rays both in
6522going in and out at the first Surface be in Fits of easy Transmission,
6523and the Intervals and Numbers of those Fits between the first and second
6524Surface, before and after Reflexion, be equal, the distances of the Fits
6525of easy Transmission from either Surface, must be in the same
6526progression after Reflexion as before; that is, from the first Surface
6527which transmitted them in the progression of the even Numbers 0, 2, 4,
65286, 8, &c. and from the second which reflected them, in that of the odd
6529Numbers 1, 3, 5, 7, &c. But these two Propositions will become much more
6530evident by the Observations in the following part of this Book.
6531
6532
6533
6534
6535THE
6536
6537SECOND BOOK
6538
6539OF
6540
6541OPTICKS
6542
6543
6544_PART IV._
6545
6546_Observations concerning the Reflexions and Colours of thick transparent
6547polish'd Plates._
6548
6549There is no Glass or Speculum how well soever polished, but, besides the
6550Light which it refracts or reflects regularly, scatters every way
6551irregularly a faint Light, by means of which the polish'd Surface, when
6552illuminated in a dark room by a beam of the Sun's Light, may be easily
6553seen in all positions of the Eye. There are certain Phænomena of this
6554scatter'd Light, which when I first observed them, seem'd very strange
6555and surprizing to me. My Observations were as follows.
6556
6557_Obs._ 1. The Sun shining into my darken'd Chamber through a hole one
6558third of an Inch wide, I let the intromitted beam of Light fall
6559perpendicularly upon a Glass Speculum ground concave on one side and
6560convex on the other, to a Sphere of five Feet and eleven Inches Radius,
6561and Quick-silver'd over on the convex side. And holding a white opake
6562Chart, or a Quire of Paper at the center of the Spheres to which the
6563Speculum was ground, that is, at the distance of about five Feet and
6564eleven Inches from the Speculum, in such manner, that the beam of Light
6565might pass through a little hole made in the middle of the Chart to the
6566Speculum, and thence be reflected back to the same hole: I observed upon
6567the Chart four or five concentric Irises or Rings of Colours, like
6568Rain-bows, encompassing the hole much after the manner that those, which
6569in the fourth and following Observations of the first part of this Book
6570appear'd between the Object-glasses, encompassed the black Spot, but yet
6571larger and fainter than those. These Rings as they grew larger and
6572larger became diluter and fainter, so that the fifth was scarce visible.
6573Yet sometimes, when the Sun shone very clear, there appear'd faint
6574Lineaments of a sixth and seventh. If the distance of the Chart from the
6575Speculum was much greater or much less than that of six Feet, the Rings
6576became dilute and vanish'd. And if the distance of the Speculum from the
6577Window was much greater than that of six Feet, the reflected beam of
6578Light would be so broad at the distance of six Feet from the Speculum
6579where the Rings appear'd, as to obscure one or two of the innermost
6580Rings. And therefore I usually placed the Speculum at about six Feet
6581from the Window; so that its Focus might there fall in with the center
6582of its concavity at the Rings upon the Chart. And this Posture is always
6583to be understood in the following Observations where no other is
6584express'd.
6585
6586_Obs._ 2. The Colours of these Rain-bows succeeded one another from the
6587center outwards, in the same form and order with those which were made
6588in the ninth Observation of the first Part of this Book by Light not
6589reflected, but transmitted through the two Object-glasses. For, first,
6590there was in their common center a white round Spot of faint Light,
6591something broader than the reflected beam of Light, which beam sometimes
6592fell upon the middle of the Spot, and sometimes by a little inclination
6593of the Speculum receded from the middle, and left the Spot white to the
6594center.
6595
6596This white Spot was immediately encompassed with a dark grey or russet,
6597and that dark grey with the Colours of the first Iris; which Colours on
6598the inside next the dark grey were a little violet and indigo, and next
6599to that a blue, which on the outside grew pale, and then succeeded a
6600little greenish yellow, and after that a brighter yellow, and then on
6601the outward edge of the Iris a red which on the outside inclined to
6602purple.
6603
6604This Iris was immediately encompassed with a second, whose Colours were
6605in order from the inside outwards, purple, blue, green, yellow, light
6606red, a red mix'd with purple.
6607
6608Then immediately follow'd the Colours of the third Iris, which were in
6609order outwards a green inclining to purple, a good green, and a red more
6610bright than that of the former Iris.
6611
6612The fourth and fifth Iris seem'd of a bluish green within, and red
6613without, 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
6616accurately as I could, I found them also in the same proportion to one
6617another with the Rings made by Light transmitted through the two
6618Object-glasses. For the Diameters of the four first of the bright Rings
6619measured between the brightest parts of their Orbits, at the distance of
6620six Feet from the Speculum were 1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches,
6621whose Squares are in arithmetical progression of the numbers 1, 2, 3, 4.
6622If the white circular Spot in the middle be reckon'd amongst the Rings,
6623and its central Light, where it seems to be most luminous, be put
6624equipollent to an infinitely little Ring; the Squares of the Diameters
6625of the Rings will be in the progression 0, 1, 2, 3, 4, &c. I measured
6626also the Diameters of the dark Circles between these luminous ones, and
6627found their Squares in the progression of the numbers 1/2, 1-1/2, 2-1/2,
66283-1/2, &c. the Diameters of the first four at the distance of six Feet
6629from the Speculum, being 1-3/16, 2-1/16, 2-2/3, 3-3/20 Inches. If the
6630distance of the Chart from the Speculum was increased or diminished, the
6631Diameters of the Circles were increased or diminished proportionally.
6632
6633_Obs._ 4. By the analogy between these Rings and those described in the
6634Observations of the first Part of this Book, I suspected that there
6635were many more of them which spread into one another, and by interfering
6636mix'd their Colours, and diluted one another so that they could not be
6637seen apart. I viewed them therefore through a Prism, as I did those in
6638the 24th Observation of the first Part of this Book. And when the Prism
6639was so placed as by refracting the Light of their mix'd Colours to
6640separate them, and distinguish the Rings from one another, as it did
6641those in that Observation, I could then see them distincter than before,
6642and easily number eight or nine of them, and sometimes twelve or
6643thirteen. And had not their Light been so very faint, I question not but
6644that I might have seen many more.
6645
6646_Obs._ 5. Placing a Prism at the Window to refract the intromitted beam
6647of Light, and cast the oblong Spectrum of Colours on the Speculum: I
6648covered the Speculum with a black Paper which had in the middle of it a
6649hole to let any one of the Colours pass through to the Speculum, whilst
6650the rest were intercepted by the Paper. And now I found Rings of that
6651Colour only which fell upon the Speculum. If the Speculum was
6652illuminated with red, the Rings were totally red with dark Intervals, if
6653with blue they were totally blue, and so of the other Colours. And when
6654they were illuminated with any one Colour, the Squares of their
6655Diameters measured between their most luminous Parts, were in the
6656arithmetical Progression of the Numbers, 0, 1, 2, 3, 4 and the Squares
6657of the Diameters of their dark Intervals in the Progression of the
6658intermediate Numbers 1/2, 1-1/2, 2-1/2, 3-1/2. But if the Colour was
6659varied, they varied their Magnitude. In the red they were largest, in
6660the indigo and violet least, and in the intermediate Colours yellow,
6661green, and blue, they were of several intermediate Bignesses answering
6662to the Colour, that is, greater in yellow than in green, and greater in
6663green than in blue. And hence I knew, that when the Speculum was
6664illuminated with white Light, the red and yellow on the outside of the
6665Rings were produced by the least refrangible Rays, and the blue and
6666violet by the most refrangible, and that the Colours of each Ring spread
6667into the Colours of the neighbouring Rings on either side, after the
6668manner explain'd in the first and second Part of this Book, and by
6669mixing diluted one another so that they could not be distinguish'd,
6670unless near the Center where they were least mix'd. For in this
6671Observation I could see the Rings more distinctly, and to a greater
6672Number than before, being able in the yellow Light to number eight or
6673nine of them, besides a faint shadow of a tenth. To satisfy my self how
6674much the Colours of the several Rings spread into one another, I
6675measured the Diameters of the second and third Rings, and found them
6676when made by the Confine of the red and orange to be to the same
6677Diameters when made by the Confine of blue and indigo, as 9 to 8, or
6678thereabouts. For it was hard to determine this Proportion accurately.
6679Also the Circles made successively by the red, yellow, and green,
6680differ'd more from one another than those made successively by the
6681green, blue, and indigo. For the Circle made by the violet was too dark
6682to be seen. To carry on the Computation, let us therefore suppose that
6683the Differences of the Diameters of the Circles made by the outmost red,
6684the Confine of red and orange, the Confine of orange and yellow, the
6685Confine of yellow and green, the Confine of green and blue, the Confine
6686of blue and indigo, the Confine of indigo and violet, and outmost
6687violet, are in proportion as the Differences of the Lengths of a
6688Monochord 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,
66902/27, 1/27, 1/18. And if the Diameter of the Circle made by the Confine
6691of red and orange be 9A, and that of the Circle made by the Confine of
6692blue and indigo be 8A as above; their difference 9A-8A will be to the
6693difference of the Diameters of the Circles made by the outmost red, and
6694by the Confine of red and orange, as 1/18 + 1/12 + 1/12 + 2/27 to 1/9,
6695that is as 8/27 to 1/9, or 8 to 3, and to the difference of the Circles
6696made by the outmost violet, and by the Confine of blue and indigo, as
66971/18 + 1/12 + 1/12 + 2/27 to 1/27 + 1/18, that is, as 8/27 to 5/54, or
6698as 16 to 5. And therefore these differences will be 3/8A and 5/16A. Add
6699the first to 9A and subduct the last from 8A, and you will have the
6700Diameters of the Circles made by the least and most refrangible Rays
670175/8A and ((61-1/2)/8)A. These diameters are therefore to one another as
670275 to 61-1/2 or 50 to 41, and their Squares as 2500 to 1681, that is, as
67033 to 2 very nearly. Which proportion differs not much from the
6704proportion of the Diameters of the Circles made by the outmost red and
6705outmost 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
6708Speculum tinged all over with Waves of Colours, (red, yellow, green,
6709blue;) like those which in the Observations of the first part of this
6710Book appeared between the Object-glasses, and upon Bubbles of Water, but
6711much larger. And after the manner of those, they were of various
6712magnitudes in various Positions of the Eye, swelling and shrinking as I
6713moved my Eye this way and that way. They were formed like Arcs of
6714concentrick Circles, as those were; and when my Eye was over against the
6715center of the concavity of the Speculum, (that is, 5 Feet and 10 Inches
6716distant from the Speculum,) their common center was in a right Line with
6717that center of concavity, and with the hole in the Window. But in other
6718postures of my Eye their center had other positions. They appear'd by
6719the Light of the Clouds propagated to the Speculum through the hole in
6720the Window; and when the Sun shone through that hole upon the Speculum,
6721his Light upon it was of the Colour of the Ring whereon it fell, but by
6722its splendor obscured the Rings made by the Light of the Clouds, unless
6723when the Speculum was removed to a great distance from the Window, so
6724that his Light upon it might be broad and faint. By varying the position
6725of my Eye, and moving it nearer to or farther from the direct beam of
6726the Sun's Light, the Colour of the Sun's reflected Light constantly
6727varied upon the Speculum, as it did upon my Eye, the same Colour always
6728appearing to a Bystander upon my Eye which to me appear'd upon the
6729Speculum. And thence I knew that the Rings of Colours upon the Chart
6730were made by these reflected Colours, propagated thither from the
6731Speculum in several Angles, and that their production depended not upon
6732the termination of Light and Shadow.
6733
6734_Obs._ 7. By the Analogy of all these Phænomena with those of the like
6735Rings of Colours described in the first part of this Book, it seemed to
6736me that these Colours were produced by this thick Plate of Glass, much
6737after the manner that those were produced by very thin Plates. For, upon
6738trial, I found that if the Quick-silver were rubb'd off from the
6739backside of the Speculum, the Glass alone would cause the same Rings of
6740Colours, but much more faint than before; and therefore the Phænomenon
6741depends not upon the Quick-silver, unless so far as the Quick-silver by
6742increasing the Reflexion of the backside of the Glass increases the
6743Light of the Rings of Colours. I found also that a Speculum of Metal
6744without Glass made some Years since for optical uses, and very well
6745wrought, produced none of those Rings; and thence I understood that
6746these Rings arise not from one specular Surface alone, but depend upon
6747the two Surfaces of the Plate of Glass whereof the Speculum was made,
6748and upon the thickness of the Glass between them. For as in the 7th and
674919th Observations of the first part of this Book a thin Plate of Air,
6750Water, or Glass of an even thickness appeared of one Colour when the
6751Rays were perpendicular to it, of another when they were a little
6752oblique, of another when more oblique, of another when still more
6753oblique, and so on; so here, in the sixth Observation, the Light which
6754emerged out of the Glass in several Obliquities, made the Glass appear
6755of several Colours, and being propagated in those Obliquities to the
6756Chart, there painted Rings of those Colours. And as the reason why a
6757thin Plate appeared of several Colours in several Obliquities of the
6758Rays, was, that the Rays of one and the same sort are reflected by the
6759thin Plate at one obliquity and transmitted at another, and those of
6760other sorts transmitted where these are reflected, and reflected where
6761these are transmitted: So the reason why the thick Plate of Glass
6762whereof the Speculum was made did appear of various Colours in various
6763Obliquities, and in those Obliquities propagated those Colours to the
6764Chart, was, that the Rays of one and the same sort did at one Obliquity
6765emerge out of the Glass, at another did not emerge, but were reflected
6766back towards the Quick-silver by the hither Surface of the Glass, and
6767accordingly as the Obliquity became greater and greater, emerged and
6768were reflected alternately for many Successions; and that in one and the
6769same Obliquity the Rays of one sort were reflected, and those of another
6770transmitted. This is manifest by the fifth Observation of this part of
6771this Book. For in that Observation, when the Speculum was illuminated by
6772any one of the prismatick Colours, that Light made many Rings of the
6773same Colour upon the Chart with dark Intervals, and therefore at its
6774emergence out of the Speculum was alternately transmitted and not
6775transmitted from the Speculum to the Chart for many Successions,
6776according to the various Obliquities of its Emergence. And when the
6777Colour cast on the Speculum by the Prism was varied, the Rings became of
6778the Colour cast on it, and varied their bigness with their Colour, and
6779therefore the Light was now alternately transmitted and not transmitted
6780from the Speculum to the Chart at other Obliquities than before. It
6781seemed to me therefore that these Rings were of one and the same
6782original with those of thin Plates, but yet with this difference, that
6783those of thin Plates are made by the alternate Reflexions and
6784Transmissions of the Rays at the second Surface of the Plate, after one
6785passage through it; but here the Rays go twice through the Plate before
6786they are alternately reflected and transmitted. First, they go through
6787it from the first Surface to the Quick-silver, and then return through
6788it from the Quick-silver to the first Surface, and there are either
6789transmitted to the Chart or reflected back to the Quick-silver,
6790accordingly as they are in their Fits of easy Reflexion or Transmission
6791when they arrive at that Surface. For the Intervals of the Fits of the
6792Rays which fall perpendicularly on the Speculum, and are reflected back
6793in the same perpendicular Lines, by reason of the equality of these
6794Angles and Lines, are of the same length and number within the Glass
6795after Reflexion as before, by the 19th Proposition of the third part of
6796this Book. And therefore since all the Rays that enter through the
6797first Surface are in their Fits of easy Transmission at their entrance,
6798and as many of these as are reflected by the second are in their Fits of
6799easy Reflexion there, all these must be again in their Fits of easy
6800Transmission at their return to the first, and by consequence there go
6801out of the Glass to the Chart, and form upon it the white Spot of Light
6802in the center of the Rings. For the reason holds good in all sorts of
6803Rays, and therefore all sorts must go out promiscuously to that Spot,
6804and by their mixture cause it to be white. But the Intervals of the Fits
6805of those Rays which are reflected more obliquely than they enter, must
6806be greater after Reflexion than before, by the 15th and 20th
6807Propositions. And thence it may happen that the Rays at their return to
6808the first Surface, may in certain Obliquities be in Fits of easy
6809Reflexion, and return back to the Quick-silver, and in other
6810intermediate Obliquities be again in Fits of easy Transmission, and so
6811go out to the Chart, and paint on it the Rings of Colours about the
6812white Spot. And because the Intervals of the Fits at equal obliquities
6813are greater and fewer in the less refrangible Rays, and less and more
6814numerous in the more refrangible, therefore the less refrangible at
6815equal obliquities shall make fewer Rings than the more refrangible, and
6816the Rings made by those shall be larger than the like number of Rings
6817made by these; that is, the red Rings shall be larger than the yellow,
6818the yellow than the green, the green than the blue, and the blue than
6819the violet, as they were really found to be in the fifth Observation.
6820And therefore the first Ring of all Colours encompassing the white Spot
6821of Light shall be red without any violet within, and yellow, and green,
6822and blue in the middle, as it was found in the second Observation; and
6823these Colours in the second Ring, and those that follow, shall be more
6824expanded, till they spread into one another, and blend one another by
6825interfering.
6826
6827These seem to be the reasons of these Rings in general; and this put me
6828upon observing the thickness of the Glass, and considering whether the
6829dimensions and proportions of the Rings may be truly derived from it by
6830computation.
6831
6832_Obs._ 8. I measured therefore the thickness of this concavo-convex
6833Plate of Glass, and found it every where 1/4 of an Inch precisely. Now,
6834by the sixth Observation of the first Part of this Book, a thin Plate of
6835Air transmits the brightest Light of the first Ring, that is, the bright
6836yellow, when its thickness is the 1/89000th part of an Inch; and by the
6837tenth Observation of the same Part, a thin Plate of Glass transmits the
6838same Light of the same Ring, when its thickness is less in proportion of
6839the Sine of Refraction to the Sine of Incidence, that is, when its
6840thickness is the 11/1513000th or 1/137545th part of an Inch, supposing
6841the Sines are as 11 to 17. And if this thickness be doubled, it
6842transmits the same bright Light of the second Ring; if tripled, it
6843transmits that of the third, and so on; the bright yellow Light in all
6844these cases being in its Fits of Transmission. And therefore if its
6845thickness be multiplied 34386 times, so as to become 1/4 of an Inch, it
6846transmits the same bright Light of the 34386th Ring. Suppose this be the
6847bright yellow Light transmitted perpendicularly from the reflecting
6848convex side of the Glass through the concave side to the white Spot in
6849the center of the Rings of Colours on the Chart: And by a Rule in the
68507th and 19th Observations in the first Part of this Book, and by the
685115th and 20th Propositions of the third Part of this Book, if the Rays
6852be made oblique to the Glass, the thickness of the Glass requisite to
6853transmit the same bright Light of the same Ring in any obliquity, is to
6854this thickness of 1/4 of an Inch, as the Secant of a certain Angle to
6855the Radius, the Sine of which Angle is the first of an hundred and six
6856arithmetical Means between the Sines of Incidence and Refraction,
6857counted from the Sine of Incidence when the Refraction is made out of
6858any plated Body into any Medium encompassing it; that is, in this case,
6859out of Glass into Air. Now if the thickness of the Glass be increased by
6860degrees, so as to bear to its first thickness, (_viz._ that of a quarter
6861of an Inch,) the Proportions which 34386 (the number of Fits of the
6862perpendicular Rays in going through the Glass towards the white Spot in
6863the center of the Rings,) hath to 34385, 34384, 34383, and 34382, (the
6864numbers of the Fits of the oblique Rays in going through the Glass
6865towards the first, second, third, and fourth Rings of Colours,) and if
6866the first thickness be divided into 100000000 equal parts, the increased
6867thicknesses will be 100002908, 100005816, 100008725, and 100011633, and
6868the Angles of which these thicknesses are Secants will be 26´ 13´´, 37´
68695´´, 45´ 6´´, and 52´ 26´´, the Radius being 100000000; and the Sines of
6870these Angles are 762, 1079, 1321, and 1525, and the proportional Sines
6871of Refraction 1172, 1659, 2031, and 2345, the Radius being 100000. For
6872since the Sines of Incidence out of Glass into Air are to the Sines of
6873Refraction as 11 to 17, and to the above-mentioned Secants as 11 to the
6874first of 106 arithmetical Means between 11 and 17, that is, as 11 to
687511-6/106, those Secants will be to the Sines of Refraction as 11-6/106,
6876to 17, and by this Analogy will give these Sines. So then, if the
6877obliquities of the Rays to the concave Surface of the Glass be such that
6878the Sines of their Refraction in passing out of the Glass through that
6879Surface into the Air be 1172, 1659, 2031, 2345, the bright Light of the
688034386th Ring shall emerge at the thicknesses of the Glass, which are to
68811/4 of an Inch as 34386 to 34385, 34384, 34383, 34382, respectively. And
6882therefore, if the thickness in all these Cases be 1/4 of an Inch (as it
6883is in the Glass of which the Speculum was made) the bright Light of the
688434385th Ring shall emerge where the Sine of Refraction is 1172, and that
6885of the 34384th, 34383th, and 34382th Ring where the Sine is 1659, 2031,
6886and 2345 respectively. And in these Angles of Refraction the Light of
6887these Rings shall be propagated from the Speculum to the Chart, and
6888there paint Rings about the white central round Spot of Light which we
6889said was the Light of the 34386th Ring. And the Semidiameters of these
6890Rings shall subtend the Angles of Refraction made at the
6891Concave-Surface of the Speculum, and by consequence their Diameters
6892shall be to the distance of the Chart from the Speculum as those Sines
6893of Refraction doubled are to the Radius, that is, as 1172, 1659, 2031,
6894and 2345, doubled are to 100000. And therefore, if the distance of the
6895Chart from the Concave-Surface of the Speculum be six Feet (as it was in
6896the third of these Observations) the Diameters of the Rings of this
6897bright yellow Light upon the Chart shall be 1'688, 2'389, 2'925, 3'375
6898Inches: For these Diameters are to six Feet, as the above-mention'd
6899Sines doubled are to the Radius. Now, these Diameters of the bright
6900yellow Rings, thus found by Computation are the very same with those
6901found in the third of these Observations by measuring them, _viz._ with
69021-11/16, 2-3/8, 2-11/12, and 3-3/8 Inches, and therefore the Theory of
6903deriving these Rings from the thickness of the Plate of Glass of which
6904the Speculum was made, and from the Obliquity of the emerging Rays
6905agrees with the Observation. In this Computation I have equalled the
6906Diameters of the bright Rings made by Light of all Colours, to the
6907Diameters of the Rings made by the bright yellow. For this yellow makes
6908the brightest Part of the Rings of all Colours. If you desire the
6909Diameters of the Rings made by the Light of any other unmix'd Colour,
6910you may find them readily by putting them to the Diameters of the bright
6911yellow ones in a subduplicate Proportion of the Intervals of the Fits of
6912the Rays of those Colours when equally inclined to the refracting or
6913reflecting Surface which caused those Fits, that is, by putting the
6914Diameters of the Rings made by the Rays in the Extremities and Limits of
6915the seven Colours, red, orange, yellow, green, blue, indigo, violet,
6916proportional to the Cube-roots of the Numbers, 1, 8/9, 5/6, 3/4, 2/3,
69173/5, 9/16, 1/2, which express the Lengths of a Monochord sounding the
6918Notes in an Eighth: For by this means the Diameters of the Rings of
6919these Colours will be found pretty nearly in the same Proportion to one
6920another, which they ought to have by the fifth of these Observations.
6921
6922And thus I satisfy'd my self, that these Rings were of the same kind and
6923Original with those of thin Plates, and by consequence that the Fits or
6924alternate Dispositions of the Rays to be reflected and transmitted are
6925propagated to great distances from every reflecting and refracting
6926Surface. But yet to put the matter out of doubt, I added the following
6927Observation.
6928
6929_Obs._ 9. If these Rings thus depend on the thickness of the Plate of
6930Glass, their Diameters at equal distances from several Speculums made of
6931such concavo-convex Plates of Glass as are ground on the same Sphere,
6932ought to be reciprocally in a subduplicate Proportion of the thicknesses
6933of the Plates of Glass. And if this Proportion be found true by
6934experience it will amount to a demonstration that these Rings (like
6935those formed in thin Plates) do depend on the thickness of the Glass. I
6936procured therefore another concavo-convex Plate of Glass ground on both
6937sides to the same Sphere with the former Plate. Its thickness was 5/62
6938Parts of an Inch; and the Diameters of the three first bright Rings
6939measured between the brightest Parts of their Orbits at the distance of
6940six Feet from the Glass were 3·4-1/6·5-1/8· Inches. Now, the thickness
6941of the other Glass being 1/4 of an Inch was to the thickness of this
6942Glass as 1/4 to 5/62, that is as 31 to 10, or 310000000 to 100000000,
6943and the Roots of these Numbers are 17607 and 10000, and in the
6944Proportion of the first of these Roots to the second are the Diameters
6945of the bright Rings made in this Observation by the thinner Glass,
69463·4-1/6·5-1/8, to the Diameters of the same Rings made in the third of
6947these Observations by the thicker Glass 1-11/16, 2-3/8. 2-11/12, that
6948is, the Diameters of the Rings are reciprocally in a subduplicate
6949Proportion of the thicknesses of the Plates of Glass.
6950
6951So then in Plates of Glass which are alike concave on one side, and
6952alike convex on the other side, and alike quick-silver'd on the convex
6953sides, and differ in nothing but their thickness, the Diameters of the
6954Rings are reciprocally in a subduplicate Proportion of the thicknesses
6955of the Plates. And this shews sufficiently that the Rings depend on both
6956the Surfaces of the Glass. They depend on the convex Surface, because
6957they are more luminous when that Surface is quick-silver'd over than
6958when it is without Quick-silver. They depend also upon the concave
6959Surface, because without that Surface a Speculum makes them not. They
6960depend on both Surfaces, and on the distances between them, because
6961their bigness is varied by varying only that distance. And this
6962dependence is of the same kind with that which the Colours of thin
6963Plates have on the distance of the Surfaces of those Plates, because the
6964bigness of the Rings, and their Proportion to one another, and the
6965variation of their bigness arising from the variation of the thickness
6966of the Glass, and the Orders of their Colours, is such as ought to
6967result from the Propositions in the end of the third Part of this Book,
6968derived from the Phænomena of the Colours of thin Plates set down in the
6969first Part.
6970
6971There are yet other Phænomena of these Rings of Colours, but such as
6972follow from the same Propositions, and therefore confirm both the Truth
6973of those Propositions, and the Analogy between these Rings and the Rings
6974of 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
6977Speculum not directly to the hole in the Window, but to a place a little
6978distant from it, the common center of that Spot, and of all the Rings of
6979Colours fell in the middle way between the beam of the incident Light,
6980and the beam of the reflected Light, and by consequence in the center of
6981the spherical concavity of the Speculum, whenever the Chart on which the
6982Rings of Colours fell was placed at that center. And as the beam of
6983reflected Light by inclining the Speculum receded more and more from the
6984beam of incident Light and from the common center of the colour'd Rings
6985between them, those Rings grew bigger and bigger, and so also did the
6986white round Spot, and new Rings of Colours emerged successively out of
6987their common center, and the white Spot became a white Ring
6988encompassing them; and the incident and reflected beams of Light always
6989fell upon the opposite parts of this white Ring, illuminating its
6990Perimeter like two mock Suns in the opposite parts of an Iris. So then
6991the Diameter of this Ring, measured from the middle of its Light on one
6992side to the middle of its Light on the other side, was always equal to
6993the distance between the middle of the incident beam of Light, and the
6994middle of the reflected beam measured at the Chart on which the Rings
6995appeared: And the Rays which form'd this Ring were reflected by the
6996Speculum in Angles equal to their Angles of Incidence, and by
6997consequence to their Angles of Refraction at their entrance into the
6998Glass, but yet their Angles of Reflexion were not in the same Planes
6999with their Angles of Incidence.
7000
7001_Obs._ 11. The Colours of the new Rings were in a contrary order to
7002those of the former, and arose after this manner. The white round Spot
7003of Light in the middle of the Rings continued white to the center till
7004the distance of the incident and reflected beams at the Chart was about
70057/8 parts of an Inch, and then it began to grow dark in the middle. And
7006when that distance was about 1-3/16 of an Inch, the white Spot was
7007become a Ring encompassing a dark round Spot which in the middle
7008inclined to violet and indigo. And the luminous Rings encompassing it
7009were grown equal to those dark ones which in the four first Observations
7010encompassed them, that is to say, the white Spot was grown a white Ring
7011equal to the first of those dark Rings, and the first of those luminous
7012Rings was now grown equal to the second of those dark ones, and the
7013second of those luminous ones to the third of those dark ones, and so
7014on. For the Diameters of the luminous Rings were now 1-3/16, 2-1/16,
70152-2/3, 3-3/20, &c. Inches.
7016
7017When the distance between the incident and reflected beams of Light
7018became a little bigger, there emerged out of the middle of the dark Spot
7019after the indigo a blue, and then out of that blue a pale green, and
7020soon after a yellow and red. And when the Colour at the center was
7021brightest, being between yellow and red, the bright Rings were grown
7022equal to those Rings which in the four first Observations next
7023encompassed them; that is to say, the white Spot in the middle of those
7024Rings was now become a white Ring equal to the first of those bright
7025Rings, and the first of those bright ones was now become equal to the
7026second of those, and so on. For the Diameters of the white Ring, and of
7027the other luminous Rings encompassing it, were now 1-11/16, 2-3/8,
70282-11/12, 3-3/8, &c. or thereabouts.
7029
7030When the distance of the two beams of Light at the Chart was a little
7031more increased, there emerged out of the middle in order after the red,
7032a purple, a blue, a green, a yellow, and a red inclining much to purple,
7033and when the Colour was brightest being between yellow and red, the
7034former indigo, blue, green, yellow and red, were become an Iris or Ring
7035of Colours equal to the first of those luminous Rings which appeared in
7036the four first Observations, and the white Ring which was now become
7037the second of the luminous Rings was grown equal to the second of those,
7038and the first of those which was now become the third Ring was become
7039equal to the third of those, and so on. For their Diameters were
70401-11/16, 2-3/8, 2-11/12, 3-3/8 Inches, the distance of the two beams of
7041Light, and the Diameter of the white Ring being 2-3/8 Inches.
7042
7043When these two beams became more distant there emerged out of the middle
7044of the purplish red, first a darker round Spot, and then out of the
7045middle of that Spot a brighter. And now the former Colours (purple,
7046blue, green, yellow, and purplish red) were become a Ring equal to the
7047first of the bright Rings mentioned in the four first Observations, and
7048the Rings about this Ring were grown equal to the Rings about that
7049respectively; the distance between the two beams of Light and the
7050Diameter of the white Ring (which was now become the third Ring) being
7051about 3 Inches.
7052
7053The Colours of the Rings in the middle began now to grow very dilute,
7054and if the distance between the two Beams was increased half an Inch, or
7055an Inch more, they vanish'd whilst the white Ring, with one or two of
7056the Rings next it on either side, continued still visible. But if the
7057distance of the two beams of Light was still more increased, these also
7058vanished: For the Light which coming from several parts of the hole in
7059the Window fell upon the Speculum in several Angles of Incidence, made
7060Rings of several bignesses, which diluted and blotted out one another,
7061as I knew by intercepting some part of that Light. For if I intercepted
7062that part which was nearest to the Axis of the Speculum the Rings would
7063be less, if the other part which was remotest from it they would be
7064bigger.
7065
7066_Obs._ 12. When the Colours of the Prism were cast successively on the
7067Speculum, that Ring which in the two last Observations was white, was of
7068the same bigness in all the Colours, but the Rings without it were
7069greater in the green than in the blue, and still greater in the yellow,
7070and greatest in the red. And, on the contrary, the Rings within that
7071white Circle were less in the green than in the blue, and still less in
7072the yellow, and least in the red. For the Angles of Reflexion of those
7073Rays which made this Ring, being equal to their Angles of Incidence, the
7074Fits of every reflected Ray within the Glass after Reflexion are equal
7075in length and number to the Fits of the same Ray within the Glass before
7076its Incidence on the reflecting Surface. And therefore since all the
7077Rays of all sorts at their entrance into the Glass were in a Fit of
7078Transmission, they were also in a Fit of Transmission at their returning
7079to the same Surface after Reflexion; and by consequence were
7080transmitted, and went out to the white Ring on the Chart. This is the
7081reason why that Ring was of the same bigness in all the Colours, and why
7082in a mixture of all it appears white. But in Rays which are reflected in
7083other Angles, the Intervals of the Fits of the least refrangible being
7084greatest, make the Rings of their Colour in their progress from this
7085white Ring, either outwards or inwards, increase or decrease by the
7086greatest steps; so that the Rings of this Colour without are greatest,
7087and within least. And this is the reason why in the last Observation,
7088when the Speculum was illuminated with white Light, the exterior Rings
7089made by all Colours appeared red without and blue within, and the
7090interior blue without and red within.
7091
7092These are the Phænomena of thick convexo-concave Plates of Glass, which
7093are every where of the same thickness. There are yet other Phænomena
7094when these Plates are a little thicker on one side than on the other,
7095and others when the Plates are more or less concave than convex, or
7096plano-convex, or double-convex. For in all these cases the Plates make
7097Rings of Colours, but after various manners; all which, so far as I have
7098yet observed, follow from the Propositions in the end of the third part
7099of this Book, and so conspire to confirm the truth of those
7100Propositions. But the Phænomena are too various, and the Calculations
7101whereby they follow from those Propositions too intricate to be here
7102prosecuted. I content my self with having prosecuted this kind of
7103Phænomena so far as to discover their Cause, and by discovering it to
7104ratify 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
7107makes the Rings of Colours above described, so it ought to make the like
7108Rings of Colours in passing through a drop of Water. At the first
7109Reflexion of the Rays within the drop, some Colours ought to be
7110transmitted, as in the case of a Lens, and others to be reflected back
7111to the Eye. For instance, if the Diameter of a small drop or globule of
7112Water be about the 500th part of an Inch, so that a red-making Ray in
7113passing through the middle of this globule has 250 Fits of easy
7114Transmission within the globule, and that all the red-making Rays which
7115are at a certain distance from this middle Ray round about it have 249
7116Fits within the globule, and all the like Rays at a certain farther
7117distance round about it have 248 Fits, and all those at a certain
7118farther distance 247 Fits, and so on; these concentrick Circles of Rays
7119after their transmission, falling on a white Paper, will make
7120concentrick Rings of red upon the Paper, supposing the Light which
7121passes through one single globule, strong enough to be sensible. And, in
7122like manner, the Rays of other Colours will make Rings of other Colours.
7123Suppose now that in a fair Day the Sun shines through a thin Cloud of
7124such globules of Water or Hail, and that the globules are all of the
7125same bigness; and the Sun seen through this Cloud shall appear
7126encompassed with the like concentrick Rings of Colours, and the Diameter
7127of the first Ring of red shall be 7-1/4 Degrees, that of the second
712810-1/4 Degrees, that of the third 12 Degrees 33 Minutes. And accordingly
7129as the Globules of Water are bigger or less, the Rings shall be less or
7130bigger. This is the Theory, and Experience answers it. For in _June_
71311692, I saw by reflexion in a Vessel of stagnating Water three Halos,
7132Crowns, or Rings of Colours about the Sun, like three little Rain-bows,
7133concentrick to his Body. The Colours of the first or innermost Crown
7134were blue next the Sun, red without, and white in the middle between the
7135blue and red. Those of the second Crown were purple and blue within, and
7136pale red without, and green in the middle. And those of the third were
7137pale blue within, and pale red without; these Crowns enclosed one
7138another immediately, so that their Colours proceeded in this continual
7139order from the Sun outward: blue, white, red; purple, blue, green, pale
7140yellow and red; pale blue, pale red. The Diameter of the second Crown
7141measured from the middle of the yellow and red on one side of the Sun,
7142to the middle of the same Colour on the other side was 9-1/3 Degrees, or
7143thereabouts. The Diameters of the first and third I had not time to
7144measure, but that of the first seemed to be about five or six Degrees,
7145and that of the third about twelve. The like Crowns appear sometimes
7146about the Moon; for in the beginning of the Year 1664, _Febr._ 19th at
7147Night, I saw two such Crowns about her. The Diameter of the first or
7148innermost was about three Degrees, and that of the second about five
7149Degrees and an half. Next about the Moon was a Circle of white, and next
7150about that the inner Crown, which was of a bluish green within next the
7151white, and of a yellow and red without, and next about these Colours
7152were blue and green on the inside of the outward Crown, and red on the
7153outside of it. At the same time there appear'd a Halo about 22 Degrees
715435´ distant from the center of the Moon. It was elliptical, and its long
7155Diameter was perpendicular to the Horizon, verging below farthest from
7156the Moon. I am told that the Moon has sometimes three or more
7157concentrick Crowns of Colours encompassing one another next about her
7158Body. The more equal the globules of Water or Ice are to one another,
7159the more Crowns of Colours will appear, and the Colours will be the more
7160lively. The Halo at the distance of 22-1/2 Degrees from the Moon is of
7161another sort. By its being oval and remoter from the Moon below than
7162above, I conclude, that it was made by Refraction in some sort of Hail
7163or Snow floating in the Air in an horizontal posture, the refracting
7164Angle being about 58 or 60 Degrees.
7165
7166
7167
7168
7169THE
7170
7171THIRD BOOK
7172
7173OF
7174
7175OPTICKS
7176
7177
7178_PART I._
7179
7180_Observations concerning the Inflexions of the Rays of Light, and the
7181Colours made thereby._
7182
7183Grimaldo has inform'd us, that if a beam of the Sun's Light be let into
7184a dark Room through a very small hole, the Shadows of things in this
7185Light will be larger than they ought to be if the Rays went on by the
7186Bodies in straight Lines, and that these Shadows have three parallel
7187Fringes, Bands or Ranks of colour'd Light adjacent to them. But if the
7188Hole be enlarged the Fringes grow broad and run into one another, so
7189that they cannot be distinguish'd. These broad Shadows and Fringes have
7190been reckon'd by some to proceed from the ordinary refraction of the
7191Air, but without due examination of the Matter. For the circumstances of
7192the 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
7195breadth was the 42d part of an Inch. For 21 of those Pins laid together
7196took up the breadth of half an Inch. Through this Hole I let into my
7197darken'd Chamber a beam of the Sun's Light, and found that the Shadows
7198of Hairs, Thred, Pins, Straws, and such like slender Substances placed
7199in this beam of Light, were considerably broader than they ought to be,
7200if the Rays of Light passed on by these Bodies in right Lines. And
7201particularly a Hair of a Man's Head, whose breadth was but the 280th
7202part of an Inch, being held in this Light, at the distance of about
7203twelve Feet from the Hole, did cast a Shadow which at the distance of
7204four Inches from the Hair was the sixtieth part of an Inch broad, that
7205is, above four times broader than the Hair, and at the distance of two
7206Feet from the Hair was about the eight and twentieth part of an Inch
7207broad, that is, ten times broader than the Hair, and at the distance of
7208ten Feet was the eighth part of an Inch broad, that is 35 times broader.
7209
7210Nor is it material whether the Hair be encompassed with Air, or with any
7211other pellucid Substance. For I wetted a polish'd Plate of Glass, and
7212laid the Hair in the Water upon the Glass, and then laying another
7213polish'd Plate of Glass upon it, so that the Water might fill up the
7214space between the Glasses, I held them in the aforesaid beam of Light,
7215so that the Light might pass through them perpendicularly, and the
7216Shadow of the Hair was at the same distances as big as before. The
7217Shadows of Scratches made in polish'd Plates of Glass were also much
7218broader than they ought to be, and the Veins in polish'd Plates of Glass
7219did also cast the like broad Shadows. And therefore the great breadth of
7220these Shadows proceeds from some other cause than the Refraction of the
7221Air.
7222
7223Let the Circle X [in _Fig._ 1.] represent the middle of the Hair; ADG,
7224BEH, CFI, three Rays passing by one side of the Hair at several
7225distances; KNQ, LOR, MPS, three other Rays passing by the other side of
7226the Hair at the like distances; D, E, F, and N, O, P, the places where
7227the Rays are bent in their passage by the Hair; G, H, I, and Q, R, S,
7228the places where the Rays fall on a Paper GQ; IS the breadth of the
7229Shadow of the Hair cast on the Paper, and TI, VS, two Rays passing to
7230the Points I and S without bending when the Hair is taken away. And it's
7231manifest that all the Light between these two Rays TI and VS is bent in
7232passing by the Hair, and turned aside from the Shadow IS, because if any
7233part of this Light were not bent it would fall on the Paper within the
7234Shadow, and there illuminate the Paper, contrary to experience. And
7235because when the Paper is at a great distance from the Hair, the Shadow
7236is broad, and therefore the Rays TI and VS are at a great distance from
7237one another, it follows that the Hair acts upon the Rays of Light at a
7238good distance in their passing by it. But the Action is strongest on the
7239Rays which pass by at least distances, and grows weaker and weaker
7240accordingly as the Rays pass by at distances greater and greater, as is
7241represented in the Scheme: For thence it comes to pass, that the Shadow
7242of the Hair is much broader in proportion to the distance of the Paper
7243from the Hair, when the Paper is nearer the Hair, than when it is at a
7244great distance from it.
7245
7246_Obs._ 2. The Shadows of all Bodies (Metals, Stones, Glass, Wood, Horn,
7247Ice, &c.) in this Light were border'd with three Parallel Fringes or
7248Bands of colour'd Light, whereof that which was contiguous to the Shadow
7249was broadest and most luminous, and that which was remotest from it was
7250narrowest, and so faint, as not easily to be visible. It was difficult
7251to distinguish the Colours, unless when the Light fell very obliquely
7252upon a smooth Paper, or some other smooth white Body, so as to make them
7253appear much broader than they would otherwise do. And then the Colours
7254were plainly visible in this Order: The first or innermost Fringe was
7255violet and deep blue next the Shadow, and then light blue, green, and
7256yellow in the middle, and red without. The second Fringe was almost
7257contiguous to the first, and the third to the second, and both were blue
7258within, and yellow and red without, but their Colours were very faint,
7259especially those of the third. The Colours therefore proceeded in this
7260order from the Shadow; violet, indigo, pale blue, green, yellow, red;
7261blue, yellow, red; pale blue, pale yellow and red. The Shadows made by
7262Scratches and Bubbles in polish'd Plates of Glass were border'd with the
7263like Fringes of colour'd Light. And if Plates of Looking-glass sloop'd
7264off near the edges with a Diamond-cut, be held in the same beam of
7265Light, the Light which passes through the parallel Planes of the Glass
7266will be border'd with the like Fringes of Colours where those Planes
7267meet with the Diamond-cut, and by this means there will sometimes appear
7268four or five Fringes of Colours. Let AB, CD [in _Fig._ 2.] represent the
7269parallel Planes of a Looking-glass, and BD the Plane of the Diamond-cut,
7270making at B a very obtuse Angle with the Plane AB. And let all the Light
7271between the Rays ENI and FBM pass directly through the parallel Planes
7272of the Glass, and fall upon the Paper between I and M, and all the Light
7273between the Rays GO and HD be refracted by the oblique Plane of the
7274Diamond-cut BD, and fall upon the Paper between K and L; and the Light
7275which passes directly through the parallel Planes of the Glass, and
7276falls upon the Paper between I and M, will be border'd with three or
7277more Fringes at M.
7278
7279[Illustration: FIG. 1.]
7280
7281[Illustration: FIG. 2.]
7282
7283So by looking on the Sun through a Feather or black Ribband held close
7284to the Eye, several Rain-bows will appear; the Shadows which the Fibres
7285or Threds cast on the _Tunica Retina_, being border'd with the like
7286Fringes of Colours.
7287
7288_Obs._ 3. When the Hair was twelve Feet distant from this Hole, and its
7289Shadow fell obliquely upon a flat white Scale of Inches and Parts of an
7290Inch placed half a Foot beyond it, and also when the Shadow fell
7291perpendicularly upon the same Scale placed nine Feet beyond it; I
7292measured the breadth of the Shadow and Fringes as accurately as I could,
7293and found them in Parts of an Inch as follows.
7294
7295-------------------------------------------+-----------+--------
7296 | half a | Nine
7297 At the Distance of | Foot | Feet
7298-------------------------------------------+-----------+--------
7299The breadth of the Shadow | 1/54 | 1/9
7300-------------------------------------------+-----------+--------
7301The 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-------------------------------------------+-----------+--------
7305The 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-------------------------------------------+-----------+--------
7309The 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-------------------------------------------+-----------+--------
7313The distance between the Middles of the | |
7314 brightest Light of the first and second | |
7315 Fringes | 1/120 | 1/21
7316-------------------------------------------+-----------+--------
7317The distance between the Middles of the | |
7318 brightest Light of the second and third | |
7319 Fringes | 1/170 | 1/31
7320-------------------------------------------+-----------+--------
7321The breadth of the luminous Part (green, | |
7322 white, yellow, and red) of the first | |
7323 Fringe | 1/170 | 1/32
7324-------------------------------------------+-----------+--------
7325The breadth of the darker Space between | |
7326 the first and second Fringes | 1/240 | 1/45
7327-------------------------------------------+-----------+--------
7328The breadth of the luminous Part of the | |
7329 second Fringe | 1/290 | 1/55
7330-------------------------------------------+-----------+--------
7331The breadth of the darker Space between | |
7332 the second and third Fringes | 1/340 | 1/63
7333-------------------------------------------+-----------+--------
7334
7335These Measures I took by letting the Shadow of the Hair, at half a Foot
7336distance, fall so obliquely on the Scale, as to appear twelve times
7337broader than when it fell perpendicularly on it at the same distance,
7338and setting down in this Table the twelfth part of the Measures I then
7339took.
7340
7341_Obs._ 4. When the Shadow and Fringes were cast obliquely upon a smooth
7342white Body, and that Body was removed farther and farther from the Hair,
7343the first Fringe began to appear and look brighter than the rest of the
7344Light at the distance of less than a quarter of an Inch from the Hair,
7345and the dark Line or Shadow between that and the second Fringe began to
7346appear at a less distance from the Hair than that of the third part of
7347an Inch. The second Fringe began to appear at a distance from the Hair
7348of less than half an Inch, and the Shadow between that and the third
7349Fringe at a distance less than an inch, and the third Fringe at a
7350distance less than three Inches. At greater distances they became much
7351more sensible, but kept very nearly the same proportion of their
7352breadths and intervals which they had at their first appearing. For the
7353distance between the middle of the first, and middle of the second
7354Fringe, was to the distance between the middle of the second and middle
7355of the third Fringe, as three to two, or ten to seven. And the last of
7356these two distances was equal to the breadth of the bright Light or
7357luminous part of the first Fringe. And this breadth was to the breadth
7358of the bright Light of the second Fringe as seven to four, and to the
7359dark Interval of the first and second Fringe as three to two, and to
7360the like dark Interval between the second and third as two to one. For
7361the breadths of the Fringes seem'd to be in the progression of the
7362Numbers 1, sqrt(1/3), sqrt(1/5), and their Intervals to be in the
7363same progression with them; that is, the Fringes and their Intervals
7364together to be in the continual progression of the Numbers 1,
7365sqrt(1/2), sqrt(1/3), sqrt(1/4), sqrt(1/5), or thereabouts. And
7366these Proportions held the same very nearly at all distances from the
7367Hair; the dark Intervals of the Fringes being as broad in proportion to
7368the breadth of the Fringes at their first appearance as afterwards at
7369great 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
7372quarter of an Inch broad, I placed at the distance of two or three Feet
7373from the Hole a Sheet of Pasteboard, which was black'd all over on both
7374sides, and in the middle of it had a hole about three quarters of an
7375Inch square for the Light to pass through. And behind the hole I
7376fasten'd to the Pasteboard with Pitch the blade of a sharp Knife, to
7377intercept some part of the Light which passed through the hole. The
7378Planes of the Pasteboard and blade of the Knife were parallel to one
7379another, and perpendicular to the Rays. And when they were so placed
7380that none of the Sun's Light fell on the Pasteboard, but all of it
7381passed through the hole to the Knife, and there part of it fell upon the
7382blade of the Knife, and part of it passed by its edge; I let this part
7383of the Light which passed by, fall on a white Paper two or three Feet
7384beyond the Knife, and there saw two streams of faint Light shoot out
7385both ways from the beam of Light into the shadow, like the Tails of
7386Comets. But because the Sun's direct Light by its brightness upon the
7387Paper obscured these faint streams, so that I could scarce see them, I
7388made a little hole in the midst of the Paper for that Light to pass
7389through and fall on a black Cloth behind it; and then I saw the two
7390streams plainly. They were like one another, and pretty nearly equal in
7391length, and breadth, and quantity of Light. Their Light at that end next
7392the Sun's direct Light was pretty strong for the space of about a
7393quarter of an Inch, or half an Inch, and in all its progress from that
7394direct Light decreased gradually till it became insensible. The whole
7395length of either of these streams measured upon the paper at the
7396distance of three Feet from the Knife was about six or eight Inches; so
7397that it subtended an Angle at the edge of the Knife of about 10 or 12,
7398or at most 14 Degrees. Yet sometimes I thought I saw it shoot three or
7399four Degrees farther, but with a Light so very faint that I could scarce
7400perceive it, and suspected it might (in some measure at least) arise
7401from some other cause than the two streams did. For placing my Eye in
7402that Light beyond the end of that stream which was behind the Knife, and
7403looking towards the Knife, I could see a line of Light upon its edge,
7404and that not only when my Eye was in the line of the Streams, but also
7405when it was without that line either towards the point of the Knife, or
7406towards the handle. This line of Light appear'd contiguous to the edge
7407of the Knife, and was narrower than the Light of the innermost Fringe,
7408and narrowest when my Eye was farthest from the direct Light, and
7409therefore seem'd to pass between the Light of that Fringe and the edge
7410of the Knife, and that which passed nearest the edge to be most bent,
7411though not all of it.
7412
7413_Obs._ 6. I placed another Knife by this, so that their edges might be
7414parallel, and look towards one another, and that the beam of Light might
7415fall upon both the Knives, and some part of it pass between their edges.
7416And when the distance of their edges was about the 400th part of an
7417Inch, the stream parted in the middle, and left a Shadow between the two
7418parts. This Shadow was so black and dark that all the Light which passed
7419between the Knives seem'd to be bent, and turn'd aside to the one hand
7420or to the other. And as the Knives still approach'd one another the
7421Shadow grew broader, and the streams shorter at their inward ends which
7422were next the Shadow, until upon the contact of the Knives the whole
7423Light vanish'd, leaving its place to the Shadow.
7424
7425And hence I gather that the Light which is least bent, and goes to the
7426inward ends of the streams, passes by the edges of the Knives at the
7427greatest distance, and this distance when the Shadow begins to appear
7428between the streams, is about the 800th part of an Inch. And the Light
7429which passes by the edges of the Knives at distances still less and
7430less, is more and more bent, and goes to those parts of the streams
7431which are farther and farther from the direct Light; because when the
7432Knives approach one another till they touch, those parts of the streams
7433vanish last which are farthest from the direct Light.
7434
7435_Obs._ 7. In the fifth Observation the Fringes did not appear, but by
7436reason of the breadth of the hole in the Window became so broad as to
7437run into one another, and by joining, to make one continued Light in the
7438beginning of the streams. But in the sixth, as the Knives approached one
7439another, a little before the Shadow appeared between the two streams,
7440the Fringes began to appear on the inner ends of the Streams on either
7441side of the direct Light; three on one side made by the edge of one
7442Knife, and three on the other side made by the edge of the other Knife.
7443They were distinctest when the Knives were placed at the greatest
7444distance from the hole in the Window, and still became more distinct by
7445making the hole less, insomuch that I could sometimes see a faint
7446lineament of a fourth Fringe beyond the three above mention'd. And as
7447the Knives continually approach'd one another, the Fringes grew
7448distincter and larger, until they vanish'd. The outmost Fringe vanish'd
7449first, and the middlemost next, and the innermost last. And after they
7450were all vanish'd, and the line of Light which was in the middle between
7451them was grown very broad, enlarging it self on both sides into the
7452streams of Light described in the fifth Observation, the above-mention'd
7453Shadow began to appear in the middle of this line, and divide it along
7454the middle into two lines of Light, and increased until the whole Light
7455vanish'd. This enlargement of the Fringes was so great that the Rays
7456which go to the innermost Fringe seem'd to be bent above twenty times
7457more when this Fringe was ready to vanish, than when one of the Knives
7458was taken away.
7459
7460And from this and the former Observation compared, I gather, that the
7461Light of the first Fringe passed by the edge of the Knife at a distance
7462greater than the 800th part of an Inch, and the Light of the second
7463Fringe passed by the edge of the Knife at a greater distance than the
7464Light of the first Fringe did, and that of the third at a greater
7465distance than that of the second, and that of the streams of Light
7466described in the fifth and sixth Observations passed by the edges of the
7467Knives 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,
7470and pricking their points into a Board so that their edges might look
7471towards one another, and meeting near their points contain a rectilinear
7472Angle, I fasten'd their Handles together with Pitch to make this Angle
7473invariable. The distance of the edges of the Knives from one another at
7474the distance of four Inches from the angular Point, where the edges of
7475the Knives met, was the eighth part of an Inch; and therefore the Angle
7476contain'd by the edges was about one Degree 54: The Knives thus fix'd
7477together I placed in a beam of the Sun's Light, let into my darken'd
7478Chamber through a Hole the 42d Part of an Inch wide, at the distance of
747910 or 15 Feet from the Hole, and let the Light which passed between
7480their edges fall very obliquely upon a smooth white Ruler at the
7481distance of half an Inch, or an Inch from the Knives, and there saw the
7482Fringes by the two edges of the Knives run along the edges of the
7483Shadows of the Knives in Lines parallel to those edges without growing
7484sensibly broader, till they met in Angles equal to the Angle contained
7485by the edges of the Knives, and where they met and joined they ended
7486without crossing one another. But if the Ruler was held at a much
7487greater distance from the Knives, the Fringes where they were farther
7488from the Place of their Meeting, were a little narrower, and became
7489something broader and broader as they approach'd nearer and nearer to
7490one another, and after they met they cross'd one another, and then
7491became much broader than before.
7492
7493Whence I gather that the distances at which the Fringes pass by the
7494Knives are not increased nor alter'd by the approach of the Knives, but
7495the Angles in which the Rays are there bent are much increased by that
7496approach; and that the Knife which is nearest any Ray determines which
7497way 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
7500distance of the third Part of an Inch from the Knives, the dark Line
7501between the first and second Fringe of the Shadow of one Knife, and the
7502dark Line between the first and second Fringe of the Shadow of the other
7503knife met with one another, at the distance of the fifth Part of an Inch
7504from the end of the Light which passed between the Knives at the
7505concourse of their edges. And therefore the distance of the edges of the
7506Knives at the meeting of these dark Lines was the 160th Part of an Inch.
7507For as four Inches to the eighth Part of an Inch, so is any Length of
7508the edges of the Knives measured from the point of their concourse to
7509the distance of the edges of the Knives at the end of that Length, and
7510so is the fifth Part of an Inch to the 160th Part. So then the dark
7511Lines above-mention'd meet in the middle of the Light which passes
7512between the Knives where they are distant the 160th Part of an Inch, and
7513the one half of that Light passes by the edge of one Knife at a distance
7514not greater than the 320th Part of an Inch, and falling upon the Paper
7515makes the Fringes of the Shadow of that Knife, and the other half passes
7516by the edge of the other Knife, at a distance not greater than the 320th
7517Part of an Inch, and falling upon the Paper makes the Fringes of the
7518Shadow of the other Knife. But if the Paper be held at a distance from
7519the Knives greater than the third Part of an Inch, the dark Lines
7520above-mention'd meet at a greater distance than the fifth Part of an
7521Inch from the end of the Light which passed between the Knives at the
7522concourse of their edges; and therefore the Light which falls upon the
7523Paper where those dark Lines meet passes between the Knives where the
7524edges are distant above the 160th part of an Inch.
7525
7526For at another time, when the two Knives were distant eight Feet and
7527five Inches from the little hole in the Window, made with a small Pin as
7528above, the Light which fell upon the Paper where the aforesaid dark
7529lines met, passed between the Knives, where the distance between their
7530edges was as in the following Table, when the distance of the Paper from
7531the 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
7546And hence I gather, that the Light which makes the Fringes upon the
7547Paper is not the same Light at all distances of the Paper from the
7548Knives, but when the Paper is held near the Knives, the Fringes are made
7549by Light which passes by the edges of the Knives at a less distance, and
7550is more bent than when the Paper is held at a greater distance from the
7551Knives.
7552
7553[Illustration: FIG. 3.]
7554
7555_Obs._ 10. When the Fringes of the Shadows of the Knives fell
7556perpendicularly upon a Paper at a great distance from the Knives, they
7557were in the form of Hyperbola's, and their Dimensions were as follows.
7558Let CA, CB [in _Fig._ 3.] represent Lines drawn upon the Paper parallel
7559to the edges of the Knives, and between which all the Light would fall,
7560if it passed between the edges of the Knives without inflexion; DE a
7561Right Line drawn through C making the Angles ACD, BCE, equal to one
7562another, and terminating all the Light which falls upon the Paper from
7563the point where the edges of the Knives meet; _eis_, _fkt_, and _glv_,
7564three hyperbolical Lines representing the Terminus of the Shadow of one
7565of the Knives, the dark Line between the first and second Fringes of
7566that Shadow, and the dark Line between the second and third Fringes of
7567the same Shadow; _xip_, _ykq_, and _zlr_, three other hyperbolical Lines
7568representing the Terminus of the Shadow of the other Knife, the dark
7569Line between the first and second Fringes of that Shadow, and the dark
7570line between the second and third Fringes of the same Shadow. And
7571conceive that these three Hyperbola's are like and equal to the former
7572three, and cross them in the points _i_, _k_, and _l_, and that the
7573Shadows of the Knives are terminated and distinguish'd from the first
7574luminous Fringes by the lines _eis_ and _xip_, until the meeting and
7575crossing of the Fringes, and then those lines cross the Fringes in the
7576form of dark lines, terminating the first luminous Fringes within side,
7577and distinguishing them from another Light which begins to appear at
7578_i_, and illuminates all the triangular space _ip_DE_s_ comprehended by
7579these dark lines, and the right line DE. Of these Hyperbola's one
7580Asymptote is the line DE, and their other Asymptotes are parallel to the
7581lines CA and CB. Let _rv_ represent a line drawn any where upon the
7582Paper parallel to the Asymptote DE, and let this line cross the right
7583lines 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
7587line _rv_ from the Asymptote DD, you may find as many points of these
7588Hyperbola's as you please, and thereby know that these curve lines are
7589Hyperbola's differing little from the conical Hyperbola. And by
7590measuring the lines C_i_, C_k_, C_l_, you may find other points of these
7591Curves.
7592
7593For instance; when the Knives were distant from the hole in the Window
7594ten Feet, and the Paper from the Knives nine Feet, and the Angle
7595contained by the edges of the Knives to which the Angle ACB is equal,
7596was subtended by a Chord which was to the Radius as 1 to 32, and the
7597distance of the line _rv_ from the Asymptote DE was half an Inch: I
7598measured the lines _ps_, _qt_, _rv_, and found them 0'35, 0'65, 0'98
7599Inches 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
7602the 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
7604them 0'5, 0'8, and 1'17 Inches.
7605
7606_Obs._ 11. The Sun shining into my darken'd Room through a small round
7607hole made in a Plate of Lead with a slender Pin, as above; I placed at
7608the hole a Prism to refract the Light, and form on the opposite Wall the
7609Spectrum of Colours, described in the third Experiment of the first
7610Book. And then I found that the Shadows of all Bodies held in the
7611colour'd Light between the Prism and the Wall, were border'd with
7612Fringes of the Colour of that Light in which they were held. In the full
7613red Light they were totally red without any sensible blue or violet, and
7614in the deep blue Light they were totally blue without any sensible red
7615or yellow; and so in the green Light they were totally green, excepting
7616a little yellow and blue, which were mixed in the green Light of the
7617Prism. And comparing the Fringes made in the several colour'd Lights, I
7618found that those made in the red Light were largest, those made in the
7619violet were least, and those made in the green were of a middle bigness.
7620For the Fringes with which the Shadow of a Man's Hair were bordered,
7621being measured cross the Shadow at the distance of six Inches from the
7622Hair, the distance between the middle and most luminous part of the
7623first or innermost Fringe on one side of the Shadow, and that of the
7624like Fringe on the other side of the Shadow, was in the full red Light
76251/37-1/4 of an Inch, and in the full violet 7/46. And the like distance
7626between the middle and most luminous parts of the second Fringes on
7627either side the Shadow was in the full red Light 1/22, and in the violet
76281/27 of an Inch. And these distances of the Fringes held the same
7629proportion at all distances from the Hair without any sensible
7630variation.
7631
7632So then the Rays which made these Fringes in the red Light passed by the
7633Hair at a greater distance than those did which made the like Fringes in
7634the violet; and therefore the Hair in causing these Fringes acted alike
7635upon the red Light or least refrangible Rays at a greater distance, and
7636upon the violet or most refrangible Rays at a less distance, and by
7637those actions disposed the red Light into Larger Fringes, and the violet
7638into smaller, and the Lights of intermediate Colours into Fringes of
7639intermediate bignesses without changing the Colour of any sort of Light.
7640
7641When therefore the Hair in the first and second of these Observations
7642was held in the white beam of the Sun's Light, and cast a Shadow which
7643was border'd with three Fringes of coloured Light, those Colours arose
7644not from any new modifications impress'd upon the Rays of Light by the
7645Hair, but only from the various inflexions whereby the several Sorts of
7646Rays were separated from one another, which before separation, by the
7647mixture of all their Colours, composed the white beam of the Sun's
7648Light, but whenever separated compose Lights of the several Colours
7649which they are originally disposed to exhibit. In this 11th Observation,
7650where the Colours are separated before the Light passes by the Hair, the
7651least refrangible Rays, which when separated from the rest make red,
7652were inflected at a greater distance from the Hair, so as to make three
7653red Fringes at a greater distance from the middle of the Shadow of the
7654Hair; and the most refrangible Rays which when separated make violet,
7655were inflected at a less distance from the Hair, so as to make three
7656violet Fringes at a less distance from the middle of the Shadow of the
7657Hair. And other Rays of intermediate degrees of Refrangibility were
7658inflected at intermediate distances from the Hair, so as to make Fringes
7659of intermediate Colours at intermediate distances from the middle of the
7660Shadow of the Hair. And in the second Observation, where all the Colours
7661are mix'd in the white Light which passes by the Hair, these Colours are
7662separated by the various inflexions of the Rays, and the Fringes which
7663they make appear all together, and the innermost Fringes being
7664contiguous make one broad Fringe composed of all the Colours in due
7665order, the violet lying on the inside of the Fringe next the Shadow, the
7666red on the outside farthest from the Shadow, and the blue, green, and
7667yellow, in the middle. And, in like manner, the middlemost Fringes of
7668all the Colours lying in order, and being contiguous, make another broad
7669Fringe composed of all the Colours; and the outmost Fringes of all the
7670Colours lying in order, and being contiguous, make a third broad Fringe
7671composed of all the Colours. These are the three Fringes of colour'd
7672Light with which the Shadows of all Bodies are border'd in the second
7673Observation.
7674
7675When I made the foregoing Observations, I design'd to repeat most of
7676them with more care and exactness, and to make some new ones for
7677determining the manner how the Rays of Light are bent in their passage
7678by Bodies, for making the Fringes of Colours with the dark lines between
7679them. But I was then interrupted, and cannot now think of taking these
7680things into farther Consideration. And since I have not finish'd this
7681part of my Design, I shall conclude with proposing only some Queries, in
7682order 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
7685action bend its Rays; and is not this action (_cæteris paribus_)
7686strongest at the least distance?
7687
7688_Qu._ 2. Do not the Rays which differ in Refrangibility differ also in
7689Flexibity; and are they not by their different Inflexions separated from
7690one another, so as after separation to make the Colours in the three
7691Fringes above described? And after what manner are they inflected to
7692make those Fringes?
7693
7694_Qu._ 3. Are not the Rays of Light in passing by the edges and sides of
7695Bodies, bent several times backwards and forwards, with a motion like
7696that of an Eel? And do not the three Fringes of colour'd Light
7697above-mention'd arise from three such bendings?
7698
7699_Qu._ 4. Do not the Rays of Light which fall upon Bodies, and are
7700reflected or refracted, begin to bend before they arrive at the Bodies;
7701and are they not reflected, refracted, and inflected, by one and the
7702same Principle, acting variously in various Circumstances?
7703
7704_Qu._ 5. Do not Bodies and Light act mutually upon one another; that is
7705to say, Bodies upon Light in emitting, reflecting, refracting and
7706inflecting it, and Light upon Bodies for heating them, and putting their
7707parts into a vibrating motion wherein heat consists?
7708
7709_Qu._ 6. Do not black Bodies conceive heat more easily from Light than
7710those of other Colours do, by reason that the Light falling on them is
7711not reflected outwards, but enters the Bodies, and is often reflected
7712and 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
7715sulphureous Bodies observed above, one reason why sulphureous Bodies
7716take 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,
7719emit Light and shine; and is not this Emission perform'd by the
7720vibrating motions of their parts? And do not all Bodies which abound
7721with terrestrial parts, and especially with sulphureous ones, emit Light
7722as often as those parts are sufficiently agitated; whether that
7723agitation be made by Heat, or by Friction, or Percussion, or
7724Putrefaction, or by any vital Motion, or any other Cause? As for
7725instance; Sea-Water in a raging Storm; Quick-silver agitated in _vacuo_;
7726the Back of a Cat, or Neck of a Horse, obliquely struck or rubbed in a
7727dark place; Wood, Flesh and Fish while they putrefy; Vapours arising
7728from putrefy'd Waters, usually call'd _Ignes Fatui_; Stacks of moist Hay
7729or Corn growing hot by fermentation; Glow-worms and the Eyes of some
7730Animals by vital Motions; the vulgar _Phosphorus_ agitated by the
7731attrition of any Body, or by the acid Particles of the Air; Amber and
7732some Diamonds by striking, pressing or rubbing them; Scrapings of Steel
7733struck off with a Flint; Iron hammer'd very nimbly till it become so hot
7734as to kindle Sulphur thrown upon it; the Axletrees of Chariots taking
7735fire by the rapid rotation of the Wheels; and some Liquors mix'd with
7736one another whose Particles come together with an Impetus, as Oil of
7737Vitriol distilled from its weight of Nitre, and then mix'd with twice
7738its weight of Oil of Anniseeds. So also a Globe of Glass about 8 or 10
7739Inches in diameter, being put into a Frame where it may be swiftly
7740turn'd round its Axis, will in turning shine where it rubs against the
7741palm of ones Hand apply'd to it: And if at the same time a piece of
7742white Paper or white Cloth, or the end of ones Finger be held at the
7743distance of about a quarter of an Inch or half an Inch from that part of
7744the Glass where it is most in motion, the electrick Vapour which is
7745excited by the friction of the Glass against the Hand, will by dashing
7746against the white Paper, Cloth or Finger, be put into such an agitation
7747as to emit Light, and make the white Paper, Cloth or Finger, appear
7748lucid like a Glowworm; and in rushing out of the Glass will sometimes
7749push against the finger so as to be felt. And the same things have been
7750found by rubbing a long and large Cylinder or Glass or Amber with a
7751Paper held in ones hand, and continuing the friction till the Glass grew
7752warm.
7753
7754_Qu._ 9. Is not Fire a Body heated so hot as to emit Light copiously?
7755For what else is a red hot Iron than Fire? And what else is a burning
7756Coal than red hot Wood?
7757
7758_Qu._ 10. Is not Flame a Vapour, Fume or Exhalation heated red hot, that
7759is, so hot as to shine? For Bodies do not flame without emitting a
7760copious Fume, and this Fume burns in the Flame. The _Ignis Fatuus_ is a
7761Vapour shining without heat, and is there not the same difference
7762between this Vapour and Flame, as between rotten Wood shining without
7763heat and burning Coals of Fire? In distilling hot Spirits, if the Head
7764of the Still be taken off, the Vapour which ascends out of the Still
7765will take fire at the Flame of a Candle, and turn into Flame, and the
7766Flame will run along the Vapour from the Candle to the Still. Some
7767Bodies heated by Motion, or Fermentation, if the heat grow intense, fume
7768copiously, and if the heat be great enough the Fumes will shine and
7769become Flame. Metals in fusion do not flame for want of a copious Fume,
7770except Spelter, which fumes copiously, and thereby flames. All flaming
7771Bodies, as Oil, Tallow, Wax, Wood, fossil Coals, Pitch, Sulphur, by
7772flaming waste and vanish into burning Smoke, which Smoke, if the Flame
7773be put out, is very thick and visible, and sometimes smells strongly,
7774but in the Flame loses its smell by burning, and according to the nature
7775of the Smoke the Flame is of several Colours, as that of Sulphur blue,
7776that of Copper open'd with sublimate green, that of Tallow yellow, that
7777of Camphire white. Smoke passing through Flame cannot but grow red hot,
7778and red hot Smoke can have no other appearance than that of Flame. When
7779Gun-powder takes fire, it goes away into Flaming Smoke. For the Charcoal
7780and Sulphur easily take fire, and set fire to the Nitre, and the Spirit
7781of the Nitre being thereby rarified into Vapour, rushes out with
7782Explosion much after the manner that the Vapour of Water rushes out of
7783an Æolipile; the Sulphur also being volatile is converted into Vapour,
7784and augments the Explosion. And the acid Vapour of the Sulphur (namely
7785that which distils under a Bell into Oil of Sulphur,) entring violently
7786into the fix'd Body of the Nitre, sets loose the Spirit of the Nitre,
7787and excites a great Fermentation, whereby the Heat is farther augmented,
7788and the fix'd Body of the Nitre is also rarified into Fume, and the
7789Explosion is thereby made more vehement and quick. For if Salt of Tartar
7790be mix'd with Gun-powder, and that Mixture be warm'd till it takes fire,
7791the Explosion will be more violent and quick than that of Gun-powder
7792alone; which cannot proceed from any other cause than the action of the
7793Vapour of the Gun-powder upon the Salt of Tartar, whereby that Salt is
7794rarified. The Explosion of Gun-powder arises therefore from the violent
7795action whereby all the Mixture being quickly and vehemently heated, is
7796rarified and converted into Fume and Vapour: which Vapour, by the
7797violence of that action, becoming so hot as to shine, appears in the
7798form of Flame.
7799
7800_Qu._ 11. Do not great Bodies conserve their heat the longest, their
7801parts heating one another, and may not great dense and fix'd Bodies,
7802when heated beyond a certain degree, emit Light so copiously, as by the
7803Emission and Re-action of its Light, and the Reflexions and Refractions
7804of its Rays within its Pores to grow still hotter, till it comes to a
7805certain period of heat, such as is that of the Sun? And are not the Sun
7806and fix'd Stars great Earths vehemently hot, whose heat is conserved by
7807the greatness of the Bodies, and the mutual Action and Reaction between
7808them, and the Light which they emit, and whose parts are kept from
7809fuming away, not only by their fixity, but also by the vast weight and
7810density of the Atmospheres incumbent upon them; and very strongly
7811compressing them, and condensing the Vapours and Exhalations which arise
7812from them? For if Water be made warm in any pellucid Vessel emptied of
7813Air, that Water in the _Vacuum_ will bubble and boil as vehemently as it
7814would in the open Air in a Vessel set upon the Fire till it conceives a
7815much greater heat. For the weight of the incumbent Atmosphere keeps down
7816the Vapours, and hinders the Water from boiling, until it grow much
7817hotter than is requisite to make it boil _in vacuo_. Also a mixture of
7818Tin and Lead being put upon a red hot Iron _in vacuo_ emits a Fume and
7819Flame, but the same Mixture in the open Air, by reason of the incumbent
7820Atmosphere, does not so much as emit any Fume which can be perceived by
7821Sight. In like manner the great weight of the Atmosphere which lies upon
7822the Globe of the Sun may hinder Bodies there from rising up and going
7823away from the Sun in the form of Vapours and Fumes, unless by means of a
7824far greater heat than that which on the Surface of our Earth would very
7825easily turn them into Vapours and Fumes. And the same great weight may
7826condense those Vapours and Exhalations as soon as they shall at any time
7827begin to ascend from the Sun, and make them presently fall back again
7828into him, and by that action increase his Heat much after the manner
7829that in our Earth the Air increases the Heat of a culinary Fire. And the
7830same weight may hinder the Globe of the Sun from being diminish'd,
7831unless by the Emission of Light, and a very small quantity of Vapours
7832and Exhalations.
7833
7834_Qu._ 12. Do not the Rays of Light in falling upon the bottom of the Eye
7835excite Vibrations in the _Tunica Retina_? Which Vibrations, being
7836propagated along the solid Fibres of the optick Nerves into the Brain,
7837cause the Sense of seeing. For because dense Bodies conserve their Heat
7838a long time, and the densest Bodies conserve their Heat the longest, the
7839Vibrations of their parts are of a lasting nature, and therefore may be
7840propagated along solid Fibres of uniform dense Matter to a great
7841distance, for conveying into the Brain the impressions made upon all the
7842Organs of Sense. For that Motion which can continue long in one and the
7843same part of a Body, can be propagated a long way from one part to
7844another, supposing the Body homogeneal, so that the Motion may not be
7845reflected, refracted, interrupted or disorder'd by any unevenness of the
7846Body.
7847
7848_Qu._ 13. Do not several sorts of Rays make Vibrations of several
7849bignesses, which according to their bignesses excite Sensations of
7850several Colours, much after the manner that the Vibrations of the Air,
7851according to their several bignesses excite Sensations of several
7852Sounds? And particularly do not the most refrangible Rays excite the
7853shortest Vibrations for making a Sensation of deep violet, the least
7854refrangible the largest for making a Sensation of deep red, and the
7855several intermediate sorts of Rays, Vibrations of several intermediate
7856bignesses to make Sensations of the several intermediate Colours?
7857
7858_Qu._ 14. May not the harmony and discord of Colours arise from the
7859proportions of the Vibrations propagated through the Fibres of the
7860optick Nerves into the Brain, as the harmony and discord of Sounds arise
7861from the proportions of the Vibrations of the Air? For some Colours, if
7862they be view'd together, are agreeable to one another, as those of Gold
7863and Indigo, and others disagree.
7864
7865_Qu._ 15. Are not the Species of Objects seen with both Eyes united
7866where the optick Nerves meet before they come into the Brain, the Fibres
7867on the right side of both Nerves uniting there, and after union going
7868thence into the Brain in the Nerve which is on the right side of the
7869Head, and the Fibres on the left side of both Nerves uniting in the same
7870place, and after union going into the Brain in the Nerve which is on the
7871left side of the Head, and these two Nerves meeting in the Brain in such
7872a manner that their Fibres make but one entire Species or Picture, half
7873of which on the right side of the Sensorium comes from the right side of
7874both Eyes through the right side of both optick Nerves to the place
7875where the Nerves meet, and from thence on the right side of the Head
7876into the Brain, and the other half on the left side of the Sensorium
7877comes in like manner from the left side of both Eyes. For the optick
7878Nerves of such Animals as look the same way with both Eyes (as of Men,
7879Dogs, Sheep, Oxen, &c.) meet before they come into the Brain, but the
7880optick 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
7882inform'd.
7883
7884_Qu._ 16. When a Man in the dark presses either corner of his Eye with
7885his Finger, and turns his Eye away from his Finger, he will see a Circle
7886of Colours like those in the Feather of a Peacock's Tail. If the Eye and
7887the Finger remain quiet these Colours vanish in a second Minute of Time,
7888but if the Finger be moved with a quavering Motion they appear again. Do
7889not these Colours arise from such Motions excited in the bottom of the
7890Eye by the Pressure and Motion of the Finger, as, at other times are
7891excited there by Light for causing Vision? And do not the Motions once
7892excited continue about a Second of Time before they cease? And when a
7893Man by a stroke upon his Eye sees a flash of Light, are not the like
7894Motions excited in the _Retina_ by the stroke? And when a Coal of Fire
7895moved nimbly in the circumference of a Circle, makes the whole
7896circumference appear like a Circle of Fire; is it not because the
7897Motions excited in the bottom of the Eye by the Rays of Light are of a
7898lasting nature, and continue till the Coal of Fire in going round
7899returns to its former place? And considering the lastingness of the
7900Motions excited in the bottom of the Eye by Light, are they not of a
7901vibrating nature?
7902
7903_Qu._ 17. If a stone be thrown into stagnating Water, the Waves excited
7904thereby continue some time to arise in the place where the Stone fell
7905into the Water, and are propagated from thence in concentrick Circles
7906upon the Surface of the Water to great distances. And the Vibrations or
7907Tremors excited in the Air by percussion, continue a little time to move
7908from the place of percussion in concentrick Spheres to great distances.
7909And in like manner, when a Ray of Light falls upon the Surface of any
7910pellucid Body, and is there refracted or reflected, may not Waves of
7911Vibrations, or Tremors, be thereby excited in the refracting or
7912reflecting Medium at the point of Incidence, and continue to arise
7913there, and to be propagated from thence as long as they continue to
7914arise and be propagated, when they are excited in the bottom of the Eye
7915by the Pressure or Motion of the Finger, or by the Light which comes
7916from the Coal of Fire in the Experiments above-mention'd? and are not
7917these Vibrations propagated from the point of Incidence to great
7918distances? And do they not overtake the Rays of Light, and by overtaking
7919them successively, do they not put them into the Fits of easy Reflexion
7920and easy Transmission described above? For if the Rays endeavour to
7921recede from the densest part of the Vibration, they may be alternately
7922accelerated and retarded by the Vibrations overtaking them.
7923
7924_Qu._ 18. If in two large tall cylindrical Vessels of Glass inverted,
7925two little Thermometers be suspended so as not to touch the Vessels, and
7926the Air be drawn out of one of these Vessels, and these Vessels thus
7927prepared 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
7929which is not _in vacuo_. And when the Vessels are carried back into the
7930cold place, the Thermometer _in vacuo_ will grow cold almost as soon as
7931the other Thermometer. Is not the Heat of the warm Room convey'd through
7932the _Vacuum_ by the Vibrations of a much subtiler Medium than Air, which
7933after the Air was drawn out remained in the _Vacuum_? And is not this
7934Medium the same with that Medium by which Light is refracted and
7935reflected, and by whose Vibrations Light communicates Heat to Bodies,
7936and is put into Fits of easy Reflexion and easy Transmission? And do not
7937the Vibrations of this Medium in hot Bodies contribute to the
7938intenseness and duration of their Heat? And do not hot Bodies
7939communicate their Heat to contiguous cold ones, by the Vibrations of
7940this Medium propagated from them into the cold ones? And is not this
7941Medium exceedingly more rare and subtile than the Air, and exceedingly
7942more elastick and active? And doth it not readily pervade all Bodies?
7943And 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
7946density of this Æthereal Medium in different places, the Light receding
7947always from the denser parts of the Medium? And is not the density
7948thereof greater in free and open Spaces void of Air and other grosser
7949Bodies, than within the Pores of Water, Glass, Crystal, Gems, and other
7950compact Bodies? For when Light passes through Glass or Crystal, and
7951falling very obliquely upon the farther Surface thereof is totally
7952reflected, the total Reflexion ought to proceed rather from the density
7953and vigour of the Medium without and beyond the Glass, than from the
7954rarity and weakness thereof.
7955
7956_Qu._ 20. Doth not this Æthereal Medium in passing out of Water, Glass,
7957Crystal, and other compact and dense Bodies into empty Spaces, grow
7958denser and denser by degrees, and by that means refract the Rays of
7959Light not in a point, but by bending them gradually in curve Lines? And
7960doth not the gradual condensation of this Medium extend to some distance
7961from the Bodies, and thereby cause the Inflexions of the Rays of Light,
7962which pass by the edges of dense Bodies, at some distance from the
7963Bodies?
7964
7965_Qu._ 21. Is not this Medium much rarer within the dense Bodies of the
7966Sun, Stars, Planets and Comets, than in the empty celestial Spaces
7967between them? And in passing from them to great distances, doth it not
7968grow denser and denser perpetually, and thereby cause the gravity of
7969those great Bodies towards one another, and of their parts towards the
7970Bodies; every Body endeavouring to go from the denser parts of the
7971Medium towards the rarer? For if this Medium be rarer within the Sun's
7972Body than at its Surface, and rarer there than at the hundredth part of
7973an Inch from its Body, and rarer there than at the fiftieth part of an
7974Inch from its Body, and rarer there than at the Orb of _Saturn_; I see
7975no reason why the Increase of density should stop any where, and not
7976rather be continued through all distances from the Sun to _Saturn_, and
7977beyond. And though this Increase of density may at great distances be
7978exceeding slow, yet if the elastick force of this Medium be exceeding
7979great, it may suffice to impel Bodies from the denser parts of the
7980Medium towards the rarer, with all that power which we call Gravity. And
7981that the elastick force of this Medium is exceeding great, may be
7982gather'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
7984of Time they move about one hundred _English_ Miles. Light moves from
7985the Sun to us in about seven or eight Minutes of Time, which distance is
7986about 70,000,000 _English_ Miles, supposing the horizontal Parallax of
7987the Sun to be about 12´´. And the Vibrations or Pulses of this Medium,
7988that they may cause the alternate Fits of easy Transmission and easy
7989Reflexion, must be swifter than Light, and by consequence above 700,000
7990times swifter than Sounds. And therefore the elastick force of this
7991Medium, 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
7993of the Air is in proportion to its density. For the Velocities of the
7994Pulses of elastick Mediums are in a subduplicate _Ratio_ of the
7995Elasticities and the Rarities of the Mediums taken together.
7996
7997As Attraction is stronger in small Magnets than in great ones in
7998proportion to their Bulk, and Gravity is greater in the Surfaces of
7999small Planets than in those of great ones in proportion to their bulk,
8000and small Bodies are agitated much more by electric attraction than
8001great ones; so the smallness of the Rays of Light may contribute very
8002much to the power of the Agent by which they are refracted. And so if
8003any one should suppose that _Æther_ (like our Air) may contain Particles
8004which 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
8006Air, or even than those of Light: The exceeding smallness of its
8007Particles may contribute to the greatness of the force by which those
8008Particles may recede from one another, and thereby make that Medium
8009exceedingly more rare and elastick than Air, and by consequence
8010exceedingly less able to resist the motions of Projectiles, and
8011exceedingly more able to press upon gross Bodies, by endeavouring to
8012expand it self.
8013
8014_Qu._ 22. May not Planets and Comets, and all gross Bodies, perform
8015their Motions more freely, and with less resistance in this Æthereal
8016Medium than in any Fluid, which fills all Space adequately without
8017leaving any Pores, and by consequence is much denser than Quick-silver
8018or Gold? And may not its resistance be so small, as to be
8019inconsiderable? For instance; If this _Æther_ (for so I will call it)
8020should be supposed 700000 times more elastick than our Air, and above
8021700000 times more rare; its resistance would be above 600,000,000 times
8022less than that of Water. And so small a resistance would scarce make any
8023sensible alteration in the Motions of the Planets in ten thousand
8024Years. If any one would ask how a Medium can be so rare, let him tell me
8025how the Air, in the upper parts of the Atmosphere, can be above an
8026hundred thousand thousand times rarer than Gold. Let him also tell me,
8027how an electrick Body can by Friction emit an Exhalation so rare and
8028subtile, and yet so potent, as by its Emission to cause no sensible
8029Diminution of the weight of the electrick Body, and to be expanded
8030through a Sphere, whose Diameter is above two Feet, and yet to be able
8031to agitate and carry up Leaf Copper, or Leaf Gold, at the distance of
8032above a Foot from the electrick Body? And how the Effluvia of a Magnet
8033can be so rare and subtile, as to pass through a Plate of Glass without
8034any Resistance or Diminution of their Force, and yet so potent as to
8035turn a magnetick Needle beyond the Glass?
8036
8037_Qu._ 23. Is not Vision perform'd chiefly by the Vibrations of this
8038Medium, excited in the bottom of the Eye by the Rays of Light, and
8039propagated through the solid, pellucid and uniform Capillamenta of the
8040optick Nerves into the place of Sensation? And is not Hearing perform'd
8041by the Vibrations either of this or some other Medium, excited in the
8042auditory Nerves by the Tremors of the Air, and propagated through the
8043solid, pellucid and uniform Capillamenta of those Nerves into the place
8044of Sensation? And so of the other Senses.
8045
8046_Qu._ 24. Is not Animal Motion perform'd by the Vibrations of this
8047Medium, excited in the Brain by the power of the Will, and propagated
8048from thence through the solid, pellucid and uniform Capillamenta of the
8049Nerves into the Muscles, for contracting and dilating them? I suppose
8050that the Capillamenta of the Nerves are each of them solid and uniform,
8051that the vibrating Motion of the Æthereal Medium may be propagated along
8052them from one end to the other uniformly, and without interruption: For
8053Obstructions in the Nerves create Palsies. And that they may be
8054sufficiently uniform, I suppose them to be pellucid when view'd singly,
8055tho' the Reflexions in their cylindrical Surfaces may make the whole
8056Nerve (composed of many Capillamenta) appear opake and white. For
8057opacity arises from reflecting Surfaces, such as may disturb and
8058interrupt 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,
8063besides those already described? An instance of another original
8064Property we have in the Refraction of Island Crystal, described first by
8065_Erasmus Bartholine_, and afterwards more exactly by _Hugenius_, in his
8066Book _De la Lumiere_. This Crystal is a pellucid fissile Stone, clear as
8067Water or Crystal of the Rock, and without Colour; enduring a red Heat
8068without losing its transparency, and in a very strong Heat calcining
8069without Fusion. Steep'd a Day or two in Water, it loses its natural
8070Polish. Being rubb'd on Cloth, it attracts pieces of Straws and other
8071light things, like Ambar or Glass; and with _Aqua fortis_ it makes an
8072Ebullition. It seems to be a sort of Talk, and is found in form of an
8073oblique Parallelopiped, with six parallelogram Sides and eight solid
8074Angles. The obtuse Angles of the Parallelograms are each of them 101
8075Degrees and 52 Minutes; the acute ones 78 Degrees and 8 Minutes. Two of
8076the solid Angles opposite to one another, as C and E, are compassed each
8077of them with three of these obtuse Angles, and each of the other six
8078with one obtuse and two acute ones. It cleaves easily in planes parallel
8079to any of its Sides, and not in any other Planes. It cleaves with a
8080glossy polite Surface not perfectly plane, but with some little
8081unevenness. It is easily scratch'd, and by reason of its softness it
8082takes a Polish very difficultly. It polishes better upon polish'd
8083Looking-glass than upon Metal, and perhaps better upon Pitch, Leather or
8084Parchment. Afterwards it must be rubb'd with a little Oil or white of an
8085Egg, to fill up its Scratches; whereby it will become very transparent
8086and polite. But for several Experiments, it is not necessary to polish
8087it. If a piece of this crystalline Stone be laid upon a Book, every
8088Letter of the Book seen through it will appear double, by means of a
8089double Refraction. And if any beam of Light falls either
8090perpendicularly, or in any oblique Angle upon any Surface of this
8091Crystal, it becomes divided into two beams by means of the same double
8092Refraction. Which beams are of the same Colour with the incident beam of
8093Light, and seem equal to one another in the quantity of their Light, or
8094very nearly equal. One of these Refractions is perform'd by the usual
8095Rule of Opticks, the Sine of Incidence out of Air into this Crystal
8096being to the Sine of Refraction, as five to three. The other
8097Refraction, which may be called the unusual Refraction, is perform'd by
8098the following Rule.
8099
8100[Illustration: FIG. 4.]
8101
8102Let ADBC represent the refracting Surface of the Crystal, C the biggest
8103solid Angle at that Surface, GEHF the opposite Surface, and CK a
8104perpendicular on that Surface. This perpendicular makes with the edge of
8105the Crystal CF, an Angle of 19 Degr. 3'. Join KF, and in it take KL, so
8106that the Angle KCL be 6 Degr. 40'. and the Angle LCF 12 Degr. 23'. And
8107if ST represent any beam of Light incident at T in any Angle upon the
8108refracting Surface ADBC, let TV be the refracted beam determin'd by the
8109given Portion of the Sines 5 to 3, according to the usual Rule of
8110Opticks. Draw VX parallel and equal to KL. Draw it the same way from V
8111in which L lieth from K; and joining TX, this line TX shall be the other
8112refracted beam carried from T to X, by the unusual Refraction.
8113
8114If therefore the incident beam ST be perpendicular to the refracting
8115Surface, the two beams TV and TX, into which it shall become divided,
8116shall be parallel to the lines CK and CL; one of those beams going
8117through the Crystal perpendicularly, as it ought to do by the usual Laws
8118of Opticks, and the other TX by an unusual Refraction diverging from the
8119perpendicular, and making with it an Angle VTX of about 6-2/3 Degrees,
8120as is found by Experience. And hence, the Plane VTX, and such like
8121Planes which are parallel to the Plane CFK, may be called the Planes of
8122perpendicular Refraction. And the Coast towards which the lines KL and
8123VX are drawn, may be call'd the Coast of unusual Refraction.
8124
8125In like manner Crystal of the Rock has a double Refraction: But the
8126difference of the two Refractions is not so great and manifest as in
8127Island Crystal.
8128
8129When the beam ST incident on Island Crystal is divided into two beams TV
8130and TX, and these two beams arrive at the farther Surface of the Glass;
8131the beam TV, which was refracted at the first Surface after the usual
8132manner, shall be again refracted entirely after the usual manner at the
8133second Surface; and the beam TX, which was refracted after the unusual
8134manner in the first Surface, shall be again refracted entirely after the
8135unusual manner in the second Surface; so that both these beams shall
8136emerge out of the second Surface in lines parallel to the first incident
8137beam ST.
8138
8139And if two pieces of Island Crystal be placed one after another, in such
8140manner that all the Surfaces of the latter be parallel to all the
8141corresponding Surfaces of the former: The Rays which are refracted after
8142the usual manner in the first Surface of the first Crystal, shall be
8143refracted after the usual manner in all the following Surfaces; and the
8144Rays which are refracted after the unusual manner in the first Surface,
8145shall be refracted after the unusual manner in all the following
8146Surfaces. And the same thing happens, though the Surfaces of the
8147Crystals be any ways inclined to one another, provided that their Planes
8148of perpendicular Refraction be parallel to one another.
8149
8150And therefore there is an original difference in the Rays of Light, by
8151means of which some Rays are in this Experiment constantly refracted
8152after the usual manner, and others constantly after the unusual manner:
8153For if the difference be not original, but arises from new Modifications
8154impress'd on the Rays at their first Refraction, it would be alter'd by
8155new Modifications in the three following Refractions; whereas it suffers
8156no alteration, but is constant, and has the same effect upon the Rays in
8157all the Refractions. The unusual Refraction is therefore perform'd by an
8158original property of the Rays. And it remains to be enquired, whether
8159the 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
8162original Properties? For if the Planes of perpendicular Refraction of
8163the second Crystal be at right Angles with the Planes of perpendicular
8164Refraction of the first Crystal, the Rays which are refracted after the
8165usual manner in passing through the first Crystal, will be all of them
8166refracted after the unusual manner in passing through the second
8167Crystal; and the Rays which are refracted after the unusual manner in
8168passing through the first Crystal, will be all of them refracted after
8169the usual manner in passing through the second Crystal. And therefore
8170there are not two sorts of Rays differing in their nature from one
8171another, one of which is constantly and in all Positions refracted after
8172the usual manner, and the other constantly and in all Positions after
8173the unusual manner. The difference between the two sorts of Rays in the
8174Experiment mention'd in the 25th Question, was only in the Positions of
8175the Sides of the Rays to the Planes of perpendicular Refraction. For one
8176and the same Ray is here refracted sometimes after the usual, and
8177sometimes after the unusual manner, according to the Position which its
8178Sides have to the Crystals. If the Sides of the Ray are posited the same
8179way to both Crystals, it is refracted after the same manner in them
8180both: But if that side of the Ray which looks towards the Coast of the
8181unusual Refraction of the first Crystal, be 90 Degrees from that side of
8182the same Ray which looks toward the Coast of the unusual Refraction of
8183the second Crystal, (which may be effected by varying the Position of
8184the second Crystal to the first, and by consequence to the Rays of
8185Light,) the Ray shall be refracted after several manners in the several
8186Crystals. There is nothing more required to determine whether the Rays
8187of Light which fall upon the second Crystal shall be refracted after
8188the usual or after the unusual manner, but to turn about this Crystal,
8189so that the Coast of this Crystal's unusual Refraction may be on this or
8190on that side of the Ray. And therefore every Ray may be consider'd as
8191having four Sides or Quarters, two of which opposite to one another
8192incline the Ray to be refracted after the unusual manner, as often as
8193either of them are turn'd towards the Coast of unusual Refraction; and
8194the other two, whenever either of them are turn'd towards the Coast of
8195unusual Refraction, do not incline it to be otherwise refracted than
8196after the usual manner. The two first may therefore be call'd the Sides
8197of unusual Refraction. And since these Dispositions were in the Rays
8198before their Incidence on the second, third, and fourth Surfaces of the
8199two Crystals, and suffered no alteration (so far as appears,) by the
8200Refraction of the Rays in their passage through those Surfaces, and the
8201Rays were refracted by the same Laws in all the four Surfaces; it
8202appears that those Dispositions were in the Rays originally, and
8203suffer'd no alteration by the first Refraction, and that by means of
8204those Dispositions the Rays were refracted at their Incidence on the
8205first Surface of the first Crystal, some of them after the usual, and
8206some of them after the unusual manner, accordingly as their Sides of
8207unusual Refraction were then turn'd towards the Coast of the unusual
8208Refraction of that Crystal, or sideways from it.
8209
8210Every Ray of Light has therefore two opposite Sides, originally endued
8211with a Property on which the unusual Refraction depends, and the other
8212two opposite Sides not endued with that Property. And it remains to be
8213enquired, whether there are not more Properties of Light by which the
8214Sides of the Rays differ, and are distinguished from one another.
8215
8216In explaining the difference of the Sides of the Rays above mention'd, I
8217have supposed that the Rays fall perpendicularly on the first Crystal.
8218But if they fall obliquely on it, the Success is the same. Those Rays
8219which are refracted after the usual manner in the first Crystal, will be
8220refracted after the unusual manner in the second Crystal, supposing the
8221Planes of perpendicular Refraction to be at right Angles with one
8222another, as above; and on the contrary.
8223
8224If the Planes of the perpendicular Refraction of the two Crystals be
8225neither parallel nor perpendicular to one another, but contain an acute
8226Angle: The two beams of Light which emerge out of the first Crystal,
8227will be each of them divided into two more at their Incidence on the
8228second Crystal. For in this case the Rays in each of the two beams will
8229some of them have their Sides of unusual Refraction, and some of them
8230their other Sides turn'd towards the Coast of the unusual Refraction of
8231the second Crystal.
8232
8233_Qu._ 27. Are not all Hypotheses erroneous which have hitherto been
8234invented for explaining the Phænomena of Light, by new Modifications of
8235the Rays? For those Phænomena depend not upon new Modifications, as has
8236been supposed, but upon the original and unchangeable Properties of the
8237Rays.
8238
8239_Qu._ 28. Are not all Hypotheses erroneous, in which Light is supposed
8240to consist in Pression or Motion, propagated through a fluid Medium? For
8241in all these Hypotheses the Phænomena of Light have been hitherto
8242explain'd by supposing that they arise from new Modifications of the
8243Rays; which is an erroneous Supposition.
8244
8245If Light consisted only in Pression propagated without actual Motion, it
8246would not be able to agitate and heat the Bodies which refract and
8247reflect it. If it consisted in Motion propagated to all distances in an
8248instant, it would require an infinite force every moment, in every
8249shining Particle, to generate that Motion. And if it consisted in
8250Pression or Motion, propagated either in an instant or in time, it would
8251bend into the Shadow. For Pression or Motion cannot be propagated in a
8252Fluid in right Lines, beyond an Obstacle which stops part of the Motion,
8253but will bend and spread every way into the quiescent Medium which lies
8254beyond the Obstacle. Gravity tends downwards, but the Pressure of Water
8255arising from Gravity tends every way with equal Force, and is propagated
8256as readily, and with as much force sideways as downwards, and through
8257crooked passages as through strait ones. The Waves on the Surface of
8258stagnating Water, passing by the sides of a broad Obstacle which stops
8259part of them, bend afterwards and dilate themselves gradually into the
8260quiet Water behind the Obstacle. The Waves, Pulses or Vibrations of the
8261Air, wherein Sounds consist, bend manifestly, though not so much as the
8262Waves of Water. For a Bell or a Cannon may be heard beyond a Hill which
8263intercepts the sight of the sounding Body, and Sounds are propagated as
8264readily through crooked Pipes as through streight ones. But Light is
8265never known to follow crooked Passages nor to bend into the Shadow. For
8266the fix'd Stars by the Interposition of any of the Planets cease to be
8267seen. 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
8269Body, are bent a little by the action of the Body, as we shew'd above;
8270but this bending is not towards but from the Shadow, and is perform'd
8271only in the passage of the Ray by the Body, and at a very small distance
8272from 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
8275jusqu' ici qui me satisfasse._ C. H. de la lumiere, c. 5, p. 91.]
8276
8277To explain the unusual Refraction of Island Crystal by Pression or
8278Motion propagated, has not hitherto been attempted (to my knowledge)
8279except by _Huygens_, who for that end supposed two several vibrating
8280Mediums within that Crystal. But when he tried the Refractions in two
8281successive pieces of that Crystal, and found them such as is mention'd
8282above; he confessed himself at a loss for explaining them. For Pressions
8283or Motions, propagated from a shining Body through an uniform Medium,
8284must be on all sides alike; whereas by those Experiments it appears,
8285that the Rays of Light have different Properties in their different
8286Sides. He suspected that the Pulses of _Æther_ in passing through the
8287first Crystal might receive certain new Modifications, which might
8288determine them to be propagated in this or that Medium within the
8289second Crystal, according to the Position of that Crystal. But what
8290Modifications those might be he could not say, nor think of any thing
8291satisfactory in that Point. And if he had known that the unusual
8292Refraction depends not on new Modifications, but on the original and
8293unchangeable Dispositions of the Rays, he would have found it as
8294difficult to explain how those Dispositions which he supposed to be
8295impress'd on the Rays by the first Crystal, could be in them before
8296their Incidence on that Crystal, and in general, how all Rays emitted by
8297shining Bodies, can have those Dispositions in them from the beginning.
8298To me, at least, this seems inexplicable, if Light be nothing else than
8299Pression or Motion propagated through _Æther_.
8300
8301And it is as difficult to explain by these Hypotheses, how Rays can be
8302alternately in Fits of easy Reflexion and easy Transmission; unless
8303perhaps one might suppose that there are in all Space two Æthereal
8304vibrating Mediums, and that the Vibrations of one of them constitute
8305Light, and the Vibrations of the other are swifter, and as often as they
8306overtake the Vibrations of the first, put them into those Fits. But how
8307two _Æthers_ can be diffused through all Space, one of which acts upon
8308the other, and by consequence is re-acted upon, without retarding,
8309shattering, dispersing and confounding one anothers Motions, is
8310inconceivable. And against filling the Heavens with fluid Mediums,
8311unless they be exceeding rare, a great Objection arises from the regular
8312and very lasting Motions of the Planets and Comets in all manner of
8313Courses through the Heavens. For thence it is manifest, that the Heavens
8314are void of all sensible Resistance, and by consequence of all sensible
8315Matter.
8316
8317For the resisting Power of fluid Mediums arises partly from the
8318Attrition of the Parts of the Medium, and partly from the _Vis inertiæ_
8319of the Matter. That part of the Resistance of a spherical Body which
8320arises from the Attrition of the Parts of the Medium is very nearly as
8321the Diameter, or, at the most, as the _Factum_ of the Diameter, and the
8322Velocity of the spherical Body together. And that part of the Resistance
8323which arises from the _Vis inertiæ_ of the Matter, is as the Square of
8324that _Factum_. And by this difference the two sorts of Resistance may be
8325distinguish'd from one another in any Medium; and these being
8326distinguish'd, it will be found that almost all the Resistance of Bodies
8327of a competent Magnitude moving in Air, Water, Quick-silver, and such
8328like Fluids with a competent Velocity, arises from the _Vis inertiæ_ of
8329the Parts of the Fluid.
8330
8331Now that part of the resisting Power of any Medium which arises from the
8332Tenacity, Friction or Attrition of the Parts of the Medium, may be
8333diminish'd by dividing the Matter into smaller Parts, and making the
8334Parts more smooth and slippery: But that part of the Resistance which
8335arises from the _Vis inertiæ_, is proportional to the Density of the
8336Matter, and cannot be diminish'd by dividing the Matter into smaller
8337Parts, nor by any other means than by decreasing the Density of the
8338Medium. And for these Reasons the Density of fluid Mediums is very
8339nearly proportional to their Resistance. Liquors which differ not much
8340in Density, as Water, Spirit of Wine, Spirit of Turpentine, hot Oil,
8341differ not much in Resistance. Water is thirteen or fourteen times
8342lighter than Quick-silver and by consequence thirteen or fourteen times
8343rarer, and its Resistance is less than that of Quick-silver in the same
8344Proportion, or thereabouts, as I have found by Experiments made with
8345Pendulums. The open Air in which we breathe is eight or nine hundred
8346times lighter than Water, and by consequence eight or nine hundred times
8347rarer, and accordingly its Resistance is less than that of Water in the
8348same Proportion, or thereabouts; as I have also found by Experiments
8349made with Pendulums. And in thinner Air the Resistance is still less,
8350and at length, by ratifying the Air, becomes insensible. For small
8351Feathers falling in the open Air meet with great Resistance, but in a
8352tall Glass well emptied of Air, they fall as fast as Lead or Gold, as I
8353have seen tried several times. Whence the Resistance seems still to
8354decrease in proportion to the Density of the Fluid. For I do not find by
8355any Experiments, that Bodies moving in Quick-silver, Water or Air, meet
8356with any other sensible Resistance than what arises from the Density and
8357Tenacity of those sensible Fluids, as they would do if the Pores of
8358those Fluids, and all other Spaces, were filled with a dense and
8359subtile Fluid. Now if the Resistance in a Vessel well emptied of Air,
8360was but an hundred times less than in the open Air, it would be about a
8361million of times less than in Quick-silver. But it seems to be much less
8362in such a Vessel, and still much less in the Heavens, at the height of
8363three or four hundred Miles from the Earth, or above. For Mr. _Boyle_
8364has shew'd that Air may be rarified above ten thousand times in Vessels
8365of Glass; and the Heavens are much emptier of Air than any _Vacuum_ we
8366can make below. For since the Air is compress'd by the Weight of the
8367incumbent Atmosphere, and the Density of Air is proportional to the
8368Force compressing it, it follows by Computation, that at the height of
8369about seven and a half _English_ Miles from the Earth, the Air is four
8370times rarer than at the Surface of the Earth; and at the height of 15
8371Miles it is sixteen times rarer than that at the Surface of the Earth;
8372and at the height of 22-1/2, 30, or 38 Miles, it is respectively 64,
8373256, or 1024 times rarer, or thereabouts; and at the height of 76, 152,
8374228 Miles, it is about 1000000, 1000000000000, or 1000000000000000000
8375times rarer; and so on.
8376
8377Heat promotes Fluidity very much by diminishing the Tenacity of Bodies.
8378It makes many Bodies fluid which are not fluid in cold, and increases
8379the Fluidity of tenacious Liquids, as of Oil, Balsam, and Honey, and
8380thereby decreases their Resistance. But it decreases not the Resistance
8381of Water considerably, as it would do if any considerable part of the
8382Resistance of Water arose from the Attrition or Tenacity of its Parts.
8383And therefore the Resistance of Water arises principally and almost
8384entirely from the _Vis inertiæ_ of its Matter; and by consequence, if
8385the Heavens were as dense as Water, they would not have much less
8386Resistance than Water; if as dense as Quick-silver, they would not have
8387much less Resistance than Quick-silver; if absolutely dense, or full of
8388Matter without any _Vacuum_, let the Matter be never so subtil and
8389fluid, they would have a greater Resistance than Quick-silver. A solid
8390Globe in such a Medium would lose above half its Motion in moving three
8391times the length of its Diameter, and a Globe not solid (such as are the
8392Planets,) would be retarded sooner. And therefore to make way for the
8393regular and lasting Motions of the Planets and Comets, it's necessary to
8394empty the Heavens of all Matter, except perhaps some very thin Vapours,
8395Steams, or Effluvia, arising from the Atmospheres of the Earth, Planets,
8396and Comets, and from such an exceedingly rare Æthereal Medium as we
8397described above. A dense Fluid can be of no use for explaining the
8398Phænomena of Nature, the Motions of the Planets and Comets being better
8399explain'd without it. It serves only to disturb and retard the Motions
8400of those great Bodies, and make the Frame of Nature languish: And in the
8401Pores of Bodies, it serves only to stop the vibrating Motions of their
8402Parts, wherein their Heat and Activity consists. And as it is of no use,
8403and hinders the Operations of Nature, and makes her languish, so there
8404is no evidence for its Existence, and therefore it ought to be rejected.
8405And if it be rejected, the Hypotheses that Light consists in Pression
8406or Motion, propagated through such a Medium, are rejected with it.
8407
8408And for rejecting such a Medium, we have the Authority of those the
8409oldest and most celebrated Philosophers of _Greece_ and _Phoenicia_,
8410who made a _Vacuum_, and Atoms, and the Gravity of Atoms, the first
8411Principles of their Philosophy; tacitly attributing Gravity to some
8412other Cause than dense Matter. Later Philosophers banish the
8413Consideration of such a Cause out of natural Philosophy, feigning
8414Hypotheses for explaining all things mechanically, and referring other
8415Causes to Metaphysicks: Whereas the main Business of natural Philosophy
8416is to argue from Phænomena without feigning Hypotheses, and to deduce
8417Causes from Effects, till we come to the very first Cause, which
8418certainly is not mechanical; and not only to unfold the Mechanism of the
8419World, but chiefly to resolve these and such like Questions. What is
8420there in places almost empty of Matter, and whence is it that the Sun
8421and Planets gravitate towards one another, without dense Matter between
8422them? Whence is it that Nature doth nothing in vain; and whence arises
8423all that Order and Beauty which we see in the World? To what end are
8424Comets, and whence is it that Planets move all one and the same way in
8425Orbs concentrick, while Comets move all manner of ways in Orbs very
8426excentrick; and what hinders the fix'd Stars from falling upon one
8427another? How came the Bodies of Animals to be contrived with so much
8428Art, and for what ends were their several Parts? Was the Eye contrived
8429without Skill in Opticks, and the Ear without Knowledge of Sounds? How
8430do the Motions of the Body follow from the Will, and whence is the
8431Instinct in Animals? Is not the Sensory of Animals that place to which
8432the sensitive Substance is present, and into which the sensible Species
8433of Things are carried through the Nerves and Brain, that there they may
8434be perceived by their immediate presence to that Substance? And these
8435things being rightly dispatch'd, does it not appear from Phænomena that
8436there is a Being incorporeal, living, intelligent, omnipresent, who in
8437infinite Space, as it were in his Sensory, sees the things themselves
8438intimately, and throughly perceives them, and comprehends them wholly by
8439their immediate presence to himself: Of which things the Images only
8440carried through the Organs of Sense into our little Sensoriums, are
8441there seen and beheld by that which in us perceives and thinks. And
8442though every true Step made in this Philosophy brings us not immediately
8443to the Knowledge of the first Cause, yet it brings us nearer to it, and
8444on that account is to be highly valued.
8445
8446_Qu._ 29. Are not the Rays of Light very small Bodies emitted from
8447shining Substances? For such Bodies will pass through uniform Mediums in
8448right Lines without bending into the Shadow, which is the Nature of the
8449Rays of Light. They will also be capable of several Properties, and be
8450able to conserve their Properties unchanged in passing through several
8451Mediums, which is another Condition of the Rays of Light. Pellucid
8452Substances act upon the Rays of Light at a distance in refracting,
8453reflecting, and inflecting them, and the Rays mutually agitate the Parts
8454of those Substances at a distance for heating them; and this Action and
8455Re-action at a distance very much resembles an attractive Force between
8456Bodies. If Refraction be perform'd by Attraction of the Rays, the Sines
8457of Incidence must be to the Sines of Refraction in a given Proportion,
8458as we shew'd in our Principles of Philosophy: And this Rule is true by
8459Experience. The Rays of Light in going out of Glass into a _Vacuum_, are
8460bent towards the Glass; and if they fall too obliquely on the _Vacuum_,
8461they are bent backwards into the Glass, and totally reflected; and this
8462Reflexion cannot be ascribed to the Resistance of an absolute _Vacuum_,
8463but must be caused by the Power of the Glass attracting the Rays at
8464their going out of it into the _Vacuum_, and bringing them back. For if
8465the farther Surface of the Glass be moisten'd with Water or clear Oil,
8466or liquid and clear Honey, the Rays which would otherwise be reflected
8467will go into the Water, Oil, or Honey; and therefore are not reflected
8468before they arrive at the farther Surface of the Glass, and begin to go
8469out of it. If they go out of it into the Water, Oil, or Honey, they go
8470on, because the Attraction of the Glass is almost balanced and rendered
8471ineffectual by the contrary Attraction of the Liquor. But if they go out
8472of it into a _Vacuum_ which has no Attraction to balance that of the
8473Glass, the Attraction of the Glass either bends and refracts them, or
8474brings them back and reflects them. And this is still more evident by
8475laying together two Prisms of Glass, or two Object-glasses of very long
8476Telescopes, the one plane, the other a little convex, and so compressing
8477them that they do not fully touch, nor are too far asunder. For the
8478Light which falls upon the farther Surface of the first Glass where the
8479Interval between the Glasses is not above the ten hundred thousandth
8480Part 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
8482explain'd in the first, fourth, and eighth Observations of the first
8483Part of the second Book. But, if the second Glass be taken away, the
8484Light which goes out of the second Surface of the first Glass into the
8485Air or _Vacuum_, will not go on forwards, but turns back into the first
8486Glass, and is reflected; and therefore it is drawn back by the Power of
8487the first Glass, there being nothing else to turn it back. Nothing more
8488is requisite for producing all the variety of Colours, and degrees of
8489Refrangibility, than that the Rays of Light be Bodies of different
8490Sizes, the least of which may take violet the weakest and darkest of the
8491Colours, and be more easily diverted by refracting Surfaces from the
8492right Course; and the rest as they are bigger and bigger, may make the
8493stronger and more lucid Colours, blue, green, yellow, and red, and be
8494more and more difficultly diverted. Nothing more is requisite for
8495putting the Rays of Light into Fits of easy Reflexion and easy
8496Transmission, than that they be small Bodies which by their attractive
8497Powers, or some other Force, stir up Vibrations in what they act upon,
8498which Vibrations being swifter than the Rays, overtake them
8499successively, and agitate them so as by turns to increase and decrease
8500their Velocities, and thereby put them into those Fits. And lastly, the
8501unusual Refraction of Island-Crystal looks very much as if it were
8502perform'd by some kind of attractive virtue lodged in certain Sides both
8503of the Rays, and of the Particles of the Crystal. For were it not for
8504some kind of Disposition or Virtue lodged in some Sides of the Particles
8505of the Crystal, and not in their other Sides, and which inclines and
8506bends the Rays towards the Coast of unusual Refraction, the Rays which
8507fall perpendicularly on the Crystal, would not be refracted towards that
8508Coast rather than towards any other Coast, both at their Incidence and
8509at their Emergence, so as to emerge perpendicularly by a contrary
8510Situation of the Coast of unusual Refraction at the second Surface; the
8511Crystal acting upon the Rays after they have pass'd through it, and are
8512emerging into the Air; or, if you please, into a _Vacuum_. And since the
8513Crystal by this Disposition or Virtue does not act upon the Rays, unless
8514when one of their Sides of unusual Refraction looks towards that Coast,
8515this argues a Virtue or Disposition in those Sides of the Rays, which
8516answers to, and sympathizes with that Virtue or Disposition of the
8517Crystal, as the Poles of two Magnets answer to one another. And as
8518Magnetism may be intended and remitted, and is found only in the Magnet
8519and in Iron: So this Virtue of refracting the perpendicular Rays is
8520greater in Island-Crystal, less in Crystal of the Rock, and is not yet
8521found in other Bodies. I do not say that this Virtue is magnetical: It
8522seems to be of another kind. I only say, that whatever it be, it's
8523difficult to conceive how the Rays of Light, unless they be Bodies, can
8524have a permanent Virtue in two of their Sides which is not in their
8525other Sides, and this without any regard to their Position to the Space
8526or Medium through which they pass.
8527
8528What I mean in this Question by a _Vacuum_, and by the Attractions of
8529the Rays of Light towards Glass or Crystal, may be understood by what
8530was said in the 18th, 19th, and 20th Questions.
8531
8532_Quest._ 30. Are not gross Bodies and Light convertible into one
8533another, and may not Bodies receive much of their Activity from the
8534Particles of Light which enter their Composition? For all fix'd Bodies
8535being heated emit Light so long as they continue sufficiently hot, and
8536Light mutually stops in Bodies as often as its Rays strike upon their
8537Parts, as we shew'd above. I know no Body less apt to shine than Water;
8538and 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
8540sufficient Heat, shines by Heat like other Bodies.
8541
8542The changing of Bodies into Light, and Light into Bodies, is very
8543conformable to the Course of Nature, which seems delighted with
8544Transmutations. Water, which is a very fluid tasteless Salt, she changes
8545by Heat into Vapour, which is a sort of Air, and by Cold into Ice, which
8546is a hard, pellucid, brittle, fusible Stone; and this Stone returns into
8547Water by Heat, and Vapour returns into Water by Cold. Earth by Heat
8548becomes Fire, and by Cold returns into Earth. Dense Bodies by
8549Fermentation rarify into several sorts of Air, and this Air by
8550Fermentation, and sometimes without it, returns into dense Bodies.
8551Mercury appears sometimes in the form of a fluid Metal, sometimes in the
8552form of a hard brittle Metal, sometimes in the form of a corrosive
8553pellucid Salt call'd Sublimate, sometimes in the form of a tasteless,
8554pellucid, volatile white Earth, call'd _Mercurius Dulcis_; or in that of
8555a red opake volatile Earth, call'd Cinnaber; or in that of a red or
8556white Precipitate, or in that of a fluid Salt; and in Distillation it
8557turns into Vapour, and being agitated _in Vacuo_, it shines like Fire.
8558And after all these Changes it returns again into its first form of
8559Mercury. Eggs grow from insensible Magnitudes, and change into Animals;
8560Tadpoles into Frogs; and Worms into Flies. All Birds, Beasts and Fishes,
8561Insects, Trees, and other Vegetables, with their several Parts, grow out
8562of Water and watry Tinctures and Salts, and by Putrefaction return again
8563into watry Substances. And Water standing a few Days in the open Air,
8564yields a Tincture, which (like that of Malt) by standing longer yields a
8565Sediment and a Spirit, but before Putrefaction is fit Nourishment for
8566Animals and Vegetables. And among such various and strange
8567Transmutations, why may not Nature change Bodies into Light, and Light
8568into Bodies?
8569
8570_Quest._ 31. Have not the small Particles of Bodies certain Powers,
8571Virtues, or Forces, by which they act at a distance, not only upon the
8572Rays of Light for reflecting, refracting, and inflecting them, but also
8573upon one another for producing a great Part of the Phænomena of Nature?
8574For it's well known, that Bodies act one upon another by the Attractions
8575of Gravity, Magnetism, and Electricity; and these Instances shew the
8576Tenor and Course of Nature, and make it not improbable but that there
8577may be more attractive Powers than these. For Nature is very consonant
8578and conformable to her self. How these Attractions may be perform'd, I
8579do not here consider. What I call Attraction may be perform'd by
8580impulse, or by some other means unknown to me. I use that Word here to
8581signify only in general any Force by which Bodies tend towards one
8582another, whatsoever be the Cause. For we must learn from the Phænomena
8583of Nature what Bodies attract one another, and what are the Laws and
8584Properties of the Attraction, before we enquire the Cause by which the
8585Attraction is perform'd. The Attractions of Gravity, Magnetism, and
8586Electricity, reach to very sensible distances, and so have been observed
8587by vulgar Eyes, and there may be others which reach to so small
8588distances as hitherto escape Observation; and perhaps electrical
8589Attraction may reach to such small distances, even without being excited
8590by Friction.
8591
8592For when Salt of Tartar runs _per Deliquium_, is not this done by an
8593Attraction between the Particles of the Salt of Tartar, and the
8594Particles of the Water which float in the Air in the form of Vapours?
8595And why does not common Salt, or Salt-petre, or Vitriol, run _per
8596Deliquium_, but for want of such an Attraction? Or why does not Salt of
8597Tartar draw more Water out of the Air than in a certain Proportion to
8598its quantity, but for want of an attractive Force after it is satiated
8599with Water? And whence is it but from this attractive Power that Water
8600which alone distils with a gentle luke-warm Heat, will not distil from
8601Salt of Tartar without a great Heat? And is it not from the like
8602attractive Power between the Particles of Oil of Vitriol and the
8603Particles of Water, that Oil of Vitriol draws to it a good quantity of
8604Water out of the Air, and after it is satiated draws no more, and in
8605Distillation lets go the Water very difficultly? And when Water and Oil
8606of Vitriol poured successively into the same Vessel grow very hot in the
8607mixing, does not this Heat argue a great Motion in the Parts of the
8608Liquors? And does not this Motion argue, that the Parts of the two
8609Liquors in mixing coalesce with Violence, and by consequence rush
8610towards one another with an accelerated Motion? And when _Aqua fortis_,
8611or Spirit of Vitriol poured upon Filings of Iron dissolves the Filings
8612with a great Heat and Ebullition, is not this Heat and Ebullition
8613effected by a violent Motion of the Parts, and does not that Motion
8614argue that the acid Parts of the Liquor rush towards the Parts of the
8615Metal with violence, and run forcibly into its Pores till they get
8616between its outmost Particles, and the main Mass of the Metal, and
8617surrounding those Particles loosen them from the main Mass, and set them
8618at liberty to float off into the Water? And when the acid Particles,
8619which alone would distil with an easy Heat, will not separate from the
8620Particles of the Metal without a very violent Heat, does not this
8621confirm the Attraction between them?
8622
8623When Spirit of Vitriol poured upon common Salt or Salt-petre makes an
8624Ebullition with the Salt, and unites with it, and in Distillation the
8625Spirit of the common Salt or Salt-petre comes over much easier than it
8626would do before, and the acid part of the Spirit of Vitriol stays
8627behind; does not this argue that the fix'd Alcaly of the Salt attracts
8628the acid Spirit of the Vitriol more strongly than its own Spirit, and
8629not being able to hold them both, lets go its own? And when Oil of
8630Vitriol is drawn off from its weight of Nitre, and from both the
8631Ingredients a compound Spirit of Nitre is distilled, and two parts of
8632this Spirit are poured on one part of Oil of Cloves or Carraway Seeds,
8633or of any ponderous Oil of vegetable or animal Substances, or Oil of
8634Turpentine thicken'd with a little Balsam of Sulphur, and the Liquors
8635grow so very hot in mixing, as presently to send up a burning Flame;
8636does not this very great and sudden Heat argue that the two Liquors mix
8637with violence, and that their Parts in mixing run towards one another
8638with an accelerated Motion, and clash with the greatest Force? And is it
8639not for the same reason that well rectified Spirit of Wine poured on the
8640same compound Spirit flashes; and that the _Pulvis fulminans_, composed
8641of Sulphur, Nitre, and Salt of Tartar, goes off with a more sudden and
8642violent Explosion than Gun-powder, the acid Spirits of the Sulphur and
8643Nitre rushing towards one another, and towards the Salt of Tartar, with
8644so great a violence, as by the shock to turn the whole at once into
8645Vapour and Flame? Where the Dissolution is slow, it makes a slow
8646Ebullition and a gentle Heat; and where it is quicker, it makes a
8647greater Ebullition with more heat; and where it is done at once, the
8648Ebullition is contracted into a sudden Blast or violent Explosion, with
8649a heat equal to that of Fire and Flame. So when a Drachm of the
8650above-mention'd compound Spirit of Nitre was poured upon half a Drachm
8651of Oil of Carraway Seeds _in vacuo_, the Mixture immediately made a
8652flash like Gun-powder, and burst the exhausted Receiver, which was a
8653Glass six Inches wide, and eight Inches deep. And even the gross Body of
8654Sulphur powder'd, and with an equal weight of Iron Filings and a little
8655Water made into Paste, acts upon the Iron, and in five or six hours
8656grows too hot to be touch'd, and emits a Flame. And by these Experiments
8657compared with the great quantity of Sulphur with which the Earth
8658abounds, and the warmth of the interior Parts of the Earth, and hot
8659Springs, and burning Mountains, and with Damps, mineral Coruscations,
8660Earthquakes, hot suffocating Exhalations, Hurricanes, and Spouts; we may
8661learn that sulphureous Steams abound in the Bowels of the Earth and
8662ferment with Minerals, and sometimes take fire with a sudden Coruscation
8663and Explosion; and if pent up in subterraneous Caverns, burst the
8664Caverns with a great shaking of the Earth, as in springing of a Mine.
8665And then the Vapour generated by the Explosion, expiring through the
8666Pores of the Earth, feels hot and suffocates, and makes Tempests and
8667Hurricanes, and sometimes causes the Land to slide, or the Sea to boil,
8668and carries up the Water thereof in Drops, which by their weight fall
8669down again in Spouts. Also some sulphureous Steams, at all times when
8670the Earth is dry, ascending into the Air, ferment there with nitrous
8671Acids, and sometimes taking fire cause Lightning and Thunder, and fiery
8672Meteors. For the Air abounds with acid Vapours fit to promote
8673Fermentations, as appears by the rusting of Iron and Copper in it, the
8674kindling of Fire by blowing, and the beating of the Heart by means of
8675Respiration. Now the above-mention'd Motions are so great and violent as
8676to shew that in Fermentations the Particles of Bodies which almost rest,
8677are put into new Motions by a very potent Principle, which acts upon
8678them only when they approach one another, and causes them to meet and
8679clash with great violence, and grow hot with the motion, and dash one
8680another into pieces, and vanish into Air, and Vapour, and Flame.
8681
8682When Salt of Tartar _per deliquium_, being poured into the Solution of
8683any Metal, precipitates the Metal and makes it fall down to the bottom
8684of the Liquor in the form of Mud: Does not this argue that the acid
8685Particles are attracted more strongly by the Salt of Tartar than by the
8686Metal, and by the stronger Attraction go from the Metal to the Salt of
8687Tartar? 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
8689dissolves Iron immersed in it and lets go the Copper, or a Solution of
8690Silver dissolves Copper and lets go the Silver, or a Solution of Mercury
8691in _Aqua fortis_ being poured upon Iron, Copper, Tin, or Lead, dissolves
8692the Metal and lets go the Mercury; does not this argue that the acid
8693Particles of the _Aqua fortis_ are attracted more strongly by the _Lapis
8694Calaminaris_ than by Iron, and more strongly by Iron than by Copper, and
8695more strongly by Copper than by Silver, and more strongly by Iron,
8696Copper, Tin, and Lead, than by Mercury? And is it not for the same
8697reason that Iron requires more _Aqua fortis_ to dissolve it than Copper,
8698and Copper more than the other Metals; and that of all Metals, Iron is
8699dissolved most easily, and is most apt to rust; and next after Iron,
8700Copper?
8701
8702When Oil of Vitriol is mix'd with a little Water, or is run _per
8703deliquium_, and in Distillation the Water ascends difficultly, and
8704brings over with it some part of the Oil of Vitriol in the form of
8705Spirit of Vitriol, and this Spirit being poured upon Iron, Copper, or
8706Salt of Tartar, unites with the Body and lets go the Water; doth not
8707this shew that the acid Spirit is attracted by the Water, and more
8708attracted by the fix'd Body than by the Water, and therefore lets go the
8709Water to close with the fix'd Body? And is it not for the same reason
8710that the Water and acid Spirits which are mix'd together in Vinegar,
8711_Aqua fortis_, and Spirit of Salt, cohere and rise together in
8712Distillation; but if the _Menstruum_ be poured on Salt of Tartar, or on
8713Lead, or Iron, or any fix'd Body which it can dissolve, the Acid by a
8714stronger Attraction adheres to the Body, and lets go the Water? And is
8715it not also from a mutual Attraction that the Spirits of Soot and
8716Sea-Salt unite and compose the Particles of Sal-armoniac, which are less
8717volatile than before, because grosser and freer from Water; and that the
8718Particles of Sal-armoniac in Sublimation carry up the Particles of
8719Antimony, which will not sublime alone; and that the Particles of
8720Mercury uniting with the acid Particles of Spirit of Salt compose
8721Mercury sublimate, and with the Particles of Sulphur, compose Cinnaber;
8722and that the Particles of Spirit of Wine and Spirit of Urine well
8723rectified unite, and letting go the Water which dissolved them, compose
8724a consistent Body; and that in subliming Cinnaber from Salt of Tartar,
8725or from quick Lime, the Sulphur by a stronger Attraction of the Salt or
8726Lime lets go the Mercury, and stays with the fix'd Body; and that when
8727Mercury sublimate is sublimed from Antimony, or from Regulus of
8728Antimony, the Spirit of Salt lets go the Mercury, and unites with the
8729antimonial metal which attracts it more strongly, and stays with it till
8730the Heat be great enough to make them both ascend together, and then
8731carries up the Metal with it in the form of a very fusible Salt, called
8732Butter of Antimony, although the Spirit of Salt alone be almost as
8733volatile as Water, and the Antimony alone as fix'd as Lead?
8734
8735When _Aqua fortis_ dissolves Silver and not Gold, and _Aqua regia_
8736dissolves Gold and not Silver, may it not be said that _Aqua fortis_ is
8737subtil enough to penetrate Gold as well as Silver, but wants the
8738attractive Force to give it Entrance; and that _Aqua regia_ is subtil
8739enough to penetrate Silver as well as Gold, but wants the attractive
8740Force to give it Entrance? For _Aqua regia_ is nothing else than _Aqua
8741fortis_ mix'd with some Spirit of Salt, or with Sal-armoniac; and even
8742common Salt dissolved in _Aqua fortis_, enables the _Menstruum_ to
8743dissolve Gold, though the Salt be a gross Body. When therefore Spirit of
8744Salt precipitates Silver out of _Aqua fortis_, is it not done by
8745attracting and mixing with the _Aqua fortis_, and not attracting, or
8746perhaps repelling Silver? And when Water precipitates Antimony out of
8747the Sublimate of Antimony and Sal-armoniac, or out of Butter of
8748Antimony, is it not done by its dissolving, mixing with, and weakening
8749the Sal-armoniac or Spirit of Salt, and its not attracting, or perhaps
8750repelling the Antimony? And is it not for want of an attractive virtue
8751between the Parts of Water and Oil, of Quick-silver and Antimony, of
8752Lead and Iron, that these Substances do not mix; and by a weak
8753Attraction, that Quick-silver and Copper mix difficultly; and from a
8754strong one, that Quick-silver and Tin, Antimony and Iron, Water and
8755Salts, mix readily? And in general, is it not from the same Principle
8756that Heat congregates homogeneal Bodies, and separates heterogeneal
8757ones?
8758
8759When Arsenick with Soap gives a Regulus, and with Mercury sublimate a
8760volatile fusible Salt, like Butter of Antimony, doth not this shew that
8761Arsenick, which is a Substance totally volatile, is compounded of fix'd
8762and volatile Parts, strongly cohering by a mutual Attraction, so that
8763the volatile will not ascend without carrying up the fixed? And so, when
8764an equal weight of Spirit of Wine and Oil of Vitriol are digested
8765together, and in Distillation yield two fragrant and volatile Spirits
8766which will not mix with one another, and a fix'd black Earth remains
8767behind; doth not this shew that Oil of Vitriol is composed of volatile
8768and fix'd Parts strongly united by Attraction, so as to ascend together
8769in form of a volatile, acid, fluid Salt, until the Spirit of Wine
8770attracts and separates the volatile Parts from the fixed? And therefore,
8771since Oil of Sulphur _per Campanam_ is of the same Nature with Oil of
8772Vitriol, may it not be inferred, that Sulphur is also a mixture of
8773volatile and fix'd Parts so strongly cohering by Attraction, as to
8774ascend together in Sublimation. By dissolving Flowers of Sulphur in Oil
8775of Turpentine, and distilling the Solution, it is found that Sulphur is
8776composed of an inflamable thick Oil or fat Bitumen, an acid Salt, a very
8777fix'd Earth, and a little Metal. The three first were found not much
8778unequal to one another, the fourth in so small a quantity as scarce to
8779be worth considering. The acid Salt dissolved in Water, is the same with
8780Oil of Sulphur _per Campanam_, and abounding much in the Bowels of the
8781Earth, and particularly in Markasites, unites it self to the other
8782Ingredients of the Markasite, which are, Bitumen, Iron, Copper, and
8783Earth, and with them compounds Allum, Vitriol, and Sulphur. With the
8784Earth alone it compounds Allum; with the Metal alone, or Metal and
8785Earth together, it compounds Vitriol; and with the Bitumen and Earth it
8786compounds Sulphur. Whence it comes to pass that Markasites abound with
8787those three Minerals. And is it not from the mutual Attraction of the
8788Ingredients that they stick together for compounding these Minerals, and
8789that the Bitumen carries up the other Ingredients of the Sulphur, which
8790without it would not sublime? And the same Question may be put
8791concerning all, or almost all the gross Bodies in Nature. For all the
8792Parts of Animals and Vegetables are composed of Substances volatile and
8793fix'd, fluid and solid, as appears by their Analysis; and so are Salts
8794and Minerals, so far as Chymists have been hitherto able to examine
8795their Composition.
8796
8797When Mercury sublimate is re-sublimed with fresh Mercury, and becomes
8798_Mercurius Dulcis_, which is a white tasteless Earth scarce dissolvable
8799in Water, and _Mercurius Dulcis_ re-sublimed with Spirit of Salt returns
8800into Mercury sublimate; and when Metals corroded with a little acid turn
8801into rust, which is an Earth tasteless and indissolvable in Water, and
8802this Earth imbibed with more acid becomes a metallick Salt; and when
8803some Stones, as Spar of Lead, dissolved in proper _Menstruums_ become
8804Salts; do not these things shew that Salts are dry Earth and watry Acid
8805united by Attraction, and that the Earth will not become a Salt without
8806so much acid as makes it dissolvable in Water? Do not the sharp and
8807pungent Tastes of Acids arise from the strong Attraction whereby the
8808acid Particles rush upon and agitate the Particles of the Tongue? And
8809when Metals are dissolved in acid _Menstruums_, and the Acids in
8810conjunction with the Metal act after a different manner, so that the
8811Compound has a different Taste much milder than before, and sometimes a
8812sweet one; is it not because the Acids adhere to the metallick
8813Particles, and thereby lose much of their Activity? And if the Acid be
8814in too small a Proportion to make the Compound dissolvable in Water,
8815will it not by adhering strongly to the Metal become unactive and lose
8816its Taste, and the Compound be a tasteless Earth? For such things as are
8817not dissolvable by the Moisture of the Tongue, act not upon the Taste.
8818
8819As Gravity makes the Sea flow round the denser and weightier Parts of
8820the Globe of the Earth, so the Attraction may make the watry Acid flow
8821round the denser and compacter Particles of Earth for composing the
8822Particles of Salt. For otherwise the Acid would not do the Office of a
8823Medium between the Earth and common Water, for making Salts dissolvable
8824in the Water; nor would Salt of Tartar readily draw off the Acid from
8825dissolved Metals, nor Metals the Acid from Mercury. Now, as in the great
8826Globe of the Earth and Sea, the densest Bodies by their Gravity sink
8827down in Water, and always endeavour to go towards the Center of the
8828Globe; so in Particles of Salt, the densest Matter may always endeavour
8829to approach the Center of the Particle: So that a Particle of Salt may
8830be compared to a Chaos; being dense, hard, dry, and earthy in the
8831Center; and rare, soft, moist, and watry in the Circumference. And
8832hence it seems to be that Salts are of a lasting Nature, being scarce
8833destroy'd, unless by drawing away their watry Parts by violence, or by
8834letting them soak into the Pores of the central Earth by a gentle Heat
8835in Putrefaction, until the Earth be dissolved by the Water, and
8836separated into smaller Particles, which by reason of their Smallness
8837make the rotten Compound appear of a black Colour. Hence also it may be,
8838that the Parts of Animals and Vegetables preserve their several Forms,
8839and assimilate their Nourishment; the soft and moist Nourishment easily
8840changing its Texture by a gentle Heat and Motion, till it becomes like
8841the dense, hard, dry, and durable Earth in the Center of each Particle.
8842But when the Nourishment grows unfit to be assimilated, or the central
8843Earth grows too feeble to assimilate it, the Motion ends in Confusion,
8844Putrefaction, and Death.
8845
8846If a very small quantity of any Salt or Vitriol be dissolved in a great
8847quantity of Water, the Particles of the Salt or Vitriol will not sink to
8848the bottom, though they be heavier in Specie than the Water, but will
8849evenly diffuse themselves into all the Water, so as to make it as saline
8850at the top as at the bottom. And does not this imply that the Parts of
8851the Salt or Vitriol recede from one another, and endeavour to expand
8852themselves, and get as far asunder as the quantity of Water in which
8853they float, will allow? And does not this Endeavour imply that they have
8854a repulsive Force by which they fly from one another, or at least, that
8855they attract the Water more strongly than they do one another? For as
8856all things ascend in Water which are less attracted than Water, by the
8857gravitating Power of the Earth; so all the Particles of Salt which float
8858in Water, and are less attracted than Water by any one Particle of Salt,
8859must recede from that Particle, and give way to the more attracted
8860Water.
8861
8862When any saline Liquor is evaporated to a Cuticle and let cool, the Salt
8863concretes in regular Figures; which argues, that the Particles of the
8864Salt before they concreted, floated in the Liquor at equal distances in
8865rank and file, and by consequence that they acted upon one another by
8866some Power which at equal distances is equal, at unequal distances
8867unequal. For by such a Power they will range themselves uniformly, and
8868without it they will float irregularly, and come together as
8869irregularly. And since the Particles of Island-Crystal act all the same
8870way upon the Rays of Light for causing the unusual Refraction, may it
8871not be supposed that in the Formation of this Crystal, the Particles not
8872only ranged themselves in rank and file for concreting in regular
8873Figures, but also by some kind of polar Virtue turned their homogeneal
8874Sides the same way.
8875
8876The Parts of all homogeneal hard Bodies which fully touch one another,
8877stick together very strongly. And for explaining how this may be, some
8878have invented hooked Atoms, which is begging the Question; and others
8879tell us that Bodies are glued together by rest, that is, by an occult
8880Quality, or rather by nothing; and others, that they stick together by
8881conspiring Motions, that is, by relative rest amongst themselves. I had
8882rather infer from their Cohesion, that their Particles attract one
8883another by some Force, which in immediate Contact is exceeding strong,
8884at small distances performs the chymical Operations above-mention'd, and
8885reaches not far from the Particles with any sensible Effect.
8886
8887All Bodies seem to be composed of hard Particles: For otherwise Fluids
8888would not congeal; as Water, Oils, Vinegar, and Spirit or Oil of Vitriol
8889do by freezing; Mercury by Fumes of Lead; Spirit of Nitre and Mercury,
8890by dissolving the Mercury and evaporating the Flegm; Spirit of Wine and
8891Spirit of Urine, by deflegming and mixing them; and Spirit of Urine and
8892Spirit of Salt, by subliming them together to make Sal-armoniac. Even
8893the Rays of Light seem to be hard Bodies; for otherwise they would not
8894retain different Properties in their different Sides. And therefore
8895Hardness may be reckon'd the Property of all uncompounded Matter. At
8896least, this seems to be as evident as the universal Impenetrability of
8897Matter. For all Bodies, so far as Experience reaches, are either hard,
8898or may be harden'd; and we have no other Evidence of universal
8899Impenetrability, besides a large Experience without an experimental
8900Exception. Now if compound Bodies are so very hard as we find some of
8901them to be, and yet are very porous, and consist of Parts which are only
8902laid together; the simple Particles which are void of Pores, and were
8903never yet divided, must be much harder. For such hard Particles being
8904heaped up together, can scarce touch one another in more than a few
8905Points, and therefore must be separable by much less Force than is
8906requisite to break a solid Particle, whose Parts touch in all the Space
8907between them, without any Pores or Interstices to weaken their Cohesion.
8908And how such very hard Particles which are only laid together and touch
8909only in a few Points, can stick together, and that so firmly as they do,
8910without the assistance of something which causes them to be attracted or
8911press'd towards one another, is very difficult to conceive.
8912
8913The 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
8915the height of 50, 60 or 70 Inches, or above, when ever it is well-purged
8916of Air and carefully poured in, so that its Parts be every where
8917contiguous both to one another and to the Glass. The Atmosphere by its
8918weight presses the Quick-silver into the Glass, to the height of 29 or
891930 Inches. And some other Agent raises it higher, not by pressing it
8920into the Glass, but by making its Parts stick to the Glass, and to one
8921another. For upon any discontinuation of Parts, made either by Bubbles
8922or by shaking the Glass, the whole Mercury falls down to the height of
892329 or 30 Inches.
8924
8925And of the same kind with these Experiments are those that follow. If
8926two plane polish'd Plates of Glass (suppose two pieces of a polish'd
8927Looking-glass) be laid together, so that their sides be parallel and at
8928a very small distance from one another, and then their lower edges be
8929dipped into Water, the Water will rise up between them. And the less
8930the distance of the Glasses is, the greater will be the height to which
8931the Water will rise. If the distance be about the hundredth part of an
8932Inch, the Water will rise to the height of about an Inch; and if the
8933distance be greater or less in any Proportion, the height will be
8934reciprocally proportional to the distance very nearly. For the
8935attractive Force of the Glasses is the same, whether the distance
8936between them be greater or less; and the weight of the Water drawn up is
8937the same, if the height of it be reciprocally proportional to the
8938distance of the Glasses. And in like manner, Water ascends between two
8939Marbles polish'd plane, when their polish'd sides are parallel, and at a
8940very little distance from one another, And if slender Pipes of Glass be
8941dipped at one end into stagnating Water, the Water will rise up within
8942the Pipe, and the height to which it rises will be reciprocally
8943proportional to the Diameter of the Cavity of the Pipe, and will equal
8944the height to which it rises between two Planes of Glass, if the
8945Semi-diameter of the Cavity of the Pipe be equal to the distance between
8946the Planes, or thereabouts. And these Experiments succeed after the same
8947manner _in vacuo_ as in the open Air, (as hath been tried before the
8948Royal Society,) and therefore are not influenced by the Weight or
8949Pressure of the Atmosphere.
8950
8951And if a large Pipe of Glass be filled with sifted Ashes well pressed
8952together in the Glass, and one end of the Pipe be dipped into stagnating
8953Water, the Water will rise up slowly in the Ashes, so as in the space
8954of a Week or Fortnight to reach up within the Glass, to the height of 30
8955or 40 Inches above the stagnating Water. And the Water rises up to this
8956height by the Action only of those Particles of the Ashes which are upon
8957the Surface of the elevated Water; the Particles which are within the
8958Water, attracting or repelling it as much downwards as upwards. And
8959therefore the Action of the Particles is very strong. But the Particles
8960of the Ashes being not so dense and close together as those of Glass,
8961their Action is not so strong as that of Glass, which keeps Quick-silver
8962suspended to the height of 60 or 70 Inches, and therefore acts with a
8963Force which would keep Water suspended to the height of above 60 Feet.
8964
8965By the same Principle, a Sponge sucks in Water, and the Glands in the
8966Bodies of Animals, according to their several Natures and Dispositions,
8967suck in various Juices from the Blood.
8968
8969If two plane polish'd Plates of Glass three or four Inches broad, and
8970twenty or twenty five long, be laid one of them parallel to the Horizon,
8971the other upon the first, so as at one of their ends to touch one
8972another, and contain an Angle of about 10 or 15 Minutes, and the same be
8973first moisten'd on their inward sides with a clean Cloth dipp'd into Oil
8974of Oranges or Spirit of Turpentine, and a Drop or two of the Oil or
8975Spirit be let fall upon the lower Glass at the other; so soon as the
8976upper Glass is laid down upon the lower, so as to touch it at one end as
8977above, and to touch the Drop at the other end, making with the lower
8978Glass an Angle of about 10 or 15 Minutes; the Drop will begin to move
8979towards the Concourse of the Glasses, and will continue to move with an
8980accelerated Motion, till it arrives at that Concourse of the Glasses.
8981For the two Glasses attract the Drop, and make it run that way towards
8982which the Attractions incline. And if when the Drop is in motion you
8983lift up that end of the Glasses where they meet, and towards which the
8984Drop moves, the Drop will ascend between the Glasses, and therefore is
8985attracted. And as you lift up the Glasses more and more, the Drop will
8986ascend slower and slower, and at length rest, being then carried
8987downward by its Weight, as much as upwards by the Attraction. And by
8988this means you may know the Force by which the Drop is attracted at all
8989distances from the Concourse of the Glasses.
8990
8991Now by some Experiments of this kind, (made by Mr. _Hauksbee_) it has
8992been found that the Attraction is almost reciprocally in a duplicate
8993Proportion of the distance of the middle of the Drop from the Concourse
8994of the Glasses, _viz._ reciprocally in a simple Proportion, by reason of
8995the spreading of the Drop, and its touching each Glass in a larger
8996Surface; and again reciprocally in a simple Proportion, by reason of the
8997Attractions growing stronger within the same quantity of attracting
8998Surface. The Attraction therefore within the same quantity of attracting
8999Surface, is reciprocally as the distance between the Glasses. And
9000therefore where the distance is exceeding small, the Attraction must be
9001exceeding great. By the Table in the second Part of the second Book,
9002wherein the thicknesses of colour'd Plates of Water between two Glasses
9003are set down, the thickness of the Plate where it appears very black, is
9004three eighths of the ten hundred thousandth part of an Inch. And where
9005the Oil of Oranges between the Glasses is of this thickness, the
9006Attraction collected by the foregoing Rule, seems to be so strong, as
9007within a Circle of an Inch in diameter, to suffice to hold up a Weight
9008equal to that of a Cylinder of Water of an Inch in diameter, and two or
9009three Furlongs in length. And where it is of a less thickness the
9010Attraction may be proportionally greater, and continue to increase,
9011until the thickness do not exceed that of a single Particle of the Oil.
9012There are therefore Agents in Nature able to make the Particles of
9013Bodies stick together by very strong Attractions. And it is the Business
9014of experimental Philosophy to find them out.
9015
9016Now the smallest Particles of Matter may cohere by the strongest
9017Attractions, and compose bigger Particles of weaker Virtue; and many of
9018these may cohere and compose bigger Particles whose Virtue is still
9019weaker, and so on for divers Successions, until the Progression end in
9020the biggest Particles on which the Operations in Chymistry, and the
9021Colours of natural Bodies depend, and which by cohering compose Bodies
9022of a sensible Magnitude. If the Body is compact, and bends or yields
9023inward to Pression without any sliding of its Parts, it is hard and
9024elastick, returning to its Figure with a Force rising from the mutual
9025Attraction of its Parts. If the Parts slide upon one another, the Body
9026is malleable or soft. If they slip easily, and are of a fit Size to be
9027agitated by Heat, and the Heat is big enough to keep them in Agitation,
9028the Body is fluid; and if it be apt to stick to things, it is humid; and
9029the Drops of every fluid affect a round Figure by the mutual Attraction
9030of their Parts, as the Globe of the Earth and Sea affects a round Figure
9031by the mutual Attraction of its Parts by Gravity.
9032
9033Since Metals dissolved in Acids attract but a small quantity of the
9034Acid, their attractive Force can reach but to a small distance from
9035them. And as in Algebra, where affirmative Quantities vanish and cease,
9036there negative ones begin; so in Mechanicks, where Attraction ceases,
9037there a repulsive Virtue ought to succeed. And that there is such a
9038Virtue, seems to follow from the Reflexions and Inflexions of the Rays
9039of Light. For the Rays are repelled by Bodies in both these Cases,
9040without the immediate Contact of the reflecting or inflecting Body. It
9041seems also to follow from the Emission of Light; the Ray so soon as it
9042is shaken off from a shining Body by the vibrating Motion of the Parts
9043of the Body, and gets beyond the reach of Attraction, being driven away
9044with exceeding great Velocity. For that Force which is sufficient to
9045turn it back in Reflexion, may be sufficient to emit it. It seems also
9046to follow from the Production of Air and Vapour. The Particles when they
9047are shaken off from Bodies by Heat or Fermentation, so soon as they are
9048beyond the reach of the Attraction of the Body, receding from it, and
9049also from one another with great Strength, and keeping at a distance,
9050so as sometimes to take up above a Million of Times more space than they
9051did before in the form of a dense Body. Which vast Contraction and
9052Expansion seems unintelligible, by feigning the Particles of Air to be
9053springy and ramous, or rolled up like Hoops, or by any other means than
9054a repulsive Power. The Particles of Fluids which do not cohere too
9055strongly, and are of such a Smallness as renders them most susceptible
9056of those Agitations which keep Liquors in a Fluor, are most easily
9057separated and rarified into Vapour, and in the Language of the Chymists,
9058they are volatile, rarifying with an easy Heat, and condensing with
9059Cold. But those which are grosser, and so less susceptible of Agitation,
9060or cohere by a stronger Attraction, are not separated without a stronger
9061Heat, or perhaps not without Fermentation. And these last are the Bodies
9062which Chymists call fix'd, and being rarified by Fermentation, become
9063true permanent Air; those Particles receding from one another with the
9064greatest Force, and being most difficultly brought together, which upon
9065Contact cohere most strongly. And because the Particles of permanent Air
9066are grosser, and arise from denser Substances than those of Vapours,
9067thence it is that true Air is more ponderous than Vapour, and that a
9068moist Atmosphere is lighter than a dry one, quantity for quantity. From
9069the same repelling Power it seems to be that Flies walk upon the Water
9070without wetting their Feet; and that the Object-glasses of long
9071Telescopes lie upon one another without touching; and that dry Powders
9072are difficultly made to touch one another so as to stick together,
9073unless by melting them, or wetting them with Water, which by exhaling
9074may bring them together; and that two polish'd Marbles, which by
9075immediate Contact stick together, are difficultly brought so close
9076together as to stick.
9077
9078And thus Nature will be very conformable to her self and very simple,
9079performing all the great Motions of the heavenly Bodies by the
9080Attraction of Gravity which intercedes those Bodies, and almost all the
9081small ones of their Particles by some other attractive and repelling
9082Powers which intercede the Particles. The _Vis inertiæ_ is a passive
9083Principle by which Bodies persist in their Motion or Rest, receive
9084Motion in proportion to the Force impressing it, and resist as much as
9085they are resisted. By this Principle alone there never could have been
9086any Motion in the World. Some other Principle was necessary for putting
9087Bodies into Motion; and now they are in Motion, some other Principle is
9088necessary for conserving the Motion. For from the various Composition of
9089two Motions, 'tis very certain that there is not always the same
9090quantity of Motion in the World. For if two Globes joined by a slender
9091Rod, revolve about their common Center of Gravity with an uniform
9092Motion, while that Center moves on uniformly in a right Line drawn in
9093the Plane of their circular Motion; the Sum of the Motions of the two
9094Globes, as often as the Globes are in the right Line described by their
9095common Center of Gravity, will be bigger than the Sum of their Motions,
9096when they are in a Line perpendicular to that right Line. By this
9097Instance it appears that Motion may be got or lost. But by reason of the
9098Tenacity of Fluids, and Attrition of their Parts, and the Weakness of
9099Elasticity in Solids, Motion is much more apt to be lost than got, and
9100is always upon the Decay. For Bodies which are either absolutely hard,
9101or so soft as to be void of Elasticity, will not rebound from one
9102another. Impenetrability makes them only stop. If two equal Bodies meet
9103directly _in vacuo_, they will by the Laws of Motion stop where they
9104meet, and lose all their Motion, and remain in rest, unless they be
9105elastick, and receive new Motion from their Spring. If they have so much
9106Elasticity as suffices to make them re-bound with a quarter, or half, or
9107three quarters of the Force with which they come together, they will
9108lose three quarters, or half, or a quarter of their Motion. And this may
9109be try'd, by letting two equal Pendulums fall against one another from
9110equal heights. If the Pendulums be of Lead or soft Clay, they will lose
9111all or almost all their Motions: If of elastick Bodies they will lose
9112all but what they recover from their Elasticity. If it be said, that
9113they can lose no Motion but what they communicate to other Bodies, the
9114consequence is, that _in vacuo_ they can lose no Motion, but when they
9115meet they must go on and penetrate one another's Dimensions. If three
9116equal round Vessels be filled, the one with Water, the other with Oil,
9117the third with molten Pitch, and the Liquors be stirred about alike to
9118give them a vortical Motion; the Pitch by its Tenacity will lose its
9119Motion quickly, the Oil being less tenacious will keep it longer, and
9120the Water being less tenacious will keep it longest, but yet will lose
9121it in a short time. Whence it is easy to understand, that if many
9122contiguous Vortices of molten Pitch were each of them as large as those
9123which some suppose to revolve about the Sun and fix'd Stars, yet these
9124and all their Parts would, by their Tenacity and Stiffness, communicate
9125their Motion to one another till they all rested among themselves.
9126Vortices of Oil or Water, or some fluider Matter, might continue longer
9127in Motion; but unless the Matter were void of all Tenacity and Attrition
9128of Parts, and Communication of Motion, (which is not to be supposed,)
9129the Motion would constantly decay. Seeing therefore the variety of
9130Motion which we find in the World is always decreasing, there is a
9131necessity of conserving and recruiting it by active Principles, such as
9132are the cause of Gravity, by which Planets and Comets keep their Motions
9133in their Orbs, and Bodies acquire great Motion in falling; and the cause
9134of Fermentation, by which the Heart and Blood of Animals are kept in
9135perpetual Motion and Heat; the inward Parts of the Earth are constantly
9136warm'd, and in some places grow very hot; Bodies burn and shine,
9137Mountains take fire, the Caverns of the Earth are blown up, and the Sun
9138continues violently hot and lucid, and warms all things by his Light.
9139For we meet with very little Motion in the World, besides what is owing
9140to these active Principles. And if it were not for these Principles, the
9141Bodies of the Earth, Planets, Comets, Sun, and all things in them,
9142would grow cold and freeze, and become inactive Masses; and all
9143Putrefaction, Generation, Vegetation and Life would cease, and the
9144Planets and Comets would not remain in their Orbs.
9145
9146All these things being consider'd, it seems probable to me, that God in
9147the Beginning form'd Matter in solid, massy, hard, impenetrable,
9148moveable Particles, of such Sizes and Figures, and with such other
9149Properties, and in such Proportion to Space, as most conduced to the End
9150for which he form'd them; and that these primitive Particles being
9151Solids, are incomparably harder than any porous Bodies compounded of
9152them; even so very hard, as never to wear or break in pieces; no
9153ordinary Power being able to divide what God himself made one in the
9154first Creation. While the Particles continue entire, they may compose
9155Bodies of one and the same Nature and Texture in all Ages: But should
9156they wear away, or break in pieces, the Nature of Things depending on
9157them, would be changed. Water and Earth, composed of old worn Particles
9158and Fragments of Particles, would not be of the same Nature and Texture
9159now, with Water and Earth composed of entire Particles in the Beginning.
9160And therefore, that Nature may be lasting, the Changes of corporeal
9161Things are to be placed only in the various Separations and new
9162Associations and Motions of these permanent Particles; compound Bodies
9163being apt to break, not in the midst of solid Particles, but where those
9164Particles are laid together, and only touch in a few Points.
9165
9166It seems to me farther, that these Particles have not only a _Vis
9167inertiæ_, accompanied with such passive Laws of Motion as naturally
9168result from that Force, but also that they are moved by certain active
9169Principles, such as is that of Gravity, and that which causes
9170Fermentation, and the Cohesion of Bodies. These Principles I consider,
9171not as occult Qualities, supposed to result from the specifick Forms of
9172Things, but as general Laws of Nature, by which the Things themselves
9173are form'd; their Truth appearing to us by Phænomena, though their
9174Causes be not yet discover'd. For these are manifest Qualities, and
9175their Causes only are occult. And the _Aristotelians_ gave the Name of
9176occult Qualities, not to manifest Qualities, but to such Qualities only
9177as they supposed to lie hid in Bodies, and to be the unknown Causes of
9178manifest Effects: Such as would be the Causes of Gravity, and of
9179magnetick and electrick Attractions, and of Fermentations, if we should
9180suppose that these Forces or Actions arose from Qualities unknown to us,
9181and uncapable of being discovered and made manifest. Such occult
9182Qualities put a stop to the Improvement of natural Philosophy, and
9183therefore of late Years have been rejected. To tell us that every
9184Species of Things is endow'd with an occult specifick Quality by which
9185it acts and produces manifest Effects, is to tell us nothing: But to
9186derive two or three general Principles of Motion from Phænomena, and
9187afterwards to tell us how the Properties and Actions of all corporeal
9188Things follow from those manifest Principles, would be a very great step
9189in Philosophy, though the Causes of those Principles were not yet
9190discover'd: And therefore I scruple not to propose the Principles of
9191Motion above-mention'd, they being of very general Extent, and leave
9192their Causes to be found out.
9193
9194Now by the help of these Principles, all material Things seem to have
9195been composed of the hard and solid Particles above-mention'd, variously
9196associated in the first Creation by the Counsel of an intelligent Agent.
9197For it became him who created them to set them in order. And if he did
9198so, it's unphilosophical to seek for any other Origin of the World, or
9199to pretend that it might arise out of a Chaos by the mere Laws of
9200Nature; though being once form'd, it may continue by those Laws for many
9201Ages. For while Comets move in very excentrick Orbs in all manner of
9202Positions, blind Fate could never make all the Planets move one and the
9203same way in Orbs concentrick, some inconsiderable Irregularities
9204excepted, which may have risen from the mutual Actions of Comets and
9205Planets upon one another, and which will be apt to increase, till this
9206System wants a Reformation. Such a wonderful Uniformity in the Planetary
9207System must be allowed the Effect of Choice. And so must the Uniformity
9208in the Bodies of Animals, they having generally a right and a left side
9209shaped alike, and on either side of their Bodies two Legs behind, and
9210either two Arms, or two Legs, or two Wings before upon their Shoulders,
9211and between their Shoulders a Neck running down into a Back-bone, and a
9212Head upon it; and in the Head two Ears, two Eyes, a Nose, a Mouth, and
9213a Tongue, alike situated. Also the first Contrivance of those very
9214artificial Parts of Animals, the Eyes, Ears, Brain, Muscles, Heart,
9215Lungs, Midriff, Glands, Larynx, Hands, Wings, swimming Bladders, natural
9216Spectacles, and other Organs of Sense and Motion; and the Instinct of
9217Brutes and Insects, can be the effect of nothing else than the Wisdom
9218and Skill of a powerful ever-living Agent, who being in all Places, is
9219more able by his Will to move the Bodies within his boundless uniform
9220Sensorium, and thereby to form and reform the Parts of the Universe,
9221than we are by our Will to move the Parts of our own Bodies. And yet we
9222are not to consider the World as the Body of God, or the several Parts
9223thereof, as the Parts of God. He is an uniform Being, void of Organs,
9224Members or Parts, and they are his Creatures subordinate to him, and
9225subservient to his Will; and he is no more the Soul of them, than the
9226Soul of Man is the Soul of the Species of Things carried through the
9227Organs of Sense into the place of its Sensation, where it perceives them
9228by means of its immediate Presence, without the Intervention of any
9229third thing. The Organs of Sense are not for enabling the Soul to
9230perceive the Species of Things in its Sensorium, but only for conveying
9231them thither; and God has no need of such Organs, he being every where
9232present to the Things themselves. And since Space is divisible _in
9233infinitum_, and Matter is not necessarily in all places, it may be also
9234allow'd that God is able to create Particles of Matter of several Sizes
9235and Figures, and in several Proportions to Space, and perhaps of
9236different Densities and Forces, and thereby to vary the Laws of Nature,
9237and make Worlds of several sorts in several Parts of the Universe. At
9238least, I see nothing of Contradiction in all this.
9239
9240As in Mathematicks, so in Natural Philosophy, the Investigation of
9241difficult Things by the Method of Analysis, ought ever to precede the
9242Method of Composition. This Analysis consists in making Experiments and
9243Observations, and in drawing general Conclusions from them by Induction,
9244and admitting of no Objections against the Conclusions, but such as are
9245taken from Experiments, or other certain Truths. For Hypotheses are not
9246to be regarded in experimental Philosophy. And although the arguing from
9247Experiments and Observations by Induction be no Demonstration of general
9248Conclusions; yet it is the best way of arguing which the Nature of
9249Things admits of, and may be looked upon as so much the stronger, by how
9250much the Induction is more general. And if no Exception occur from
9251Phænomena, the Conclusion may be pronounced generally. But if at any
9252time afterwards any Exception shall occur from Experiments, it may then
9253begin to be pronounced with such Exceptions as occur. By this way of
9254Analysis we may proceed from Compounds to Ingredients, and from Motions
9255to the Forces producing them; and in general, from Effects to their
9256Causes, and from particular Causes to more general ones, till the
9257Argument end in the most general. This is the Method of Analysis: And
9258the Synthesis consists in assuming the Causes discover'd, and
9259establish'd as Principles, and by them explaining the Phænomena
9260proceeding from them, and proving the Explanations.
9261
9262In the two first Books of these Opticks, I proceeded by this Analysis to
9263discover and prove the original Differences of the Rays of Light in
9264respect of Refrangibility, Reflexibility, and Colour, and their
9265alternate Fits of easy Reflexion and easy Transmission, and the
9266Properties of Bodies, both opake and pellucid, on which their Reflexions
9267and Colours depend. And these Discoveries being proved, may be assumed
9268in the Method of Composition for explaining the Phænomena arising from
9269them: An Instance of which Method I gave in the End of the first Book.
9270In this third Book I have only begun the Analysis of what remains to be
9271discover'd about Light and its Effects upon the Frame of Nature, hinting
9272several things about it, and leaving the Hints to be examin'd and
9273improv'd by the farther Experiments and Observations of such as are
9274inquisitive. And if natural Philosophy in all its Parts, by pursuing
9275this Method, shall at length be perfected, the Bounds of Moral
9276Philosophy will be also enlarged. For so far as we can know by natural
9277Philosophy what is the first Cause, what Power he has over us, and what
9278Benefits we receive from him, so far our Duty towards him, as well as
9279that towards one another, will appear to us by the Light of Nature. And
9280no doubt, if the Worship of false Gods had not blinded the Heathen,
9281their moral Philosophy would have gone farther than to the four
9282Cardinal Virtues; and instead of teaching the Transmigration of Souls,
9283and to worship the Sun and Moon, and dead Heroes, they would have taught
9284us to worship our true Author and Benefactor, as their Ancestors did
9285under the Government of _Noah_ and his Sons before they corrupted
9286themselves.View as plain text