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    10  OPTICKS:
    12  OR, A
    14  TREATISE
    16  OF THE
    18  _Reflections_, _Refractions_,
    19  _Inflections_ and _Colours_
    21  OF
    23  LIGHT.
    25  _The_ FOURTH EDITION, _corrected_.
    27  By Sir _ISAAC NEWTON_, Knt.
    29  LONDON:
    31  Printed for WILLIAM INNYS at the West-End of St. _Paul's_. MDCCXXX.
    43  Advertisement I
    46  _Part of the ensuing Discourse about Light was written at the Desire of
    47  some Gentlemen of the_ Royal-Society, _in the Year 1675, and then sent
    48  to their Secretary, and read at their Meetings, and the rest was added
    49  about twelve Years after to complete the Theory; except the third Book,
    50  and the last Proposition of the Second, which were since put together
    51  out of scatter'd Papers. To avoid being engaged in Disputes about these
    52  Matters, I have hitherto delayed the printing, and should still have
    53  delayed it, had not the Importunity of Friends prevailed upon me. If any
    54  other Papers writ on this Subject are got out of my Hands they are
    55  imperfect, and were perhaps written before I had tried all the
    56  Experiments here set down, and fully satisfied my self about the Laws of
    57  Refractions and Composition of Colours. I have here publish'd what I
    58  think proper to come abroad, wishing that it may not be translated into
    59  another Language without my Consent._
    61  _The Crowns of Colours, which sometimes appear about the Sun and Moon, I
    62  have endeavoured to give an Account of; but for want of sufficient
    63  Observations leave that Matter to be farther examined. The Subject of
    64  the Third Book I have also left imperfect, not having tried all the
    65  Experiments which I intended when I was about these Matters, nor
    66  repeated some of those which I did try, until I had satisfied my self
    67  about all their Circumstances. To communicate what I have tried, and
    68  leave the rest to others for farther Enquiry, is all my Design in
    69  publishing these Papers._
    71  _In a Letter written to Mr._ Leibnitz _in the year 1679, and published
    72  by Dr._ Wallis, _I mention'd a Method by which I had found some general
    73  Theorems about squaring Curvilinear Figures, or comparing them with the
    74  Conic Sections, or other the simplest Figures with which they may be
    75  compared. And some Years ago I lent out a Manuscript containing such
    76  Theorems, and having since met with some Things copied out of it, I have
    77  on this Occasion made it publick, prefixing to it an_ Introduction, _and
    78  subjoining a_ Scholium _concerning that Method. And I have joined with
    79  it another small Tract concerning the Curvilinear Figures of the Second
    80  Kind, which was also written many Years ago, and made known to some
    81  Friends, who have solicited the making it publick._
    83                                          _I. N._
    85  April 1, 1704.
    88  Advertisement II
    90  _In this Second Edition of these Opticks I have omitted the Mathematical
    91  Tracts publish'd at the End of the former Edition, as not belonging to
    92  the Subject. And at the End of the Third Book I have added some
    93  Questions. And to shew that I do not take Gravity for an essential
    94  Property of Bodies, I have added one Question concerning its Cause,
    95  chusing to propose it by way of a Question, because I am not yet
    96  satisfied about it for want of Experiments._
    98                                          _I. N._
   100  July 16, 1717.
   103  Advertisement to this Fourth Edition
   105  _This new Edition of Sir_ Isaac Newton's Opticks _is carefully printed
   106  from the Third Edition, as it was corrected by the Author's own Hand,
   107  and left before his Death with the Bookseller. Since Sir_ Isaac's
   108  Lectiones Opticæ, _which he publickly read in the University of_
   109  Cambridge _in the Years 1669, 1670, and 1671, are lately printed, it has
   110  been thought proper to make at the bottom of the Pages several Citations
   111  from thence, where may be found the Demonstrations, which the Author
   112  omitted in these_ Opticks.
   114         *       *       *       *       *
   116  Transcriber's Note: There are several greek letters used in the
   117  descriptions of the illustrations. They are signified by [Greek:
   118  letter]. Square roots are noted by the letters sqrt before the equation.
   120         *       *       *       *       *
   127  _PART I._
   130  My Design in this Book is not to explain the Properties of Light by
   131  Hypotheses, but to propose and prove them by Reason and Experiments: In
   132  order to which I shall premise the following Definitions and Axioms.
   140  DEFIN. I.
   142  _By the Rays of Light I understand its least Parts, and those as well
   143  Successive in the same Lines, as Contemporary in several Lines._ For it
   144  is manifest that Light consists of Parts, both Successive and
   145  Contemporary; because in the same place you may stop that which comes
   146  one moment, and let pass that which comes presently after; and in the
   147  same time you may stop it in any one place, and let it pass in any
   148  other. For that part of Light which is stopp'd cannot be the same with
   149  that which is let pass. The least Light or part of Light, which may be
   150  stopp'd alone without the rest of the Light, or propagated alone, or do
   151  or suffer any thing alone, which the rest of the Light doth not or
   152  suffers not, I call a Ray of Light.
   155  DEFIN. II.
   157  _Refrangibility of the Rays of Light, is their Disposition to be
   158  refracted or turned out of their Way in passing out of one transparent
   159  Body or Medium into another. And a greater or less Refrangibility of
   160  Rays, is their Disposition to be turned more or less out of their Way in
   161  like Incidences on the same Medium._ Mathematicians usually consider the
   162  Rays of Light to be Lines reaching from the luminous Body to the Body
   163  illuminated, and the refraction of those Rays to be the bending or
   164  breaking of those lines in their passing out of one Medium into another.
   165  And thus may Rays and Refractions be considered, if Light be propagated
   166  in an instant. But by an Argument taken from the Æquations of the times
   167  of the Eclipses of _Jupiter's Satellites_, it seems that Light is
   168  propagated in time, spending in its passage from the Sun to us about
   169  seven Minutes of time: And therefore I have chosen to define Rays and
   170  Refractions in such general terms as may agree to Light in both cases.
   173  DEFIN. III.
   175  _Reflexibility of Rays, is their Disposition to be reflected or turned
   176  back into the same Medium from any other Medium upon whose Surface they
   177  fall. And Rays are more or less reflexible, which are turned back more
   178  or less easily._ As if Light pass out of a Glass into Air, and by being
   179  inclined more and more to the common Surface of the Glass and Air,
   180  begins at length to be totally reflected by that Surface; those sorts of
   181  Rays which at like Incidences are reflected most copiously, or by
   182  inclining the Rays begin soonest to be totally reflected, are most
   183  reflexible.
   186  DEFIN. IV.
   188  _The Angle of Incidence is that Angle, which the Line described by the
   189  incident Ray contains with the Perpendicular to the reflecting or
   190  refracting Surface at the Point of Incidence._
   193  DEFIN. V.
   195  _The Angle of Reflexion or Refraction, is the Angle which the line
   196  described by the reflected or refracted Ray containeth with the
   197  Perpendicular to the reflecting or refracting Surface at the Point of
   198  Incidence._
   201  DEFIN. VI.
   203  _The Sines of Incidence, Reflexion, and Refraction, are the Sines of the
   204  Angles of Incidence, Reflexion, and Refraction._
   207  DEFIN. VII
   209  _The Light whose Rays are all alike Refrangible, I call Simple,
   210  Homogeneal and Similar; and that whose Rays are some more Refrangible
   211  than others, I call Compound, Heterogeneal and Dissimilar._ The former
   212  Light I call Homogeneal, not because I would affirm it so in all
   213  respects, but because the Rays which agree in Refrangibility, agree at
   214  least in all those their other Properties which I consider in the
   215  following Discourse.
   218  DEFIN. VIII.
   220  _The Colours of Homogeneal Lights, I call Primary, Homogeneal and
   221  Simple; and those of Heterogeneal Lights, Heterogeneal and Compound._
   222  For these are always compounded of the colours of Homogeneal Lights; as
   223  will appear in the following Discourse.
   228  _AXIOMS._
   231  AX. I.
   233  _The Angles of Reflexion and Refraction, lie in one and the same Plane
   234  with the Angle of Incidence._
   237  AX. II.
   239  _The Angle of Reflexion is equal to the Angle of Incidence._
   242  AX. III.
   244  _If the refracted Ray be returned directly back to the Point of
   245  Incidence, it shall be refracted into the Line before described by the
   246  incident Ray._
   249  AX. IV.
   251  _Refraction out of the rarer Medium into the denser, is made towards the
   252  Perpendicular; that is, so that the Angle of Refraction be less than the
   253  Angle of Incidence._
   256  AX. V.
   258  _The Sine of Incidence is either accurately or very nearly in a given
   259  Ratio to the Sine of Refraction._
   261  Whence if that Proportion be known in any one Inclination of the
   262  incident Ray, 'tis known in all the Inclinations, and thereby the
   263  Refraction in all cases of Incidence on the same refracting Body may be
   264  determined. Thus if the Refraction be made out of Air into Water, the
   265  Sine of Incidence of the red Light is to the Sine of its Refraction as 4
   266  to 3. If out of Air into Glass, the Sines are as 17 to 11. In Light of
   267  other Colours the Sines have other Proportions: but the difference is so
   268  little that it need seldom be considered.
   270  [Illustration: FIG. 1]
   272  Suppose therefore, that RS [in _Fig._ 1.] represents the Surface of
   273  stagnating Water, and that C is the point of Incidence in which any Ray
   274  coming in the Air from A in the Line AC is reflected or refracted, and I
   275  would know whither this Ray shall go after Reflexion or Refraction: I
   276  erect upon the Surface of the Water from the point of Incidence the
   277  Perpendicular CP and produce it downwards to Q, and conclude by the
   278  first Axiom, that the Ray after Reflexion and Refraction, shall be
   279  found somewhere in the Plane of the Angle of Incidence ACP produced. I
   280  let fall therefore upon the Perpendicular CP the Sine of Incidence AD;
   281  and if the reflected Ray be desired, I produce AD to B so that DB be
   282  equal to AD, and draw CB. For this Line CB shall be the reflected Ray;
   283  the Angle of Reflexion BCP and its Sine BD being equal to the Angle and
   284  Sine of Incidence, as they ought to be by the second Axiom, But if the
   285  refracted Ray be desired, I produce AD to H, so that DH may be to AD as
   286  the Sine of Refraction to the Sine of Incidence, that is, (if the Light
   287  be red) as 3 to 4; and about the Center C and in the Plane ACP with the
   288  Radius CA describing a Circle ABE, I draw a parallel to the
   289  Perpendicular CPQ, the Line HE cutting the Circumference in E, and
   290  joining CE, this Line CE shall be the Line of the refracted Ray. For if
   291  EF be let fall perpendicularly on the Line PQ, this Line EF shall be the
   292  Sine of Refraction of the Ray CE, the Angle of Refraction being ECQ; and
   293  this Sine EF is equal to DH, and consequently in Proportion to the Sine
   294  of Incidence AD as 3 to 4.
   296  In like manner, if there be a Prism of Glass (that is, a Glass bounded
   297  with two Equal and Parallel Triangular ends, and three plain and well
   298  polished Sides, which meet in three Parallel Lines running from the
   299  three Angles of one end to the three Angles of the other end) and if the
   300  Refraction of the Light in passing cross this Prism be desired: Let ACB
   301  [in _Fig._ 2.] represent a Plane cutting this Prism transversly to its
   302  three Parallel lines or edges there where the Light passeth through it,
   303  and let DE be the Ray incident upon the first side of the Prism AC where
   304  the Light goes into the Glass; and by putting the Proportion of the Sine
   305  of Incidence to the Sine of Refraction as 17 to 11 find EF the first
   306  refracted Ray. Then taking this Ray for the Incident Ray upon the second
   307  side of the Glass BC where the Light goes out, find the next refracted
   308  Ray FG by putting the Proportion of the Sine of Incidence to the Sine of
   309  Refraction as 11 to 17. For if the Sine of Incidence out of Air into
   310  Glass be to the Sine of Refraction as 17 to 11, the Sine of Incidence
   311  out of Glass into Air must on the contrary be to the Sine of Refraction
   312  as 11 to 17, by the third Axiom.
   314  [Illustration: FIG. 2.]
   316  Much after the same manner, if ACBD [in _Fig._ 3.] represent a Glass
   317  spherically convex on both sides (usually called a _Lens_, such as is a
   318  Burning-glass, or Spectacle-glass, or an Object-glass of a Telescope)
   319  and it be required to know how Light falling upon it from any lucid
   320  point Q shall be refracted, let QM represent a Ray falling upon any
   321  point M of its first spherical Surface ACB, and by erecting a
   322  Perpendicular to the Glass at the point M, find the first refracted Ray
   323  MN by the Proportion of the Sines 17 to 11. Let that Ray in going out of
   324  the Glass be incident upon N, and then find the second refracted Ray
   325  N_q_ by the Proportion of the Sines 11 to 17. And after the same manner
   326  may the Refraction be found when the Lens is convex on one side and
   327  plane or concave on the other, or concave on both sides.
   329  [Illustration: FIG. 3.]
   332  AX. VI.
   334  _Homogeneal Rays which flow from several Points of any Object, and fall
   335  perpendicularly or almost perpendicularly on any reflecting or
   336  refracting Plane or spherical Surface, shall afterwards diverge from so
   337  many other Points, or be parallel to so many other Lines, or converge to
   338  so many other Points, either accurately or without any sensible Error.
   339  And the same thing will happen, if the Rays be reflected or refracted
   340  successively by two or three or more Plane or Spherical Surfaces._
   342  The Point from which Rays diverge or to which they converge may be
   343  called their _Focus_. And the Focus of the incident Rays being given,
   344  that of the reflected or refracted ones may be found by finding the
   345  Refraction of any two Rays, as above; or more readily thus.
   347  _Cas._ 1. Let ACB [in _Fig._ 4.] be a reflecting or refracting Plane,
   348  and Q the Focus of the incident Rays, and Q_q_C a Perpendicular to that
   349  Plane. And if this Perpendicular be produced to _q_, so that _q_C be
   350  equal to QC, the Point _q_ shall be the Focus of the reflected Rays: Or
   351  if _q_C be taken on the same side of the Plane with QC, and in
   352  proportion to QC as the Sine of Incidence to the Sine of Refraction, the
   353  Point _q_ shall be the Focus of the refracted Rays.
   355  [Illustration: FIG. 4.]
   357  _Cas._ 2. Let ACB [in _Fig._ 5.] be the reflecting Surface of any Sphere
   358  whose Centre is E. Bisect any Radius thereof, (suppose EC) in T, and if
   359  in that Radius on the same side the Point T you take the Points Q and
   360  _q_, so that TQ, TE, and T_q_, be continual Proportionals, and the Point
   361  Q be the Focus of the incident Rays, the Point _q_ shall be the Focus of
   362  the reflected ones.
   364  [Illustration: FIG. 5.]
   366  _Cas._ 3. Let ACB [in _Fig._ 6.] be the refracting Surface of any Sphere
   367  whose Centre is E. In any Radius thereof EC produced both ways take ET
   368  and C_t_ equal to one another and severally in such Proportion to that
   369  Radius as the lesser of the Sines of Incidence and Refraction hath to
   370  the difference of those Sines. And then if in the same Line you find any
   371  two Points Q and _q_, so that TQ be to ET as E_t_ to _tq_, taking _tq_
   372  the contrary way from _t_ which TQ lieth from T, and if the Point Q be
   373  the Focus of any incident Rays, the Point _q_ shall be the Focus of the
   374  refracted ones.
   376  [Illustration: FIG. 6.]
   378  And by the same means the Focus of the Rays after two or more Reflexions
   379  or Refractions may be found.
   381  [Illustration: FIG. 7.]
   383  _Cas._ 4. Let ACBD [in _Fig._ 7.] be any refracting Lens, spherically
   384  Convex or Concave or Plane on either side, and let CD be its Axis (that
   385  is, the Line which cuts both its Surfaces perpendicularly, and passes
   386  through the Centres of the Spheres,) and in this Axis produced let F and
   387  _f_ be the Foci of the refracted Rays found as above, when the incident
   388  Rays on both sides the Lens are parallel to the same Axis; and upon the
   389  Diameter F_f_ bisected in E, describe a Circle. Suppose now that any
   390  Point Q be the Focus of any incident Rays. Draw QE cutting the said
   391  Circle in T and _t_, and therein take _tq_ in such proportion to _t_E as
   392  _t_E or TE hath to TQ. Let _tq_ lie the contrary way from _t_ which TQ
   393  doth from T, and _q_ shall be the Focus of the refracted Rays without
   394  any sensible Error, provided the Point Q be not so remote from the Axis,
   395  nor the Lens so broad as to make any of the Rays fall too obliquely on
   396  the refracting Surfaces.[A]
   398  And by the like Operations may the reflecting or refracting Surfaces be
   399  found when the two Foci are given, and thereby a Lens be formed, which
   400  shall make the Rays flow towards or from what Place you please.[B]
   402  So then the Meaning of this Axiom is, that if Rays fall upon any Plane
   403  or Spherical Surface or Lens, and before their Incidence flow from or
   404  towards any Point Q, they shall after Reflexion or Refraction flow from
   405  or towards the Point _q_ found by the foregoing Rules. And if the
   406  incident Rays flow from or towards several points Q, the reflected or
   407  refracted Rays shall flow from or towards so many other Points _q_
   408  found by the same Rules. Whether the reflected and refracted Rays flow
   409  from or towards the Point _q_ is easily known by the situation of that
   410  Point. For if that Point be on the same side of the reflecting or
   411  refracting Surface or Lens with the Point Q, and the incident Rays flow
   412  from the Point Q, the reflected flow towards the Point _q_ and the
   413  refracted from it; and if the incident Rays flow towards Q, the
   414  reflected flow from _q_, and the refracted towards it. And the contrary
   415  happens when _q_ is on the other side of the Surface.
   418  AX. VII.
   420  _Wherever the Rays which come from all the Points of any Object meet
   421  again in so many Points after they have been made to converge by
   422  Reflection or Refraction, there they will make a Picture of the Object
   423  upon any white Body on which they fall._
   425  So if PR [in _Fig._ 3.] represent any Object without Doors, and AB be a
   426  Lens placed at a hole in the Window-shut of a dark Chamber, whereby the
   427  Rays that come from any Point Q of that Object are made to converge and
   428  meet again in the Point _q_; and if a Sheet of white Paper be held at
   429  _q_ for the Light there to fall upon it, the Picture of that Object PR
   430  will appear upon the Paper in its proper shape and Colours. For as the
   431  Light which comes from the Point Q goes to the Point _q_, so the Light
   432  which comes from other Points P and R of the Object, will go to so many
   433  other correspondent Points _p_ and _r_ (as is manifest by the sixth
   434  Axiom;) so that every Point of the Object shall illuminate a
   435  correspondent Point of the Picture, and thereby make a Picture like the
   436  Object in Shape and Colour, this only excepted, that the Picture shall
   437  be inverted. And this is the Reason of that vulgar Experiment of casting
   438  the Species of Objects from abroad upon a Wall or Sheet of white Paper
   439  in a dark Room.
   441  In like manner, when a Man views any Object PQR, [in _Fig._ 8.] the
   442  Light which comes from the several Points of the Object is so refracted
   443  by the transparent skins and humours of the Eye, (that is, by the
   444  outward coat EFG, called the _Tunica Cornea_, and by the crystalline
   445  humour AB which is beyond the Pupil _mk_) as to converge and meet again
   446  in so many Points in the bottom of the Eye, and there to paint the
   447  Picture of the Object upon that skin (called the _Tunica Retina_) with
   448  which the bottom of the Eye is covered. For Anatomists, when they have
   449  taken off from the bottom of the Eye that outward and most thick Coat
   450  called the _Dura Mater_, can then see through the thinner Coats, the
   451  Pictures of Objects lively painted thereon. And these Pictures,
   452  propagated by Motion along the Fibres of the Optick Nerves into the
   453  Brain, are the cause of Vision. For accordingly as these Pictures are
   454  perfect or imperfect, the Object is seen perfectly or imperfectly. If
   455  the Eye be tinged with any colour (as in the Disease of the _Jaundice_)
   456  so as to tinge the Pictures in the bottom of the Eye with that Colour,
   457  then all Objects appear tinged with the same Colour. If the Humours of
   458  the Eye by old Age decay, so as by shrinking to make the _Cornea_ and
   459  Coat of the _Crystalline Humour_ grow flatter than before, the Light
   460  will not be refracted enough, and for want of a sufficient Refraction
   461  will not converge to the bottom of the Eye but to some place beyond it,
   462  and by consequence paint in the bottom of the Eye a confused Picture,
   463  and according to the Indistinctness of this Picture the Object will
   464  appear confused. This is the reason of the decay of sight in old Men,
   465  and shews why their Sight is mended by Spectacles. For those Convex
   466  glasses supply the defect of plumpness in the Eye, and by increasing the
   467  Refraction make the Rays converge sooner, so as to convene distinctly at
   468  the bottom of the Eye if the Glass have a due degree of convexity. And
   469  the contrary happens in short-sighted Men whose Eyes are too plump. For
   470  the Refraction being now too great, the Rays converge and convene in the
   471  Eyes before they come at the bottom; and therefore the Picture made in
   472  the bottom and the Vision caused thereby will not be distinct, unless
   473  the Object be brought so near the Eye as that the place where the
   474  converging Rays convene may be removed to the bottom, or that the
   475  plumpness of the Eye be taken off and the Refractions diminished by a
   476  Concave-glass of a due degree of Concavity, or lastly that by Age the
   477  Eye grow flatter till it come to a due Figure: For short-sighted Men see
   478  remote Objects best in Old Age, and therefore they are accounted to have
   479  the most lasting Eyes.
   481  [Illustration: FIG. 8.]
   484  AX. VIII.
   486  _An Object seen by Reflexion or Refraction, appears in that place from
   487  whence the Rays after their last Reflexion or Refraction diverge in
   488  falling on the Spectator's Eye._
   490  [Illustration: FIG. 9.]
   492  If the Object A [in FIG. 9.] be seen by Reflexion of a Looking-glass
   493  _mn_, it shall appear, not in its proper place A, but behind the Glass
   494  at _a_, from whence any Rays AB, AC, AD, which flow from one and the
   495  same Point of the Object, do after their Reflexion made in the Points B,
   496  C, D, diverge in going from the Glass to E, F, G, where they are
   497  incident on the Spectator's Eyes. For these Rays do make the same
   498  Picture in the bottom of the Eyes as if they had come from the Object
   499  really placed at _a_ without the Interposition of the Looking-glass; and
   500  all Vision is made according to the place and shape of that Picture.
   502  In like manner the Object D [in FIG. 2.] seen through a Prism, appears
   503  not in its proper place D, but is thence translated to some other place
   504  _d_ situated in the last refracted Ray FG drawn backward from F to _d_.
   506  [Illustration: FIG. 10.]
   508  And so the Object Q [in FIG. 10.] seen through the Lens AB, appears at
   509  the place _q_ from whence the Rays diverge in passing from the Lens to
   510  the Eye. Now it is to be noted, that the Image of the Object at _q_ is
   511  so much bigger or lesser than the Object it self at Q, as the distance
   512  of the Image at _q_ from the Lens AB is bigger or less than the distance
   513  of the Object at Q from the same Lens. And if the Object be seen through
   514  two or more such Convex or Concave-glasses, every Glass shall make a new
   515  Image, and the Object shall appear in the place of the bigness of the
   516  last Image. Which consideration unfolds the Theory of Microscopes and
   517  Telescopes. For that Theory consists in almost nothing else than the
   518  describing such Glasses as shall make the last Image of any Object as
   519  distinct and large and luminous as it can conveniently be made.
   521  I have now given in Axioms and their Explications the sum of what hath
   522  hitherto been treated of in Opticks. For what hath been generally
   523  agreed on I content my self to assume under the notion of Principles, in
   524  order to what I have farther to write. And this may suffice for an
   525  Introduction to Readers of quick Wit and good Understanding not yet
   526  versed in Opticks: Although those who are already acquainted with this
   527  Science, and have handled Glasses, will more readily apprehend what
   528  followeth.
   530  FOOTNOTES:
   532  [A] In our Author's _Lectiones Opticæ_, Part I. Sect. IV. Prop 29, 30,
   533  there is an elegant Method of determining these _Foci_; not only in
   534  spherical Surfaces, but likewise in any other curved Figure whatever:
   535  And in Prop. 32, 33, the same thing is done for any Ray lying out of the
   536  Axis.
   538  [B] _Ibid._ Prop. 34.
   547  _PROP._ I. THEOR. I.
   549  _Lights which differ in Colour, differ also in Degrees of
   550  Refrangibility._
   552  The PROOF by Experiments.
   554  _Exper._ 1.
   556  I took a black oblong stiff Paper terminated by Parallel Sides, and with
   557  a Perpendicular right Line drawn cross from one Side to the other,
   558  distinguished it into two equal Parts. One of these parts I painted with
   559  a red colour and the other with a blue. The Paper was very black, and
   560  the Colours intense and thickly laid on, that the Phænomenon might be
   561  more conspicuous. This Paper I view'd through a Prism of solid Glass,
   562  whose two Sides through which the Light passed to the Eye were plane and
   563  well polished, and contained an Angle of about sixty degrees; which
   564  Angle I call the refracting Angle of the Prism. And whilst I view'd it,
   565  I held it and the Prism before a Window in such manner that the Sides of
   566  the Paper were parallel to the Prism, and both those Sides and the Prism
   567  were parallel to the Horizon, and the cross Line was also parallel to
   568  it: and that the Light which fell from the Window upon the Paper made an
   569  Angle with the Paper, equal to that Angle which was made with the same
   570  Paper by the Light reflected from it to the Eye. Beyond the Prism was
   571  the Wall of the Chamber under the Window covered over with black Cloth,
   572  and the Cloth was involved in Darkness that no Light might be reflected
   573  from thence, which in passing by the Edges of the Paper to the Eye,
   574  might mingle itself with the Light of the Paper, and obscure the
   575  Phænomenon thereof. These things being thus ordered, I found that if the
   576  refracting Angle of the Prism be turned upwards, so that the Paper may
   577  seem to be lifted upwards by the Refraction, its blue half will be
   578  lifted higher by the Refraction than its red half. But if the refracting
   579  Angle of the Prism be turned downward, so that the Paper may seem to be
   580  carried lower by the Refraction, its blue half will be carried something
   581  lower thereby than its red half. Wherefore in both Cases the Light which
   582  comes from the blue half of the Paper through the Prism to the Eye, does
   583  in like Circumstances suffer a greater Refraction than the Light which
   584  comes from the red half, and by consequence is more refrangible.
   586  _Illustration._ In the eleventh Figure, MN represents the Window, and DE
   587  the Paper terminated with parallel Sides DJ and HE, and by the
   588  transverse Line FG distinguished into two halfs, the one DG of an
   589  intensely blue Colour, the other FE of an intensely red. And BAC_cab_
   590  represents the Prism whose refracting Planes AB_ba_ and AC_ca_ meet in
   591  the Edge of the refracting Angle A_a_. This Edge A_a_ being upward, is
   592  parallel both to the Horizon, and to the Parallel-Edges of the Paper DJ
   593  and HE, and the transverse Line FG is perpendicular to the Plane of the
   594  Window. And _de_ represents the Image of the Paper seen by Refraction
   595  upwards in such manner, that the blue half DG is carried higher to _dg_
   596  than the red half FE is to _fe_, and therefore suffers a greater
   597  Refraction. If the Edge of the refracting Angle be turned downward, the
   598  Image of the Paper will be refracted downward; suppose to [Greek: de],
   599  and the blue half will be refracted lower to [Greek: dg] than the red
   600  half is to [Greek: pe].
   602  [Illustration: FIG. 11.]
   604  _Exper._ 2. About the aforesaid Paper, whose two halfs were painted over
   605  with red and blue, and which was stiff like thin Pasteboard, I lapped
   606  several times a slender Thred of very black Silk, in such manner that
   607  the several parts of the Thred might appear upon the Colours like so
   608  many black Lines drawn over them, or like long and slender dark Shadows
   609  cast upon them. I might have drawn black Lines with a Pen, but the
   610  Threds were smaller and better defined. This Paper thus coloured and
   611  lined I set against a Wall perpendicularly to the Horizon, so that one
   612  of the Colours might stand to the Right Hand, and the other to the Left.
   613  Close before the Paper, at the Confine of the Colours below, I placed a
   614  Candle to illuminate the Paper strongly: For the Experiment was tried in
   615  the Night. The Flame of the Candle reached up to the lower edge of the
   616  Paper, or a very little higher. Then at the distance of six Feet, and
   617  one or two Inches from the Paper upon the Floor I erected a Glass Lens
   618  four Inches and a quarter broad, which might collect the Rays coming
   619  from the several Points of the Paper, and make them converge towards so
   620  many other Points at the same distance of six Feet, and one or two
   621  Inches on the other side of the Lens, and so form the Image of the
   622  coloured Paper upon a white Paper placed there, after the same manner
   623  that a Lens at a Hole in a Window casts the Images of Objects abroad
   624  upon a Sheet of white Paper in a dark Room. The aforesaid white Paper,
   625  erected perpendicular to the Horizon, and to the Rays which fell upon it
   626  from the Lens, I moved sometimes towards the Lens, sometimes from it, to
   627  find the Places where the Images of the blue and red Parts of the
   628  coloured Paper appeared most distinct. Those Places I easily knew by the
   629  Images of the black Lines which I had made by winding the Silk about the
   630  Paper. For the Images of those fine and slender Lines (which by reason
   631  of their Blackness were like Shadows on the Colours) were confused and
   632  scarce visible, unless when the Colours on either side of each Line were
   633  terminated most distinctly, Noting therefore, as diligently as I could,
   634  the Places where the Images of the red and blue halfs of the coloured
   635  Paper appeared most distinct, I found that where the red half of the
   636  Paper appeared distinct, the blue half appeared confused, so that the
   637  black Lines drawn upon it could scarce be seen; and on the contrary,
   638  where the blue half appeared most distinct, the red half appeared
   639  confused, so that the black Lines upon it were scarce visible. And
   640  between the two Places where these Images appeared distinct there was
   641  the distance of an Inch and a half; the distance of the white Paper from
   642  the Lens, when the Image of the red half of the coloured Paper appeared
   643  most distinct, being greater by an Inch and an half than the distance of
   644  the same white Paper from the Lens, when the Image of the blue half
   645  appeared most distinct. In like Incidences therefore of the blue and red
   646  upon the Lens, the blue was refracted more by the Lens than the red, so
   647  as to converge sooner by an Inch and a half, and therefore is more
   648  refrangible.
   650  _Illustration._ In the twelfth Figure (p. 27), DE signifies the coloured
   651  Paper, DG the blue half, FE the red half, MN the Lens, HJ the white
   652  Paper in that Place where the red half with its black Lines appeared
   653  distinct, and _hi_ the same Paper in that Place where the blue half
   654  appeared distinct. The Place _hi_ was nearer to the Lens MN than the
   655  Place HJ by an Inch and an half.
   657  _Scholium._ The same Things succeed, notwithstanding that some of the
   658  Circumstances be varied; as in the first Experiment when the Prism and
   659  Paper are any ways inclined to the Horizon, and in both when coloured
   660  Lines are drawn upon very black Paper. But in the Description of these
   661  Experiments, I have set down such Circumstances, by which either the
   662  Phænomenon might be render'd more conspicuous, or a Novice might more
   663  easily try them, or by which I did try them only. The same Thing, I have
   664  often done in the following Experiments: Concerning all which, this one
   665  Admonition may suffice. Now from these Experiments it follows not, that
   666  all the Light of the blue is more refrangible than all the Light of the
   667  red: For both Lights are mixed of Rays differently refrangible, so that
   668  in the red there are some Rays not less refrangible than those of the
   669  blue, and in the blue there are some Rays not more refrangible than
   670  those of the red: But these Rays, in proportion to the whole Light, are
   671  but few, and serve to diminish the Event of the Experiment, but are not
   672  able to destroy it. For, if the red and blue Colours were more dilute
   673  and weak, the distance of the Images would be less than an Inch and a
   674  half; and if they were more intense and full, that distance would be
   675  greater, as will appear hereafter. These Experiments may suffice for the
   676  Colours of Natural Bodies. For in the Colours made by the Refraction of
   677  Prisms, this Proposition will appear by the Experiments which are now to
   678  follow in the next Proposition.
   681  _PROP._ II. THEOR. II.
   683  _The Light of the Sun consists of Rays differently Refrangible._
   685  The PROOF by Experiments.
   687  [Illustration: FIG. 12.]
   689  [Illustration: FIG. 13.]
   691  _Exper._ 3.
   693  In a very dark Chamber, at a round Hole, about one third Part of an Inch
   694  broad, made in the Shut of a Window, I placed a Glass Prism, whereby the
   695  Beam of the Sun's Light, which came in at that Hole, might be refracted
   696  upwards toward the opposite Wall of the Chamber, and there form a
   697  colour'd Image of the Sun. The Axis of the Prism (that is, the Line
   698  passing through the middle of the Prism from one end of it to the other
   699  end parallel to the edge of the Refracting Angle) was in this and the
   700  following Experiments perpendicular to the incident Rays. About this
   701  Axis I turned the Prism slowly, and saw the refracted Light on the Wall,
   702  or coloured Image of the Sun, first to descend, and then to ascend.
   703  Between the Descent and Ascent, when the Image seemed Stationary, I
   704  stopp'd the Prism, and fix'd it in that Posture, that it should be moved
   705  no more. For in that Posture the Refractions of the Light at the two
   706  Sides of the refracting Angle, that is, at the Entrance of the Rays into
   707  the Prism, and at their going out of it, were equal to one another.[C]
   708  So also in other Experiments, as often as I would have the Refractions
   709  on both sides the Prism to be equal to one another, I noted the Place
   710  where the Image of the Sun formed by the refracted Light stood still
   711  between its two contrary Motions, in the common Period of its Progress
   712  and Regress; and when the Image fell upon that Place, I made fast the
   713  Prism. And in this Posture, as the most convenient, it is to be
   714  understood that all the Prisms are placed in the following Experiments,
   715  unless where some other Posture is described. The Prism therefore being
   716  placed in this Posture, I let the refracted Light fall perpendicularly
   717  upon a Sheet of white Paper at the opposite Wall of the Chamber, and
   718  observed the Figure and Dimensions of the Solar Image formed on the
   719  Paper by that Light. This Image was Oblong and not Oval, but terminated
   720  with two Rectilinear and Parallel Sides, and two Semicircular Ends. On
   721  its Sides it was bounded pretty distinctly, but on its Ends very
   722  confusedly and indistinctly, the Light there decaying and vanishing by
   723  degrees. The Breadth of this Image answered to the Sun's Diameter, and
   724  was about two Inches and the eighth Part of an Inch, including the
   725  Penumbra. For the Image was eighteen Feet and an half distant from the
   726  Prism, and at this distance that Breadth, if diminished by the Diameter
   727  of the Hole in the Window-shut, that is by a quarter of an Inch,
   728  subtended an Angle at the Prism of about half a Degree, which is the
   729  Sun's apparent Diameter. But the Length of the Image was about ten
   730  Inches and a quarter, and the Length of the Rectilinear Sides about
   731  eight Inches; and the refracting Angle of the Prism, whereby so great a
   732  Length was made, was 64 degrees. With a less Angle the Length of the
   733  Image was less, the Breadth remaining the same. If the Prism was turned
   734  about its Axis that way which made the Rays emerge more obliquely out of
   735  the second refracting Surface of the Prism, the Image soon became an
   736  Inch or two longer, or more; and if the Prism was turned about the
   737  contrary way, so as to make the Rays fall more obliquely on the first
   738  refracting Surface, the Image soon became an Inch or two shorter. And
   739  therefore in trying this Experiment, I was as curious as I could be in
   740  placing the Prism by the above-mention'd Rule exactly in such a Posture,
   741  that the Refractions of the Rays at their Emergence out of the Prism
   742  might be equal to that at their Incidence on it. This Prism had some
   743  Veins running along within the Glass from one end to the other, which
   744  scattered some of the Sun's Light irregularly, but had no sensible
   745  Effect in increasing the Length of the coloured Spectrum. For I tried
   746  the same Experiment with other Prisms with the same Success. And
   747  particularly with a Prism which seemed free from such Veins, and whose
   748  refracting Angle was 62-1/2 Degrees, I found the Length of the Image
   749  9-3/4 or 10 Inches at the distance of 18-1/2 Feet from the Prism, the
   750  Breadth of the Hole in the Window-shut being 1/4 of an Inch, as before.
   751  And because it is easy to commit a Mistake in placing the Prism in its
   752  due Posture, I repeated the Experiment four or five Times, and always
   753  found the Length of the Image that which is set down above. With another
   754  Prism of clearer Glass and better Polish, which seemed free from Veins,
   755  and whose refracting Angle was 63-1/2 Degrees, the Length of this Image
   756  at the same distance of 18-1/2 Feet was also about 10 Inches, or 10-1/8.
   757  Beyond these Measures for about a 1/4 or 1/3 of an Inch at either end of
   758  the Spectrum the Light of the Clouds seemed to be a little tinged with
   759  red and violet, but so very faintly, that I suspected that Tincture
   760  might either wholly, or in great Measure arise from some Rays of the
   761  Spectrum scattered irregularly by some Inequalities in the Substance and
   762  Polish of the Glass, and therefore I did not include it in these
   763  Measures. Now the different Magnitude of the hole in the Window-shut,
   764  and different thickness of the Prism where the Rays passed through it,
   765  and different inclinations of the Prism to the Horizon, made no sensible
   766  changes in the length of the Image. Neither did the different matter of
   767  the Prisms make any: for in a Vessel made of polished Plates of Glass
   768  cemented together in the shape of a Prism and filled with Water, there
   769  is the like Success of the Experiment according to the quantity of the
   770  Refraction. It is farther to be observed, that the Rays went on in right
   771  Lines from the Prism to the Image, and therefore at their very going out
   772  of the Prism had all that Inclination to one another from which the
   773  length of the Image proceeded, that is, the Inclination of more than two
   774  degrees and an half. And yet according to the Laws of Opticks vulgarly
   775  received, they could not possibly be so much inclined to one another.[D]
   776  For let EG [_Fig._ 13. (p. 27)] represent the Window-shut, F the hole
   777  made therein through which a beam of the Sun's Light was transmitted
   778  into the darkened Chamber, and ABC a Triangular Imaginary Plane whereby
   779  the Prism is feigned to be cut transversely through the middle of the
   780  Light. Or if you please, let ABC represent the Prism it self, looking
   781  directly towards the Spectator's Eye with its nearer end: And let XY be
   782  the Sun, MN the Paper upon which the Solar Image or Spectrum is cast,
   783  and PT the Image it self whose sides towards _v_ and _w_ are Rectilinear
   784  and Parallel, and ends towards P and T Semicircular. YKHP and XLJT are
   785  two Rays, the first of which comes from the lower part of the Sun to the
   786  higher part of the Image, and is refracted in the Prism at K and H, and
   787  the latter comes from the higher part of the Sun to the lower part of
   788  the Image, and is refracted at L and J. Since the Refractions on both
   789  sides the Prism are equal to one another, that is, the Refraction at K
   790  equal to the Refraction at J, and the Refraction at L equal to the
   791  Refraction at H, so that the Refractions of the incident Rays at K and L
   792  taken together, are equal to the Refractions of the emergent Rays at H
   793  and J taken together: it follows by adding equal things to equal things,
   794  that the Refractions at K and H taken together, are equal to the
   795  Refractions at J and L taken together, and therefore the two Rays being
   796  equally refracted, have the same Inclination to one another after
   797  Refraction which they had before; that is, the Inclination of half a
   798  Degree answering to the Sun's Diameter. For so great was the inclination
   799  of the Rays to one another before Refraction. So then, the length of the
   800  Image PT would by the Rules of Vulgar Opticks subtend an Angle of half a
   801  Degree at the Prism, and by Consequence be equal to the breadth _vw_;
   802  and therefore the Image would be round. Thus it would be were the two
   803  Rays XLJT and YKHP, and all the rest which form the Image P_w_T_v_,
   804  alike refrangible. And therefore seeing by Experience it is found that
   805  the Image is not round, but about five times longer than broad, the Rays
   806  which going to the upper end P of the Image suffer the greatest
   807  Refraction, must be more refrangible than those which go to the lower
   808  end T, unless the Inequality of Refraction be casual.
   810  This Image or Spectrum PT was coloured, being red at its least refracted
   811  end T, and violet at its most refracted end P, and yellow green and
   812  blue in the intermediate Spaces. Which agrees with the first
   813  Proposition, that Lights which differ in Colour, do also differ in
   814  Refrangibility. The length of the Image in the foregoing Experiments, I
   815  measured from the faintest and outmost red at one end, to the faintest
   816  and outmost blue at the other end, excepting only a little Penumbra,
   817  whose breadth scarce exceeded a quarter of an Inch, as was said above.
   819  _Exper._ 4. In the Sun's Beam which was propagated into the Room through
   820  the hole in the Window-shut, at the distance of some Feet from the hole,
   821  I held the Prism in such a Posture, that its Axis might be perpendicular
   822  to that Beam. Then I looked through the Prism upon the hole, and turning
   823  the Prism to and fro about its Axis, to make the Image of the Hole
   824  ascend and descend, when between its two contrary Motions it seemed
   825  Stationary, I stopp'd the Prism, that the Refractions of both sides of
   826  the refracting Angle might be equal to each other, as in the former
   827  Experiment. In this situation of the Prism viewing through it the said
   828  Hole, I observed the length of its refracted Image to be many times
   829  greater than its breadth, and that the most refracted part thereof
   830  appeared violet, the least refracted red, the middle parts blue, green
   831  and yellow in order. The same thing happen'd when I removed the Prism
   832  out of the Sun's Light, and looked through it upon the hole shining by
   833  the Light of the Clouds beyond it. And yet if the Refraction were done
   834  regularly according to one certain Proportion of the Sines of Incidence
   835  and Refraction as is vulgarly supposed, the refracted Image ought to
   836  have appeared round.
   838  So then, by these two Experiments it appears, that in Equal Incidences
   839  there is a considerable inequality of Refractions. But whence this
   840  inequality arises, whether it be that some of the incident Rays are
   841  refracted more, and others less, constantly, or by chance, or that one
   842  and the same Ray is by Refraction disturbed, shatter'd, dilated, and as
   843  it were split and spread into many diverging Rays, as _Grimaldo_
   844  supposes, does not yet appear by these Experiments, but will appear by
   845  those that follow.
   847  _Exper._ 5. Considering therefore, that if in the third Experiment the
   848  Image of the Sun should be drawn out into an oblong Form, either by a
   849  Dilatation of every Ray, or by any other casual inequality of the
   850  Refractions, the same oblong Image would by a second Refraction made
   851  sideways be drawn out as much in breadth by the like Dilatation of the
   852  Rays, or other casual inequality of the Refractions sideways, I tried
   853  what would be the Effects of such a second Refraction. For this end I
   854  ordered all things as in the third Experiment, and then placed a second
   855  Prism immediately after the first in a cross Position to it, that it
   856  might again refract the beam of the Sun's Light which came to it through
   857  the first Prism. In the first Prism this beam was refracted upwards, and
   858  in the second sideways. And I found that by the Refraction of the second
   859  Prism, the breadth of the Image was not increased, but its superior
   860  part, which in the first Prism suffered the greater Refraction, and
   861  appeared violet and blue, did again in the second Prism suffer a greater
   862  Refraction than its inferior part, which appeared red and yellow, and
   863  this without any Dilatation of the Image in breadth.
   865  [Illustration: FIG. 14]
   867  _Illustration._ Let S [_Fig._ 14, 15.] represent the Sun, F the hole in
   868  the Window, ABC the first Prism, DH the second Prism, Y the round Image
   869  of the Sun made by a direct beam of Light when the Prisms are taken
   870  away, PT the oblong Image of the Sun made by that beam passing through
   871  the first Prism alone, when the second Prism is taken away, and _pt_ the
   872  Image made by the cross Refractions of both Prisms together. Now if the
   873  Rays which tend towards the several Points of the round Image Y were
   874  dilated and spread by the Refraction of the first Prism, so that they
   875  should not any longer go in single Lines to single Points, but that
   876  every Ray being split, shattered, and changed from a Linear Ray to a
   877  Superficies of Rays diverging from the Point of Refraction, and lying in
   878  the Plane of the Angles of Incidence and Refraction, they should go in
   879  those Planes to so many Lines reaching almost from one end of the Image
   880  PT to the other, and if that Image should thence become oblong: those
   881  Rays and their several parts tending towards the several Points of the
   882  Image PT ought to be again dilated and spread sideways by the transverse
   883  Refraction of the second Prism, so as to compose a four square Image,
   884  such as is represented at [Greek: pt]. For the better understanding of
   885  which, let the Image PT be distinguished into five equal parts PQK,
   886  KQRL, LRSM, MSVN, NVT. And by the same irregularity that the orbicular
   887  Light Y is by the Refraction of the first Prism dilated and drawn out
   888  into a long Image PT, the Light PQK which takes up a space of the same
   889  length and breadth with the Light Y ought to be by the Refraction of the
   890  second Prism dilated and drawn out into the long Image _[Greek: p]qkp_,
   891  and the Light KQRL into the long Image _kqrl_, and the Lights LRSM,
   892  MSVN, NVT, into so many other long Images _lrsm_, _msvn_, _nvt[Greek:
   893  t]_; and all these long Images would compose the four square Images
   894  _[Greek: pt]_. Thus it ought to be were every Ray dilated by Refraction,
   895  and spread into a triangular Superficies of Rays diverging from the
   896  Point of Refraction. For the second Refraction would spread the Rays one
   897  way as much as the first doth another, and so dilate the Image in
   898  breadth as much as the first doth in length. And the same thing ought to
   899  happen, were some rays casually refracted more than others. But the
   900  Event is otherwise. The Image PT was not made broader by the Refraction
   901  of the second Prism, but only became oblique, as 'tis represented at
   902  _pt_, its upper end P being by the Refraction translated to a greater
   903  distance than its lower end T. So then the Light which went towards the
   904  upper end P of the Image, was (at equal Incidences) more refracted in
   905  the second Prism, than the Light which tended towards the lower end T,
   906  that is the blue and violet, than the red and yellow; and therefore was
   907  more refrangible. The same Light was by the Refraction of the first
   908  Prism translated farther from the place Y to which it tended before
   909  Refraction; and therefore suffered as well in the first Prism as in the
   910  second a greater Refraction than the rest of the Light, and by
   911  consequence was more refrangible than the rest, even before its
   912  incidence on the first Prism.
   914  Sometimes I placed a third Prism after the second, and sometimes also a
   915  fourth after the third, by all which the Image might be often refracted
   916  sideways: but the Rays which were more refracted than the rest in the
   917  first Prism were also more refracted in all the rest, and that without
   918  any Dilatation of the Image sideways: and therefore those Rays for their
   919  constancy of a greater Refraction are deservedly reputed more
   920  refrangible.
   922  [Illustration: FIG. 15]
   924  But that the meaning of this Experiment may more clearly appear, it is
   925  to be considered that the Rays which are equally refrangible do fall
   926  upon a Circle answering to the Sun's Disque. For this was proved in the
   927  third Experiment. By a Circle I understand not here a perfect
   928  geometrical Circle, but any orbicular Figure whose length is equal to
   929  its breadth, and which, as to Sense, may seem circular. Let therefore AG
   930  [in _Fig._ 15.] represent the Circle which all the most refrangible Rays
   931  propagated from the whole Disque of the Sun, would illuminate and paint
   932  upon the opposite Wall if they were alone; EL the Circle which all the
   933  least refrangible Rays would in like manner illuminate and paint if they
   934  were alone; BH, CJ, DK, the Circles which so many intermediate sorts of
   935  Rays would successively paint upon the Wall, if they were singly
   936  propagated from the Sun in successive order, the rest being always
   937  intercepted; and conceive that there are other intermediate Circles
   938  without Number, which innumerable other intermediate sorts of Rays would
   939  successively paint upon the Wall if the Sun should successively emit
   940  every sort apart. And seeing the Sun emits all these sorts at once, they
   941  must all together illuminate and paint innumerable equal Circles, of all
   942  which, being according to their degrees of Refrangibility placed in
   943  order in a continual Series, that oblong Spectrum PT is composed which I
   944  described in the third Experiment. Now if the Sun's circular Image Y [in
   945  _Fig._ 15.] which is made by an unrefracted beam of Light was by any
   946  Dilation of the single Rays, or by any other irregularity in the
   947  Refraction of the first Prism, converted into the oblong Spectrum, PT:
   948  then ought every Circle AG, BH, CJ, &c. in that Spectrum, by the cross
   949  Refraction of the second Prism again dilating or otherwise scattering
   950  the Rays as before, to be in like manner drawn out and transformed into
   951  an oblong Figure, and thereby the breadth of the Image PT would be now
   952  as much augmented as the length of the Image Y was before by the
   953  Refraction of the first Prism; and thus by the Refractions of both
   954  Prisms together would be formed a four square Figure _p[Greek:
   955  p]t[Greek: t]_, as I described above. Wherefore since the breadth of the
   956  Spectrum PT is not increased by the Refraction sideways, it is certain
   957  that the Rays are not split or dilated, or otherways irregularly
   958  scatter'd by that Refraction, but that every Circle is by a regular and
   959  uniform Refraction translated entire into another Place, as the Circle
   960  AG by the greatest Refraction into the place _ag_, the Circle BH by a
   961  less Refraction into the place _bh_, the Circle CJ by a Refraction still
   962  less into the place _ci_, and so of the rest; by which means a new
   963  Spectrum _pt_ inclined to the former PT is in like manner composed of
   964  Circles lying in a right Line; and these Circles must be of the same
   965  bigness with the former, because the breadths of all the Spectrums Y, PT
   966  and _pt_ at equal distances from the Prisms are equal.
   968  I considered farther, that by the breadth of the hole F through which
   969  the Light enters into the dark Chamber, there is a Penumbra made in the
   970  Circuit of the Spectrum Y, and that Penumbra remains in the rectilinear
   971  Sides of the Spectrums PT and _pt_. I placed therefore at that hole a
   972  Lens or Object-glass of a Telescope which might cast the Image of the
   973  Sun distinctly on Y without any Penumbra at all, and found that the
   974  Penumbra of the rectilinear Sides of the oblong Spectrums PT and _pt_
   975  was also thereby taken away, so that those Sides appeared as distinctly
   976  defined as did the Circumference of the first Image Y. Thus it happens
   977  if the Glass of the Prisms be free from Veins, and their sides be
   978  accurately plane and well polished without those numberless Waves or
   979  Curles which usually arise from Sand-holes a little smoothed in
   980  polishing with Putty. If the Glass be only well polished and free from
   981  Veins, and the Sides not accurately plane, but a little Convex or
   982  Concave, as it frequently happens; yet may the three Spectrums Y, PT and
   983  _pt_ want Penumbras, but not in equal distances from the Prisms. Now
   984  from this want of Penumbras, I knew more certainly that every one of the
   985  Circles was refracted according to some most regular, uniform and
   986  constant Law. For if there were any irregularity in the Refraction, the
   987  right Lines AE and GL, which all the Circles in the Spectrum PT do
   988  touch, could not by that Refraction be translated into the Lines _ae_
   989  and _gl_ as distinct and straight as they were before, but there would
   990  arise in those translated Lines some Penumbra or Crookedness or
   991  Undulation, or other sensible Perturbation contrary to what is found by
   992  Experience. Whatsoever Penumbra or Perturbation should be made in the
   993  Circles by the cross Refraction of the second Prism, all that Penumbra
   994  or Perturbation would be conspicuous in the right Lines _ae_ and _gl_
   995  which touch those Circles. And therefore since there is no such Penumbra
   996  or Perturbation in those right Lines, there must be none in the
   997  Circles. Since the distance between those Tangents or breadth of the
   998  Spectrum is not increased by the Refractions, the Diameters of the
   999  Circles are not increased thereby. Since those Tangents continue to be
  1000  right Lines, every Circle which in the first Prism is more or less
  1001  refracted, is exactly in the same proportion more or less refracted in
  1002  the second. And seeing all these things continue to succeed after the
  1003  same manner when the Rays are again in a third Prism, and again in a
  1004  fourth refracted sideways, it is evident that the Rays of one and the
  1005  same Circle, as to their degree of Refrangibility, continue always
  1006  uniform and homogeneal to one another, and that those of several Circles
  1007  do differ in degree of Refrangibility, and that in some certain and
  1008  constant Proportion. Which is the thing I was to prove.
  1010  There is yet another Circumstance or two of this Experiment by which it
  1011  becomes still more plain and convincing. Let the second Prism DH [in
  1012  _Fig._ 16.] be placed not immediately after the first, but at some
  1013  distance from it; suppose in the mid-way between it and the Wall on
  1014  which the oblong Spectrum PT is cast, so that the Light from the first
  1015  Prism may fall upon it in the form of an oblong Spectrum [Greek: pt]
  1016  parallel to this second Prism, and be refracted sideways to form the
  1017  oblong Spectrum _pt_ upon the Wall. And you will find as before, that
  1018  this Spectrum _pt_ is inclined to that Spectrum PT, which the first
  1019  Prism forms alone without the second; the blue ends P and _p_ being
  1020  farther distant from one another than the red ones T and _t_, and by
  1021  consequence that the Rays which go to the blue end [Greek: p] of the
  1022  Image [Greek: pt], and which therefore suffer the greatest Refraction in
  1023  the first Prism, are again in the second Prism more refracted than the
  1024  rest.
  1026  [Illustration: FIG. 16.]
  1028  [Illustration: FIG. 17.]
  1030  The same thing I try'd also by letting the Sun's Light into a dark Room
  1031  through two little round holes F and [Greek: ph] [in _Fig._ 17.] made in
  1032  the Window, and with two parallel Prisms ABC and [Greek: abg] placed at
  1033  those holes (one at each) refracting those two beams of Light to the
  1034  opposite Wall of the Chamber, in such manner that the two colour'd
  1035  Images PT and MN which they there painted were joined end to end and lay
  1036  in one straight Line, the red end T of the one touching the blue end M
  1037  of the other. For if these two refracted Beams were again by a third
  1038  Prism DH placed cross to the two first, refracted sideways, and the
  1039  Spectrums thereby translated to some other part of the Wall of the
  1040  Chamber, suppose the Spectrum PT to _pt_ and the Spectrum MN to _mn_,
  1041  these translated Spectrums _pt_ and _mn_ would not lie in one straight
  1042  Line with their ends contiguous as before, but be broken off from one
  1043  another and become parallel, the blue end _m_ of the Image _mn_ being by
  1044  a greater Refraction translated farther from its former place MT, than
  1045  the red end _t_ of the other Image _pt_ from the same place MT; which
  1046  puts the Proposition past Dispute. And this happens whether the third
  1047  Prism DH be placed immediately after the two first, or at a great
  1048  distance from them, so that the Light refracted in the two first Prisms
  1049  be either white and circular, or coloured and oblong when it falls on
  1050  the third.
  1052  _Exper._ 6. In the middle of two thin Boards I made round holes a third
  1053  part of an Inch in diameter, and in the Window-shut a much broader hole
  1054  being made to let into my darkned Chamber a large Beam of the Sun's
  1055  Light; I placed a Prism behind the Shut in that beam to refract it
  1056  towards the opposite Wall, and close behind the Prism I fixed one of the
  1057  Boards, in such manner that the middle of the refracted Light might pass
  1058  through the hole made in it, and the rest be intercepted by the Board.
  1059  Then at the distance of about twelve Feet from the first Board I fixed
  1060  the other Board in such manner that the middle of the refracted Light
  1061  which came through the hole in the first Board, and fell upon the
  1062  opposite Wall, might pass through the hole in this other Board, and the
  1063  rest being intercepted by the Board might paint upon it the coloured
  1064  Spectrum of the Sun. And close behind this Board I fixed another Prism
  1065  to refract the Light which came through the hole. Then I returned
  1066  speedily to the first Prism, and by turning it slowly to and fro about
  1067  its Axis, I caused the Image which fell upon the second Board to move up
  1068  and down upon that Board, that all its parts might successively pass
  1069  through the hole in that Board and fall upon the Prism behind it. And in
  1070  the mean time, I noted the places on the opposite Wall to which that
  1071  Light after its Refraction in the second Prism did pass; and by the
  1072  difference of the places I found that the Light which being most
  1073  refracted in the first Prism did go to the blue end of the Image, was
  1074  again more refracted in the second Prism than the Light which went to
  1075  the red end of that Image, which proves as well the first Proposition as
  1076  the second. And this happened whether the Axis of the two Prisms were
  1077  parallel, or inclined to one another, and to the Horizon in any given
  1078  Angles.
  1080  _Illustration._ Let F [in _Fig._ 18.] be the wide hole in the
  1081  Window-shut, through which the Sun shines upon the first Prism ABC, and
  1082  let the refracted Light fall upon the middle of the Board DE, and the
  1083  middle part of that Light upon the hole G made in the middle part of
  1084  that Board. Let this trajected part of that Light fall again upon the
  1085  middle of the second Board _de_, and there paint such an oblong coloured
  1086  Image of the Sun as was described in the third Experiment. By turning
  1087  the Prism ABC slowly to and fro about its Axis, this Image will be made
  1088  to move up and down the Board _de_, and by this means all its parts from
  1089  one end to the other may be made to pass successively through the hole
  1090  _g_ which is made in the middle of that Board. In the mean while another
  1091  Prism _abc_ is to be fixed next after that hole _g_, to refract the
  1092  trajected Light a second time. And these things being thus ordered, I
  1093  marked the places M and N of the opposite Wall upon which the refracted
  1094  Light fell, and found that whilst the two Boards and second Prism
  1095  remained unmoved, those places by turning the first Prism about its Axis
  1096  were changed perpetually. For when the lower part of the Light which
  1097  fell upon the second Board _de_ was cast through the hole _g_, it went
  1098  to a lower place M on the Wall and when the higher part of that Light
  1099  was cast through the same hole _g_, it went to a higher place N on the
  1100  Wall, and when any intermediate part of the Light was cast through that
  1101  hole, it went to some place on the Wall between M and N. The unchanged
  1102  Position of the holes in the Boards, made the Incidence of the Rays upon
  1103  the second Prism to be the same in all cases. And yet in that common
  1104  Incidence some of the Rays were more refracted, and others less. And
  1105  those were more refracted in this Prism, which by a greater Refraction
  1106  in the first Prism were more turned out of the way, and therefore for
  1107  their Constancy of being more refracted are deservedly called more
  1108  refrangible.
  1110  [Illustration: FIG. 18.]
  1112  [Illustration: FIG. 20.]
  1114  _Exper._ 7. At two holes made near one another in my Window-shut I
  1115  placed two Prisms, one at each, which might cast upon the opposite Wall
  1116  (after the manner of the third Experiment) two oblong coloured Images of
  1117  the Sun. And at a little distance from the Wall I placed a long slender
  1118  Paper with straight and parallel edges, and ordered the Prisms and Paper
  1119  so, that the red Colour of one Image might fall directly upon one half
  1120  of the Paper, and the violet Colour of the other Image upon the other
  1121  half of the same Paper; so that the Paper appeared of two Colours, red
  1122  and violet, much after the manner of the painted Paper in the first and
  1123  second Experiments. Then with a black Cloth I covered the Wall behind
  1124  the Paper, that no Light might be reflected from it to disturb the
  1125  Experiment, and viewing the Paper through a third Prism held parallel
  1126  to it, I saw that half of it which was illuminated by the violet Light
  1127  to be divided from the other half by a greater Refraction, especially
  1128  when I went a good way off from the Paper. For when I viewed it too near
  1129  at hand, the two halfs of the Paper did not appear fully divided from
  1130  one another, but seemed contiguous at one of their Angles like the
  1131  painted Paper in the first Experiment. Which also happened when the
  1132  Paper was too broad.
  1134  [Illustration: FIG. 19.]
  1136  Sometimes instead of the Paper I used a white Thred, and this appeared
  1137  through the Prism divided into two parallel Threds as is represented in
  1138  the nineteenth Figure, where DG denotes the Thred illuminated with
  1139  violet Light from D to E and with red Light from F to G, and _defg_ are
  1140  the parts of the Thred seen by Refraction. If one half of the Thred be
  1141  constantly illuminated with red, and the other half be illuminated with
  1142  all the Colours successively, (which may be done by causing one of the
  1143  Prisms to be turned about its Axis whilst the other remains unmoved)
  1144  this other half in viewing the Thred through the Prism, will appear in
  1145  a continual right Line with the first half when illuminated with red,
  1146  and begin to be a little divided from it when illuminated with Orange,
  1147  and remove farther from it when illuminated with yellow, and still
  1148  farther when with green, and farther when with blue, and go yet farther
  1149  off when illuminated with Indigo, and farthest when with deep violet.
  1150  Which plainly shews, that the Lights of several Colours are more and
  1151  more refrangible one than another, in this Order of their Colours, red,
  1152  orange, yellow, green, blue, indigo, deep violet; and so proves as well
  1153  the first Proposition as the second.
  1155  I caused also the coloured Spectrums PT [in _Fig._ 17.] and MN made in a
  1156  dark Chamber by the Refractions of two Prisms to lie in a Right Line end
  1157  to end, as was described above in the fifth Experiment, and viewing them
  1158  through a third Prism held parallel to their Length, they appeared no
  1159  longer in a Right Line, but became broken from one another, as they are
  1160  represented at _pt_ and _mn_, the violet end _m_ of the Spectrum _mn_
  1161  being by a greater Refraction translated farther from its former Place
  1162  MT than the red end _t_ of the other Spectrum _pt_.
  1164  I farther caused those two Spectrums PT [in _Fig._ 20.] and MN to become
  1165  co-incident in an inverted Order of their Colours, the red end of each
  1166  falling on the violet end of the other, as they are represented in the
  1167  oblong Figure PTMN; and then viewing them through a Prism DH held
  1168  parallel to their Length, they appeared not co-incident, as when view'd
  1169  with the naked Eye, but in the form of two distinct Spectrums _pt_ and
  1170  _mn_ crossing one another in the middle after the manner of the Letter
  1171  X. Which shews that the red of the one Spectrum and violet of the other,
  1172  which were co-incident at PN and MT, being parted from one another by a
  1173  greater Refraction of the violet to _p_ and _m_ than of the red to _n_
  1174  and _t_, do differ in degrees of Refrangibility.
  1176  I illuminated also a little Circular Piece of white Paper all over with
  1177  the Lights of both Prisms intermixed, and when it was illuminated with
  1178  the red of one Spectrum, and deep violet of the other, so as by the
  1179  Mixture of those Colours to appear all over purple, I viewed the Paper,
  1180  first at a less distance, and then at a greater, through a third Prism;
  1181  and as I went from the Paper, the refracted Image thereof became more
  1182  and more divided by the unequal Refraction of the two mixed Colours, and
  1183  at length parted into two distinct Images, a red one and a violet one,
  1184  whereof the violet was farthest from the Paper, and therefore suffered
  1185  the greatest Refraction. And when that Prism at the Window, which cast
  1186  the violet on the Paper was taken away, the violet Image disappeared;
  1187  but when the other Prism was taken away the red vanished; which shews,
  1188  that these two Images were nothing else than the Lights of the two
  1189  Prisms, which had been intermixed on the purple Paper, but were parted
  1190  again by their unequal Refractions made in the third Prism, through
  1191  which the Paper was view'd. This also was observable, that if one of the
  1192  Prisms at the Window, suppose that which cast the violet on the Paper,
  1193  was turned about its Axis to make all the Colours in this order,
  1194  violet, indigo, blue, green, yellow, orange, red, fall successively on
  1195  the Paper from that Prism, the violet Image changed Colour accordingly,
  1196  turning successively to indigo, blue, green, yellow and red, and in
  1197  changing Colour came nearer and nearer to the red Image made by the
  1198  other Prism, until when it was also red both Images became fully
  1199  co-incident.
  1201  I placed also two Paper Circles very near one another, the one in the
  1202  red Light of one Prism, and the other in the violet Light of the other.
  1203  The Circles were each of them an Inch in diameter, and behind them the
  1204  Wall was dark, that the Experiment might not be disturbed by any Light
  1205  coming from thence. These Circles thus illuminated, I viewed through a
  1206  Prism, so held, that the Refraction might be made towards the red
  1207  Circle, and as I went from them they came nearer and nearer together,
  1208  and at length became co-incident; and afterwards when I went still
  1209  farther off, they parted again in a contrary Order, the violet by a
  1210  greater Refraction being carried beyond the red.
  1212  _Exper._ 8. In Summer, when the Sun's Light uses to be strongest, I
  1213  placed a Prism at the Hole of the Window-shut, as in the third
  1214  Experiment, yet so that its Axis might be parallel to the Axis of the
  1215  World, and at the opposite Wall in the Sun's refracted Light, I placed
  1216  an open Book. Then going six Feet and two Inches from the Book, I placed
  1217  there the above-mentioned Lens, by which the Light reflected from the
  1218  Book might be made to converge and meet again at the distance of six
  1219  Feet and two Inches behind the Lens, and there paint the Species of the
  1220  Book upon a Sheet of white Paper much after the manner of the second
  1221  Experiment. The Book and Lens being made fast, I noted the Place where
  1222  the Paper was, when the Letters of the Book, illuminated by the fullest
  1223  red Light of the Solar Image falling upon it, did cast their Species on
  1224  that Paper most distinctly: And then I stay'd till by the Motion of the
  1225  Sun, and consequent Motion of his Image on the Book, all the Colours
  1226  from that red to the middle of the blue pass'd over those Letters; and
  1227  when those Letters were illuminated by that blue, I noted again the
  1228  Place of the Paper when they cast their Species most distinctly upon it:
  1229  And I found that this last Place of the Paper was nearer to the Lens
  1230  than its former Place by about two Inches and an half, or two and three
  1231  quarters. So much sooner therefore did the Light in the violet end of
  1232  the Image by a greater Refraction converge and meet, than the Light in
  1233  the red end. But in trying this, the Chamber was as dark as I could make
  1234  it. For, if these Colours be diluted and weakned by the Mixture of any
  1235  adventitious Light, the distance between the Places of the Paper will
  1236  not be so great. This distance in the second Experiment, where the
  1237  Colours of natural Bodies were made use of, was but an Inch and an half,
  1238  by reason of the Imperfection of those Colours. Here in the Colours of
  1239  the Prism, which are manifestly more full, intense, and lively than
  1240  those of natural Bodies, the distance is two Inches and three quarters.
  1241  And were the Colours still more full, I question not but that the
  1242  distance would be considerably greater. For the coloured Light of the
  1243  Prism, by the interfering of the Circles described in the second Figure
  1244  of the fifth Experiment, and also by the Light of the very bright Clouds
  1245  next the Sun's Body intermixing with these Colours, and by the Light
  1246  scattered by the Inequalities in the Polish of the Prism, was so very
  1247  much compounded, that the Species which those faint and dark Colours,
  1248  the indigo and violet, cast upon the Paper were not distinct enough to
  1249  be well observed.
  1251  _Exper._ 9. A Prism, whose two Angles at its Base were equal to one
  1252  another, and half right ones, and the third a right one, I placed in a
  1253  Beam of the Sun's Light let into a dark Chamber through a Hole in the
  1254  Window-shut, as in the third Experiment. And turning the Prism slowly
  1255  about its Axis, until all the Light which went through one of its
  1256  Angles, and was refracted by it began to be reflected by its Base, at
  1257  which till then it went out of the Glass, I observed that those Rays
  1258  which had suffered the greatest Refraction were sooner reflected than
  1259  the rest. I conceived therefore, that those Rays of the reflected Light,
  1260  which were most refrangible, did first of all by a total Reflexion
  1261  become more copious in that Light than the rest, and that afterwards the
  1262  rest also, by a total Reflexion, became as copious as these. To try
  1263  this, I made the reflected Light pass through another Prism, and being
  1264  refracted by it to fall afterwards upon a Sheet of white Paper placed
  1265  at some distance behind it, and there by that Refraction to paint the
  1266  usual Colours of the Prism. And then causing the first Prism to be
  1267  turned about its Axis as above, I observed that when those Rays, which
  1268  in this Prism had suffered the greatest Refraction, and appeared of a
  1269  blue and violet Colour began to be totally reflected, the blue and
  1270  violet Light on the Paper, which was most refracted in the second Prism,
  1271  received a sensible Increase above that of the red and yellow, which was
  1272  least refracted; and afterwards, when the rest of the Light which was
  1273  green, yellow, and red, began to be totally reflected in the first
  1274  Prism, the Light of those Colours on the Paper received as great an
  1275  Increase as the violet and blue had done before. Whence 'tis manifest,
  1276  that the Beam of Light reflected by the Base of the Prism, being
  1277  augmented first by the more refrangible Rays, and afterwards by the less
  1278  refrangible ones, is compounded of Rays differently refrangible. And
  1279  that all such reflected Light is of the same Nature with the Sun's Light
  1280  before its Incidence on the Base of the Prism, no Man ever doubted; it
  1281  being generally allowed, that Light by such Reflexions suffers no
  1282  Alteration in its Modifications and Properties. I do not here take
  1283  Notice of any Refractions made in the sides of the first Prism, because
  1284  the Light enters it perpendicularly at the first side, and goes out
  1285  perpendicularly at the second side, and therefore suffers none. So then,
  1286  the Sun's incident Light being of the same Temper and Constitution with
  1287  his emergent Light, and the last being compounded of Rays differently
  1288  refrangible, the first must be in like manner compounded.
  1290  [Illustration: FIG. 21.]
  1292  _Illustration._ In the twenty-first Figure, ABC is the first Prism, BC
  1293  its Base, B and C its equal Angles at the Base, each of 45 Degrees, A
  1294  its rectangular Vertex, FM a beam of the Sun's Light let into a dark
  1295  Room through a hole F one third part of an Inch broad, M its Incidence
  1296  on the Base of the Prism, MG a less refracted Ray, MH a more refracted
  1297  Ray, MN the beam of Light reflected from the Base, VXY the second Prism
  1298  by which this beam in passing through it is refracted, N_t_ the less
  1299  refracted Light of this beam, and N_p_ the more refracted part thereof.
  1300  When the first Prism ABC is turned about its Axis according to the order
  1301  of the Letters ABC, the Rays MH emerge more and more obliquely out of
  1302  that Prism, and at length after their most oblique Emergence are
  1303  reflected towards N, and going on to _p_ do increase the Number of the
  1304  Rays N_p_. Afterwards by continuing the Motion of the first Prism, the
  1305  Rays MG are also reflected to N and increase the number of the Rays
  1306  N_t_. And therefore the Light MN admits into its Composition, first the
  1307  more refrangible Rays, and then the less refrangible Rays, and yet after
  1308  this Composition is of the same Nature with the Sun's immediate Light
  1309  FM, the Reflexion of the specular Base BC causing no Alteration therein.
  1311  _Exper._ 10. Two Prisms, which were alike in Shape, I tied so together,
  1312  that their Axis and opposite Sides being parallel, they composed a
  1313  Parallelopiped. And, the Sun shining into my dark Chamber through a
  1314  little hole in the Window-shut, I placed that Parallelopiped in his beam
  1315  at some distance from the hole, in such a Posture, that the Axes of the
  1316  Prisms might be perpendicular to the incident Rays, and that those Rays
  1317  being incident upon the first Side of one Prism, might go on through the
  1318  two contiguous Sides of both Prisms, and emerge out of the last Side of
  1319  the second Prism. This Side being parallel to the first Side of the
  1320  first Prism, caused the emerging Light to be parallel to the incident.
  1321  Then, beyond these two Prisms I placed a third, which might refract that
  1322  emergent Light, and by that Refraction cast the usual Colours of the
  1323  Prism upon the opposite Wall, or upon a sheet of white Paper held at a
  1324  convenient Distance behind the Prism for that refracted Light to fall
  1325  upon it. After this I turned the Parallelopiped about its Axis, and
  1326  found that when the contiguous Sides of the two Prisms became so oblique
  1327  to the incident Rays, that those Rays began all of them to be
  1328  reflected, those Rays which in the third Prism had suffered the greatest
  1329  Refraction, and painted the Paper with violet and blue, were first of
  1330  all by a total Reflexion taken out of the transmitted Light, the rest
  1331  remaining and on the Paper painting their Colours of green, yellow,
  1332  orange and red, as before; and afterwards by continuing the Motion of
  1333  the two Prisms, the rest of the Rays also by a total Reflexion vanished
  1334  in order, according to their degrees of Refrangibility. The Light
  1335  therefore which emerged out of the two Prisms is compounded of Rays
  1336  differently refrangible, seeing the more refrangible Rays may be taken
  1337  out of it, while the less refrangible remain. But this Light being
  1338  trajected only through the parallel Superficies of the two Prisms, if it
  1339  suffer'd any change by the Refraction of one Superficies it lost that
  1340  Impression by the contrary Refraction of the other Superficies, and so
  1341  being restor'd to its pristine Constitution, became of the same Nature
  1342  and Condition as at first before its Incidence on those Prisms; and
  1343  therefore, before its Incidence, was as much compounded of Rays
  1344  differently refrangible, as afterwards.
  1346  [Illustration: FIG. 22.]
  1348  _Illustration._ In the twenty second Figure ABC and BCD are the two
  1349  Prisms tied together in the form of a Parallelopiped, their Sides BC and
  1350  CB being contiguous, and their Sides AB and CD parallel. And HJK is the
  1351  third Prism, by which the Sun's Light propagated through the hole F into
  1352  the dark Chamber, and there passing through those sides of the Prisms
  1353  AB, BC, CB and CD, is refracted at O to the white Paper PT, falling
  1354  there partly upon P by a greater Refraction, partly upon T by a less
  1355  Refraction, and partly upon R and other intermediate places by
  1356  intermediate Refractions. By turning the Parallelopiped ACBD about its
  1357  Axis, according to the order of the Letters A, C, D, B, at length when
  1358  the contiguous Planes BC and CB become sufficiently oblique to the Rays
  1359  FM, which are incident upon them at M, there will vanish totally out of
  1360  the refracted Light OPT, first of all the most refracted Rays OP, (the
  1361  rest OR and OT remaining as before) then the Rays OR and other
  1362  intermediate ones, and lastly, the least refracted Rays OT. For when
  1363  the Plane BC becomes sufficiently oblique to the Rays incident upon it,
  1364  those Rays will begin to be totally reflected by it towards N; and first
  1365  the most refrangible Rays will be totally reflected (as was explained in
  1366  the preceding Experiment) and by Consequence must first disappear at P,
  1367  and afterwards the rest as they are in order totally reflected to N,
  1368  they must disappear in the same order at R and T. So then the Rays which
  1369  at O suffer the greatest Refraction, may be taken out of the Light MO
  1370  whilst the rest of the Rays remain in it, and therefore that Light MO is
  1371  compounded of Rays differently refrangible. And because the Planes AB
  1372  and CD are parallel, and therefore by equal and contrary Refractions
  1373  destroy one anothers Effects, the incident Light FM must be of the same
  1374  Kind and Nature with the emergent Light MO, and therefore doth also
  1375  consist of Rays differently refrangible. These two Lights FM and MO,
  1376  before the most refrangible Rays are separated out of the emergent Light
  1377  MO, agree in Colour, and in all other Properties so far as my
  1378  Observation reaches, and therefore are deservedly reputed of the same
  1379  Nature and Constitution, and by Consequence the one is compounded as
  1380  well as the other. But after the most refrangible Rays begin to be
  1381  totally reflected, and thereby separated out of the emergent Light MO,
  1382  that Light changes its Colour from white to a dilute and faint yellow, a
  1383  pretty good orange, a very full red successively, and then totally
  1384  vanishes. For after the most refrangible Rays which paint the Paper at
  1385  P with a purple Colour, are by a total Reflexion taken out of the beam
  1386  of Light MO, the rest of the Colours which appear on the Paper at R and
  1387  T being mix'd in the Light MO compound there a faint yellow, and after
  1388  the blue and part of the green which appear on the Paper between P and R
  1389  are taken away, the rest which appear between R and T (that is the
  1390  yellow, orange, red and a little green) being mixed in the beam MO
  1391  compound there an orange; and when all the Rays are by Reflexion taken
  1392  out of the beam MO, except the least refrangible, which at T appear of a
  1393  full red, their Colour is the same in that beam MO as afterwards at T,
  1394  the Refraction of the Prism HJK serving only to separate the differently
  1395  refrangible Rays, without making any Alteration in their Colours, as
  1396  shall be more fully proved hereafter. All which confirms as well the
  1397  first Proposition as the second.
  1399  _Scholium._ If this Experiment and the former be conjoined and made one
  1400  by applying a fourth Prism VXY [in _Fig._ 22.] to refract the reflected
  1401  beam MN towards _tp_, the Conclusion will be clearer. For then the Light
  1402  N_p_ which in the fourth Prism is more refracted, will become fuller and
  1403  stronger when the Light OP, which in the third Prism HJK is more
  1404  refracted, vanishes at P; and afterwards when the less refracted Light
  1405  OT vanishes at T, the less refracted Light N_t_ will become increased
  1406  whilst the more refracted Light at _p_ receives no farther increase. And
  1407  as the trajected beam MO in vanishing is always of such a Colour as
  1408  ought to result from the mixture of the Colours which fall upon the
  1409  Paper PT, so is the reflected beam MN always of such a Colour as ought
  1410  to result from the mixture of the Colours which fall upon the Paper
  1411  _pt_. For when the most refrangible Rays are by a total Reflexion taken
  1412  out of the beam MO, and leave that beam of an orange Colour, the Excess
  1413  of those Rays in the reflected Light, does not only make the violet,
  1414  indigo and blue at _p_ more full, but also makes the beam MN change from
  1415  the yellowish Colour of the Sun's Light, to a pale white inclining to
  1416  blue, and afterward recover its yellowish Colour again, so soon as all
  1417  the rest of the transmitted Light MOT is reflected.
  1419  Now seeing that in all this variety of Experiments, whether the Trial be
  1420  made in Light reflected, and that either from natural Bodies, as in the
  1421  first and second Experiment, or specular, as in the ninth; or in Light
  1422  refracted, and that either before the unequally refracted Rays are by
  1423  diverging separated from one another, and losing their whiteness which
  1424  they have altogether, appear severally of several Colours, as in the
  1425  fifth Experiment; or after they are separated from one another, and
  1426  appear colour'd as in the sixth, seventh, and eighth Experiments; or in
  1427  Light trajected through parallel Superficies, destroying each others
  1428  Effects, as in the tenth Experiment; there are always found Rays, which
  1429  at equal Incidences on the same Medium suffer unequal Refractions, and
  1430  that without any splitting or dilating of single Rays, or contingence in
  1431  the inequality of the Refractions, as is proved in the fifth and sixth
  1432  Experiments. And seeing the Rays which differ in Refrangibility may be
  1433  parted and sorted from one another, and that either by Refraction as in
  1434  the third Experiment, or by Reflexion as in the tenth, and then the
  1435  several sorts apart at equal Incidences suffer unequal Refractions, and
  1436  those sorts are more refracted than others after Separation, which were
  1437  more refracted before it, as in the sixth and following Experiments, and
  1438  if the Sun's Light be trajected through three or more cross Prisms
  1439  successively, those Rays which in the first Prism are refracted more
  1440  than others, are in all the following Prisms refracted more than others
  1441  in the same Rate and Proportion, as appears by the fifth Experiment;
  1442  it's manifest that the Sun's Light is an heterogeneous Mixture of Rays,
  1443  some of which are constantly more refrangible than others, as was
  1444  proposed.
  1447  _PROP._ III. THEOR. III.
  1449  _The Sun's Light consists of Rays differing in Reflexibility, and those
  1450  Rays are more reflexible than others which are more refrangible._
  1452  This is manifest by the ninth and tenth Experiments: For in the ninth
  1453  Experiment, by turning the Prism about its Axis, until the Rays within
  1454  it which in going out into the Air were refracted by its Base, became so
  1455  oblique to that Base, as to begin to be totally reflected thereby; those
  1456  Rays became first of all totally reflected, which before at equal
  1457  Incidences with the rest had suffered the greatest Refraction. And the
  1458  same thing happens in the Reflexion made by the common Base of the two
  1459  Prisms in the tenth Experiment.
  1462  _PROP._ IV. PROB. I.
  1464  _To separate from one another the heterogeneous Rays of compound Light._
  1466  [Illustration: FIG. 23.]
  1468  The heterogeneous Rays are in some measure separated from one another by
  1469  the Refraction of the Prism in the third Experiment, and in the fifth
  1470  Experiment, by taking away the Penumbra from the rectilinear sides of
  1471  the coloured Image, that Separation in those very rectilinear sides or
  1472  straight edges of the Image becomes perfect. But in all places between
  1473  those rectilinear edges, those innumerable Circles there described,
  1474  which are severally illuminated by homogeneal Rays, by interfering with
  1475  one another, and being every where commix'd, do render the Light
  1476  sufficiently compound. But if these Circles, whilst their Centers keep
  1477  their Distances and Positions, could be made less in Diameter, their
  1478  interfering one with another, and by Consequence the Mixture of the
  1479  heterogeneous Rays would be proportionally diminish'd. In the twenty
  1480  third Figure let AG, BH, CJ, DK, EL, FM be the Circles which so many
  1481  sorts of Rays flowing from the same disque of the Sun, do in the third
  1482  Experiment illuminate; of all which and innumerable other intermediate
  1483  ones lying in a continual Series between the two rectilinear and
  1484  parallel edges of the Sun's oblong Image PT, that Image is compos'd, as
  1485  was explained in the fifth Experiment. And let _ag_, _bh_, _ci_, _dk_,
  1486  _el_, _fm_ be so many less Circles lying in a like continual Series
  1487  between two parallel right Lines _af_ and _gm_ with the same distances
  1488  between their Centers, and illuminated by the same sorts of Rays, that
  1489  is the Circle _ag_ with the same sort by which the corresponding Circle
  1490  AG was illuminated, and the Circle _bh_ with the same sort by which the
  1491  corresponding Circle BH was illuminated, and the rest of the Circles
  1492  _ci_, _dk_, _el_, _fm_ respectively, with the same sorts of Rays by
  1493  which the several corresponding Circles CJ, DK, EL, FM were illuminated.
  1494  In the Figure PT composed of the greater Circles, three of those Circles
  1495  AG, BH, CJ, are so expanded into one another, that the three sorts of
  1496  Rays by which those Circles are illuminated, together with other
  1497  innumerable sorts of intermediate Rays, are mixed at QR in the middle
  1498  of the Circle BH. And the like Mixture happens throughout almost the
  1499  whole length of the Figure PT. But in the Figure _pt_ composed of the
  1500  less Circles, the three less Circles _ag_, _bh_, _ci_, which answer to
  1501  those three greater, do not extend into one another; nor are there any
  1502  where mingled so much as any two of the three sorts of Rays by which
  1503  those Circles are illuminated, and which in the Figure PT are all of
  1504  them intermingled at BH.
  1506  Now he that shall thus consider it, will easily understand that the
  1507  Mixture is diminished in the same Proportion with the Diameters of the
  1508  Circles. If the Diameters of the Circles whilst their Centers remain the
  1509  same, be made three times less than before, the Mixture will be also
  1510  three times less; if ten times less, the Mixture will be ten times less,
  1511  and so of other Proportions. That is, the Mixture of the Rays in the
  1512  greater Figure PT will be to their Mixture in the less _pt_, as the
  1513  Latitude of the greater Figure is to the Latitude of the less. For the
  1514  Latitudes of these Figures are equal to the Diameters of their Circles.
  1515  And hence it easily follows, that the Mixture of the Rays in the
  1516  refracted Spectrum _pt_ is to the Mixture of the Rays in the direct and
  1517  immediate Light of the Sun, as the breadth of that Spectrum is to the
  1518  difference between the length and breadth of the same Spectrum.
  1520  So then, if we would diminish the Mixture of the Rays, we are to
  1521  diminish the Diameters of the Circles. Now these would be diminished if
  1522  the Sun's Diameter to which they answer could be made less than it is,
  1523  or (which comes to the same Purpose) if without Doors, at a great
  1524  distance from the Prism towards the Sun, some opake Body were placed,
  1525  with a round hole in the middle of it, to intercept all the Sun's Light,
  1526  excepting so much as coming from the middle of his Body could pass
  1527  through that Hole to the Prism. For so the Circles AG, BH, and the rest,
  1528  would not any longer answer to the whole Disque of the Sun, but only to
  1529  that Part of it which could be seen from the Prism through that Hole,
  1530  that it is to the apparent Magnitude of that Hole view'd from the Prism.
  1531  But that these Circles may answer more distinctly to that Hole, a Lens
  1532  is to be placed by the Prism to cast the Image of the Hole, (that is,
  1533  every one of the Circles AG, BH, &c.) distinctly upon the Paper at PT,
  1534  after such a manner, as by a Lens placed at a Window, the Species of
  1535  Objects abroad are cast distinctly upon a Paper within the Room, and the
  1536  rectilinear Sides of the oblong Solar Image in the fifth Experiment
  1537  became distinct without any Penumbra. If this be done, it will not be
  1538  necessary to place that Hole very far off, no not beyond the Window. And
  1539  therefore instead of that Hole, I used the Hole in the Window-shut, as
  1540  follows.
  1542  _Exper._ 11. In the Sun's Light let into my darken'd Chamber through a
  1543  small round Hole in my Window-shut, at about ten or twelve Feet from the
  1544  Window, I placed a Lens, by which the Image of the Hole might be
  1545  distinctly cast upon a Sheet of white Paper, placed at the distance of
  1546  six, eight, ten, or twelve Feet from the Lens. For, according to the
  1547  difference of the Lenses I used various distances, which I think not
  1548  worth the while to describe. Then immediately after the Lens I placed a
  1549  Prism, by which the trajected Light might be refracted either upwards or
  1550  sideways, and thereby the round Image, which the Lens alone did cast
  1551  upon the Paper might be drawn out into a long one with Parallel Sides,
  1552  as in the third Experiment. This oblong Image I let fall upon another
  1553  Paper at about the same distance from the Prism as before, moving the
  1554  Paper either towards the Prism or from it, until I found the just
  1555  distance where the Rectilinear Sides of the Image became most distinct.
  1556  For in this Case, the Circular Images of the Hole, which compose that
  1557  Image after the same manner that the Circles _ag_, _bh_, _ci_, &c. do
  1558  the Figure _pt_ [in _Fig._ 23.] were terminated most distinctly without
  1559  any Penumbra, and therefore extended into one another the least that
  1560  they could, and by consequence the Mixture of the heterogeneous Rays was
  1561  now the least of all. By this means I used to form an oblong Image (such
  1562  as is _pt_) [in _Fig._ 23, and 24.] of Circular Images of the Hole,
  1563  (such as are _ag_, _bh_, _ci_, &c.) and by using a greater or less Hole
  1564  in the Window-shut, I made the Circular Images _ag_, _bh_, _ci_, &c. of
  1565  which it was formed, to become greater or less at pleasure, and thereby
  1566  the Mixture of the Rays in the Image _pt_ to be as much, or as little as
  1567  I desired.
  1569  [Illustration: FIG. 24.]
  1571  _Illustration._ In the twenty-fourth Figure, F represents the Circular
  1572  Hole in the Window-shut, MN the Lens, whereby the Image or Species of
  1573  that Hole is cast distinctly upon a Paper at J, ABC the Prism, whereby
  1574  the Rays are at their emerging out of the Lens refracted from J towards
  1575  another Paper at _pt_, and the round Image at J is turned into an oblong
  1576  Image _pt_ falling on that other Paper. This Image _pt_ consists of
  1577  Circles placed one after another in a Rectilinear Order, as was
  1578  sufficiently explained in the fifth Experiment; and these Circles are
  1579  equal to the Circle J, and consequently answer in magnitude to the Hole
  1580  F; and therefore by diminishing that Hole they may be at pleasure
  1581  diminished, whilst their Centers remain in their Places. By this means I
  1582  made the Breadth of the Image _pt_ to be forty times, and sometimes
  1583  sixty or seventy times less than its Length. As for instance, if the
  1584  Breadth of the Hole F be one tenth of an Inch, and MF the distance of
  1585  the Lens from the Hole be 12 Feet; and if _p_B or _p_M the distance of
  1586  the Image _pt_ from the Prism or Lens be 10 Feet, and the refracting
  1587  Angle of the Prism be 62 Degrees, the Breadth of the Image _pt_ will be
  1588  one twelfth of an Inch, and the Length about six Inches, and therefore
  1589  the Length to the Breadth as 72 to 1, and by consequence the Light of
  1590  this Image 71 times less compound than the Sun's direct Light. And Light
  1591  thus far simple and homogeneal, is sufficient for trying all the
  1592  Experiments in this Book about simple Light. For the Composition of
  1593  heterogeneal Rays is in this Light so little, that it is scarce to be
  1594  discovered and perceiv'd by Sense, except perhaps in the indigo and
  1595  violet. For these being dark Colours do easily suffer a sensible Allay
  1596  by that little scattering Light which uses to be refracted irregularly
  1597  by the Inequalities of the Prism.
  1599  Yet instead of the Circular Hole F, 'tis better to substitute an oblong
  1600  Hole shaped like a long Parallelogram with its Length parallel to the
  1601  Prism ABC. For if this Hole be an Inch or two long, and but a tenth or
  1602  twentieth Part of an Inch broad, or narrower; the Light of the Image
  1603  _pt_ will be as simple as before, or simpler, and the Image will become
  1604  much broader, and therefore more fit to have Experiments try'd in its
  1605  Light than before.
  1607  Instead of this Parallelogram Hole may be substituted a triangular one
  1608  of equal Sides, whose Base, for instance, is about the tenth Part of an
  1609  Inch, and its Height an Inch or more. For by this means, if the Axis of
  1610  the Prism be parallel to the Perpendicular of the Triangle, the Image
  1611  _pt_ [in _Fig._ 25.] will now be form'd of equicrural Triangles _ag_,
  1612  _bh_, _ci_, _dk_, _el_, _fm_, &c. and innumerable other intermediate
  1613  ones answering to the triangular Hole in Shape and Bigness, and lying
  1614  one after another in a continual Series between two Parallel Lines _af_
  1615  and _gm_. These Triangles are a little intermingled at their Bases, but
  1616  not at their Vertices; and therefore the Light on the brighter Side _af_
  1617  of the Image, where the Bases of the Triangles are, is a little
  1618  compounded, but on the darker Side _gm_ is altogether uncompounded, and
  1619  in all Places between the Sides the Composition is proportional to the
  1620  distances of the Places from that obscurer Side _gm_. And having a
  1621  Spectrum _pt_ of such a Composition, we may try Experiments either in
  1622  its stronger and less simple Light near the Side _af_, or in its weaker
  1623  and simpler Light near the other Side _gm_, as it shall seem most
  1624  convenient.
  1626  [Illustration: FIG. 25.]
  1628  But in making Experiments of this kind, the Chamber ought to be made as
  1629  dark as can be, lest any Foreign Light mingle it self with the Light of
  1630  the Spectrum _pt_, and render it compound; especially if we would try
  1631  Experiments in the more simple Light next the Side _gm_ of the Spectrum;
  1632  which being fainter, will have a less proportion to the Foreign Light;
  1633  and so by the mixture of that Light be more troubled, and made more
  1634  compound. The Lens also ought to be good, such as may serve for optical
  1635  Uses, and the Prism ought to have a large Angle, suppose of 65 or 70
  1636  Degrees, and to be well wrought, being made of Glass free from Bubbles
  1637  and Veins, with its Sides not a little convex or concave, as usually
  1638  happens, but truly plane, and its Polish elaborate, as in working
  1639  Optick-glasses, and not such as is usually wrought with Putty, whereby
  1640  the edges of the Sand-holes being worn away, there are left all over the
  1641  Glass a numberless Company of very little convex polite Risings like
  1642  Waves. The edges also of the Prism and Lens, so far as they may make any
  1643  irregular Refraction, must be covered with a black Paper glewed on. And
  1644  all the Light of the Sun's Beam let into the Chamber, which is useless
  1645  and unprofitable to the Experiment, ought to be intercepted with black
  1646  Paper, or other black Obstacles. For otherwise the useless Light being
  1647  reflected every way in the Chamber, will mix with the oblong Spectrum,
  1648  and help to disturb it. In trying these Things, so much diligence is not
  1649  altogether necessary, but it will promote the Success of the
  1650  Experiments, and by a very scrupulous Examiner of Things deserves to be
  1651  apply'd. It's difficult to get Glass Prisms fit for this Purpose, and
  1652  therefore I used sometimes prismatick Vessels made with pieces of broken
  1653  Looking-glasses, and filled with Rain Water. And to increase the
  1654  Refraction, I sometimes impregnated the Water strongly with _Saccharum
  1655  Saturni_.
  1658  _PROP._ V. THEOR. IV.
  1660  _Homogeneal Light is refracted regularly without any Dilatation
  1661  splitting or shattering of the Rays, and the confused Vision of Objects
  1662  seen through refracting Bodies by heterogeneal Light arises from the
  1663  different Refrangibility of several sorts of Rays._
  1665  The first Part of this Proposition has been already sufficiently proved
  1666  in the fifth Experiment, and will farther appear by the Experiments
  1667  which follow.
  1669  _Exper._ 12. In the middle of a black Paper I made a round Hole about a
  1670  fifth or sixth Part of an Inch in diameter. Upon this Paper I caused the
  1671  Spectrum of homogeneal Light described in the former Proposition, so to
  1672  fall, that some part of the Light might pass through the Hole of the
  1673  Paper. This transmitted part of the Light I refracted with a Prism
  1674  placed behind the Paper, and letting this refracted Light fall
  1675  perpendicularly upon a white Paper two or three Feet distant from the
  1676  Prism, I found that the Spectrum formed on the Paper by this Light was
  1677  not oblong, as when 'tis made (in the third Experiment) by refracting
  1678  the Sun's compound Light, but was (so far as I could judge by my Eye)
  1679  perfectly circular, the Length being no greater than the Breadth. Which
  1680  shews, that this Light is refracted regularly without any Dilatation of
  1681  the Rays.
  1683  _Exper._ 13. In the homogeneal Light I placed a Paper Circle of a
  1684  quarter of an Inch in diameter, and in the Sun's unrefracted
  1685  heterogeneal white Light I placed another Paper Circle of the same
  1686  Bigness. And going from the Papers to the distance of some Feet, I
  1687  viewed both Circles through a Prism. The Circle illuminated by the Sun's
  1688  heterogeneal Light appeared very oblong, as in the fourth Experiment,
  1689  the Length being many times greater than the Breadth; but the other
  1690  Circle, illuminated with homogeneal Light, appeared circular and
  1691  distinctly defined, as when 'tis view'd with the naked Eye. Which proves
  1692  the whole Proposition.
  1694  _Exper._ 14. In the homogeneal Light I placed Flies, and such-like
  1695  minute Objects, and viewing them through a Prism, I saw their Parts as
  1696  distinctly defined, as if I had viewed them with the naked Eye. The same
  1697  Objects placed in the Sun's unrefracted heterogeneal Light, which was
  1698  white, I viewed also through a Prism, and saw them most confusedly
  1699  defined, so that I could not distinguish their smaller Parts from one
  1700  another. I placed also the Letters of a small print, one while in the
  1701  homogeneal Light, and then in the heterogeneal, and viewing them through
  1702  a Prism, they appeared in the latter Case so confused and indistinct,
  1703  that I could not read them; but in the former they appeared so distinct,
  1704  that I could read readily, and thought I saw them as distinct, as when I
  1705  view'd them with my naked Eye. In both Cases I view'd the same Objects,
  1706  through the same Prism at the same distance from me, and in the same
  1707  Situation. There was no difference, but in the Light by which the
  1708  Objects were illuminated, and which in one Case was simple, and in the
  1709  other compound; and therefore, the distinct Vision in the former Case,
  1710  and confused in the latter, could arise from nothing else than from that
  1711  difference of the Lights. Which proves the whole Proposition.
  1713  And in these three Experiments it is farther very remarkable, that the
  1714  Colour of homogeneal Light was never changed by the Refraction.
  1717  _PROP._ VI. THEOR. V.
  1719  _The Sine of Incidence of every Ray considered apart, is to its Sine of
  1720  Refraction in a given Ratio._
  1722  That every Ray consider'd apart, is constant to it self in some degree
  1723  of Refrangibility, is sufficiently manifest out of what has been said.
  1724  Those Rays, which in the first Refraction, are at equal Incidences most
  1725  refracted, are also in the following Refractions at equal Incidences
  1726  most refracted; and so of the least refrangible, and the rest which have
  1727  any mean Degree of Refrangibility, as is manifest by the fifth, sixth,
  1728  seventh, eighth, and ninth Experiments. And those which the first Time
  1729  at like Incidences are equally refracted, are again at like Incidences
  1730  equally and uniformly refracted, and that whether they be refracted
  1731  before they be separated from one another, as in the fifth Experiment,
  1732  or whether they be refracted apart, as in the twelfth, thirteenth and
  1733  fourteenth Experiments. The Refraction therefore of every Ray apart is
  1734  regular, and what Rule that Refraction observes we are now to shew.[E]
  1736  The late Writers in Opticks teach, that the Sines of Incidence are in a
  1737  given Proportion to the Sines of Refraction, as was explained in the
  1738  fifth Axiom, and some by Instruments fitted for measuring of
  1739  Refractions, or otherwise experimentally examining this Proportion, do
  1740  acquaint us that they have found it accurate. But whilst they, not
  1741  understanding the different Refrangibility of several Rays, conceived
  1742  them all to be refracted according to one and the same Proportion, 'tis
  1743  to be presumed that they adapted their Measures only to the middle of
  1744  the refracted Light; so that from their Measures we may conclude only
  1745  that the Rays which have a mean Degree of Refrangibility, that is, those
  1746  which when separated from the rest appear green, are refracted according
  1747  to a given Proportion of their Sines. And therefore we are now to shew,
  1748  that the like given Proportions obtain in all the rest. That it should
  1749  be so is very reasonable, Nature being ever conformable to her self; but
  1750  an experimental Proof is desired. And such a Proof will be had, if we
  1751  can shew that the Sines of Refraction of Rays differently refrangible
  1752  are one to another in a given Proportion when their Sines of Incidence
  1753  are equal. For, if the Sines of Refraction of all the Rays are in given
  1754  Proportions to the Sine of Refractions of a Ray which has a mean Degree
  1755  of Refrangibility, and this Sine is in a given Proportion to the equal
  1756  Sines of Incidence, those other Sines of Refraction will also be in
  1757  given Proportions to the equal Sines of Incidence. Now, when the Sines
  1758  of Incidence are equal, it will appear by the following Experiment, that
  1759  the Sines of Refraction are in a given Proportion to one another.
  1761  [Illustration: FIG. 26.]
  1763  _Exper._ 15. The Sun shining into a dark Chamber through a little round
  1764  Hole in the Window-shut, let S [in _Fig._ 26.] represent his round white
  1765  Image painted on the opposite Wall by his direct Light, PT his oblong
  1766  coloured Image made by refracting that Light with a Prism placed at the
  1767  Window; and _pt_, or _2p 2t_, _3p 3t_, his oblong colour'd Image made by
  1768  refracting again the same Light sideways with a second Prism placed
  1769  immediately after the first in a cross Position to it, as was explained
  1770  in the fifth Experiment; that is to say, _pt_ when the Refraction of the
  1771  second Prism is small, _2p 2t_ when its Refraction is greater, and _3p
  1772  3t_ when it is greatest. For such will be the diversity of the
  1773  Refractions, if the refracting Angle of the second Prism be of various
  1774  Magnitudes; suppose of fifteen or twenty Degrees to make the Image _pt_,
  1775  of thirty or forty to make the Image _2p 2t_, and of sixty to make the
  1776  Image _3p 3t_. But for want of solid Glass Prisms with Angles of
  1777  convenient Bignesses, there may be Vessels made of polished Plates of
  1778  Glass cemented together in the form of Prisms and filled with Water.
  1779  These things being thus ordered, I observed that all the solar Images or
  1780  coloured Spectrums PT, _pt_, _2p 2t_, _3p 3t_ did very nearly converge
  1781  to the place S on which the direct Light of the Sun fell and painted his
  1782  white round Image when the Prisms were taken away. The Axis of the
  1783  Spectrum PT, that is the Line drawn through the middle of it parallel to
  1784  its rectilinear Sides, did when produced pass exactly through the middle
  1785  of that white round Image S. And when the Refraction of the second Prism
  1786  was equal to the Refraction of the first, the refracting Angles of them
  1787  both being about 60 Degrees, the Axis of the Spectrum _3p 3t_ made by
  1788  that Refraction, did when produced pass also through the middle of the
  1789  same white round Image S. But when the Refraction of the second Prism
  1790  was less than that of the first, the produced Axes of the Spectrums _tp_
  1791  or _2t 2p_ made by that Refraction did cut the produced Axis of the
  1792  Spectrum TP in the points _m_ and _n_, a little beyond the Center of
  1793  that white round Image S. Whence the proportion of the Line 3_t_T to the
  1794  Line 3_p_P was a little greater than the Proportion of 2_t_T or 2_p_P,
  1795  and this Proportion a little greater than that of _t_T to _p_P. Now when
  1796  the Light of the Spectrum PT falls perpendicularly upon the Wall, those
  1797  Lines 3_t_T, 3_p_P, and 2_t_T, and 2_p_P, and _t_T, _p_P, are the
  1798  Tangents of the Refractions, and therefore by this Experiment the
  1799  Proportions of the Tangents of the Refractions are obtained, from whence
  1800  the Proportions of the Sines being derived, they come out equal, so far
  1801  as by viewing the Spectrums, and using some mathematical Reasoning I
  1802  could estimate. For I did not make an accurate Computation. So then the
  1803  Proposition holds true in every Ray apart, so far as appears by
  1804  Experiment. And that it is accurately true, may be demonstrated upon
  1805  this Supposition. _That Bodies refract Light by acting upon its Rays in
  1806  Lines perpendicular to their Surfaces._ But in order to this
  1807  Demonstration, I must distinguish the Motion of every Ray into two
  1808  Motions, the one perpendicular to the refracting Surface, the other
  1809  parallel to it, and concerning the perpendicular Motion lay down the
  1810  following Proposition.
  1812  If any Motion or moving thing whatsoever be incident with any Velocity
  1813  on any broad and thin space terminated on both sides by two parallel
  1814  Planes, and in its Passage through that space be urged perpendicularly
  1815  towards the farther Plane by any force which at given distances from the
  1816  Plane is of given Quantities; the perpendicular velocity of that Motion
  1817  or Thing, at its emerging out of that space, shall be always equal to
  1818  the square Root of the sum of the square of the perpendicular velocity
  1819  of that Motion or Thing at its Incidence on that space; and of the
  1820  square of the perpendicular velocity which that Motion or Thing would
  1821  have at its Emergence, if at its Incidence its perpendicular velocity
  1822  was infinitely little.
  1824  And the same Proposition holds true of any Motion or Thing
  1825  perpendicularly retarded in its passage through that space, if instead
  1826  of the sum of the two Squares you take their difference. The
  1827  Demonstration Mathematicians will easily find out, and therefore I shall
  1828  not trouble the Reader with it.
  1830  Suppose now that a Ray coming most obliquely in the Line MC [in _Fig._
  1831  1.] be refracted at C by the Plane RS into the Line CN, and if it be
  1832  required to find the Line CE, into which any other Ray AC shall be
  1833  refracted; let MC, AD, be the Sines of Incidence of the two Rays, and
  1834  NG, EF, their Sines of Refraction, and let the equal Motions of the
  1835  incident Rays be represented by the equal Lines MC and AC, and the
  1836  Motion MC being considered as parallel to the refracting Plane, let the
  1837  other Motion AC be distinguished into two Motions AD and DC, one of
  1838  which AD is parallel, and the other DC perpendicular to the refracting
  1839  Surface. In like manner, let the Motions of the emerging Rays be
  1840  distinguish'd into two, whereof the perpendicular ones are MC/NG × CG
  1841  and AD/EF × CF. And if the force of the refracting Plane begins to act
  1842  upon the Rays either in that Plane or at a certain distance from it on
  1843  the one side, and ends at a certain distance from it on the other side,
  1844  and in all places between those two limits acts upon the Rays in Lines
  1845  perpendicular to that refracting Plane, and the Actions upon the Rays at
  1846  equal distances from the refracting Plane be equal, and at unequal ones
  1847  either equal or unequal according to any rate whatever; that Motion of
  1848  the Ray which is parallel to the refracting Plane, will suffer no
  1849  Alteration by that Force; and that Motion which is perpendicular to it
  1850  will be altered according to the rule of the foregoing Proposition. If
  1851  therefore for the perpendicular velocity of the emerging Ray CN you
  1852  write MC/NG × CG as above, then the perpendicular velocity of any other
  1853  emerging Ray CE which was AD/EF × CF, will be equal to the square Root
  1854  of CD_q_ + (_MCq/NGq_ × CG_q_). And by squaring these Equals, and adding
  1855  to them the Equals AD_q_ and MC_q_ - CD_q_, and dividing the Sums by the
  1856  Equals CF_q_ + EF_q_ and CG_q_ + NG_q_, you will have _MCq/NGq_ equal to
  1857  _ADq/EFq_. Whence AD, the Sine of Incidence, is to EF the Sine of
  1858  Refraction, as MC to NG, that is, in a given _ratio_. And this
  1859  Demonstration being general, without determining what Light is, or by
  1860  what kind of Force it is refracted, or assuming any thing farther than
  1861  that the refracting Body acts upon the Rays in Lines perpendicular to
  1862  its Surface; I take it to be a very convincing Argument of the full
  1863  truth of this Proposition.
  1865  So then, if the _ratio_ of the Sines of Incidence and Refraction of any
  1866  sort of Rays be found in any one case, 'tis given in all cases; and this
  1867  may be readily found by the Method in the following Proposition.
  1870  _PROP._ VII. THEOR. VI.
  1872  _The Perfection of Telescopes is impeded by the different Refrangibility
  1873  of the Rays of Light._
  1875  The Imperfection of Telescopes is vulgarly attributed to the spherical
  1876  Figures of the Glasses, and therefore Mathematicians have propounded to
  1877  figure them by the conical Sections. To shew that they are mistaken, I
  1878  have inserted this Proposition; the truth of which will appear by the
  1879  measure of the Refractions of the several sorts of Rays; and these
  1880  measures I thus determine.
  1882  In the third Experiment of this first Part, where the refracting Angle
  1883  of the Prism was 62-1/2 Degrees, the half of that Angle 31 deg. 15 min.
  1884  is the Angle of Incidence of the Rays at their going out of the Glass
  1885  into the Air[F]; and the Sine of this Angle is 5188, the Radius being
  1886  10000. When the Axis of this Prism was parallel to the Horizon, and the
  1887  Refraction of the Rays at their Incidence on this Prism equal to that at
  1888  their Emergence out of it, I observed with a Quadrant the Angle which
  1889  the mean refrangible Rays, (that is those which went to the middle of
  1890  the Sun's coloured Image) made with the Horizon, and by this Angle and
  1891  the Sun's altitude observed at the same time, I found the Angle which
  1892  the emergent Rays contained with the incident to be 44 deg. and 40 min.
  1893  and the half of this Angle added to the Angle of Incidence 31 deg. 15
  1894  min. makes the Angle of Refraction, which is therefore 53 deg. 35 min.
  1895  and its Sine 8047. These are the Sines of Incidence and Refraction of
  1896  the mean refrangible Rays, and their Proportion in round Numbers is 20
  1897  to 31. This Glass was of a Colour inclining to green. The last of the
  1898  Prisms mentioned in the third Experiment was of clear white Glass. Its
  1899  refracting Angle 63-1/2 Degrees. The Angle which the emergent Rays
  1900  contained, with the incident 45 deg. 50 min. The Sine of half the first
  1901  Angle 5262. The Sine of half the Sum of the Angles 8157. And their
  1902  Proportion in round Numbers 20 to 31, as before.
  1904  From the Length of the Image, which was about 9-3/4 or 10 Inches,
  1905  subduct its Breadth, which was 2-1/8 Inches, and the Remainder 7-3/4
  1906  Inches would be the Length of the Image were the Sun but a Point, and
  1907  therefore subtends the Angle which the most and least refrangible Rays,
  1908  when incident on the Prism in the same Lines, do contain with one
  1909  another after their Emergence. Whence this Angle is 2 deg. 0´. 7´´. For
  1910  the distance between the Image and the Prism where this Angle is made,
  1911  was 18-1/2 Feet, and at that distance the Chord 7-3/4 Inches subtends an
  1912  Angle of 2 deg. 0´. 7´´. Now half this Angle is the Angle which these
  1913  emergent Rays contain with the emergent mean refrangible Rays, and a
  1914  quarter thereof, that is 30´. 2´´. may be accounted the Angle which they
  1915  would contain with the same emergent mean refrangible Rays, were they
  1916  co-incident to them within the Glass, and suffered no other Refraction
  1917  than that at their Emergence. For, if two equal Refractions, the one at
  1918  the Incidence of the Rays on the Prism, the other at their Emergence,
  1919  make half the Angle 2 deg. 0´. 7´´. then one of those Refractions will
  1920  make about a quarter of that Angle, and this quarter added to, and
  1921  subducted from the Angle of Refraction of the mean refrangible Rays,
  1922  which was 53 deg. 35´, gives the Angles of Refraction of the most and
  1923  least refrangible Rays 54 deg. 5´ 2´´, and 53 deg. 4´ 58´´, whose Sines
  1924  are 8099 and 7995, the common Angle of Incidence being 31 deg. 15´, and
  1925  its Sine 5188; and these Sines in the least round Numbers are in
  1926  proportion to one another, as 78 and 77 to 50.
  1928  Now, if you subduct the common Sine of Incidence 50 from the Sines of
  1929  Refraction 77 and 78, the Remainders 27 and 28 shew, that in small
  1930  Refractions the Refraction of the least refrangible Rays is to the
  1931  Refraction of the most refrangible ones, as 27 to 28 very nearly, and
  1932  that the difference of the Refractions of the least refrangible and most
  1933  refrangible Rays is about the 27-1/2th Part of the whole Refraction of
  1934  the mean refrangible Rays.
  1936  Whence they that are skilled in Opticks will easily understand,[G] that
  1937  the Breadth of the least circular Space, into which Object-glasses of
  1938  Telescopes can collect all sorts of Parallel Rays, is about the 27-1/2th
  1939  Part of half the Aperture of the Glass, or 55th Part of the whole
  1940  Aperture; and that the Focus of the most refrangible Rays is nearer to
  1941  the Object-glass than the Focus of the least refrangible ones, by about
  1942  the 27-1/2th Part of the distance between the Object-glass and the Focus
  1943  of the mean refrangible ones.
  1945  And if Rays of all sorts, flowing from any one lucid Point in the Axis
  1946  of any convex Lens, be made by the Refraction of the Lens to converge to
  1947  Points not too remote from the Lens, the Focus of the most refrangible
  1948  Rays shall be nearer to the Lens than the Focus of the least refrangible
  1949  ones, by a distance which is to the 27-1/2th Part of the distance of the
  1950  Focus of the mean refrangible Rays from the Lens, as the distance
  1951  between that Focus and the lucid Point, from whence the Rays flow, is to
  1952  the distance between that lucid Point and the Lens very nearly.
  1954  Now to examine whether the Difference between the Refractions, which the
  1955  most refrangible and the least refrangible Rays flowing from the same
  1956  Point suffer in the Object-glasses of Telescopes and such-like Glasses,
  1957  be so great as is here described, I contrived the following Experiment.
  1959  _Exper._ 16. The Lens which I used in the second and eighth Experiments,
  1960  being placed six Feet and an Inch distant from any Object, collected the
  1961  Species of that Object by the mean refrangible Rays at the distance of
  1962  six Feet and an Inch from the Lens on the other side. And therefore by
  1963  the foregoing Rule, it ought to collect the Species of that Object by
  1964  the least refrangible Rays at the distance of six Feet and 3-2/3 Inches
  1965  from the Lens, and by the most refrangible ones at the distance of five
  1966  Feet and 10-1/3 Inches from it: So that between the two Places, where
  1967  these least and most refrangible Rays collect the Species, there may be
  1968  the distance of about 5-1/3 Inches. For by that Rule, as six Feet and an
  1969  Inch (the distance of the Lens from the lucid Object) is to twelve Feet
  1970  and two Inches (the distance of the lucid Object from the Focus of the
  1971  mean refrangible Rays) that is, as One is to Two; so is the 27-1/2th
  1972  Part of six Feet and an Inch (the distance between the Lens and the same
  1973  Focus) to the distance between the Focus of the most refrangible Rays
  1974  and the Focus of the least refrangible ones, which is therefore 5-17/55
  1975  Inches, that is very nearly 5-1/3 Inches. Now to know whether this
  1976  Measure was true, I repeated the second and eighth Experiment with
  1977  coloured Light, which was less compounded than that I there made use of:
  1978  For I now separated the heterogeneous Rays from one another by the
  1979  Method I described in the eleventh Experiment, so as to make a coloured
  1980  Spectrum about twelve or fifteen Times longer than broad. This Spectrum
  1981  I cast on a printed Book, and placing the above-mentioned Lens at the
  1982  distance of six Feet and an Inch from this Spectrum to collect the
  1983  Species of the illuminated Letters at the same distance on the other
  1984  side, I found that the Species of the Letters illuminated with blue were
  1985  nearer to the Lens than those illuminated with deep red by about three
  1986  Inches, or three and a quarter; but the Species of the Letters
  1987  illuminated with indigo and violet appeared so confused and indistinct,
  1988  that I could not read them: Whereupon viewing the Prism, I found it was
  1989  full of Veins running from one end of the Glass to the other; so that
  1990  the Refraction could not be regular. I took another Prism therefore
  1991  which was free from Veins, and instead of the Letters I used two or
  1992  three Parallel black Lines a little broader than the Strokes of the
  1993  Letters, and casting the Colours upon these Lines in such manner, that
  1994  the Lines ran along the Colours from one end of the Spectrum to the
  1995  other, I found that the Focus where the indigo, or confine of this
  1996  Colour and violet cast the Species of the black Lines most distinctly,
  1997  to be about four Inches, or 4-1/4 nearer to the Lens than the Focus,
  1998  where the deepest red cast the Species of the same black Lines most
  1999  distinctly. The violet was so faint and dark, that I could not discern
  2000  the Species of the Lines distinctly by that Colour; and therefore
  2001  considering that the Prism was made of a dark coloured Glass inclining
  2002  to green, I took another Prism of clear white Glass; but the Spectrum of
  2003  Colours which this Prism made had long white Streams of faint Light
  2004  shooting out from both ends of the Colours, which made me conclude that
  2005  something was amiss; and viewing the Prism, I found two or three little
  2006  Bubbles in the Glass, which refracted the Light irregularly. Wherefore I
  2007  covered that Part of the Glass with black Paper, and letting the Light
  2008  pass through another Part of it which was free from such Bubbles, the
  2009  Spectrum of Colours became free from those irregular Streams of Light,
  2010  and was now such as I desired. But still I found the violet so dark and
  2011  faint, that I could scarce see the Species of the Lines by the violet,
  2012  and not at all by the deepest Part of it, which was next the end of the
  2013  Spectrum. I suspected therefore, that this faint and dark Colour might
  2014  be allayed by that scattering Light which was refracted, and reflected
  2015  irregularly, partly by some very small Bubbles in the Glasses, and
  2016  partly by the Inequalities of their Polish; which Light, tho' it was but
  2017  little, yet it being of a white Colour, might suffice to affect the
  2018  Sense so strongly as to disturb the Phænomena of that weak and dark
  2019  Colour the violet, and therefore I tried, as in the 12th, 13th, and 14th
  2020  Experiments, whether the Light of this Colour did not consist of a
  2021  sensible Mixture of heterogeneous Rays, but found it did not. Nor did
  2022  the Refractions cause any other sensible Colour than violet to emerge
  2023  out of this Light, as they would have done out of white Light, and by
  2024  consequence out of this violet Light had it been sensibly compounded
  2025  with white Light. And therefore I concluded, that the reason why I could
  2026  not see the Species of the Lines distinctly by this Colour, was only
  2027  the Darkness of this Colour, and Thinness of its Light, and its distance
  2028  from the Axis of the Lens; I divided therefore those Parallel black
  2029  Lines into equal Parts, by which I might readily know the distances of
  2030  the Colours in the Spectrum from one another, and noted the distances of
  2031  the Lens from the Foci of such Colours, as cast the Species of the Lines
  2032  distinctly, and then considered whether the difference of those
  2033  distances bear such proportion to 5-1/3 Inches, the greatest Difference
  2034  of the distances, which the Foci of the deepest red and violet ought to
  2035  have from the Lens, as the distance of the observed Colours from one
  2036  another in the Spectrum bear to the greatest distance of the deepest red
  2037  and violet measured in the Rectilinear Sides of the Spectrum, that is,
  2038  to the Length of those Sides, or Excess of the Length of the Spectrum
  2039  above its Breadth. And my Observations were as follows.
  2041  When I observed and compared the deepest sensible red, and the Colour in
  2042  the Confine of green and blue, which at the Rectilinear Sides of the
  2043  Spectrum was distant from it half the Length of those Sides, the Focus
  2044  where the Confine of green and blue cast the Species of the Lines
  2045  distinctly on the Paper, was nearer to the Lens than the Focus, where
  2046  the red cast those Lines distinctly on it by about 2-1/2 or 2-3/4
  2047  Inches. For sometimes the Measures were a little greater, sometimes a
  2048  little less, but seldom varied from one another above 1/3 of an Inch.
  2049  For it was very difficult to define the Places of the Foci, without some
  2050  little Errors. Now, if the Colours distant half the Length of the
  2051  Image, (measured at its Rectilinear Sides) give 2-1/2 or 2-3/4
  2052  Difference of the distances of their Foci from the Lens, then the
  2053  Colours distant the whole Length ought to give 5 or 5-1/2 Inches
  2054  difference of those distances.
  2056  But here it's to be noted, that I could not see the red to the full end
  2057  of the Spectrum, but only to the Center of the Semicircle which bounded
  2058  that end, or a little farther; and therefore I compared this red not
  2059  with that Colour which was exactly in the middle of the Spectrum, or
  2060  Confine of green and blue, but with that which verged a little more to
  2061  the blue than to the green: And as I reckoned the whole Length of the
  2062  Colours not to be the whole Length of the Spectrum, but the Length of
  2063  its Rectilinear Sides, so compleating the semicircular Ends into
  2064  Circles, when either of the observed Colours fell within those Circles,
  2065  I measured the distance of that Colour from the semicircular End of the
  2066  Spectrum, and subducting half this distance from the measured distance
  2067  of the two Colours, I took the Remainder for their corrected distance;
  2068  and in these Observations set down this corrected distance for the
  2069  difference of the distances of their Foci from the Lens. For, as the
  2070  Length of the Rectilinear Sides of the Spectrum would be the whole
  2071  Length of all the Colours, were the Circles of which (as we shewed) that
  2072  Spectrum consists contracted and reduced to Physical Points, so in that
  2073  Case this corrected distance would be the real distance of the two
  2074  observed Colours.
  2076  When therefore I farther observed the deepest sensible red, and that
  2077  blue whose corrected distance from it was 7/12 Parts of the Length of
  2078  the Rectilinear Sides of the Spectrum, the difference of the distances
  2079  of their Foci from the Lens was about 3-1/4 Inches, and as 7 to 12, so
  2080  is 3-1/4 to 5-4/7.
  2082  When I observed the deepest sensible red, and that indigo whose
  2083  corrected distance was 8/12 or 2/3 of the Length of the Rectilinear
  2084  Sides of the Spectrum, the difference of the distances of their Foci
  2085  from the Lens, was about 3-2/3 Inches, and as 2 to 3, so is 3-2/3 to
  2086  5-1/2.
  2088  When I observed the deepest sensible red, and that deep indigo whose
  2089  corrected distance from one another was 9/12 or 3/4 of the Length of the
  2090  Rectilinear Sides of the Spectrum, the difference of the distances of
  2091  their Foci from the Lens was about 4 Inches; and as 3 to 4, so is 4 to
  2092  5-1/3.
  2094  When I observed the deepest sensible red, and that Part of the violet
  2095  next the indigo, whose corrected distance from the red was 10/12 or 5/6
  2096  of the Length of the Rectilinear Sides of the Spectrum, the difference
  2097  of the distances of their Foci from the Lens was about 4-1/2 Inches, and
  2098  as 5 to 6, so is 4-1/2 to 5-2/5. For sometimes, when the Lens was
  2099  advantageously placed, so that its Axis respected the blue, and all
  2100  Things else were well ordered, and the Sun shone clear, and I held my
  2101  Eye very near to the Paper on which the Lens cast the Species of the
  2102  Lines, I could see pretty distinctly the Species of those Lines by that
  2103  Part of the violet which was next the indigo; and sometimes I could see
  2104  them by above half the violet, For in making these Experiments I had
  2105  observed, that the Species of those Colours only appear distinct, which
  2106  were in or near the Axis of the Lens: So that if the blue or indigo were
  2107  in the Axis, I could see their Species distinctly; and then the red
  2108  appeared much less distinct than before. Wherefore I contrived to make
  2109  the Spectrum of Colours shorter than before, so that both its Ends might
  2110  be nearer to the Axis of the Lens. And now its Length was about 2-1/2
  2111  Inches, and Breadth about 1/5 or 1/6 of an Inch. Also instead of the
  2112  black Lines on which the Spectrum was cast, I made one black Line
  2113  broader than those, that I might see its Species more easily; and this
  2114  Line I divided by short cross Lines into equal Parts, for measuring the
  2115  distances of the observed Colours. And now I could sometimes see the
  2116  Species of this Line with its Divisions almost as far as the Center of
  2117  the semicircular violet End of the Spectrum, and made these farther
  2118  Observations.
  2120  When I observed the deepest sensible red, and that Part of the violet,
  2121  whose corrected distance from it was about 8/9 Parts of the Rectilinear
  2122  Sides of the Spectrum, the Difference of the distances of the Foci of
  2123  those Colours from the Lens, was one time 4-2/3, another time 4-3/4,
  2124  another time 4-7/8 Inches; and as 8 to 9, so are 4-2/3, 4-3/4, 4-7/8, to
  2125  5-1/4, 5-11/32, 5-31/64 respectively.
  2127  When I observed the deepest sensible red, and deepest sensible violet,
  2128  (the corrected distance of which Colours, when all Things were ordered
  2129  to the best Advantage, and the Sun shone very clear, was about 11/12 or
  2130  15/16 Parts of the Length of the Rectilinear Sides of the coloured
  2131  Spectrum) I found the Difference of the distances of their Foci from the
  2132  Lens sometimes 4-3/4 sometimes 5-1/4, and for the most part 5 Inches or
  2133  thereabouts; and as 11 to 12, or 15 to 16, so is five Inches to 5-2/2 or
  2134  5-1/3 Inches.
  2136  And by this Progression of Experiments I satisfied my self, that had the
  2137  Light at the very Ends of the Spectrum been strong enough to make the
  2138  Species of the black Lines appear plainly on the Paper, the Focus of the
  2139  deepest violet would have been found nearer to the Lens, than the Focus
  2140  of the deepest red, by about 5-1/3 Inches at least. And this is a
  2141  farther Evidence, that the Sines of Incidence and Refraction of the
  2142  several sorts of Rays, hold the same Proportion to one another in the
  2143  smallest Refractions which they do in the greatest.
  2145  My Progress in making this nice and troublesome Experiment I have set
  2146  down more at large, that they that shall try it after me may be aware of
  2147  the Circumspection requisite to make it succeed well. And if they cannot
  2148  make it succeed so well as I did, they may notwithstanding collect by
  2149  the Proportion of the distance of the Colours of the Spectrum, to the
  2150  Difference of the distances of their Foci from the Lens, what would be
  2151  the Success in the more distant Colours by a better trial. And yet, if
  2152  they use a broader Lens than I did, and fix it to a long strait Staff,
  2153  by means of which it may be readily and truly directed to the Colour
  2154  whose Focus is desired, I question not but the Experiment will succeed
  2155  better with them than it did with me. For I directed the Axis as nearly
  2156  as I could to the middle of the Colours, and then the faint Ends of the
  2157  Spectrum being remote from the Axis, cast their Species less distinctly
  2158  on the Paper than they would have done, had the Axis been successively
  2159  directed to them.
  2161  Now by what has been said, it's certain that the Rays which differ in
  2162  Refrangibility do not converge to the same Focus; but if they flow from
  2163  a lucid Point, as far from the Lens on one side as their Foci are on the
  2164  other, the Focus of the most refrangible Rays shall be nearer to the
  2165  Lens than that of the least refrangible, by above the fourteenth Part of
  2166  the whole distance; and if they flow from a lucid Point, so very remote
  2167  from the Lens, that before their Incidence they may be accounted
  2168  parallel, the Focus of the most refrangible Rays shall be nearer to the
  2169  Lens than the Focus of the least refrangible, by about the 27th or 28th
  2170  Part of their whole distance from it. And the Diameter of the Circle in
  2171  the middle Space between those two Foci which they illuminate, when they
  2172  fall there on any Plane, perpendicular to the Axis (which Circle is the
  2173  least into which they can all be gathered) is about the 55th Part of the
  2174  Diameter of the Aperture of the Glass. So that 'tis a wonder, that
  2175  Telescopes represent Objects so distinct as they do. But were all the
  2176  Rays of Light equally refrangible, the Error arising only from the
  2177  Sphericalness of the Figures of Glasses would be many hundred times
  2178  less. For, if the Object-glass of a Telescope be Plano-convex, and the
  2179  Plane side be turned towards the Object, and the Diameter of the
  2180  Sphere, whereof this Glass is a Segment, be called D, and the
  2181  Semi-diameter of the Aperture of the Glass be called S, and the Sine of
  2182  Incidence out of Glass into Air, be to the Sine of Refraction as I to R;
  2183  the Rays which come parallel to the Axis of the Glass, shall in the
  2184  Place where the Image of the Object is most distinctly made, be
  2185  scattered all over a little Circle, whose Diameter is _(Rq/Iq) × (S
  2186  cub./D quad.)_ very nearly,[H] as I gather by computing the Errors of
  2187  the Rays by the Method of infinite Series, and rejecting the Terms,
  2188  whose Quantities are inconsiderable. As for instance, if the Sine of
  2189  Incidence I, be to the Sine of Refraction R, as 20 to 31, and if D the
  2190  Diameter of the Sphere, to which the Convex-side of the Glass is ground,
  2191  be 100 Feet or 1200 Inches, and S the Semi-diameter of the Aperture be
  2192  two Inches, the Diameter of the little Circle, (that is (_Rq × S
  2193  cub.)/(Iq × D quad._)) will be (31 × 31 × 8)/(20 × 20 × 1200 × 1200) (or
  2194  961/72000000) Parts of an Inch. But the Diameter of the little Circle,
  2195  through which these Rays are scattered by unequal Refrangibility, will
  2196  be about the 55th Part of the Aperture of the Object-glass, which here
  2197  is four Inches. And therefore, the Error arising from the Spherical
  2198  Figure of the Glass, is to the Error arising from the different
  2199  Refrangibility of the Rays, as 961/72000000 to 4/55, that is as 1 to
  2200  5449; and therefore being in comparison so very little, deserves not to
  2201  be considered.
  2203  [Illustration: FIG. 27.]
  2205  But you will say, if the Errors caused by the different Refrangibility
  2206  be so very great, how comes it to pass, that Objects appear through
  2207  Telescopes so distinct as they do? I answer, 'tis because the erring
  2208  Rays are not scattered uniformly over all that Circular Space, but
  2209  collected infinitely more densely in the Center than in any other Part
  2210  of the Circle, and in the Way from the Center to the Circumference, grow
  2211  continually rarer and rarer, so as at the Circumference to become
  2212  infinitely rare; and by reason of their Rarity are not strong enough to
  2213  be visible, unless in the Center and very near it. Let ADE [in _Fig._
  2214  27.] represent one of those Circles described with the Center C, and
  2215  Semi-diameter AC, and let BFG be a smaller Circle concentrick to the
  2216  former, cutting with its Circumference the Diameter AC in B, and bisect
  2217  AC in N; and by my reckoning, the Density of the Light in any Place B,
  2218  will be to its Density in N, as AB to BC; and the whole Light within the
  2219  lesser Circle BFG, will be to the whole Light within the greater AED, as
  2220  the Excess of the Square of AC above the Square of AB, is to the Square
  2221  of AC. As if BC be the fifth Part of AC, the Light will be four times
  2222  denser in B than in N, and the whole Light within the less Circle, will
  2223  be to the whole Light within the greater, as nine to twenty-five. Whence
  2224  it's evident, that the Light within the less Circle, must strike the
  2225  Sense much more strongly, than that faint and dilated Light round about
  2226  between it and the Circumference of the greater.
  2228  But it's farther to be noted, that the most luminous of the Prismatick
  2229  Colours are the yellow and orange. These affect the Senses more strongly
  2230  than all the rest together, and next to these in strength are the red
  2231  and green. The blue compared with these is a faint and dark Colour, and
  2232  the indigo and violet are much darker and fainter, so that these
  2233  compared with the stronger Colours are little to be regarded. The Images
  2234  of Objects are therefore to be placed, not in the Focus of the mean
  2235  refrangible Rays, which are in the Confine of green and blue, but in the
  2236  Focus of those Rays which are in the middle of the orange and yellow;
  2237  there where the Colour is most luminous and fulgent, that is in the
  2238  brightest yellow, that yellow which inclines more to orange than to
  2239  green. And by the Refraction of these Rays (whose Sines of Incidence and
  2240  Refraction in Glass are as 17 and 11) the Refraction of Glass and
  2241  Crystal for Optical Uses is to be measured. Let us therefore place the
  2242  Image of the Object in the Focus of these Rays, and all the yellow and
  2243  orange will fall within a Circle, whose Diameter is about the 250th
  2244  Part of the Diameter of the Aperture of the Glass. And if you add the
  2245  brighter half of the red, (that half which is next the orange) and the
  2246  brighter half of the green, (that half which is next the yellow) about
  2247  three fifth Parts of the Light of these two Colours will fall within the
  2248  same Circle, and two fifth Parts will fall without it round about; and
  2249  that which falls without will be spread through almost as much more
  2250  space as that which falls within, and so in the gross be almost three
  2251  times rarer. Of the other half of the red and green, (that is of the
  2252  deep dark red and willow green) about one quarter will fall within this
  2253  Circle, and three quarters without, and that which falls without will be
  2254  spread through about four or five times more space than that which falls
  2255  within; and so in the gross be rarer, and if compared with the whole
  2256  Light within it, will be about 25 times rarer than all that taken in the
  2257  gross; or rather more than 30 or 40 times rarer, because the deep red in
  2258  the end of the Spectrum of Colours made by a Prism is very thin and
  2259  rare, and the willow green is something rarer than the orange and
  2260  yellow. The Light of these Colours therefore being so very much rarer
  2261  than that within the Circle, will scarce affect the Sense, especially
  2262  since the deep red and willow green of this Light, are much darker
  2263  Colours than the rest. And for the same reason the blue and violet being
  2264  much darker Colours than these, and much more rarified, may be
  2265  neglected. For the dense and bright Light of the Circle, will obscure
  2266  the rare and weak Light of these dark Colours round about it, and
  2267  render them almost insensible. The sensible Image of a lucid Point is
  2268  therefore scarce broader than a Circle, whose Diameter is the 250th Part
  2269  of the Diameter of the Aperture of the Object-glass of a good Telescope,
  2270  or not much broader, if you except a faint and dark misty Light round
  2271  about it, which a Spectator will scarce regard. And therefore in a
  2272  Telescope, whose Aperture is four Inches, and Length an hundred Feet, it
  2273  exceeds not 2´´ 45´´´, or 3´´. And in a Telescope whose Aperture is two
  2274  Inches, and Length 20 or 30 Feet, it may be 5´´ or 6´´, and scarce
  2275  above. And this answers well to Experience: For some Astronomers have
  2276  found the Diameters of the fix'd Stars, in Telescopes of between 20 and
  2277  60 Feet in length, to be about 5´´ or 6´´, or at most 8´´ or 10´´ in
  2278  diameter. But if the Eye-Glass be tincted faintly with the Smoak of a
  2279  Lamp or Torch, to obscure the Light of the Star, the fainter Light in
  2280  the Circumference of the Star ceases to be visible, and the Star (if the
  2281  Glass be sufficiently soiled with Smoak) appears something more like a
  2282  mathematical Point. And for the same Reason, the enormous Part of the
  2283  Light in the Circumference of every lucid Point ought to be less
  2284  discernible in shorter Telescopes than in longer, because the shorter
  2285  transmit less Light to the Eye.
  2287  Now, that the fix'd Stars, by reason of their immense Distance, appear
  2288  like Points, unless so far as their Light is dilated by Refraction, may
  2289  appear from hence; that when the Moon passes over them and eclipses
  2290  them, their Light vanishes, not gradually like that of the Planets, but
  2291  all at once; and in the end of the Eclipse it returns into Sight all at
  2292  once, or certainly in less time than the second of a Minute; the
  2293  Refraction of the Moon's Atmosphere a little protracting the time in
  2294  which the Light of the Star first vanishes, and afterwards returns into
  2295  Sight.
  2297  Now, if we suppose the sensible Image of a lucid Point, to be even 250
  2298  times narrower than the Aperture of the Glass; yet this Image would be
  2299  still much greater than if it were only from the spherical Figure of the
  2300  Glass. For were it not for the different Refrangibility of the Rays, its
  2301  breadth in an 100 Foot Telescope whose aperture is 4 Inches, would be
  2302  but 961/72000000 parts of an Inch, as is manifest by the foregoing
  2303  Computation. And therefore in this case the greatest Errors arising from
  2304  the spherical Figure of the Glass, would be to the greatest sensible
  2305  Errors arising from the different Refrangibility of the Rays as
  2306  961/72000000 to 4/250 at most, that is only as 1 to 1200. And this
  2307  sufficiently shews that it is not the spherical Figures of Glasses, but
  2308  the different Refrangibility of the Rays which hinders the perfection of
  2309  Telescopes.
  2311  There is another Argument by which it may appear that the different
  2312  Refrangibility of Rays, is the true cause of the imperfection of
  2313  Telescopes. For the Errors of the Rays arising from the spherical
  2314  Figures of Object-glasses, are as the Cubes of the Apertures of the
  2315  Object Glasses; and thence to make Telescopes of various Lengths magnify
  2316  with equal distinctness, the Apertures of the Object-glasses, and the
  2317  Charges or magnifying Powers ought to be as the Cubes of the square
  2318  Roots of their lengths; which doth not answer to Experience. But the
  2319  Errors of the Rays arising from the different Refrangibility, are as the
  2320  Apertures of the Object-glasses; and thence to make Telescopes of
  2321  various lengths, magnify with equal distinctness, their Apertures and
  2322  Charges ought to be as the square Roots of their lengths; and this
  2323  answers to Experience, as is well known. For Instance, a Telescope of 64
  2324  Feet in length, with an Aperture of 2-2/3 Inches, magnifies about 120
  2325  times, with as much distinctness as one of a Foot in length, with 1/3 of
  2326  an Inch aperture, magnifies 15 times.
  2328  [Illustration: FIG. 28.]
  2330  Now were it not for this different Refrangibility of Rays, Telescopes
  2331  might be brought to a greater perfection than we have yet describ'd, by
  2332  composing the Object-glass of two Glasses with Water between them. Let
  2333  ADFC [in _Fig._ 28.] represent the Object-glass composed of two Glasses
  2334  ABED and BEFC, alike convex on the outsides AGD and CHF, and alike
  2335  concave on the insides BME, BNE, with Water in the concavity BMEN. Let
  2336  the Sine of Incidence out of Glass into Air be as I to R, and out of
  2337  Water into Air, as K to R, and by consequence out of Glass into Water,
  2338  as I to K: and let the Diameter of the Sphere to which the convex sides
  2339  AGD and CHF are ground be D, and the Diameter of the Sphere to which the
  2340  concave sides BME and BNE, are ground be to D, as the Cube Root of
  2341  KK--KI to the Cube Root of RK--RI: and the Refractions on the concave
  2342  sides of the Glasses, will very much correct the Errors of the
  2343  Refractions on the convex sides, so far as they arise from the
  2344  sphericalness of the Figure. And by this means might Telescopes be
  2345  brought to sufficient perfection, were it not for the different
  2346  Refrangibility of several sorts of Rays. But by reason of this different
  2347  Refrangibility, I do not yet see any other means of improving Telescopes
  2348  by Refractions alone, than that of increasing their lengths, for which
  2349  end the late Contrivance of _Hugenius_ seems well accommodated. For very
  2350  long Tubes are cumbersome, and scarce to be readily managed, and by
  2351  reason of their length are very apt to bend, and shake by bending, so as
  2352  to cause a continual trembling in the Objects, whereby it becomes
  2353  difficult to see them distinctly: whereas by his Contrivance the Glasses
  2354  are readily manageable, and the Object-glass being fix'd upon a strong
  2355  upright Pole becomes more steady.
  2357  Seeing therefore the Improvement of Telescopes of given lengths by
  2358  Refractions is desperate; I contrived heretofore a Perspective by
  2359  Reflexion, using instead of an Object-glass a concave Metal. The
  2360  diameter of the Sphere to which the Metal was ground concave was about
  2361  25 _English_ Inches, and by consequence the length of the Instrument
  2362  about six Inches and a quarter. The Eye-glass was Plano-convex, and the
  2363  diameter of the Sphere to which the convex side was ground was about 1/5
  2364  of an Inch, or a little less, and by consequence it magnified between 30
  2365  and 40 times. By another way of measuring I found that it magnified
  2366  about 35 times. The concave Metal bore an Aperture of an Inch and a
  2367  third part; but the Aperture was limited not by an opake Circle,
  2368  covering the Limb of the Metal round about, but by an opake Circle
  2369  placed between the Eyeglass and the Eye, and perforated in the middle
  2370  with a little round hole for the Rays to pass through to the Eye. For
  2371  this Circle by being placed here, stopp'd much of the erroneous Light,
  2372  which otherwise would have disturbed the Vision. By comparing it with a
  2373  pretty good Perspective of four Feet in length, made with a concave
  2374  Eye-glass, I could read at a greater distance with my own Instrument
  2375  than with the Glass. Yet Objects appeared much darker in it than in the
  2376  Glass, and that partly because more Light was lost by Reflexion in the
  2377  Metal, than by Refraction in the Glass, and partly because my Instrument
  2378  was overcharged. Had it magnified but 30 or 25 times, it would have made
  2379  the Object appear more brisk and pleasant. Two of these I made about 16
  2380  Years ago, and have one of them still by me, by which I can prove the
  2381  truth of what I write. Yet it is not so good as at the first. For the
  2382  concave has been divers times tarnished and cleared again, by rubbing
  2383  it with very soft Leather. When I made these an Artist in _London_
  2384  undertook to imitate it; but using another way of polishing them than I
  2385  did, he fell much short of what I had attained to, as I afterwards
  2386  understood by discoursing the Under-workman he had employed. The Polish
  2387  I used was in this manner. I had two round Copper Plates, each six
  2388  Inches in Diameter, the one convex, the other concave, ground very true
  2389  to one another. On the convex I ground the Object-Metal or Concave which
  2390  was to be polish'd, 'till it had taken the Figure of the Convex and was
  2391  ready for a Polish. Then I pitched over the convex very thinly, by
  2392  dropping melted Pitch upon it, and warming it to keep the Pitch soft,
  2393  whilst I ground it with the concave Copper wetted to make it spread
  2394  eavenly all over the convex. Thus by working it well I made it as thin
  2395  as a Groat, and after the convex was cold I ground it again to give it
  2396  as true a Figure as I could. Then I took Putty which I had made very
  2397  fine by washing it from all its grosser Particles, and laying a little
  2398  of this upon the Pitch, I ground it upon the Pitch with the concave
  2399  Copper, till it had done making a Noise; and then upon the Pitch I
  2400  ground the Object-Metal with a brisk motion, for about two or three
  2401  Minutes of time, leaning hard upon it. Then I put fresh Putty upon the
  2402  Pitch, and ground it again till it had done making a noise, and
  2403  afterwards ground the Object-Metal upon it as before. And this Work I
  2404  repeated till the Metal was polished, grinding it the last time with all
  2405  my strength for a good while together, and frequently breathing upon
  2406  the Pitch, to keep it moist without laying on any more fresh Putty. The
  2407  Object-Metal was two Inches broad, and about one third part of an Inch
  2408  thick, to keep it from bending. I had two of these Metals, and when I
  2409  had polished them both, I tried which was best, and ground the other
  2410  again, to see if I could make it better than that which I kept. And thus
  2411  by many Trials I learn'd the way of polishing, till I made those two
  2412  reflecting Perspectives I spake of above. For this Art of polishing will
  2413  be better learn'd by repeated Practice than by my Description. Before I
  2414  ground the Object-Metal on the Pitch, I always ground the Putty on it
  2415  with the concave Copper, till it had done making a noise, because if the
  2416  Particles of the Putty were not by this means made to stick fast in the
  2417  Pitch, they would by rolling up and down grate and fret the Object-Metal
  2418  and fill it full of little holes.
  2420  But because Metal is more difficult to polish than Glass, and is
  2421  afterwards very apt to be spoiled by tarnishing, and reflects not so
  2422  much Light as Glass quick-silver'd over does: I would propound to use
  2423  instead of the Metal, a Glass ground concave on the foreside, and as
  2424  much convex on the backside, and quick-silver'd over on the convex side.
  2425  The Glass must be every where of the same thickness exactly. Otherwise
  2426  it will make Objects look colour'd and indistinct. By such a Glass I
  2427  tried about five or six Years ago to make a reflecting Telescope of four
  2428  Feet in length to magnify about 150 times, and I satisfied my self that
  2429  there wants nothing but a good Artist to bring the Design to
  2430  perfection. For the Glass being wrought by one of our _London_ Artists
  2431  after such a manner as they grind Glasses for Telescopes, though it
  2432  seemed as well wrought as the Object-glasses use to be, yet when it was
  2433  quick-silver'd, the Reflexion discovered innumerable Inequalities all
  2434  over the Glass. And by reason of these Inequalities, Objects appeared
  2435  indistinct in this Instrument. For the Errors of reflected Rays caused
  2436  by any Inequality of the Glass, are about six times greater than the
  2437  Errors of refracted Rays caused by the like Inequalities. Yet by this
  2438  Experiment I satisfied my self that the Reflexion on the concave side of
  2439  the Glass, which I feared would disturb the Vision, did no sensible
  2440  prejudice to it, and by consequence that nothing is wanting to perfect
  2441  these Telescopes, but good Workmen who can grind and polish Glasses
  2442  truly spherical. An Object-glass of a fourteen Foot Telescope, made by
  2443  an Artificer at _London_, I once mended considerably, by grinding it on
  2444  Pitch with Putty, and leaning very easily on it in the grinding, lest
  2445  the Putty should scratch it. Whether this way may not do well enough for
  2446  polishing these reflecting Glasses, I have not yet tried. But he that
  2447  shall try either this or any other way of polishing which he may think
  2448  better, may do well to make his Glasses ready for polishing, by grinding
  2449  them without that Violence, wherewith our _London_ Workmen press their
  2450  Glasses in grinding. For by such violent pressure, Glasses are apt to
  2451  bend a little in the grinding, and such bending will certainly spoil
  2452  their Figure. To recommend therefore the consideration of these
  2453  reflecting Glasses to such Artists as are curious in figuring Glasses, I
  2454  shall describe this optical Instrument in the following Proposition.
  2457  _PROP._ VIII. PROB. II.
  2459  _To shorten Telescopes._
  2461  Let ABCD [in _Fig._ 29.] represent a Glass spherically concave on the
  2462  foreside AB, and as much convex on the backside CD, so that it be every
  2463  where of an equal thickness. Let it not be thicker on one side than on
  2464  the other, lest it make Objects appear colour'd and indistinct, and let
  2465  it be very truly wrought and quick-silver'd over on the backside; and
  2466  set in the Tube VXYZ which must be very black within. Let EFG represent
  2467  a Prism of Glass or Crystal placed near the other end of the Tube, in
  2468  the middle of it, by means of a handle of Brass or Iron FGK, to the end
  2469  of which made flat it is cemented. Let this Prism be rectangular at E,
  2470  and let the other two Angles at F and G be accurately equal to each
  2471  other, and by consequence equal to half right ones, and let the plane
  2472  sides FE and GE be square, and by consequence the third side FG a
  2473  rectangular Parallelogram, whose length is to its breadth in a
  2474  subduplicate proportion of two to one. Let it be so placed in the Tube,
  2475  that the Axis of the Speculum may pass through the middle of the square
  2476  side EF perpendicularly and by consequence through the middle of the
  2477  side FG at an Angle of 45 Degrees, and let the side EF be turned towards
  2478  the Speculum, and the distance of this Prism from the Speculum be such
  2479  that the Rays of the Light PQ, RS, &c. which are incident upon the
  2480  Speculum in Lines parallel to the Axis thereof, may enter the Prism at
  2481  the side EF, and be reflected by the side FG, and thence go out of it
  2482  through the side GE, to the Point T, which must be the common Focus of
  2483  the Speculum ABDC, and of a Plano-convex Eye-glass H, through which
  2484  those Rays must pass to the Eye. And let the Rays at their coming out of
  2485  the Glass pass through a small round hole, or aperture made in a little
  2486  plate of Lead, Brass, or Silver, wherewith the Glass is to be covered,
  2487  which hole must be no bigger than is necessary for Light enough to pass
  2488  through. For so it will render the Object distinct, the Plate in which
  2489  'tis made intercepting all the erroneous part of the Light which comes
  2490  from the verges of the Speculum AB. Such an Instrument well made, if it
  2491  be six Foot long, (reckoning the length from the Speculum to the Prism,
  2492  and thence to the Focus T) will bear an aperture of six Inches at the
  2493  Speculum, and magnify between two and three hundred times. But the hole
  2494  H here limits the aperture with more advantage, than if the aperture was
  2495  placed at the Speculum. If the Instrument be made longer or shorter, the
  2496  aperture must be in proportion as the Cube of the square-square Root of
  2497  the length, and the magnifying as the aperture. But it's convenient that
  2498  the Speculum be an Inch or two broader than the aperture at the least,
  2499  and that the Glass of the Speculum be thick, that it bend not in the
  2500  working. The Prism EFG must be no bigger than is necessary, and its back
  2501  side FG must not be quick-silver'd over. For without quicksilver it will
  2502  reflect all the Light incident on it from the Speculum.
  2504  [Illustration: FIG. 29.]
  2506  In this Instrument the Object will be inverted, but may be erected by
  2507  making the square sides FF and EG of the Prism EFG not plane but
  2508  spherically convex, that the Rays may cross as well before they come at
  2509  it as afterwards between it and the Eye-glass. If it be desired that the
  2510  Instrument bear a larger aperture, that may be also done by composing
  2511  the Speculum of two Glasses with Water between them.
  2513  If the Theory of making Telescopes could at length be fully brought into
  2514  Practice, yet there would be certain Bounds beyond which Telescopes
  2515  could not perform. For the Air through which we look upon the Stars, is
  2516  in a perpetual Tremor; as may be seen by the tremulous Motion of Shadows
  2517  cast from high Towers, and by the twinkling of the fix'd Stars. But
  2518  these Stars do not twinkle when viewed through Telescopes which have
  2519  large apertures. For the Rays of Light which pass through divers parts
  2520  of the aperture, tremble each of them apart, and by means of their
  2521  various and sometimes contrary Tremors, fall at one and the same time
  2522  upon different points in the bottom of the Eye, and their trembling
  2523  Motions are too quick and confused to be perceived severally. And all
  2524  these illuminated Points constitute one broad lucid Point, composed of
  2525  those many trembling Points confusedly and insensibly mixed with one
  2526  another by very short and swift Tremors, and thereby cause the Star to
  2527  appear broader than it is, and without any trembling of the whole. Long
  2528  Telescopes may cause Objects to appear brighter and larger than short
  2529  ones can do, but they cannot be so formed as to take away that confusion
  2530  of the Rays which arises from the Tremors of the Atmosphere. The only
  2531  Remedy is a most serene and quiet Air, such as may perhaps be found on
  2532  the tops of the highest Mountains above the grosser Clouds.
  2534  FOOTNOTES:
  2536  [C] _See our_ Author's Lectiones Opticæ § 10. _Sect. II. § 29. and Sect.
  2537  III. Prop. 25._
  2539  [D] See our Author's _Lectiones Opticæ_, Part. I. Sect. 1. §5.
  2541  [E] _This is very fully treated of in our_ Author's Lect. Optic. _Part_
  2542  I. _Sect._ II.
  2544  [F] _See our_ Author's Lect. Optic. Part I. Sect. II. § 29.
  2546  [G] _This is demonstrated in our_ Author's Lect. Optic. _Part_ I.
  2547  _Sect._ IV. _Prop._ 37.
  2549  [H] _How to do this, is shewn in our_ Author's Lect. Optic. _Part_ I.
  2550  _Sect._ IV. _Prop._ 31.
  2560  _PART II._
  2563  _PROP._ I. THEOR. I.
  2565  _The Phænomena of Colours in refracted or reflected Light are not caused
  2566  by new Modifications of the Light variously impress'd, according to the
  2567  various Terminations of the Light and Shadow_.
  2569  The PROOF by Experiments.
  2571  _Exper._ 1. For if the Sun shine into a very dark Chamber through an
  2572  oblong hole F, [in _Fig._ 1.] whose breadth is the sixth or eighth part
  2573  of an Inch, or something less; and his beam FH do afterwards pass first
  2574  through a very large Prism ABC, distant about 20 Feet from the hole, and
  2575  parallel to it, and then (with its white part) through an oblong hole H,
  2576  whose breadth is about the fortieth or sixtieth part of an Inch, and
  2577  which is made in a black opake Body GI, and placed at the distance of
  2578  two or three Feet from the Prism, in a parallel Situation both to the
  2579  Prism and to the former hole, and if this white Light thus transmitted
  2580  through the hole H, fall afterwards upon a white Paper _pt_, placed
  2581  after that hole H, at the distance of three or four Feet from it, and
  2582  there paint the usual Colours of the Prism, suppose red at _t_, yellow
  2583  at _s_, green at _r_, blue at _q_, and violet at _p_; you may with an
  2584  Iron Wire, or any such like slender opake Body, whose breadth is about
  2585  the tenth part of an Inch, by intercepting the Rays at _k_, _l_, _m_,
  2586  _n_ or _o_, take away any one of the Colours at _t_, _s_, _r_, _q_ or
  2587  _p_, whilst the other Colours remain upon the Paper as before; or with
  2588  an Obstacle something bigger you may take away any two, or three, or
  2589  four Colours together, the rest remaining: So that any one of the
  2590  Colours as well as violet may become outmost in the Confine of the
  2591  Shadow towards _p_, and any one of them as well as red may become
  2592  outmost in the Confine of the Shadow towards _t_, and any one of them
  2593  may also border upon the Shadow made within the Colours by the Obstacle
  2594  R intercepting some intermediate part of the Light; and, lastly, any one
  2595  of them by being left alone, may border upon the Shadow on either hand.
  2596  All the Colours have themselves indifferently to any Confines of Shadow,
  2597  and therefore the differences of these Colours from one another, do not
  2598  arise from the different Confines of Shadow, whereby Light is variously
  2599  modified, as has hitherto been the Opinion of Philosophers. In trying
  2600  these things 'tis to be observed, that by how much the holes F and H are
  2601  narrower, and the Intervals between them and the Prism greater, and the
  2602  Chamber darker, by so much the better doth the Experiment succeed;
  2603  provided the Light be not so far diminished, but that the Colours at
  2604  _pt_ be sufficiently visible. To procure a Prism of solid Glass large
  2605  enough for this Experiment will be difficult, and therefore a prismatick
  2606  Vessel must be made of polish'd Glass Plates cemented together, and
  2607  filled with salt Water or clear Oil.
  2609  [Illustration: FIG. 1.]
  2611  _Exper._ 2. The Sun's Light let into a dark Chamber through the round
  2612  hole F, [in _Fig._ 2.] half an Inch wide, passed first through the Prism
  2613  ABC placed at the hole, and then through a Lens PT something more than
  2614  four Inches broad, and about eight Feet distant from the Prism, and
  2615  thence converged to O the Focus of the Lens distant from it about three
  2616  Feet, and there fell upon a white Paper DE. If that Paper was
  2617  perpendicular to that Light incident upon it, as 'tis represented in the
  2618  posture DE, all the Colours upon it at O appeared white. But if the
  2619  Paper being turned about an Axis parallel to the Prism, became very much
  2620  inclined to the Light, as 'tis represented in the Positions _de_ and
  2621  _[Greek: de]_; the same Light in the one case appeared yellow and red,
  2622  in the other blue. Here one and the same part of the Light in one and
  2623  the same place, according to the various Inclinations of the Paper,
  2624  appeared in one case white, in another yellow or red, in a third blue,
  2625  whilst the Confine of Light and shadow, and the Refractions of the Prism
  2626  in all these cases remained the same.
  2628  [Illustration: FIG. 2.]
  2630  [Illustration: FIG. 3.]
  2632  _Exper._ 3. Such another Experiment may be more easily tried as follows.
  2633  Let a broad beam of the Sun's Light coming into a dark Chamber through a
  2634  hole in the Window-shut be refracted by a large Prism ABC, [in _Fig._
  2635  3.] whose refracting Angle C is more than 60 Degrees, and so soon as it
  2636  comes out of the Prism, let it fall upon the white Paper DE glewed upon
  2637  a stiff Plane; and this Light, when the Paper is perpendicular to it, as
  2638  'tis represented in DE, will appear perfectly white upon the Paper; but
  2639  when the Paper is very much inclin'd to it in such a manner as to keep
  2640  always parallel to the Axis of the Prism, the whiteness of the whole
  2641  Light upon the Paper will according to the inclination of the Paper this
  2642  way or that way, change either into yellow and red, as in the posture
  2643  _de_, or into blue and violet, as in the posture [Greek: de]. And if the
  2644  Light before it fall upon the Paper be twice refracted the same way by
  2645  two parallel Prisms, these Colours will become the more conspicuous.
  2646  Here all the middle parts of the broad beam of white Light which fell
  2647  upon the Paper, did without any Confine of Shadow to modify it, become
  2648  colour'd all over with one uniform Colour, the Colour being always the
  2649  same in the middle of the Paper as at the edges, and this Colour changed
  2650  according to the various Obliquity of the reflecting Paper, without any
  2651  change in the Refractions or Shadow, or in the Light which fell upon the
  2652  Paper. And therefore these Colours are to be derived from some other
  2653  Cause than the new Modifications of Light by Refractions and Shadows.
  2655  If it be asked, what then is their Cause? I answer, That the Paper in
  2656  the posture _de_, being more oblique to the more refrangible Rays than
  2657  to the less refrangible ones, is more strongly illuminated by the latter
  2658  than by the former, and therefore the less refrangible Rays are
  2659  predominant in the reflected Light. And where-ever they are predominant
  2660  in any Light, they tinge it with red or yellow, as may in some measure
  2661  appear by the first Proposition of the first Part of this Book, and will
  2662  more fully appear hereafter. And the contrary happens in the posture of
  2663  the Paper [Greek: de], the more refrangible Rays being then predominant
  2664  which always tinge Light with blues and violets.
  2666  _Exper._ 4. The Colours of Bubbles with which Children play are various,
  2667  and change their Situation variously, without any respect to any Confine
  2668  or Shadow. If such a Bubble be cover'd with a concave Glass, to keep it
  2669  from being agitated by any Wind or Motion of the Air, the Colours will
  2670  slowly and regularly change their situation, even whilst the Eye and the
  2671  Bubble, and all Bodies which emit any Light, or cast any Shadow, remain
  2672  unmoved. And therefore their Colours arise from some regular Cause which
  2673  depends not on any Confine of Shadow. What this Cause is will be shewed
  2674  in the next Book.
  2676  To these Experiments may be added the tenth Experiment of the first Part
  2677  of this first Book, where the Sun's Light in a dark Room being
  2678  trajected through the parallel Superficies of two Prisms tied together
  2679  in the form of a Parallelopipede, became totally of one uniform yellow
  2680  or red Colour, at its emerging out of the Prisms. Here, in the
  2681  production of these Colours, the Confine of Shadow can have nothing to
  2682  do. For the Light changes from white to yellow, orange and red
  2683  successively, without any alteration of the Confine of Shadow: And at
  2684  both edges of the emerging Light where the contrary Confines of Shadow
  2685  ought to produce different Effects, the Colour is one and the same,
  2686  whether it be white, yellow, orange or red: And in the middle of the
  2687  emerging Light, where there is no Confine of Shadow at all, the Colour
  2688  is the very same as at the edges, the whole Light at its very first
  2689  Emergence being of one uniform Colour, whether white, yellow, orange or
  2690  red, and going on thence perpetually without any change of Colour, such
  2691  as the Confine of Shadow is vulgarly supposed to work in refracted Light
  2692  after its Emergence. Neither can these Colours arise from any new
  2693  Modifications of the Light by Refractions, because they change
  2694  successively from white to yellow, orange and red, while the Refractions
  2695  remain the same, and also because the Refractions are made contrary ways
  2696  by parallel Superficies which destroy one another's Effects. They arise
  2697  not therefore from any Modifications of Light made by Refractions and
  2698  Shadows, but have some other Cause. What that Cause is we shewed above
  2699  in this tenth Experiment, and need not here repeat it.
  2701  There is yet another material Circumstance of this Experiment. For this
  2702  emerging Light being by a third Prism HIK [in _Fig._ 22. _Part_ I.][I]
  2703  refracted towards the Paper PT, and there painting the usual Colours of
  2704  the Prism, red, yellow, green, blue, violet: If these Colours arose from
  2705  the Refractions of that Prism modifying the Light, they would not be in
  2706  the Light before its Incidence on that Prism. And yet in that Experiment
  2707  we found, that when by turning the two first Prisms about their common
  2708  Axis all the Colours were made to vanish but the red; the Light which
  2709  makes that red being left alone, appeared of the very same red Colour
  2710  before its Incidence on the third Prism. And in general we find by other
  2711  Experiments, that when the Rays which differ in Refrangibility are
  2712  separated from one another, and any one Sort of them is considered
  2713  apart, the Colour of the Light which they compose cannot be changed by
  2714  any Refraction or Reflexion whatever, as it ought to be were Colours
  2715  nothing else than Modifications of Light caused by Refractions, and
  2716  Reflexions, and Shadows. This Unchangeableness of Colour I am now to
  2717  describe in the following Proposition.
  2720  _PROP._ II. THEOR. II.
  2722  _All homogeneal Light has its proper Colour answering to its Degree of
  2723  Refrangibility, and that Colour cannot be changed by Reflexions and
  2724  Refractions._
  2726  In the Experiments of the fourth Proposition of the first Part of this
  2727  first Book, when I had separated the heterogeneous Rays from one
  2728  another, the Spectrum _pt_ formed by the separated Rays, did in the
  2729  Progress from its End _p_, on which the most refrangible Rays fell, unto
  2730  its other End _t_, on which the least refrangible Rays fell, appear
  2731  tinged with this Series of Colours, violet, indigo, blue, green, yellow,
  2732  orange, red, together with all their intermediate Degrees in a continual
  2733  Succession perpetually varying. So that there appeared as many Degrees
  2734  of Colours, as there were sorts of Rays differing in Refrangibility.
  2736  _Exper._ 5. Now, that these Colours could not be changed by Refraction,
  2737  I knew by refracting with a Prism sometimes one very little Part of this
  2738  Light, sometimes another very little Part, as is described in the
  2739  twelfth Experiment of the first Part of this Book. For by this
  2740  Refraction the Colour of the Light was never changed in the least. If
  2741  any Part of the red Light was refracted, it remained totally of the same
  2742  red Colour as before. No orange, no yellow, no green or blue, no other
  2743  new Colour was produced by that Refraction. Neither did the Colour any
  2744  ways change by repeated Refractions, but continued always the same red
  2745  entirely as at first. The like Constancy and Immutability I found also
  2746  in the blue, green, and other Colours. So also, if I looked through a
  2747  Prism upon any Body illuminated with any part of this homogeneal Light,
  2748  as in the fourteenth Experiment of the first Part of this Book is
  2749  described; I could not perceive any new Colour generated this way. All
  2750  Bodies illuminated with compound Light appear through Prisms confused,
  2751  (as was said above) and tinged with various new Colours, but those
  2752  illuminated with homogeneal Light appeared through Prisms neither less
  2753  distinct, nor otherwise colour'd, than when viewed with the naked Eyes.
  2754  Their Colours were not in the least changed by the Refraction of the
  2755  interposed Prism. I speak here of a sensible Change of Colour: For the
  2756  Light which I here call homogeneal, being not absolutely homogeneal,
  2757  there ought to arise some little Change of Colour from its
  2758  Heterogeneity. But, if that Heterogeneity was so little as it might be
  2759  made by the said Experiments of the fourth Proposition, that Change was
  2760  not sensible, and therefore in Experiments, where Sense is Judge, ought
  2761  to be accounted none at all.
  2763  _Exper._ 6. And as these Colours were not changeable by Refractions, so
  2764  neither were they by Reflexions. For all white, grey, red, yellow,
  2765  green, blue, violet Bodies, as Paper, Ashes, red Lead, Orpiment, Indico
  2766  Bise, Gold, Silver, Copper, Grass, blue Flowers, Violets, Bubbles of
  2767  Water tinged with various Colours, Peacock's Feathers, the Tincture of
  2768  _Lignum Nephriticum_, and such-like, in red homogeneal Light appeared
  2769  totally red, in blue Light totally blue, in green Light totally green,
  2770  and so of other Colours. In the homogeneal Light of any Colour they all
  2771  appeared totally of that same Colour, with this only Difference, that
  2772  some of them reflected that Light more strongly, others more faintly. I
  2773  never yet found any Body, which by reflecting homogeneal Light could
  2774  sensibly change its Colour.
  2776  From all which it is manifest, that if the Sun's Light consisted of but
  2777  one sort of Rays, there would be but one Colour in the whole World, nor
  2778  would it be possible to produce any new Colour by Reflexions and
  2779  Refractions, and by consequence that the variety of Colours depends upon
  2780  the Composition of Light.
  2783  _DEFINITION._
  2785  The homogeneal Light and Rays which appear red, or rather make Objects
  2786  appear so, I call Rubrifick or Red-making; those which make Objects
  2787  appear yellow, green, blue, and violet, I call Yellow-making,
  2788  Green-making, Blue-making, Violet-making, and so of the rest. And if at
  2789  any time I speak of Light and Rays as coloured or endued with Colours, I
  2790  would be understood to speak not philosophically and properly, but
  2791  grossly, and accordingly to such Conceptions as vulgar People in seeing
  2792  all these Experiments would be apt to frame. For the Rays to speak
  2793  properly are not coloured. In them there is nothing else than a certain
  2794  Power and Disposition to stir up a Sensation of this or that Colour.
  2795  For as Sound in a Bell or musical String, or other sounding Body, is
  2796  nothing but a trembling Motion, and in the Air nothing but that Motion
  2797  propagated from the Object, and in the Sensorium 'tis a Sense of that
  2798  Motion under the Form of Sound; so Colours in the Object are nothing but
  2799  a Disposition to reflect this or that sort of Rays more copiously than
  2800  the rest; in the Rays they are nothing but their Dispositions to
  2801  propagate this or that Motion into the Sensorium, and in the Sensorium
  2802  they are Sensations of those Motions under the Forms of Colours.
  2805  _PROP._ III. PROB. I.
  2807  _To define the Refrangibility of the several sorts of homogeneal Light
  2808  answering to the several Colours._
  2810  For determining this Problem I made the following Experiment.[J]
  2812  _Exper._ 7. When I had caused the Rectilinear Sides AF, GM, [in _Fig._
  2813  4.] of the Spectrum of Colours made by the Prism to be distinctly
  2814  defined, as in the fifth Experiment of the first Part of this Book is
  2815  described, there were found in it all the homogeneal Colours in the same
  2816  Order and Situation one among another as in the Spectrum of simple
  2817  Light, described in the fourth Proposition of that Part. For the Circles
  2818  of which the Spectrum of compound Light PT is composed, and which in
  2819  the middle Parts of the Spectrum interfere, and are intermix'd with one
  2820  another, are not intermix'd in their outmost Parts where they touch
  2821  those Rectilinear Sides AF and GM. And therefore, in those Rectilinear
  2822  Sides when distinctly defined, there is no new Colour generated by
  2823  Refraction. I observed also, that if any where between the two outmost
  2824  Circles TMF and PGA a Right Line, as [Greek: gd], was cross to the
  2825  Spectrum, so as both Ends to fall perpendicularly upon its Rectilinear
  2826  Sides, there appeared one and the same Colour, and degree of Colour from
  2827  one End of this Line to the other. I delineated therefore in a Paper the
  2828  Perimeter of the Spectrum FAP GMT, and in trying the third Experiment of
  2829  the first Part of this Book, I held the Paper so that the Spectrum might
  2830  fall upon this delineated Figure, and agree with it exactly, whilst an
  2831  Assistant, whose Eyes for distinguishing Colours were more critical than
  2832  mine, did by Right Lines [Greek: ab, gd, ez,] &c. drawn cross the
  2833  Spectrum, note the Confines of the Colours, that is of the red M[Greek:
  2834  ab]F, of the orange [Greek: agdb], of the yellow [Greek: gezd], of the
  2835  green [Greek: eêthz], of the blue [Greek: êikth], of the indico [Greek:
  2836  ilmk], and of the violet [Greek: l]GA[Greek: m]. And this Operation
  2837  being divers times repeated both in the same, and in several Papers, I
  2838  found that the Observations agreed well enough with one another, and
  2839  that the Rectilinear Sides MG and FA were by the said cross Lines
  2840  divided after the manner of a Musical Chord. Let GM be produced to X,
  2841  that MX may be equal to GM, and conceive GX, [Greek: l]X, [Greek: i]X,
  2842  [Greek: ê]X, [Greek: e]X, [Greek: g]X, [Greek: a]X, MX, to be in
  2843  proportion to one another, as the Numbers, 1, 8/9, 5/6, 3/4, 2/3, 3/5,
  2844  9/16, 1/2, and so to represent the Chords of the Key, and of a Tone, a
  2845  third Minor, a fourth, a fifth, a sixth Major, a seventh and an eighth
  2846  above that Key: And the Intervals M[Greek: a], [Greek: ag], [Greek: ge],
  2847  [Greek: eê], [Greek: êi], [Greek: il], and [Greek: l]G, will be the
  2848  Spaces which the several Colours (red, orange, yellow, green, blue,
  2849  indigo, violet) take up.
  2851  [Illustration: FIG. 4.]
  2853  [Illustration: FIG. 5.]
  2855  Now these Intervals or Spaces subtending the Differences of the
  2856  Refractions of the Rays going to the Limits of those Colours, that is,
  2857  to the Points M, [Greek: a], [Greek: g], [Greek: e], [Greek: ê], [Greek:
  2858  i], [Greek: l], G, may without any sensible Error be accounted
  2859  proportional to the Differences of the Sines of Refraction of those Rays
  2860  having one common Sine of Incidence, and therefore since the common Sine
  2861  of Incidence of the most and least refrangible Rays out of Glass into
  2862  Air was (by a Method described above) found in proportion to their Sines
  2863  of Refraction, as 50 to 77 and 78, divide the Difference between the
  2864  Sines of Refraction 77 and 78, as the Line GM is divided by those
  2865  Intervals, and you will have 77, 77-1/8, 77-1/5, 77-1/3, 77-1/2, 77-2/3,
  2866  77-7/9, 78, the Sines of Refraction of those Rays out of Glass into Air,
  2867  their common Sine of Incidence being 50. So then the Sines of the
  2868  Incidences of all the red-making Rays out of Glass into Air, were to the
  2869  Sines of their Refractions, not greater than 50 to 77, nor less than 50
  2870  to 77-1/8, but they varied from one another according to all
  2871  intermediate Proportions. And the Sines of the Incidences of the
  2872  green-making Rays were to the Sines of their Refractions in all
  2873  Proportions from that of 50 to 77-1/3, unto that of 50 to 77-1/2. And
  2874  by the like Limits above-mentioned were the Refractions of the Rays
  2875  belonging to the rest of the Colours defined, the Sines of the
  2876  red-making Rays extending from 77 to 77-1/8, those of the orange-making
  2877  from 77-1/8 to 77-1/5, those of the yellow-making from 77-1/5 to 77-1/3,
  2878  those of the green-making from 77-1/3 to 77-1/2, those of the
  2879  blue-making from 77-1/2 to 77-2/3, those of the indigo-making from
  2880  77-2/3 to 77-7/9, and those of the violet from 77-7/9, to 78.
  2882  These are the Laws of the Refractions made out of Glass into Air, and
  2883  thence by the third Axiom of the first Part of this Book, the Laws of
  2884  the Refractions made out of Air into Glass are easily derived.
  2886  _Exper._ 8. I found moreover, that when Light goes out of Air through
  2887  several contiguous refracting Mediums as through Water and Glass, and
  2888  thence goes out again into Air, whether the refracting Superficies be
  2889  parallel or inclin'd to one another, that Light as often as by contrary
  2890  Refractions 'tis so corrected, that it emergeth in Lines parallel to
  2891  those in which it was incident, continues ever after to be white. But if
  2892  the emergent Rays be inclined to the incident, the Whiteness of the
  2893  emerging Light will by degrees in passing on from the Place of
  2894  Emergence, become tinged in its Edges with Colours. This I try'd by
  2895  refracting Light with Prisms of Glass placed within a Prismatick Vessel
  2896  of Water. Now those Colours argue a diverging and separation of the
  2897  heterogeneous Rays from one another by means of their unequal
  2898  Refractions, as in what follows will more fully appear. And, on the
  2899  contrary, the permanent whiteness argues, that in like Incidences of the
  2900  Rays there is no such separation of the emerging Rays, and by
  2901  consequence no inequality of their whole Refractions. Whence I seem to
  2902  gather the two following Theorems.
  2904  1. The Excesses of the Sines of Refraction of several sorts of Rays
  2905  above their common Sine of Incidence when the Refractions are made out
  2906  of divers denser Mediums immediately into one and the same rarer Medium,
  2907  suppose of Air, are to one another in a given Proportion.
  2909  2. The Proportion of the Sine of Incidence to the Sine of Refraction of
  2910  one and the same sort of Rays out of one Medium into another, is
  2911  composed of the Proportion of the Sine of Incidence to the Sine of
  2912  Refraction out of the first Medium into any third Medium, and of the
  2913  Proportion of the Sine of Incidence to the Sine of Refraction out of
  2914  that third Medium into the second Medium.
  2916  By the first Theorem the Refractions of the Rays of every sort made out
  2917  of any Medium into Air are known by having the Refraction of the Rays of
  2918  any one sort. As for instance, if the Refractions of the Rays of every
  2919  sort out of Rain-water into Air be desired, let the common Sine of
  2920  Incidence out of Glass into Air be subducted from the Sines of
  2921  Refraction, and the Excesses will be 27, 27-1/8, 27-1/5, 27-1/3, 27-1/2,
  2922  27-2/3, 27-7/9, 28. Suppose now that the Sine of Incidence of the least
  2923  refrangible Rays be to their Sine of Refraction out of Rain-water into
  2924  Air as 3 to 4, and say as 1 the difference of those Sines is to 3 the
  2925  Sine of Incidence, so is 27 the least of the Excesses above-mentioned to
  2926  a fourth Number 81; and 81 will be the common Sine of Incidence out of
  2927  Rain-water into Air, to which Sine if you add all the above-mentioned
  2928  Excesses, you will have the desired Sines of the Refractions 108,
  2929  108-1/8, 108-1/5, 108-1/3, 108-1/2, 108-2/3, 108-7/9, 109.
  2931  By the latter Theorem the Refraction out of one Medium into another is
  2932  gathered as often as you have the Refractions out of them both into any
  2933  third Medium. As if the Sine of Incidence of any Ray out of Glass into
  2934  Air be to its Sine of Refraction, as 20 to 31, and the Sine of Incidence
  2935  of the same Ray out of Air into Water, be to its Sine of Refraction as 4
  2936  to 3; the Sine of Incidence of that Ray out of Glass into Water will be
  2937  to its Sine of Refraction as 20 to 31 and 4 to 3 jointly, that is, as
  2938  the Factum of 20 and 4 to the Factum of 31 and 3, or as 80 to 93.
  2940  And these Theorems being admitted into Opticks, there would be scope
  2941  enough of handling that Science voluminously after a new manner,[K] not
  2942  only by teaching those things which tend to the perfection of Vision,
  2943  but also by determining mathematically all kinds of Phænomena of Colours
  2944  which could be produced by Refractions. For to do this, there is nothing
  2945  else requisite than to find out the Separations of heterogeneous Rays,
  2946  and their various Mixtures and Proportions in every Mixture. By this
  2947  way of arguing I invented almost all the Phænomena described in these
  2948  Books, beside some others less necessary to the Argument; and by the
  2949  successes I met with in the Trials, I dare promise, that to him who
  2950  shall argue truly, and then try all things with good Glasses and
  2951  sufficient Circumspection, the expected Event will not be wanting. But
  2952  he is first to know what Colours will arise from any others mix'd in any
  2953  assigned Proportion.
  2956  _PROP._ IV. THEOR. III.
  2958  _Colours may be produced by Composition which shall be like to the
  2959  Colours of homogeneal Light as to the Appearance of Colour, but not as
  2960  to the Immutability of Colour and Constitution of Light. And those
  2961  Colours by how much they are more compounded by so much are they less
  2962  full and intense, and by too much Composition they maybe diluted and
  2963  weaken'd till they cease, and the Mixture becomes white or grey. There
  2964  may be also Colours produced by Composition, which are not fully like
  2965  any of the Colours of homogeneal Light._
  2967  For a Mixture of homogeneal red and yellow compounds an Orange, like in
  2968  appearance of Colour to that orange which in the series of unmixed
  2969  prismatick Colours lies between them; but the Light of one orange is
  2970  homogeneal as to Refrangibility, and that of the other is heterogeneal,
  2971  and the Colour of the one, if viewed through a Prism, remains unchanged,
  2972  that of the other is changed and resolved into its component Colours red
  2973  and yellow. And after the same manner other neighbouring homogeneal
  2974  Colours may compound new Colours, like the intermediate homogeneal ones,
  2975  as yellow and green, the Colour between them both, and afterwards, if
  2976  blue be added, there will be made a green the middle Colour of the three
  2977  which enter the Composition. For the yellow and blue on either hand, if
  2978  they are equal in quantity they draw the intermediate green equally
  2979  towards themselves in Composition, and so keep it as it were in
  2980  Æquilibrion, that it verge not more to the yellow on the one hand, and
  2981  to the blue on the other, but by their mix'd Actions remain still a
  2982  middle Colour. To this mix'd green there may be farther added some red
  2983  and violet, and yet the green will not presently cease, but only grow
  2984  less full and vivid, and by increasing the red and violet, it will grow
  2985  more and more dilute, until by the prevalence of the added Colours it be
  2986  overcome and turned into whiteness, or some other Colour. So if to the
  2987  Colour of any homogeneal Light, the Sun's white Light composed of all
  2988  sorts of Rays be added, that Colour will not vanish or change its
  2989  Species, but be diluted, and by adding more and more white it will be
  2990  diluted more and more perpetually. Lastly, If red and violet be mingled,
  2991  there will be generated according to their various Proportions various
  2992  Purples, such as are not like in appearance to the Colour of any
  2993  homogeneal Light, and of these Purples mix'd with yellow and blue may be
  2994  made other new Colours.
  2997  _PROP._ V. THEOR. IV.
  2999  _Whiteness and all grey Colours between white and black, may be
  3000  compounded of Colours, and the whiteness of the Sun's Light is
  3001  compounded of all the primary Colours mix'd in a due Proportion._
  3003  The PROOF by Experiments.
  3005  _Exper._ 9. The Sun shining into a dark Chamber through a little round
  3006  hole in the Window-shut, and his Light being there refracted by a Prism
  3007  to cast his coloured Image PT [in _Fig._ 5.] upon the opposite Wall: I
  3008  held a white Paper V to that image in such manner that it might be
  3009  illuminated by the colour'd Light reflected from thence, and yet not
  3010  intercept any part of that Light in its passage from the Prism to the
  3011  Spectrum. And I found that when the Paper was held nearer to any Colour
  3012  than to the rest, it appeared of that Colour to which it approached
  3013  nearest; but when it was equally or almost equally distant from all the
  3014  Colours, so that it might be equally illuminated by them all it appeared
  3015  white. And in this last situation of the Paper, if some Colours were
  3016  intercepted, the Paper lost its white Colour, and appeared of the Colour
  3017  of the rest of the Light which was not intercepted. So then the Paper
  3018  was illuminated with Lights of various Colours, namely, red, yellow,
  3019  green, blue and violet, and every part of the Light retained its proper
  3020  Colour, until it was incident on the Paper, and became reflected thence
  3021  to the Eye; so that if it had been either alone (the rest of the Light
  3022  being intercepted) or if it had abounded most, and been predominant in
  3023  the Light reflected from the Paper, it would have tinged the Paper with
  3024  its own Colour; and yet being mixed with the rest of the Colours in a
  3025  due proportion, it made the Paper look white, and therefore by a
  3026  Composition with the rest produced that Colour. The several parts of the
  3027  coloured Light reflected from the Spectrum, whilst they are propagated
  3028  from thence through the Air, do perpetually retain their proper Colours,
  3029  because wherever they fall upon the Eyes of any Spectator, they make the
  3030  several parts of the Spectrum to appear under their proper Colours. They
  3031  retain therefore their proper Colours when they fall upon the Paper V,
  3032  and so by the confusion and perfect mixture of those Colours compound
  3033  the whiteness of the Light reflected from thence.
  3035  _Exper._ 10. Let that Spectrum or solar Image PT [in _Fig._ 6.] fall now
  3036  upon the Lens MN above four Inches broad, and about six Feet distant
  3037  from the Prism ABC and so figured that it may cause the coloured Light
  3038  which divergeth from the Prism to converge and meet again at its Focus
  3039  G, about six or eight Feet distant from the Lens, and there to fall
  3040  perpendicularly upon a white Paper DE. And if you move this Paper to and
  3041  fro, you will perceive that near the Lens, as at _de_, the whole solar
  3042  Image (suppose at _pt_) will appear upon it intensely coloured after the
  3043  manner above-explained, and that by receding from the Lens those Colours
  3044  will perpetually come towards one another, and by mixing more and more
  3045  dilute one another continually, until at length the Paper come to the
  3046  Focus G, where by a perfect mixture they will wholly vanish and be
  3047  converted into whiteness, the whole Light appearing now upon the Paper
  3048  like a little white Circle. And afterwards by receding farther from the
  3049  Lens, the Rays which before converged will now cross one another in the
  3050  Focus G, and diverge from thence, and thereby make the Colours to appear
  3051  again, but yet in a contrary order; suppose at [Greek: de], where the
  3052  red _t_ is now above which before was below, and the violet _p_ is below
  3053  which before was above.
  3055  Let us now stop the Paper at the Focus G, where the Light appears
  3056  totally white and circular, and let us consider its whiteness. I say,
  3057  that this is composed of the converging Colours. For if any of those
  3058  Colours be intercepted at the Lens, the whiteness will cease and
  3059  degenerate into that Colour which ariseth from the composition of the
  3060  other Colours which are not intercepted. And then if the intercepted
  3061  Colours be let pass and fall upon that compound Colour, they mix with
  3062  it, and by their mixture restore the whiteness. So if the violet, blue
  3063  and green be intercepted, the remaining yellow, orange and red will
  3064  compound upon the Paper an orange, and then if the intercepted Colours
  3065  be let pass, they will fall upon this compounded orange, and together
  3066  with it decompound a white. So also if the red and violet be
  3067  intercepted, the remaining yellow, green and blue, will compound a green
  3068  upon the Paper, and then the red and violet being let pass will fall
  3069  upon this green, and together with it decompound a white. And that in
  3070  this Composition of white the several Rays do not suffer any Change in
  3071  their colorific Qualities by acting upon one another, but are only
  3072  mixed, and by a mixture of their Colours produce white, may farther
  3073  appear by these Arguments.
  3075  [Illustration: FIG. 6.]
  3077  If the Paper be placed beyond the Focus G, suppose at [Greek: de], and
  3078  then the red Colour at the Lens be alternately intercepted, and let pass
  3079  again, the violet Colour on the Paper will not suffer any Change
  3080  thereby, as it ought to do if the several sorts of Rays acted upon one
  3081  another in the Focus G, where they cross. Neither will the red upon the
  3082  Paper be changed by any alternate stopping, and letting pass the violet
  3083  which crosseth it.
  3085  And if the Paper be placed at the Focus G, and the white round Image at
  3086  G be viewed through the Prism HIK, and by the Refraction of that Prism
  3087  be translated to the place _rv_, and there appear tinged with various
  3088  Colours, namely, the violet at _v_ and red at _r_, and others between,
  3089  and then the red Colours at the Lens be often stopp'd and let pass by
  3090  turns, the red at _r_ will accordingly disappear, and return as often,
  3091  but the violet at _v_ will not thereby suffer any Change. And so by
  3092  stopping and letting pass alternately the blue at the Lens, the blue at
  3093  _v_ will accordingly disappear and return, without any Change made in
  3094  the red at _r_. The red therefore depends on one sort of Rays, and the
  3095  blue on another sort, which in the Focus G where they are commix'd, do
  3096  not act on one another. And there is the same Reason of the other
  3097  Colours.
  3099  I considered farther, that when the most refrangible Rays P_p_, and the
  3100  least refrangible ones T_t_, are by converging inclined to one another,
  3101  the Paper, if held very oblique to those Rays in the Focus G, might
  3102  reflect one sort of them more copiously than the other sort, and by that
  3103  Means the reflected Light would be tinged in that Focus with the Colour
  3104  of the predominant Rays, provided those Rays severally retained their
  3105  Colours, or colorific Qualities in the Composition of White made by them
  3106  in that Focus. But if they did not retain them in that White, but became
  3107  all of them severally endued there with a Disposition to strike the
  3108  Sense with the Perception of White, then they could never lose their
  3109  Whiteness by such Reflexions. I inclined therefore the Paper to the Rays
  3110  very obliquely, as in the second Experiment of this second Part of the
  3111  first Book, that the most refrangible Rays, might be more copiously
  3112  reflected than the rest, and the Whiteness at Length changed
  3113  successively into blue, indigo, and violet. Then I inclined it the
  3114  contrary Way, that the least refrangible Rays might be more copious in
  3115  the reflected Light than the rest, and the Whiteness turned successively
  3116  to yellow, orange, and red.
  3118  Lastly, I made an Instrument XY in fashion of a Comb, whose Teeth being
  3119  in number sixteen, were about an Inch and a half broad, and the
  3120  Intervals of the Teeth about two Inches wide. Then by interposing
  3121  successively the Teeth of this Instrument near the Lens, I intercepted
  3122  Part of the Colours by the interposed Tooth, whilst the rest of them
  3123  went on through the Interval of the Teeth to the Paper DE, and there
  3124  painted a round Solar Image. But the Paper I had first placed so, that
  3125  the Image might appear white as often as the Comb was taken away; and
  3126  then the Comb being as was said interposed, that Whiteness by reason of
  3127  the intercepted Part of the Colours at the Lens did always change into
  3128  the Colour compounded of those Colours which were not intercepted, and
  3129  that Colour was by the Motion of the Comb perpetually varied so, that in
  3130  the passing of every Tooth over the Lens all these Colours, red, yellow,
  3131  green, blue, and purple, did always succeed one another. I caused
  3132  therefore all the Teeth to pass successively over the Lens, and when the
  3133  Motion was slow, there appeared a perpetual Succession of the Colours
  3134  upon the Paper: But if I so much accelerated the Motion, that the
  3135  Colours by reason of their quick Succession could not be distinguished
  3136  from one another, the Appearance of the single Colours ceased. There was
  3137  no red, no yellow, no green, no blue, nor purple to be seen any longer,
  3138  but from a Confusion of them all there arose one uniform white Colour.
  3139  Of the Light which now by the Mixture of all the Colours appeared white,
  3140  there was no Part really white. One Part was red, another yellow, a
  3141  third green, a fourth blue, a fifth purple, and every Part retains its
  3142  proper Colour till it strike the Sensorium. If the Impressions follow
  3143  one another slowly, so that they may be severally perceived, there is
  3144  made a distinct Sensation of all the Colours one after another in a
  3145  continual Succession. But if the Impressions follow one another so
  3146  quickly, that they cannot be severally perceived, there ariseth out of
  3147  them all one common Sensation, which is neither of this Colour alone nor
  3148  of that alone, but hath it self indifferently to 'em all, and this is a
  3149  Sensation of Whiteness. By the Quickness of the Successions, the
  3150  Impressions of the several Colours are confounded in the Sensorium, and
  3151  out of that Confusion ariseth a mix'd Sensation. If a burning Coal be
  3152  nimbly moved round in a Circle with Gyrations continually repeated, the
  3153  whole Circle will appear like Fire; the reason of which is, that the
  3154  Sensation of the Coal in the several Places of that Circle remains
  3155  impress'd on the Sensorium, until the Coal return again to the same
  3156  Place. And so in a quick Consecution of the Colours the Impression of
  3157  every Colour remains in the Sensorium, until a Revolution of all the
  3158  Colours be compleated, and that first Colour return again. The
  3159  Impressions therefore of all the successive Colours are at once in the
  3160  Sensorium, and jointly stir up a Sensation of them all; and so it is
  3161  manifest by this Experiment, that the commix'd Impressions of all the
  3162  Colours do stir up and beget a Sensation of white, that is, that
  3163  Whiteness is compounded of all the Colours.
  3165  And if the Comb be now taken away, that all the Colours may at once pass
  3166  from the Lens to the Paper, and be there intermixed, and together
  3167  reflected thence to the Spectator's Eyes; their Impressions on the
  3168  Sensorium being now more subtilly and perfectly commixed there, ought
  3169  much more to stir up a Sensation of Whiteness.
  3171  You may instead of the Lens use two Prisms HIK and LMN, which by
  3172  refracting the coloured Light the contrary Way to that of the first
  3173  Refraction, may make the diverging Rays converge and meet again in G, as
  3174  you see represented in the seventh Figure. For where they meet and mix,
  3175  they will compose a white Light, as when a Lens is used.
  3177  _Exper._ 11. Let the Sun's coloured Image PT [in _Fig._ 8.] fall upon
  3178  the Wall of a dark Chamber, as in the third Experiment of the first
  3179  Book, and let the same be viewed through a Prism _abc_, held parallel to
  3180  the Prism ABC, by whose Refraction that Image was made, and let it now
  3181  appear lower than before, suppose in the Place S over-against the red
  3182  Colour T. And if you go near to the Image PT, the Spectrum S will appear
  3183  oblong and coloured like the Image PT; but if you recede from it, the
  3184  Colours of the spectrum S will be contracted more and more, and at
  3185  length vanish, that Spectrum S becoming perfectly round and white; and
  3186  if you recede yet farther, the Colours will emerge again, but in a
  3187  contrary Order. Now that Spectrum S appears white in that Case, when the
  3188  Rays of several sorts which converge from the several Parts of the Image
  3189  PT, to the Prism _abc_, are so refracted unequally by it, that in their
  3190  Passage from the Prism to the Eye they may diverge from one and the same
  3191  Point of the Spectrum S, and so fall afterwards upon one and the same
  3192  Point in the bottom of the Eye, and there be mingled.
  3194  [Illustration: FIG. 7.]
  3196  [Illustration: FIG. 8.]
  3198  And farther, if the Comb be here made use of, by whose Teeth the Colours
  3199  at the Image PT may be successively intercepted; the Spectrum S, when
  3200  the Comb is moved slowly, will be perpetually tinged with successive
  3201  Colours: But when by accelerating the Motion of the Comb, the Succession
  3202  of the Colours is so quick that they cannot be severally seen, that
  3203  Spectrum S, by a confused and mix'd Sensation of them all, will appear
  3204  white.
  3206  _Exper._ 12. The Sun shining through a large Prism ABC [in _Fig._ 9.]
  3207  upon a Comb XY, placed immediately behind the Prism, his Light which
  3208  passed through the Interstices of the Teeth fell upon a white Paper DE.
  3209  The Breadths of the Teeth were equal to their Interstices, and seven
  3210  Teeth together with their Interstices took up an Inch in Breadth. Now,
  3211  when the Paper was about two or three Inches distant from the Comb, the
  3212  Light which passed through its several Interstices painted so many
  3213  Ranges of Colours, _kl_, _mn_, _op_, _qr_, &c. which were parallel to
  3214  one another, and contiguous, and without any Mixture of white. And these
  3215  Ranges of Colours, if the Comb was moved continually up and down with a
  3216  reciprocal Motion, ascended and descended in the Paper, and when the
  3217  Motion of the Comb was so quick, that the Colours could not be
  3218  distinguished from one another, the whole Paper by their Confusion and
  3219  Mixture in the Sensorium appeared white.
  3221  [Illustration: FIG. 9.]
  3223  Let the Comb now rest, and let the Paper be removed farther from the
  3224  Prism, and the several Ranges of Colours will be dilated and expanded
  3225  into one another more and more, and by mixing their Colours will dilute
  3226  one another, and at length, when the distance of the Paper from the Comb
  3227  is about a Foot, or a little more (suppose in the Place 2D 2E) they will
  3228  so far dilute one another, as to become white.
  3230  With any Obstacle, let all the Light be now stopp'd which passes through
  3231  any one Interval of the Teeth, so that the Range of Colours which comes
  3232  from thence may be taken away, and you will see the Light of the rest of
  3233  the Ranges to be expanded into the Place of the Range taken away, and
  3234  there to be coloured. Let the intercepted Range pass on as before, and
  3235  its Colours falling upon the Colours of the other Ranges, and mixing
  3236  with them, will restore the Whiteness.
  3238  Let the Paper 2D 2E be now very much inclined to the Rays, so that the
  3239  most refrangible Rays may be more copiously reflected than the rest, and
  3240  the white Colour of the Paper through the Excess of those Rays will be
  3241  changed into blue and violet. Let the Paper be as much inclined the
  3242  contrary way, that the least refrangible Rays may be now more copiously
  3243  reflected than the rest, and by their Excess the Whiteness will be
  3244  changed into yellow and red. The several Rays therefore in that white
  3245  Light do retain their colorific Qualities, by which those of any sort,
  3246  whenever they become more copious than the rest, do by their Excess and
  3247  Predominance cause their proper Colour to appear.
  3249  And by the same way of arguing, applied to the third Experiment of this
  3250  second Part of the first Book, it may be concluded, that the white
  3251  Colour of all refracted Light at its very first Emergence, where it
  3252  appears as white as before its Incidence, is compounded of various
  3253  Colours.
  3255  [Illustration: FIG. 10.]
  3257  _Exper._ 13. In the foregoing Experiment the several Intervals of the
  3258  Teeth of the Comb do the Office of so many Prisms, every Interval
  3259  producing the Phænomenon of one Prism. Whence instead of those Intervals
  3260  using several Prisms, I try'd to compound Whiteness by mixing their
  3261  Colours, and did it by using only three Prisms, as also by using only
  3262  two as follows. Let two Prisms ABC and _abc_, [in _Fig._ 10.] whose
  3263  refracting Angles B and _b_ are equal, be so placed parallel to one
  3264  another, that the refracting Angle B of the one may touch the Angle _c_
  3265  at the Base of the other, and their Planes CB and _cb_, at which the
  3266  Rays emerge, may lie in Directum. Then let the Light trajected through
  3267  them fall upon the Paper MN, distant about 8 or 12 Inches from the
  3268  Prisms. And the Colours generated by the interior Limits B and _c_ of
  3269  the two Prisms, will be mingled at PT, and there compound white. For if
  3270  either Prism be taken away, the Colours made by the other will appear in
  3271  that Place PT, and when the Prism is restored to its Place again, so
  3272  that its Colours may there fall upon the Colours of the other, the
  3273  Mixture of them both will restore the Whiteness.
  3275  This Experiment succeeds also, as I have tried, when the Angle _b_ of
  3276  the lower Prism, is a little greater than the Angle B of the upper, and
  3277  between the interior Angles B and _c_, there intercedes some Space B_c_,
  3278  as is represented in the Figure, and the refracting Planes BC and _bc_,
  3279  are neither in Directum, nor parallel to one another. For there is
  3280  nothing more requisite to the Success of this Experiment, than that the
  3281  Rays of all sorts may be uniformly mixed upon the Paper in the Place PT.
  3282  If the most refrangible Rays coming from the superior Prism take up all
  3283  the Space from M to P, the Rays of the same sort which come from the
  3284  inferior Prism ought to begin at P, and take up all the rest of the
  3285  Space from thence towards N. If the least refrangible Rays coming from
  3286  the superior Prism take up the Space MT, the Rays of the same kind which
  3287  come from the other Prism ought to begin at T, and take up the
  3288  remaining Space TN. If one sort of the Rays which have intermediate
  3289  Degrees of Refrangibility, and come from the superior Prism be extended
  3290  through the Space MQ, and another sort of those Rays through the Space
  3291  MR, and a third sort of them through the Space MS, the same sorts of
  3292  Rays coming from the lower Prism, ought to illuminate the remaining
  3293  Spaces QN, RN, SN, respectively. And the same is to be understood of all
  3294  the other sorts of Rays. For thus the Rays of every sort will be
  3295  scattered uniformly and evenly through the whole Space MN, and so being
  3296  every where mix'd in the same Proportion, they must every where produce
  3297  the same Colour. And therefore, since by this Mixture they produce white
  3298  in the Exterior Spaces MP and TN, they must also produce white in the
  3299  Interior Space PT. This is the reason of the Composition by which
  3300  Whiteness was produced in this Experiment, and by what other way soever
  3301  I made the like Composition, the Result was Whiteness.
  3303  Lastly, If with the Teeth of a Comb of a due Size, the coloured Lights
  3304  of the two Prisms which fall upon the Space PT be alternately
  3305  intercepted, that Space PT, when the Motion of the Comb is slow, will
  3306  always appear coloured, but by accelerating the Motion of the Comb so
  3307  much that the successive Colours cannot be distinguished from one
  3308  another, it will appear white.
  3310  _Exper._ 14. Hitherto I have produced Whiteness by mixing the Colours of
  3311  Prisms. If now the Colours of natural Bodies are to be mingled, let
  3312  Water a little thicken'd with Soap be agitated to raise a Froth, and
  3313  after that Froth has stood a little, there will appear to one that shall
  3314  view it intently various Colours every where in the Surfaces of the
  3315  several Bubbles; but to one that shall go so far off, that he cannot
  3316  distinguish the Colours from one another, the whole Froth will grow
  3317  white with a perfect Whiteness.
  3319  _Exper._ 15. Lastly, In attempting to compound a white, by mixing the
  3320  coloured Powders which Painters use, I consider'd that all colour'd
  3321  Powders do suppress and stop in them a very considerable Part of the
  3322  Light by which they are illuminated. For they become colour'd by
  3323  reflecting the Light of their own Colours more copiously, and that of
  3324  all other Colours more sparingly, and yet they do not reflect the Light
  3325  of their own Colours so copiously as white Bodies do. If red Lead, for
  3326  instance, and a white Paper, be placed in the red Light of the colour'd
  3327  Spectrum made in a dark Chamber by the Refraction of a Prism, as is
  3328  described in the third Experiment of the first Part of this Book; the
  3329  Paper will appear more lucid than the red Lead, and therefore reflects
  3330  the red-making Rays more copiously than red Lead doth. And if they be
  3331  held in the Light of any other Colour, the Light reflected by the Paper
  3332  will exceed the Light reflected by the red Lead in a much greater
  3333  Proportion. And the like happens in Powders of other Colours. And
  3334  therefore by mixing such Powders, we are not to expect a strong and
  3335  full White, such as is that of Paper, but some dusky obscure one, such
  3336  as might arise from a Mixture of Light and Darkness, or from white and
  3337  black, that is, a grey, or dun, or russet brown, such as are the Colours
  3338  of a Man's Nail, of a Mouse, of Ashes, of ordinary Stones, of Mortar, of
  3339  Dust and Dirt in High-ways, and the like. And such a dark white I have
  3340  often produced by mixing colour'd Powders. For thus one Part of red
  3341  Lead, and five Parts of _Viride Æris_, composed a dun Colour like that
  3342  of a Mouse. For these two Colours were severally so compounded of
  3343  others, that in both together were a Mixture of all Colours; and there
  3344  was less red Lead used than _Viride Æris_, because of the Fulness of its
  3345  Colour. Again, one Part of red Lead, and four Parts of blue Bise,
  3346  composed a dun Colour verging a little to purple, and by adding to this
  3347  a certain Mixture of Orpiment and _Viride Æris_ in a due Proportion, the
  3348  Mixture lost its purple Tincture, and became perfectly dun. But the
  3349  Experiment succeeded best without Minium thus. To Orpiment I added by
  3350  little and little a certain full bright purple, which Painters use,
  3351  until the Orpiment ceased to be yellow, and became of a pale red. Then I
  3352  diluted that red by adding a little _Viride Æris_, and a little more
  3353  blue Bise than _Viride Æris_, until it became of such a grey or pale
  3354  white, as verged to no one of the Colours more than to another. For thus
  3355  it became of a Colour equal in Whiteness to that of Ashes, or of Wood
  3356  newly cut, or of a Man's Skin. The Orpiment reflected more Light than
  3357  did any other of the Powders, and therefore conduced more to the
  3358  Whiteness of the compounded Colour than they. To assign the Proportions
  3359  accurately may be difficult, by reason of the different Goodness of
  3360  Powders of the same kind. Accordingly, as the Colour of any Powder is
  3361  more or less full and luminous, it ought to be used in a less or greater
  3362  Proportion.
  3364  Now, considering that these grey and dun Colours may be also produced by
  3365  mixing Whites and Blacks, and by consequence differ from perfect Whites,
  3366  not in Species of Colours, but only in degree of Luminousness, it is
  3367  manifest that there is nothing more requisite to make them perfectly
  3368  white than to increase their Light sufficiently; and, on the contrary,
  3369  if by increasing their Light they can be brought to perfect Whiteness,
  3370  it will thence also follow, that they are of the same Species of Colour
  3371  with the best Whites, and differ from them only in the Quantity of
  3372  Light. And this I tried as follows. I took the third of the
  3373  above-mention'd grey Mixtures, (that which was compounded of Orpiment,
  3374  Purple, Bise, and _Viride Æris_) and rubbed it thickly upon the Floor of
  3375  my Chamber, where the Sun shone upon it through the opened Casement; and
  3376  by it, in the shadow, I laid a Piece of white Paper of the same Bigness.
  3377  Then going from them to the distance of 12 or 18 Feet, so that I could
  3378  not discern the Unevenness of the Surface of the Powder, nor the little
  3379  Shadows let fall from the gritty Particles thereof; the Powder appeared
  3380  intensely white, so as to transcend even the Paper it self in Whiteness,
  3381  especially if the Paper were a little shaded from the Light of the
  3382  Clouds, and then the Paper compared with the Powder appeared of such a
  3383  grey Colour as the Powder had done before. But by laying the Paper where
  3384  the Sun shines through the Glass of the Window, or by shutting the
  3385  Window that the Sun might shine through the Glass upon the Powder, and
  3386  by such other fit Means of increasing or decreasing the Lights wherewith
  3387  the Powder and Paper were illuminated, the Light wherewith the Powder is
  3388  illuminated may be made stronger in such a due Proportion than the Light
  3389  wherewith the Paper is illuminated, that they shall both appear exactly
  3390  alike in Whiteness. For when I was trying this, a Friend coming to visit
  3391  me, I stopp'd him at the Door, and before I told him what the Colours
  3392  were, or what I was doing; I asked him, Which of the two Whites were the
  3393  best, and wherein they differed? And after he had at that distance
  3394  viewed them well, he answer'd, that they were both good Whites, and that
  3395  he could not say which was best, nor wherein their Colours differed.
  3396  Now, if you consider, that this White of the Powder in the Sun-shine was
  3397  compounded of the Colours which the component Powders (Orpiment, Purple,
  3398  Bise, and _Viride Æris_) have in the same Sun-shine, you must
  3399  acknowledge by this Experiment, as well as by the former, that perfect
  3400  Whiteness may be compounded of Colours.
  3402  From what has been said it is also evident, that the Whiteness of the
  3403  Sun's Light is compounded of all the Colours wherewith the several sorts
  3404  of Rays whereof that Light consists, when by their several
  3405  Refrangibilities they are separated from one another, do tinge Paper or
  3406  any other white Body whereon they fall. For those Colours (by _Prop._
  3407  II. _Part_ 2.) are unchangeable, and whenever all those Rays with those
  3408  their Colours are mix'd again, they reproduce the same white Light as
  3409  before.
  3412  _PROP._ VI. PROB. II.
  3414  _In a mixture of Primary Colours, the Quantity and Quality of each being
  3415  given, to know the Colour of the Compound._
  3417  [Illustration: FIG. 11.]
  3419  With the Center O [in _Fig._ 11.] and Radius OD describe a Circle ADF,
  3420  and distinguish its Circumference into seven Parts DE, EF, FG, GA, AB,
  3421  BC, CD, proportional to the seven Musical Tones or Intervals of the
  3422  eight Sounds, _Sol_, _la_, _fa_, _sol_, _la_, _mi_, _fa_, _sol_,
  3423  contained in an eight, that is, proportional to the Number 1/9, 1/16,
  3424  1/10, 1/9, 1/16, 1/16, 1/9. Let the first Part DE represent a red
  3425  Colour, the second EF orange, the third FG yellow, the fourth CA green,
  3426  the fifth AB blue, the sixth BC indigo, and the seventh CD violet. And
  3427  conceive that these are all the Colours of uncompounded Light gradually
  3428  passing into one another, as they do when made by Prisms; the
  3429  Circumference DEFGABCD, representing the whole Series of Colours from
  3430  one end of the Sun's colour'd Image to the other, so that from D to E be
  3431  all degrees of red, at E the mean Colour between red and orange, from E
  3432  to F all degrees of orange, at F the mean between orange and yellow,
  3433  from F to G all degrees of yellow, and so on. Let _p_ be the Center of
  3434  Gravity of the Arch DE, and _q_, _r_, _s_, _t_, _u_, _x_, the Centers of
  3435  Gravity of the Arches EF, FG, GA, AB, BC, and CD respectively, and about
  3436  those Centers of Gravity let Circles proportional to the Number of Rays
  3437  of each Colour in the given Mixture be describ'd: that is, the Circle
  3438  _p_ proportional to the Number of the red-making Rays in the Mixture,
  3439  the Circle _q_ proportional to the Number of the orange-making Rays in
  3440  the Mixture, and so of the rest. Find the common Center of Gravity of
  3441  all those Circles, _p_, _q_, _r_, _s_, _t_, _u_, _x_. Let that Center be
  3442  Z; and from the Center of the Circle ADF, through Z to the
  3443  Circumference, drawing the Right Line OY, the Place of the Point Y in
  3444  the Circumference shall shew the Colour arising from the Composition of
  3445  all the Colours in the given Mixture, and the Line OZ shall be
  3446  proportional to the Fulness or Intenseness of the Colour, that is, to
  3447  its distance from Whiteness. As if Y fall in the middle between F and G,
  3448  the compounded Colour shall be the best yellow; if Y verge from the
  3449  middle towards F or G, the compound Colour shall accordingly be a
  3450  yellow, verging towards orange or green. If Z fall upon the
  3451  Circumference, the Colour shall be intense and florid in the highest
  3452  Degree; if it fall in the mid-way between the Circumference and Center,
  3453  it shall be but half so intense, that is, it shall be such a Colour as
  3454  would be made by diluting the intensest yellow with an equal quantity of
  3455  whiteness; and if it fall upon the center O, the Colour shall have lost
  3456  all its intenseness, and become a white. But it is to be noted, That if
  3457  the point Z fall in or near the line OD, the main ingredients being the
  3458  red and violet, the Colour compounded shall not be any of the prismatick
  3459  Colours, but a purple, inclining to red or violet, accordingly as the
  3460  point Z lieth on the side of the line DO towards E or towards C, and in
  3461  general the compounded violet is more bright and more fiery than the
  3462  uncompounded. Also if only two of the primary Colours which in the
  3463  circle are opposite to one another be mixed in an equal proportion, the
  3464  point Z shall fall upon the center O, and yet the Colour compounded of
  3465  those two shall not be perfectly white, but some faint anonymous Colour.
  3466  For I could never yet by mixing only two primary Colours produce a
  3467  perfect white. Whether it may be compounded of a mixture of three taken
  3468  at equal distances in the circumference I do not know, but of four or
  3469  five I do not much question but it may. But these are Curiosities of
  3470  little or no moment to the understanding the Phænomena of Nature. For in
  3471  all whites produced by Nature, there uses to be a mixture of all sorts
  3472  of Rays, and by consequence a composition of all Colours.
  3474  To give an instance of this Rule; suppose a Colour is compounded of
  3475  these homogeneal Colours, of violet one part, of indigo one part, of
  3476  blue two parts, of green three parts, of yellow five parts, of orange
  3477  six parts, and of red ten parts. Proportional to these parts describe
  3478  the Circles _x_, _v_, _t_, _s_, _r_, _q_, _p_, respectively, that is, so
  3479  that if the Circle _x_ be one, the Circle _v_ may be one, the Circle _t_
  3480  two, the Circle _s_ three, and the Circles _r_, _q_ and _p_, five, six
  3481  and ten. Then I find Z the common center of gravity of these Circles,
  3482  and through Z drawing the Line OY, the Point Y falls upon the
  3483  circumference between E and F, something nearer to E than to F, and
  3484  thence I conclude, that the Colour compounded of these Ingredients will
  3485  be an orange, verging a little more to red than to yellow. Also I find
  3486  that OZ is a little less than one half of OY, and thence I conclude,
  3487  that this orange hath a little less than half the fulness or intenseness
  3488  of an uncompounded orange; that is to say, that it is such an orange as
  3489  may be made by mixing an homogeneal orange with a good white in the
  3490  proportion of the Line OZ to the Line ZY, this Proportion being not of
  3491  the quantities of mixed orange and white Powders, but of the quantities
  3492  of the Lights reflected from them.
  3494  This Rule I conceive accurate enough for practice, though not
  3495  mathematically accurate; and the truth of it may be sufficiently proved
  3496  to Sense, by stopping any of the Colours at the Lens in the tenth
  3497  Experiment of this Book. For the rest of the Colours which are not
  3498  stopp'd, but pass on to the Focus of the Lens, will there compound
  3499  either accurately or very nearly such a Colour, as by this Rule ought to
  3500  result from their Mixture.
  3503  _PROP._ VII. THEOR. V.
  3505  _All the Colours in the Universe which are made by Light, and depend not
  3506  on the Power of Imagination, are either the Colours of homogeneal
  3507  Lights, or compounded of these, and that either accurately or very
  3508  nearly, according to the Rule of the foregoing Problem._
  3510  For it has been proved (in _Prop. 1. Part 2._) that the changes of
  3511  Colours made by Refractions do not arise from any new Modifications of
  3512  the Rays impress'd by those Refractions, and by the various Terminations
  3513  of Light and Shadow, as has been the constant and general Opinion of
  3514  Philosophers. It has also been proved that the several Colours of the
  3515  homogeneal Rays do constantly answer to their degrees of Refrangibility,
  3516  (_Prop._ 1. _Part_ 1. and _Prop._ 2. _Part_ 2.) and that their degrees
  3517  of Refrangibility cannot be changed by Refractions and Reflexions
  3518  (_Prop._ 2. _Part_ 1.) and by consequence that those their Colours are
  3519  likewise immutable. It has also been proved directly by refracting and
  3520  reflecting homogeneal Lights apart, that their Colours cannot be
  3521  changed, (_Prop._ 2. _Part_ 2.) It has been proved also, that when the
  3522  several sorts of Rays are mixed, and in crossing pass through the same
  3523  space, they do not act on one another so as to change each others
  3524  colorific qualities. (_Exper._ 10. _Part_ 2.) but by mixing their
  3525  Actions in the Sensorium beget a Sensation differing from what either
  3526  would do apart, that is a Sensation of a mean Colour between their
  3527  proper Colours; and particularly when by the concourse and mixtures of
  3528  all sorts of Rays, a white Colour is produced, the white is a mixture of
  3529  all the Colours which the Rays would have apart, (_Prop._ 5. _Part_ 2.)
  3530  The Rays in that mixture do not lose or alter their several colorific
  3531  qualities, but by all their various kinds of Actions mix'd in the
  3532  Sensorium, beget a Sensation of a middling Colour between all their
  3533  Colours, which is whiteness. For whiteness is a mean between all
  3534  Colours, having it self indifferently to them all, so as with equal
  3535  facility to be tinged with any of them. A red Powder mixed with a little
  3536  blue, or a blue with a little red, doth not presently lose its Colour,
  3537  but a white Powder mix'd with any Colour is presently tinged with that
  3538  Colour, and is equally capable of being tinged with any Colour whatever.
  3539  It has been shewed also, that as the Sun's Light is mix'd of all sorts
  3540  of Rays, so its whiteness is a mixture of the Colours of all sorts of
  3541  Rays; those Rays having from the beginning their several colorific
  3542  qualities as well as their several Refrangibilities, and retaining them
  3543  perpetually unchanged notwithstanding any Refractions or Reflexions they
  3544  may at any time suffer, and that whenever any sort of the Sun's Rays is
  3545  by any means (as by Reflexion in _Exper._ 9, and 10. _Part_ 1. or by
  3546  Refraction as happens in all Refractions) separated from the rest, they
  3547  then manifest their proper Colours. These things have been prov'd, and
  3548  the sum of all this amounts to the Proposition here to be proved. For if
  3549  the Sun's Light is mix'd of several sorts of Rays, each of which have
  3550  originally their several Refrangibilities and colorific Qualities, and
  3551  notwithstanding their Refractions and Reflexions, and their various
  3552  Separations or Mixtures, keep those their original Properties
  3553  perpetually the same without alteration; then all the Colours in the
  3554  World must be such as constantly ought to arise from the original
  3555  colorific qualities of the Rays whereof the Lights consist by which
  3556  those Colours are seen. And therefore if the reason of any Colour
  3557  whatever be required, we have nothing else to do than to consider how
  3558  the Rays in the Sun's Light have by Reflexions or Refractions, or other
  3559  causes, been parted from one another, or mixed together; or otherwise to
  3560  find out what sorts of Rays are in the Light by which that Colour is
  3561  made, and in what Proportion; and then by the last Problem to learn the
  3562  Colour which ought to arise by mixing those Rays (or their Colours) in
  3563  that proportion. I speak here of Colours so far as they arise from
  3564  Light. For they appear sometimes by other Causes, as when by the power
  3565  of Phantasy we see Colours in a Dream, or a Mad-man sees things before
  3566  him which are not there; or when we see Fire by striking the Eye, or see
  3567  Colours like the Eye of a Peacock's Feather, by pressing our Eyes in
  3568  either corner whilst we look the other way. Where these and such like
  3569  Causes interpose not, the Colour always answers to the sort or sorts of
  3570  the Rays whereof the Light consists, as I have constantly found in
  3571  whatever Phænomena of Colours I have hitherto been able to examine. I
  3572  shall in the following Propositions give instances of this in the
  3573  Phænomena of chiefest note.
  3576  _PROP._ VIII. PROB. III.
  3578  _By the discovered Properties of Light to explain the Colours made by
  3579  Prisms._
  3581  Let ABC [in _Fig._ 12.] represent a Prism refracting the Light of the
  3582  Sun, which comes into a dark Chamber through a hole F[Greek: ph] almost
  3583  as broad as the Prism, and let MN represent a white Paper on which the
  3584  refracted Light is cast, and suppose the most refrangible or deepest
  3585  violet-making Rays fall upon the Space P[Greek: p], the least
  3586  refrangible or deepest red-making Rays upon the Space T[Greek: t], the
  3587  middle sort between the indigo-making and blue-making Rays upon the
  3588  Space Q[Greek: ch], the middle sort of the green-making Rays upon the
  3589  Space R, the middle sort between the yellow-making and orange-making
  3590  Rays upon the Space S[Greek: s], and other intermediate sorts upon
  3591  intermediate Spaces. For so the Spaces upon which the several sorts
  3592  adequately fall will by reason of the different Refrangibility of those
  3593  sorts be one lower than another. Now if the Paper MN be so near the
  3594  Prism that the Spaces PT and [Greek: pt] do not interfere with one
  3595  another, the distance between them T[Greek: p] will be illuminated by
  3596  all the sorts of Rays in that proportion to one another which they have
  3597  at their very first coming out of the Prism, and consequently be white.
  3598  But the Spaces PT and [Greek: pt] on either hand, will not be
  3599  illuminated by them all, and therefore will appear coloured. And
  3600  particularly at P, where the outmost violet-making Rays fall alone, the
  3601  Colour must be the deepest violet. At Q where the violet-making and
  3602  indigo-making Rays are mixed, it must be a violet inclining much to
  3603  indigo. At R where the violet-making, indigo-making, blue-making, and
  3604  one half of the green-making Rays are mixed, their Colours must (by the
  3605  construction of the second Problem) compound a middle Colour between
  3606  indigo and blue. At S where all the Rays are mixed, except the
  3607  red-making and orange-making, their Colours ought by the same Rule to
  3608  compound a faint blue, verging more to green than indigo. And in the
  3609  progress from S to T, this blue will grow more and more faint and
  3610  dilute, till at T, where all the Colours begin to be mixed, it ends in
  3611  whiteness.
  3613  [Illustration: FIG. 12.]
  3615  So again, on the other side of the white at [Greek: t], where the least
  3616  refrangible or utmost red-making Rays are alone, the Colour must be the
  3617  deepest red. At [Greek: s] the mixture of red and orange will compound a
  3618  red inclining to orange. At [Greek: r] the mixture of red, orange,
  3619  yellow, and one half of the green must compound a middle Colour between
  3620  orange and yellow. At [Greek: ch] the mixture of all Colours but violet
  3621  and indigo will compound a faint yellow, verging more to green than to
  3622  orange. And this yellow will grow more faint and dilute continually in
  3623  its progress from [Greek: ch] to [Greek: p], where by a mixture of all
  3624  sorts of Rays it will become white.
  3626  These Colours ought to appear were the Sun's Light perfectly white: But
  3627  because it inclines to yellow, the Excess of the yellow-making Rays
  3628  whereby 'tis tinged with that Colour, being mixed with the faint blue
  3629  between S and T, will draw it to a faint green. And so the Colours in
  3630  order from P to [Greek: t] ought to be violet, indigo, blue, very faint
  3631  green, white, faint yellow, orange, red. Thus it is by the computation:
  3632  And they that please to view the Colours made by a Prism will find it so
  3633  in Nature.
  3635  These are the Colours on both sides the white when the Paper is held
  3636  between the Prism and the Point X where the Colours meet, and the
  3637  interjacent white vanishes. For if the Paper be held still farther off
  3638  from the Prism, the most refrangible and least refrangible Rays will be
  3639  wanting in the middle of the Light, and the rest of the Rays which are
  3640  found there, will by mixture produce a fuller green than before. Also
  3641  the yellow and blue will now become less compounded, and by consequence
  3642  more intense than before. And this also agrees with experience.
  3644  And if one look through a Prism upon a white Object encompassed with
  3645  blackness or darkness, the reason of the Colours arising on the edges is
  3646  much the same, as will appear to one that shall a little consider it. If
  3647  a black Object be encompassed with a white one, the Colours which appear
  3648  through the Prism are to be derived from the Light of the white one,
  3649  spreading into the Regions of the black, and therefore they appear in a
  3650  contrary order to that, when a white Object is surrounded with black.
  3651  And the same is to be understood when an Object is viewed, whose parts
  3652  are some of them less luminous than others. For in the borders of the
  3653  more and less luminous Parts, Colours ought always by the same
  3654  Principles to arise from the Excess of the Light of the more luminous,
  3655  and to be of the same kind as if the darker parts were black, but yet to
  3656  be more faint and dilute.
  3658  What is said of Colours made by Prisms may be easily applied to Colours
  3659  made by the Glasses of Telescopes or Microscopes, or by the Humours of
  3660  the Eye. For if the Object-glass of a Telescope be thicker on one side
  3661  than on the other, or if one half of the Glass, or one half of the Pupil
  3662  of the Eye be cover'd with any opake substance; the Object-glass, or
  3663  that part of it or of the Eye which is not cover'd, may be consider'd as
  3664  a Wedge with crooked Sides, and every Wedge of Glass or other pellucid
  3665  Substance has the effect of a Prism in refracting the Light which passes
  3666  through it.[L]
  3668  How the Colours in the ninth and tenth Experiments of the first Part
  3669  arise from the different Reflexibility of Light, is evident by what was
  3670  there said. But it is observable in the ninth Experiment, that whilst
  3671  the Sun's direct Light is yellow, the Excess of the blue-making Rays in
  3672  the reflected beam of Light MN, suffices only to bring that yellow to a
  3673  pale white inclining to blue, and not to tinge it with a manifestly blue
  3674  Colour. To obtain therefore a better blue, I used instead of the yellow
  3675  Light of the Sun the white Light of the Clouds, by varying a little the
  3676  Experiment, as follows.
  3678  [Illustration: FIG. 13.]
  3680  _Exper._ 16 Let HFG [in _Fig._ 13.] represent a Prism in the open Air,
  3681  and S the Eye of the Spectator, viewing the Clouds by their Light coming
  3682  into the Prism at the Plane Side FIGK, and reflected in it by its Base
  3683  HEIG, and thence going out through its Plane Side HEFK to the Eye. And
  3684  when the Prism and Eye are conveniently placed, so that the Angles of
  3685  Incidence and Reflexion at the Base may be about 40 Degrees, the
  3686  Spectator will see a Bow MN of a blue Colour, running from one End of
  3687  the Base to the other, with the Concave Side towards him, and the Part
  3688  of the Base IMNG beyond this Bow will be brighter than the other Part
  3689  EMNH on the other Side of it. This blue Colour MN being made by nothing
  3690  else than by Reflexion of a specular Superficies, seems so odd a
  3691  Phænomenon, and so difficult to be explained by the vulgar Hypothesis of
  3692  Philosophers, that I could not but think it deserved to be taken Notice
  3693  of. Now for understanding the Reason of it, suppose the Plane ABC to cut
  3694  the Plane Sides and Base of the Prism perpendicularly. From the Eye to
  3695  the Line BC, wherein that Plane cuts the Base, draw the Lines S_p_ and
  3696  S_t_, in the Angles S_pc_ 50 degr. 1/9, and S_tc_ 49 degr. 1/28, and the
  3697  Point _p_ will be the Limit beyond which none of the most refrangible
  3698  Rays can pass through the Base of the Prism, and be refracted, whose
  3699  Incidence is such that they may be reflected to the Eye; and the Point
  3700  _t_ will be the like Limit for the least refrangible Rays, that is,
  3701  beyond which none of them can pass through the Base, whose Incidence is
  3702  such that by Reflexion they may come to the Eye. And the Point _r_ taken
  3703  in the middle Way between _p_ and _t_, will be the like Limit for the
  3704  meanly refrangible Rays. And therefore all the least refrangible Rays
  3705  which fall upon the Base beyond _t_, that is, between _t_ and B, and can
  3706  come from thence to the Eye, will be reflected thither: But on this side
  3707  _t_, that is, between _t_ and _c_, many of these Rays will be
  3708  transmitted through the Base. And all the most refrangible Rays which
  3709  fall upon the Base beyond _p_, that is, between, _p_ and B, and can by
  3710  Reflexion come from thence to the Eye, will be reflected thither, but
  3711  every where between _p_ and _c_, many of these Rays will get through the
  3712  Base, and be refracted; and the same is to be understood of the meanly
  3713  refrangible Rays on either side of the Point _r_. Whence it follows,
  3714  that the Base of the Prism must every where between _t_ and B, by a
  3715  total Reflexion of all sorts of Rays to the Eye, look white and bright.
  3716  And every where between _p_ and C, by reason of the Transmission of many
  3717  Rays of every sort, look more pale, obscure, and dark. But at _r_, and
  3718  in other Places between _p_ and _t_, where all the more refrangible Rays
  3719  are reflected to the Eye, and many of the less refrangible are
  3720  transmitted, the Excess of the most refrangible in the reflected Light
  3721  will tinge that Light with their Colour, which is violet and blue. And
  3722  this happens by taking the Line C _prt_ B any where between the Ends of
  3723  the Prism HG and EI.
  3726  _PROP._ IX. PROB. IV.
  3728  _By the discovered Properties of Light to explain the Colours of the
  3729  Rain-bow._
  3731  [Illustration: FIG. 14.]
  3733  This Bow never appears, but where it rains in the Sun-shine, and may be
  3734  made artificially by spouting up Water which may break aloft, and
  3735  scatter into Drops, and fall down like Rain. For the Sun shining upon
  3736  these Drops certainly causes the Bow to appear to a Spectator standing
  3737  in a due Position to the Rain and Sun. And hence it is now agreed upon,
  3738  that this Bow is made by Refraction of the Sun's Light in drops of
  3739  falling Rain. This was understood by some of the Antients, and of late
  3740  more fully discover'd and explain'd by the famous _Antonius de Dominis_
  3741  Archbishop of _Spalato_, in his book _De Radiis Visûs & Lucis_,
  3742  published by his Friend _Bartolus_ at _Venice_, in the Year 1611, and
  3743  written above 20 Years before. For he teaches there how the interior Bow
  3744  is made in round Drops of Rain by two Refractions of the Sun's Light,
  3745  and one Reflexion between them, and the exterior by two Refractions, and
  3746  two sorts of Reflexions between them in each Drop of Water, and proves
  3747  his Explications by Experiments made with a Phial full of Water, and
  3748  with Globes of Glass filled with Water, and placed in the Sun to make
  3749  the Colours of the two Bows appear in them. The same Explication
  3750  _Des-Cartes_ hath pursued in his Meteors, and mended that of the
  3751  exterior Bow. But whilst they understood not the true Origin of Colours,
  3752  it's necessary to pursue it here a little farther. For understanding
  3753  therefore how the Bow is made, let a Drop of Rain, or any other
  3754  spherical transparent Body be represented by the Sphere BNFG, [in _Fig._
  3755  14.] described with the Center C, and Semi-diameter CN. And let AN be
  3756  one of the Sun's Rays incident upon it at N, and thence refracted to F,
  3757  where let it either go out of the Sphere by Refraction towards V, or be
  3758  reflected to G; and at G let it either go out by Refraction to R, or be
  3759  reflected to H; and at H let it go out by Refraction towards S, cutting
  3760  the incident Ray in Y. Produce AN and RG, till they meet in X, and upon
  3761  AX and NF, let fall the Perpendiculars CD and CE, and produce CD till it
  3762  fall upon the Circumference at L. Parallel to the incident Ray AN draw
  3763  the Diameter BQ, and let the Sine of Incidence out of Air into Water be
  3764  to the Sine of Refraction as I to R. Now, if you suppose the Point of
  3765  Incidence N to move from the Point B, continually till it come to L, the
  3766  Arch QF will first increase and then decrease, and so will the Angle AXR
  3767  which the Rays AN and GR contain; and the Arch QF and Angle AXR will be
  3768  biggest when ND is to CN as sqrt(II - RR) to sqrt(3)RR, in which
  3769  case NE will be to ND as 2R to I. Also the Angle AYS, which the Rays AN
  3770  and HS contain will first decrease, and then increase and grow least
  3771  when ND is to CN as sqrt(II - RR) to sqrt(8)RR, in which case NE
  3772  will be to ND, as 3R to I. And so the Angle which the next emergent Ray
  3773  (that is, the emergent Ray after three Reflexions) contains with the
  3774  incident Ray AN will come to its Limit when ND is to CN as sqrt(II -
  3775  RR) to sqrt(15)RR, in which case NE will be to ND as 4R to I. And the
  3776  Angle which the Ray next after that Emergent, that is, the Ray emergent
  3777  after four Reflexions, contains with the Incident, will come to its
  3778  Limit, when ND is to CN as sqrt(II - RR) to sqrt(24)RR, in which
  3779  case NE will be to ND as 5R to I; and so on infinitely, the Numbers 3,
  3780  8, 15, 24, &c. being gather'd by continual Addition of the Terms of the
  3781  arithmetical Progression 3, 5, 7, 9, &c. The Truth of all this
  3782  Mathematicians will easily examine.[M]
  3784  Now it is to be observed, that as when the Sun comes to his Tropicks,
  3785  Days increase and decrease but a very little for a great while together;
  3786  so when by increasing the distance CD, these Angles come to their
  3787  Limits, they vary their quantity but very little for some time together,
  3788  and therefore a far greater number of the Rays which fall upon all the
  3789  Points N in the Quadrant BL, shall emerge in the Limits of these Angles,
  3790  than in any other Inclinations. And farther it is to be observed, that
  3791  the Rays which differ in Refrangibility will have different Limits of
  3792  their Angles of Emergence, and by consequence according to their
  3793  different Degrees of Refrangibility emerge most copiously in different
  3794  Angles, and being separated from one another appear each in their proper
  3795  Colours. And what those Angles are may be easily gather'd from the
  3796  foregoing Theorem by Computation.
  3798  For in the least refrangible Rays the Sines I and R (as was found above)
  3799  are 108 and 81, and thence by Computation the greatest Angle AXR will be
  3800  found 42 Degrees and 2 Minutes, and the least Angle AYS, 50 Degrees and
  3801  57 Minutes. And in the most refrangible Rays the Sines I and R are 109
  3802  and 81, and thence by Computation the greatest Angle AXR will be found
  3803  40 Degrees and 17 Minutes, and the least Angle AYS 54 Degrees and 7
  3804  Minutes.
  3806  Suppose now that O [in _Fig._ 15.] is the Spectator's Eye, and OP a Line
  3807  drawn parallel to the Sun's Rays and let POE, POF, POG, POH, be Angles
  3808  of 40 Degr. 17 Min. 42 Degr. 2 Min. 50 Degr. 57 Min. and 54 Degr. 7 Min.
  3809  respectively, and these Angles turned about their common Side OP, shall
  3810  with their other Sides OE, OF; OG, OH, describe the Verges of two
  3811  Rain-bows AF, BE and CHDG. For if E, F, G, H, be drops placed any where
  3812  in the conical Superficies described by OE, OF, OG, OH, and be
  3813  illuminated by the Sun's Rays SE, SF, SG, SH; the Angle SEO being equal
  3814  to the Angle POE, or 40 Degr. 17 Min. shall be the greatest Angle in
  3815  which the most refrangible Rays can after one Reflexion be refracted to
  3816  the Eye, and therefore all the Drops in the Line OE shall send the most
  3817  refrangible Rays most copiously to the Eye, and thereby strike the
  3818  Senses with the deepest violet Colour in that Region. And in like
  3819  manner the Angle SFO being equal to the Angle POF, or 42 Degr. 2 Min.
  3820  shall be the greatest in which the least refrangible Rays after one
  3821  Reflexion can emerge out of the Drops, and therefore those Rays shall
  3822  come most copiously to the Eye from the Drops in the Line OF, and strike
  3823  the Senses with the deepest red Colour in that Region. And by the same
  3824  Argument, the Rays which have intermediate Degrees of Refrangibility
  3825  shall come most copiously from Drops between E and F, and strike the
  3826  Senses with the intermediate Colours, in the Order which their Degrees
  3827  of Refrangibility require, that is in the Progress from E to F, or from
  3828  the inside of the Bow to the outside in this order, violet, indigo,
  3829  blue, green, yellow, orange, red. But the violet, by the mixture of the
  3830  white Light of the Clouds, will appear faint and incline to purple.
  3832  [Illustration: FIG. 15.]
  3834  Again, the Angle SGO being equal to the Angle POG, or 50 Gr. 51 Min.
  3835  shall be the least Angle in which the least refrangible Rays can after
  3836  two Reflexions emerge out of the Drops, and therefore the least
  3837  refrangible Rays shall come most copiously to the Eye from the Drops in
  3838  the Line OG, and strike the Sense with the deepest red in that Region.
  3839  And the Angle SHO being equal to the Angle POH, or 54 Gr. 7 Min. shall
  3840  be the least Angle, in which the most refrangible Rays after two
  3841  Reflexions can emerge out of the Drops; and therefore those Rays shall
  3842  come most copiously to the Eye from the Drops in the Line OH, and strike
  3843  the Senses with the deepest violet in that Region. And by the same
  3844  Argument, the Drops in the Regions between G and H shall strike the
  3845  Sense with the intermediate Colours in the Order which their Degrees of
  3846  Refrangibility require, that is, in the Progress from G to H, or from
  3847  the inside of the Bow to the outside in this order, red, orange, yellow,
  3848  green, blue, indigo, violet. And since these four Lines OE, OF, OG, OH,
  3849  may be situated any where in the above-mention'd conical Superficies;
  3850  what is said of the Drops and Colours in these Lines is to be understood
  3851  of the Drops and Colours every where in those Superficies.
  3853  Thus shall there be made two Bows of Colours, an interior and stronger,
  3854  by one Reflexion in the Drops, and an exterior and fainter by two; for
  3855  the Light becomes fainter by every Reflexion. And their Colours shall
  3856  lie in a contrary Order to one another, the red of both Bows bordering
  3857  upon the Space GF, which is between the Bows. The Breadth of the
  3858  interior Bow EOF measured cross the Colours shall be 1 Degr. 45 Min. and
  3859  the Breadth of the exterior GOH shall be 3 Degr. 10 Min. and the
  3860  distance between them GOF shall be 8 Gr. 15 Min. the greatest
  3861  Semi-diameter of the innermost, that is, the Angle POF being 42 Gr. 2
  3862  Min. and the least Semi-diameter of the outermost POG, being 50 Gr. 57
  3863  Min. These are the Measures of the Bows, as they would be were the Sun
  3864  but a Point; for by the Breadth of his Body, the Breadth of the Bows
  3865  will be increased, and their Distance decreased by half a Degree, and so
  3866  the breadth of the interior Iris will be 2 Degr. 15 Min. that of the
  3867  exterior 3 Degr. 40 Min. their distance 8 Degr. 25 Min. the greatest
  3868  Semi-diameter of the interior Bow 42 Degr. 17 Min. and the least of the
  3869  exterior 50 Degr. 42 Min. And such are the Dimensions of the Bows in the
  3870  Heavens found to be very nearly, when their Colours appear strong and
  3871  perfect. For once, by such means as I then had, I measured the greatest
  3872  Semi-diameter of the interior Iris about 42 Degrees, and the breadth of
  3873  the red, yellow and green in that Iris 63 or 64 Minutes, besides the
  3874  outmost faint red obscured by the brightness of the Clouds, for which we
  3875  may allow 3 or 4 Minutes more. The breadth of the blue was about 40
  3876  Minutes more besides the violet, which was so much obscured by the
  3877  brightness of the Clouds, that I could not measure its breadth. But
  3878  supposing the breadth of the blue and violet together to equal that of
  3879  the red, yellow and green together, the whole breadth of this Iris will
  3880  be about 2-1/4 Degrees, as above. The least distance between this Iris
  3881  and the exterior Iris was about 8 Degrees and 30 Minutes. The exterior
  3882  Iris was broader than the interior, but so faint, especially on the blue
  3883  side, that I could not measure its breadth distinctly. At another time
  3884  when both Bows appeared more distinct, I measured the breadth of the
  3885  interior Iris 2 Gr. 10´, and the breadth of the red, yellow and green in
  3886  the exterior Iris, was to the breadth of the same Colours in the
  3887  interior as 3 to 2.
  3889  This Explication of the Rain-bow is yet farther confirmed by the known
  3890  Experiment (made by _Antonius de Dominis_ and _Des-Cartes_) of hanging
  3891  up any where in the Sun-shine a Glass Globe filled with Water, and
  3892  viewing it in such a posture, that the Rays which come from the Globe to
  3893  the Eye may contain with the Sun's Rays an Angle of either 42 or 50
  3894  Degrees. For if the Angle be about 42 or 43 Degrees, the Spectator
  3895  (suppose at O) shall see a full red Colour in that side of the Globe
  3896  opposed to the Sun as 'tis represented at F, and if that Angle become
  3897  less (suppose by depressing the Globe to E) there will appear other
  3898  Colours, yellow, green and blue successive in the same side of the
  3899  Globe. But if the Angle be made about 50 Degrees (suppose by lifting up
  3900  the Globe to G) there will appear a red Colour in that side of the Globe
  3901  towards the Sun, and if the Angle be made greater (suppose by lifting
  3902  up the Globe to H) the red will turn successively to the other Colours,
  3903  yellow, green and blue. The same thing I have tried, by letting a Globe
  3904  rest, and raising or depressing the Eye, or otherwise moving it to make
  3905  the Angle of a just magnitude.
  3907  I have heard it represented, that if the Light of a Candle be refracted
  3908  by a Prism to the Eye; when the blue Colour falls upon the Eye, the
  3909  Spectator shall see red in the Prism, and when the red falls upon the
  3910  Eye he shall see blue; and if this were certain, the Colours of the
  3911  Globe and Rain-bow ought to appear in a contrary order to what we find.
  3912  But the Colours of the Candle being very faint, the mistake seems to
  3913  arise from the difficulty of discerning what Colours fall on the Eye.
  3914  For, on the contrary, I have sometimes had occasion to observe in the
  3915  Sun's Light refracted by a Prism, that the Spectator always sees that
  3916  Colour in the Prism which falls upon his Eye. And the same I have found
  3917  true also in Candle-light. For when the Prism is moved slowly from the
  3918  Line which is drawn directly from the Candle to the Eye, the red appears
  3919  first in the Prism and then the blue, and therefore each of them is seen
  3920  when it falls upon the Eye. For the red passes over the Eye first, and
  3921  then the blue.
  3923  The Light which comes through drops of Rain by two Refractions without
  3924  any Reflexion, ought to appear strongest at the distance of about 26
  3925  Degrees from the Sun, and to decay gradually both ways as the distance
  3926  from him increases and decreases. And the same is to be understood of
  3927  Light transmitted through spherical Hail-stones. And if the Hail be a
  3928  little flatted, as it often is, the Light transmitted may grow so strong
  3929  at a little less distance than that of 26 Degrees, as to form a Halo
  3930  about the Sun or Moon; which Halo, as often as the Hail-stones are duly
  3931  figured may be colour'd, and then it must be red within by the least
  3932  refrangible Rays, and blue without by the most refrangible ones,
  3933  especially if the Hail-stones have opake Globules of Snow in their
  3934  center to intercept the Light within the Halo (as _Hugenius_ has
  3935  observ'd) and make the inside thereof more distinctly defined than it
  3936  would otherwise be. For such Hail-stones, though spherical, by
  3937  terminating the Light by the Snow, may make a Halo red within and
  3938  colourless without, and darker in the red than without, as Halos used to
  3939  be. For of those Rays which pass close by the Snow the Rubriform will be
  3940  least refracted, and so come to the Eye in the directest Lines.
  3942  The Light which passes through a drop of Rain after two Refractions, and
  3943  three or more Reflexions, is scarce strong enough to cause a sensible
  3944  Bow; but in those Cylinders of Ice by which _Hugenius_ explains the
  3945  _Parhelia_, it may perhaps be sensible.
  3948  _PROP._ X. PROB. V.
  3950  _By the discovered Properties of Light to explain the permanent Colours
  3951  of Natural Bodies._
  3953  These Colours arise from hence, that some natural Bodies reflect some
  3954  sorts of Rays, others other sorts more copiously than the rest. Minium
  3955  reflects the least refrangible or red-making Rays most copiously, and
  3956  thence appears red. Violets reflect the most refrangible most copiously,
  3957  and thence have their Colour, and so of other Bodies. Every Body
  3958  reflects the Rays of its own Colour more copiously than the rest, and
  3959  from their excess and predominance in the reflected Light has its
  3960  Colour.
  3962  _Exper._ 17. For if in the homogeneal Lights obtained by the solution of
  3963  the Problem proposed in the fourth Proposition of the first Part of this
  3964  Book, you place Bodies of several Colours, you will find, as I have
  3965  done, that every Body looks most splendid and luminous in the Light of
  3966  its own Colour. Cinnaber in the homogeneal red Light is most
  3967  resplendent, in the green Light it is manifestly less resplendent, and
  3968  in the blue Light still less. Indigo in the violet blue Light is most
  3969  resplendent, and its splendor is gradually diminish'd, as it is removed
  3970  thence by degrees through the green and yellow Light to the red. By a
  3971  Leek the green Light, and next that the blue and yellow which compound
  3972  green, are more strongly reflected than the other Colours red and
  3973  violet, and so of the rest. But to make these Experiments the more
  3974  manifest, such Bodies ought to be chosen as have the fullest and most
  3975  vivid Colours, and two of those Bodies are to be compared together.
  3976  Thus, for instance, if Cinnaber and _ultra_-marine blue, or some other
  3977  full blue be held together in the red homogeneal Light, they will both
  3978  appear red, but the Cinnaber will appear of a strongly luminous and
  3979  resplendent red, and the _ultra_-marine blue of a faint obscure and dark
  3980  red; and if they be held together in the blue homogeneal Light, they
  3981  will both appear blue, but the _ultra_-marine will appear of a strongly
  3982  luminous and resplendent blue, and the Cinnaber of a faint and dark
  3983  blue. Which puts it out of dispute that the Cinnaber reflects the red
  3984  Light much more copiously than the _ultra_-marine doth, and the
  3985  _ultra_-marine reflects the blue Light much more copiously than the
  3986  Cinnaber doth. The same Experiment may be tried successfully with red
  3987  Lead and Indigo, or with any other two colour'd Bodies, if due allowance
  3988  be made for the different strength or weakness of their Colour and
  3989  Light.
  3991  And as the reason of the Colours of natural Bodies is evident by these
  3992  Experiments, so it is farther confirmed and put past dispute by the two
  3993  first Experiments of the first Part, whereby 'twas proved in such Bodies
  3994  that the reflected Lights which differ in Colours do differ also in
  3995  degrees of Refrangibility. For thence it's certain, that some Bodies
  3996  reflect the more refrangible, others the less refrangible Rays more
  3997  copiously.
  3999  And that this is not only a true reason of these Colours, but even the
  4000  only reason, may appear farther from this Consideration, that the Colour
  4001  of homogeneal Light cannot be changed by the Reflexion of natural
  4002  Bodies.
  4004  For if Bodies by Reflexion cannot in the least change the Colour of any
  4005  one sort of Rays, they cannot appear colour'd by any other means than by
  4006  reflecting those which either are of their own Colour, or which by
  4007  mixture must produce it.
  4009  But in trying Experiments of this kind care must be had that the Light
  4010  be sufficiently homogeneal. For if Bodies be illuminated by the ordinary
  4011  prismatick Colours, they will appear neither of their own Day-light
  4012  Colours, nor of the Colour of the Light cast on them, but of some middle
  4013  Colour between both, as I have found by Experience. Thus red Lead (for
  4014  instance) illuminated with the ordinary prismatick green will not appear
  4015  either red or green, but orange or yellow, or between yellow and green,
  4016  accordingly as the green Light by which 'tis illuminated is more or less
  4017  compounded. For because red Lead appears red when illuminated with white
  4018  Light, wherein all sorts of Rays are equally mix'd, and in the green
  4019  Light all sorts of Rays are not equally mix'd, the Excess of the
  4020  yellow-making, green-making and blue-making Rays in the incident green
  4021  Light, will cause those Rays to abound so much in the reflected Light,
  4022  as to draw the Colour from red towards their Colour. And because the red
  4023  Lead reflects the red-making Rays most copiously in proportion to their
  4024  number, and next after them the orange-making and yellow-making Rays;
  4025  these Rays in the reflected Light will be more in proportion to the
  4026  Light than they were in the incident green Light, and thereby will draw
  4027  the reflected Light from green towards their Colour. And therefore the
  4028  red Lead will appear neither red nor green, but of a Colour between
  4029  both.
  4031  In transparently colour'd Liquors 'tis observable, that their Colour
  4032  uses to vary with their thickness. Thus, for instance, a red Liquor in a
  4033  conical Glass held between the Light and the Eye, looks of a pale and
  4034  dilute yellow at the bottom where 'tis thin, and a little higher where
  4035  'tis thicker grows orange, and where 'tis still thicker becomes red, and
  4036  where 'tis thickest the red is deepest and darkest. For it is to be
  4037  conceiv'd that such a Liquor stops the indigo-making and violet-making
  4038  Rays most easily, the blue-making Rays more difficultly, the
  4039  green-making Rays still more difficultly, and the red-making most
  4040  difficultly: And that if the thickness of the Liquor be only so much as
  4041  suffices to stop a competent number of the violet-making and
  4042  indigo-making Rays, without diminishing much the number of the rest, the
  4043  rest must (by _Prop._ 6. _Part_ 2.) compound a pale yellow. But if the
  4044  Liquor be so much thicker as to stop also a great number of the
  4045  blue-making Rays, and some of the green-making, the rest must compound
  4046  an orange; and where it is so thick as to stop also a great number of
  4047  the green-making and a considerable number of the yellow-making, the
  4048  rest must begin to compound a red, and this red must grow deeper and
  4049  darker as the yellow-making and orange-making Rays are more and more
  4050  stopp'd by increasing the thickness of the Liquor, so that few Rays
  4051  besides the red-making can get through.
  4053  Of this kind is an Experiment lately related to me by Mr. _Halley_, who,
  4054  in diving deep into the Sea in a diving Vessel, found in a clear
  4055  Sun-shine Day, that when he was sunk many Fathoms deep into the Water
  4056  the upper part of his Hand on which the Sun shone directly through the
  4057  Water and through a small Glass Window in the Vessel appeared of a red
  4058  Colour, like that of a Damask Rose, and the Water below and the under
  4059  part of his Hand illuminated by Light reflected from the Water below
  4060  look'd green. For thence it may be gather'd, that the Sea-Water reflects
  4061  back the violet and blue-making Rays most easily, and lets the
  4062  red-making Rays pass most freely and copiously to great Depths. For
  4063  thereby the Sun's direct Light at all great Depths, by reason of the
  4064  predominating red-making Rays, must appear red; and the greater the
  4065  Depth is, the fuller and intenser must that red be. And at such Depths
  4066  as the violet-making Rays scarce penetrate unto, the blue-making,
  4067  green-making, and yellow-making Rays being reflected from below more
  4068  copiously than the red-making ones, must compound a green.
  4070  Now, if there be two Liquors of full Colours, suppose a red and blue,
  4071  and both of them so thick as suffices to make their Colours sufficiently
  4072  full; though either Liquor be sufficiently transparent apart, yet will
  4073  you not be able to see through both together. For, if only the
  4074  red-making Rays pass through one Liquor, and only the blue-making
  4075  through the other, no Rays can pass through both. This Mr. _Hook_ tried
  4076  casually with Glass Wedges filled with red and blue Liquors, and was
  4077  surprized at the unexpected Event, the reason of it being then unknown;
  4078  which makes me trust the more to his Experiment, though I have not tried
  4079  it my self. But he that would repeat it, must take care the Liquors be
  4080  of very good and full Colours.
  4082  Now, whilst Bodies become coloured by reflecting or transmitting this or
  4083  that sort of Rays more copiously than the rest, it is to be conceived
  4084  that they stop and stifle in themselves the Rays which they do not
  4085  reflect or transmit. For, if Gold be foliated and held between your Eye
  4086  and the Light, the Light looks of a greenish blue, and therefore massy
  4087  Gold lets into its Body the blue-making Rays to be reflected to and fro
  4088  within it till they be stopp'd and stifled, whilst it reflects the
  4089  yellow-making outwards, and thereby looks yellow. And much after the
  4090  same manner that Leaf Gold is yellow by reflected, and blue by
  4091  transmitted Light, and massy Gold is yellow in all Positions of the Eye;
  4092  there are some Liquors, as the Tincture of _Lignum Nephriticum_, and
  4093  some sorts of Glass which transmit one sort of Light most copiously, and
  4094  reflect another sort, and thereby look of several Colours, according to
  4095  the Position of the Eye to the Light. But, if these Liquors or Glasses
  4096  were so thick and massy that no Light could get through them, I question
  4097  not but they would like all other opake Bodies appear of one and the
  4098  same Colour in all Positions of the Eye, though this I cannot yet affirm
  4099  by Experience. For all colour'd Bodies, so far as my Observation
  4100  reaches, may be seen through if made sufficiently thin, and therefore
  4101  are in some measure transparent, and differ only in degrees of
  4102  Transparency from tinged transparent Liquors; these Liquors, as well as
  4103  those Bodies, by a sufficient Thickness becoming opake. A transparent
  4104  Body which looks of any Colour by transmitted Light, may also look of
  4105  the same Colour by reflected Light, the Light of that Colour being
  4106  reflected by the farther Surface of the Body, or by the Air beyond it.
  4107  And then the reflected Colour will be diminished, and perhaps cease, by
  4108  making the Body very thick, and pitching it on the backside to diminish
  4109  the Reflexion of its farther Surface, so that the Light reflected from
  4110  the tinging Particles may predominate. In such Cases, the Colour of the
  4111  reflected Light will be apt to vary from that of the Light transmitted.
  4112  But whence it is that tinged Bodies and Liquors reflect some sort of
  4113  Rays, and intromit or transmit other sorts, shall be said in the next
  4114  Book. In this Proposition I content my self to have put it past dispute,
  4115  that Bodies have such Properties, and thence appear colour'd.
  4118  _PROP._ XI. PROB. VI.
  4120  _By mixing colour'd Lights to compound a beam of Light of the same
  4121  Colour and Nature with a beam of the Sun's direct Light, and therein to
  4122  experience the Truth of the foregoing Propositions._
  4124  [Illustration: FIG. 16.]
  4126  Let ABC _abc_ [in _Fig._ 16.] represent a Prism, by which the Sun's
  4127  Light let into a dark Chamber through the Hole F, may be refracted
  4128  towards the Lens MN, and paint upon it at _p_, _q_, _r_, _s_, and _t_,
  4129  the usual Colours violet, blue, green, yellow, and red, and let the
  4130  diverging Rays by the Refraction of this Lens converge again towards X,
  4131  and there, by the mixture of all those their Colours, compound a white
  4132  according to what was shewn above. Then let another Prism DEG _deg_,
  4133  parallel to the former, be placed at X, to refract that white Light
  4134  upwards towards Y. Let the refracting Angles of the Prisms, and their
  4135  distances from the Lens be equal, so that the Rays which converged from
  4136  the Lens towards X, and without Refraction, would there have crossed and
  4137  diverged again, may by the Refraction of the second Prism be reduced
  4138  into Parallelism and diverge no more. For then those Rays will recompose
  4139  a beam of white Light XY. If the refracting Angle of either Prism be the
  4140  bigger, that Prism must be so much the nearer to the Lens. You will know
  4141  when the Prisms and the Lens are well set together, by observing if the
  4142  beam of Light XY, which comes out of the second Prism be perfectly white
  4143  to the very edges of the Light, and at all distances from the Prism
  4144  continue perfectly and totally white like a beam of the Sun's Light. For
  4145  till this happens, the Position of the Prisms and Lens to one another
  4146  must be corrected; and then if by the help of a long beam of Wood, as is
  4147  represented in the Figure, or by a Tube, or some other such Instrument,
  4148  made for that Purpose, they be made fast in that Situation, you may try
  4149  all the same Experiments in this compounded beam of Light XY, which have
  4150  been made in the Sun's direct Light. For this compounded beam of Light
  4151  has the same appearance, and is endow'd with all the same Properties
  4152  with a direct beam of the Sun's Light, so far as my Observation reaches.
  4153  And in trying Experiments in this beam you may by stopping any of the
  4154  Colours, _p_, _q_, _r_, _s_, and _t_, at the Lens, see how the Colours
  4155  produced in the Experiments are no other than those which the Rays had
  4156  at the Lens before they entered the Composition of this Beam: And by
  4157  consequence, that they arise not from any new Modifications of the Light
  4158  by Refractions and Reflexions, but from the various Separations and
  4159  Mixtures of the Rays originally endow'd with their colour-making
  4160  Qualities.
  4162  So, for instance, having with a Lens 4-1/4 Inches broad, and two Prisms
  4163  on either hand 6-1/4 Feet distant from the Lens, made such a beam of
  4164  compounded Light; to examine the reason of the Colours made by Prisms, I
  4165  refracted this compounded beam of Light XY with another Prism HIK _kh_,
  4166  and thereby cast the usual Prismatick Colours PQRST upon the Paper LV
  4167  placed behind. And then by stopping any of the Colours _p_, _q_, _r_,
  4168  _s_, _t_, at the Lens, I found that the same Colour would vanish at the
  4169  Paper. So if the Purple _p_ was stopp'd at the Lens, the Purple P upon
  4170  the Paper would vanish, and the rest of the Colours would remain
  4171  unalter'd, unless perhaps the blue, so far as some purple latent in it
  4172  at the Lens might be separated from it by the following Refractions. And
  4173  so by intercepting the green upon the Lens, the green R upon the Paper
  4174  would vanish, and so of the rest; which plainly shews, that as the white
  4175  beam of Light XY was compounded of several Lights variously colour'd at
  4176  the Lens, so the Colours which afterwards emerge out of it by new
  4177  Refractions are no other than those of which its Whiteness was
  4178  compounded. The Refraction of the Prism HIK _kh_ generates the Colours
  4179  PQRST upon the Paper, not by changing the colorific Qualities of the
  4180  Rays, but by separating the Rays which had the very same colorific
  4181  Qualities before they enter'd the Composition of the refracted beam of
  4182  white Light XY. For otherwise the Rays which were of one Colour at the
  4183  Lens might be of another upon the Paper, contrary to what we find.
  4185  So again, to examine the reason of the Colours of natural Bodies, I
  4186  placed such Bodies in the Beam of Light XY, and found that they all
  4187  appeared there of those their own Colours which they have in Day-light,
  4188  and that those Colours depend upon the Rays which had the same Colours
  4189  at the Lens before they enter'd the Composition of that beam. Thus, for
  4190  instance, Cinnaber illuminated by this beam appears of the same red
  4191  Colour as in Day-light; and if at the Lens you intercept the
  4192  green-making and blue-making Rays, its redness will become more full and
  4193  lively: But if you there intercept the red-making Rays, it will not any
  4194  longer appear red, but become yellow or green, or of some other Colour,
  4195  according to the sorts of Rays which you do not intercept. So Gold in
  4196  this Light XY appears of the same yellow Colour as in Day-light, but by
  4197  intercepting at the Lens a due Quantity of the yellow-making Rays it
  4198  will appear white like Silver (as I have tried) which shews that its
  4199  yellowness arises from the Excess of the intercepted Rays tinging that
  4200  Whiteness with their Colour when they are let pass. So the Infusion of
  4201  _Lignum Nephriticum_ (as I have also tried) when held in this beam of
  4202  Light XY, looks blue by the reflected Part of the Light, and red by the
  4203  transmitted Part of it, as when 'tis view'd in Day-light; but if you
  4204  intercept the blue at the Lens the Infusion will lose its reflected blue
  4205  Colour, whilst its transmitted red remains perfect, and by the loss of
  4206  some blue-making Rays, wherewith it was allay'd, becomes more intense
  4207  and full. And, on the contrary, if the red and orange-making Rays be
  4208  intercepted at the Lens, the Infusion will lose its transmitted red,
  4209  whilst its blue will remain and become more full and perfect. Which
  4210  shews, that the Infusion does not tinge the Rays with blue and red, but
  4211  only transmits those most copiously which were red-making before, and
  4212  reflects those most copiously which were blue-making before. And after
  4213  the same manner may the Reasons of other Phænomena be examined, by
  4214  trying them in this artificial beam of Light XY.
  4216  FOOTNOTES:
  4218  [I] See p. 59.
  4220  [J] _See our_ Author's Lect. Optic. _Part_ II. _Sect._ II. _p._ 239.
  4222  [K] _As is done in our_ Author's Lect. Optic. _Part_ I. _Sect._ III.
  4223  _and_ IV. _and Part_ II. _Sect._ II.
  4225  [L] _See our_ Author's Lect. Optic. _Part_ II. _Sect._ II. _pag._ 269,
  4226  &c.
  4228  [M] _This is demonstrated in our_ Author's Lect. Optic. _Part_ I.
  4229  _Sect._ IV. _Prop._ 35 _and_ 36.
  4234  THE
  4238  OF
  4240  OPTICKS
  4245  _PART I._
  4247  _Observations concerning the Reflexions, Refractions, and Colours of
  4248  thin transparent Bodies._
  4251  It has been observed by others, that transparent Substances, as Glass,
  4252  Water, Air, &c. when made very thin by being blown into Bubbles, or
  4253  otherwise formed into Plates, do exhibit various Colours according to
  4254  their various thinness, altho' at a greater thickness they appear very
  4255  clear and colourless. In the former Book I forbore to treat of these
  4256  Colours, because they seemed of a more difficult Consideration, and were
  4257  not necessary for establishing the Properties of Light there discoursed
  4258  of. But because they may conduce to farther Discoveries for compleating
  4259  the Theory of Light, especially as to the constitution of the parts of
  4260  natural Bodies, on which their Colours or Transparency depend; I have
  4261  here set down an account of them. To render this Discourse short and
  4262  distinct, I have first described the principal of my Observations, and
  4263  then consider'd and made use of them. The Observations are these.
  4265  _Obs._ 1. Compressing two Prisms hard together that their sides (which
  4266  by chance were a very little convex) might somewhere touch one another:
  4267  I found the place in which they touched to become absolutely
  4268  transparent, as if they had there been one continued piece of Glass. For
  4269  when the Light fell so obliquely on the Air, which in other places was
  4270  between them, as to be all reflected; it seemed in that place of contact
  4271  to be wholly transmitted, insomuch that when look'd upon, it appeared
  4272  like a black or dark spot, by reason that little or no sensible Light
  4273  was reflected from thence, as from other places; and when looked through
  4274  it seemed (as it were) a hole in that Air which was formed into a thin
  4275  Plate, by being compress'd between the Glasses. And through this hole
  4276  Objects that were beyond might be seen distinctly, which could not at
  4277  all be seen through other parts of the Glasses where the Air was
  4278  interjacent. Although the Glasses were a little convex, yet this
  4279  transparent spot was of a considerable breadth, which breadth seemed
  4280  principally to proceed from the yielding inwards of the parts of the
  4281  Glasses, by reason of their mutual pressure. For by pressing them very
  4282  hard together it would become much broader than otherwise.
  4284  _Obs._ 2. When the Plate of Air, by turning the Prisms about their
  4285  common Axis, became so little inclined to the incident Rays, that some
  4286  of them began to be transmitted, there arose in it many slender Arcs of
  4287  Colours which at first were shaped almost like the Conchoid, as you see
  4288  them delineated in the first Figure. And by continuing the Motion of the
  4289  Prisms, these Arcs increased and bended more and more about the said
  4290  transparent spot, till they were compleated into Circles or Rings
  4291  incompassing it, and afterwards continually grew more and more
  4292  contracted.
  4294  [Illustration: FIG. 1.]
  4296  These Arcs at their first appearance were of a violet and blue Colour,
  4297  and between them were white Arcs of Circles, which presently by
  4298  continuing the Motion of the Prisms became a little tinged in their
  4299  inward Limbs with red and yellow, and to their outward Limbs the blue
  4300  was adjacent. So that the order of these Colours from the central dark
  4301  spot, was at that time white, blue, violet; black, red, orange, yellow,
  4302  white, blue, violet, &c. But the yellow and red were much fainter than
  4303  the blue and violet.
  4305  The Motion of the Prisms about their Axis being continued, these Colours
  4306  contracted more and more, shrinking towards the whiteness on either
  4307  side of it, until they totally vanished into it. And then the Circles in
  4308  those parts appear'd black and white, without any other Colours
  4309  intermix'd. But by farther moving the Prisms about, the Colours again
  4310  emerged out of the whiteness, the violet and blue at its inward Limb,
  4311  and at its outward Limb the red and yellow. So that now their order from
  4312  the central Spot was white, yellow, red; black; violet, blue, white,
  4313  yellow, red, &c. contrary to what it was before.
  4315  _Obs._ 3. When the Rings or some parts of them appeared only black and
  4316  white, they were very distinct and well defined, and the blackness
  4317  seemed as intense as that of the central Spot. Also in the Borders of
  4318  the Rings, where the Colours began to emerge out of the whiteness, they
  4319  were pretty distinct, which made them visible to a very great multitude.
  4320  I have sometimes number'd above thirty Successions (reckoning every
  4321  black and white Ring for one Succession) and seen more of them, which by
  4322  reason of their smalness I could not number. But in other Positions of
  4323  the Prisms, at which the Rings appeared of many Colours, I could not
  4324  distinguish above eight or nine of them, and the Exterior of those were
  4325  very confused and dilute.
  4327  In these two Observations to see the Rings distinct, and without any
  4328  other Colour than Black and white, I found it necessary to hold my Eye
  4329  at a good distance from them. For by approaching nearer, although in the
  4330  same inclination of my Eye to the Plane of the Rings, there emerged a
  4331  bluish Colour out of the white, which by dilating it self more and more
  4332  into the black, render'd the Circles less distinct, and left the white a
  4333  little tinged with red and yellow. I found also by looking through a
  4334  slit or oblong hole, which was narrower than the pupil of my Eye, and
  4335  held close to it parallel to the Prisms, I could see the Circles much
  4336  distincter and visible to a far greater number than otherwise.
  4338  _Obs._ 4. To observe more nicely the order of the Colours which arose
  4339  out of the white Circles as the Rays became less and less inclined to
  4340  the Plate of Air; I took two Object-glasses, the one a Plano-convex for
  4341  a fourteen Foot Telescope, and the other a large double Convex for one
  4342  of about fifty Foot; and upon this, laying the other with its plane side
  4343  downwards, I pressed them slowly together, to make the Colours
  4344  successively emerge in the middle of the Circles, and then slowly lifted
  4345  the upper Glass from the lower to make them successively vanish again in
  4346  the same place. The Colour, which by pressing the Glasses together,
  4347  emerged last in the middle of the other Colours, would upon its first
  4348  appearance look like a Circle of a Colour almost uniform from the
  4349  circumference to the center and by compressing the Glasses still more,
  4350  grow continually broader until a new Colour emerged in its center, and
  4351  thereby it became a Ring encompassing that new Colour. And by
  4352  compressing the Glasses still more, the diameter of this Ring would
  4353  increase, and the breadth of its Orbit or Perimeter decrease until
  4354  another new Colour emerged in the center of the last: And so on until a
  4355  third, a fourth, a fifth, and other following new Colours successively
  4356  emerged there, and became Rings encompassing the innermost Colour, the
  4357  last of which was the black Spot. And, on the contrary, by lifting up
  4358  the upper Glass from the lower, the diameter of the Rings would
  4359  decrease, and the breadth of their Orbit increase, until their Colours
  4360  reached successively to the center; and then they being of a
  4361  considerable breadth, I could more easily discern and distinguish their
  4362  Species than before. And by this means I observ'd their Succession and
  4363  Quantity to be as followeth.
  4365  Next to the pellucid central Spot made by the contact of the Glasses
  4366  succeeded blue, white, yellow, and red. The blue was so little in
  4367  quantity, that I could not discern it in the Circles made by the Prisms,
  4368  nor could I well distinguish any violet in it, but the yellow and red
  4369  were pretty copious, and seemed about as much in extent as the white,
  4370  and four or five times more than the blue. The next Circuit in order of
  4371  Colours immediately encompassing these were violet, blue, green, yellow,
  4372  and red: and these were all of them copious and vivid, excepting the
  4373  green, which was very little in quantity, and seemed much more faint and
  4374  dilute than the other Colours. Of the other four, the violet was the
  4375  least in extent, and the blue less than the yellow or red. The third
  4376  Circuit or Order was purple, blue, green, yellow, and red; in which the
  4377  purple seemed more reddish than the violet in the former Circuit, and
  4378  the green was much more conspicuous, being as brisk and copious as any
  4379  of the other Colours, except the yellow, but the red began to be a
  4380  little faded, inclining very much to purple. After this succeeded the
  4381  fourth Circuit of green and red. The green was very copious and lively,
  4382  inclining on the one side to blue, and on the other side to yellow. But
  4383  in this fourth Circuit there was neither violet, blue, nor yellow, and
  4384  the red was very imperfect and dirty. Also the succeeding Colours became
  4385  more and more imperfect and dilute, till after three or four revolutions
  4386  they ended in perfect whiteness. Their form, when the Glasses were most
  4387  compress'd so as to make the black Spot appear in the center, is
  4388  delineated in the second Figure; where _a_, _b_, _c_, _d_, _e_: _f_,
  4389  _g_, _h_, _i_, _k_: _l_, _m_, _n_, _o_, _p_: _q_, _r_: _s_, _t_: _v_,
  4390  _x_: _y_, _z_, denote the Colours reckon'd in order from the center,
  4391  black, blue, white, yellow, red: violet, blue, green, yellow, red:
  4392  purple, blue, green, yellow, red: green, red: greenish blue, red:
  4393  greenish blue, pale red: greenish blue, reddish white.
  4395  [Illustration: FIG. 2.]
  4397  _Obs._ 5. To determine the interval of the Glasses, or thickness of the
  4398  interjacent Air, by which each Colour was produced, I measured the
  4399  Diameters of the first six Rings at the most lucid part of their Orbits,
  4400  and squaring them, I found their Squares to be in the arithmetical
  4401  Progression of the odd Numbers, 1, 3, 5, 7, 9, 11. And since one of
  4402  these Glasses was plane, and the other spherical, their Intervals at
  4403  those Rings must be in the same Progression. I measured also the
  4404  Diameters of the dark or faint Rings between the more lucid Colours, and
  4405  found their Squares to be in the arithmetical Progression of the even
  4406  Numbers, 2, 4, 6, 8, 10, 12. And it being very nice and difficult to
  4407  take these measures exactly; I repeated them divers times at divers
  4408  parts of the Glasses, that by their Agreement I might be confirmed in
  4409  them. And the same method I used in determining some others of the
  4410  following Observations.
  4412  _Obs._ 6. The Diameter of the sixth Ring at the most lucid part of its
  4413  Orbit was 58/100 parts of an Inch, and the Diameter of the Sphere on
  4414  which the double convex Object-glass was ground was about 102 Feet, and
  4415  hence I gathered the thickness of the Air or Aereal Interval of the
  4416  Glasses at that Ring. But some time after, suspecting that in making
  4417  this Observation I had not determined the Diameter of the Sphere with
  4418  sufficient accurateness, and being uncertain whether the Plano-convex
  4419  Glass was truly plane, and not something concave or convex on that side
  4420  which I accounted plane; and whether I had not pressed the Glasses
  4421  together, as I often did, to make them touch; (For by pressing such
  4422  Glasses together their parts easily yield inwards, and the Rings thereby
  4423  become sensibly broader than they would be, did the Glasses keep their
  4424  Figures.) I repeated the Experiment, and found the Diameter of the sixth
  4425  lucid Ring about 55/100 parts of an Inch. I repeated the Experiment also
  4426  with such an Object-glass of another Telescope as I had at hand. This
  4427  was a double Convex ground on both sides to one and the same Sphere, and
  4428  its Focus was distant from it 83-2/5 Inches. And thence, if the Sines of
  4429  Incidence and Refraction of the bright yellow Light be assumed in
  4430  proportion as 11 to 17, the Diameter of the Sphere to which the Glass
  4431  was figured will by computation be found 182 Inches. This Glass I laid
  4432  upon a flat one, so that the black Spot appeared in the middle of the
  4433  Rings of Colours without any other Pressure than that of the weight of
  4434  the Glass. And now measuring the Diameter of the fifth dark Circle as
  4435  accurately as I could, I found it the fifth part of an Inch precisely.
  4436  This Measure was taken with the points of a pair of Compasses on the
  4437  upper Surface on the upper Glass, and my Eye was about eight or nine
  4438  Inches distance from the Glass, almost perpendicularly over it, and the
  4439  Glass was 1/6 of an Inch thick, and thence it is easy to collect that
  4440  the true Diameter of the Ring between the Glasses was greater than its
  4441  measur'd Diameter above the Glasses in the Proportion of 80 to 79, or
  4442  thereabouts, and by consequence equal to 16/79 parts of an Inch, and its
  4443  true Semi-diameter equal to 8/79 parts. Now as the Diameter of the
  4444  Sphere (182 Inches) is to the Semi-diameter of this fifth dark Ring
  4445  (8/79 parts of an Inch) so is this Semi-diameter to the thickness of the
  4446  Air at this fifth dark Ring; which is therefore 32/567931 or
  4447  100/1774784. Parts of an Inch; and the fifth Part thereof, _viz._ the
  4448  1/88739 Part of an Inch, is the Thickness of the Air at the first of
  4449  these dark Rings.
  4451  The same Experiment I repeated with another double convex Object-glass
  4452  ground on both sides to one and the same Sphere. Its Focus was distant
  4453  from it 168-1/2 Inches, and therefore the Diameter of that Sphere was
  4454  184 Inches. This Glass being laid upon the same plain Glass, the
  4455  Diameter of the fifth of the dark Rings, when the black Spot in their
  4456  Center appear'd plainly without pressing the Glasses, was by the measure
  4457  of the Compasses upon the upper Glass 121/600 Parts of an Inch, and by
  4458  consequence between the Glasses it was 1222/6000: For the upper Glass
  4459  was 1/8 of an Inch thick, and my Eye was distant from it 8 Inches. And a
  4460  third proportional to half this from the Diameter of the Sphere is
  4461  5/88850 Parts of an Inch. This is therefore the Thickness of the Air at
  4462  this Ring, and a fifth Part thereof, _viz._ the 1/88850th Part of an
  4463  Inch is the Thickness thereof at the first of the Rings, as above.
  4465  I tried the same Thing, by laying these Object-glasses upon flat Pieces
  4466  of a broken Looking-glass, and found the same Measures of the Rings:
  4467  Which makes me rely upon them till they can be determin'd more
  4468  accurately by Glasses ground to larger Spheres, though in such Glasses
  4469  greater care must be taken of a true Plane.
  4471  These Dimensions were taken, when my Eye was placed almost
  4472  perpendicularly over the Glasses, being about an Inch, or an Inch and a
  4473  quarter, distant from the incident Rays, and eight Inches distant from
  4474  the Glass; so that the Rays were inclined to the Glass in an Angle of
  4475  about four Degrees. Whence by the following Observation you will
  4476  understand, that had the Rays been perpendicular to the Glasses, the
  4477  Thickness of the Air at these Rings would have been less in the
  4478  Proportion of the Radius to the Secant of four Degrees, that is, of
  4479  10000 to 10024. Let the Thicknesses found be therefore diminish'd in
  4480  this Proportion, and they will become 1/88952 and 1/89063, or (to use
  4481  the nearest round Number) the 1/89000th Part of an Inch. This is the
  4482  Thickness of the Air at the darkest Part of the first dark Ring made by
  4483  perpendicular Rays; and half this Thickness multiplied by the
  4484  Progression, 1, 3, 5, 7, 9, 11, &c. gives the Thicknesses of the Air at
  4485  the most luminous Parts of all the brightest Rings, _viz._ 1/178000,
  4486  3/178000, 5/178000, 7/178000, &c. their arithmetical Means 2/178000,
  4487  4/178000, 6/178000, &c. being its Thicknesses at the darkest Parts of
  4488  all the dark ones.
  4490  _Obs._ 7. The Rings were least, when my Eye was placed perpendicularly
  4491  over the Glasses in the Axis of the Rings: And when I view'd them
  4492  obliquely they became bigger, continually swelling as I removed my Eye
  4493  farther from the Axis. And partly by measuring the Diameter of the same
  4494  Circle at several Obliquities of my Eye, partly by other Means, as also
  4495  by making use of the two Prisms for very great Obliquities, I found its
  4496  Diameter, and consequently the Thickness of the Air at its Perimeter in
  4497  all those Obliquities to be very nearly in the Proportions express'd in
  4498  this Table.
  4500  -------------------+--------------------+----------+----------
  4501  Angle of Incidence |Angle of Refraction |Diameter  |Thickness
  4502          on         |         into       |  of the  |   of the
  4503        the Air.     |       the Air.     |   Ring.  |    Air.
  4504  -------------------+--------------------+----------+----------
  4505      Deg.    Min.   |                    |          |
  4506                     |                    |          |
  4507      00      00     |     00      00     |  10      |  10
  4508                     |                    |          |
  4509      06      26     |     10      00     |  10-1/13 |  10-2/13
  4510                     |                    |          |
  4511      12      45     |     20      00     |  10-1/3  |  10-2/3
  4512                     |                    |          |
  4513      18      49     |     30      00     |  10-3/4  |  11-1/2
  4514                     |                    |          |
  4515      24      30     |     40      00     |  11-2/5  |  13
  4516                     |                    |          |
  4517      29      37     |     50      00     |  12-1/2  |  15-1/2
  4518                     |                    |          |
  4519      33      58     |     60      00     |  14      |  20
  4520                     |                    |          |
  4521      35      47     |     65      00     |  15-1/4  |  23-1/4
  4522                     |                    |          |
  4523      37      19     |     70      00     |  16-4/5  |  28-1/4
  4524                     |                    |          |
  4525      38      33     |     75      00     |  19-1/4  |  37
  4526                     |                    |          |
  4527      39      27     |     80      00     |  22-6/7  |  52-1/4
  4528                     |                    |          |
  4529      40      00     |     85      00     |  29      |  84-1/12
  4530                     |                    |          |
  4531      40      11     |     90      00     |  35      | 122-1/2
  4532  -------------------+--------------------+----------+----------
  4534  In the two first Columns are express'd the Obliquities of the incident
  4535  and emergent Rays to the Plate of the Air, that is, their Angles of
  4536  Incidence and Refraction. In the third Column the Diameter of any
  4537  colour'd Ring at those Obliquities is expressed in Parts, of which ten
  4538  constitute that Diameter when the Rays are perpendicular. And in the
  4539  fourth Column the Thickness of the Air at the Circumference of that Ring
  4540  is expressed in Parts, of which also ten constitute its Thickness when
  4541  the Rays are perpendicular.
  4543  And from these Measures I seem to gather this Rule: That the Thickness
  4544  of the Air is proportional to the Secant of an Angle, whose Sine is a
  4545  certain mean Proportional between the Sines of Incidence and Refraction.
  4546  And that mean Proportional, so far as by these Measures I can determine
  4547  it, is the first of an hundred and six arithmetical mean Proportionals
  4548  between those Sines counted from the bigger Sine, that is, from the Sine
  4549  of Refraction when the Refraction is made out of the Glass into the
  4550  Plate of Air, or from the Sine of Incidence when the Refraction is made
  4551  out of the Plate of Air into the Glass.
  4553  _Obs._ 8. The dark Spot in the middle of the Rings increased also by the
  4554  Obliquation of the Eye, although almost insensibly. But, if instead of
  4555  the Object-glasses the Prisms were made use of, its Increase was more
  4556  manifest when viewed so obliquely that no Colours appear'd about it. It
  4557  was least when the Rays were incident most obliquely on the interjacent
  4558  Air, and as the obliquity decreased it increased more and more until the
  4559  colour'd Rings appear'd, and then decreased again, but not so much as it
  4560  increased before. And hence it is evident, that the Transparency was
  4561  not only at the absolute Contact of the Glasses, but also where they had
  4562  some little Interval. I have sometimes observed the Diameter of that
  4563  Spot to be between half and two fifth parts of the Diameter of the
  4564  exterior Circumference of the red in the first Circuit or Revolution of
  4565  Colours when view'd almost perpendicularly; whereas when view'd
  4566  obliquely it hath wholly vanish'd and become opake and white like the
  4567  other parts of the Glass; whence it may be collected that the Glasses
  4568  did then scarcely, or not at all, touch one another, and that their
  4569  Interval at the perimeter of that Spot when view'd perpendicularly was
  4570  about a fifth or sixth part of their Interval at the circumference of
  4571  the said red.
  4573  _Obs._ 9. By looking through the two contiguous Object-glasses, I found
  4574  that the interjacent Air exhibited Rings of Colours, as well by
  4575  transmitting Light as by reflecting it. The central Spot was now white,
  4576  and from it the order of the Colours were yellowish red; black, violet,
  4577  blue, white, yellow, red; violet, blue, green, yellow, red, &c. But
  4578  these Colours were very faint and dilute, unless when the Light was
  4579  trajected very obliquely through the Glasses: For by that means they
  4580  became pretty vivid. Only the first yellowish red, like the blue in the
  4581  fourth Observation, was so little and faint as scarcely to be discern'd.
  4582  Comparing the colour'd Rings made by Reflexion, with these made by
  4583  transmission of the Light; I found that white was opposite to black, red
  4584  to blue, yellow to violet, and green to a Compound of red and violet.
  4585  That is, those parts of the Glass were black when looked through, which
  4586  when looked upon appeared white, and on the contrary. And so those which
  4587  in one case exhibited blue, did in the other case exhibit red. And the
  4588  like of the other Colours. The manner you have represented in the third
  4589  Figure, where AB, CD, are the Surfaces of the Glasses contiguous at E,
  4590  and the black Lines between them are their Distances in arithmetical
  4591  Progression, and the Colours written above are seen by reflected Light,
  4592  and those below by Light transmitted (p. 209).
  4594  _Obs._ 10. Wetting the Object-glasses a little at their edges, the Water
  4595  crept in slowly between them, and the Circles thereby became less and
  4596  the Colours more faint: Insomuch that as the Water crept along, one half
  4597  of them at which it first arrived would appear broken off from the other
  4598  half, and contracted into a less Room. By measuring them I found the
  4599  Proportions of their Diameters to the Diameters of the like Circles made
  4600  by Air to be about seven to eight, and consequently the Intervals of the
  4601  Glasses at like Circles, caused by those two Mediums Water and Air, are
  4602  as about three to four. Perhaps it may be a general Rule, That if any
  4603  other Medium more or less dense than Water be compress'd between the
  4604  Glasses, their Intervals at the Rings caused thereby will be to their
  4605  Intervals caused by interjacent Air, as the Sines are which measure the
  4606  Refraction made out of that Medium into Air.
  4608  _Obs._ 11. When the Water was between the Glasses, if I pressed the
  4609  upper Glass variously at its edges to make the Rings move nimbly from
  4610  one place to another, a little white Spot would immediately follow the
  4611  center of them, which upon creeping in of the ambient Water into that
  4612  place would presently vanish. Its appearance was such as interjacent Air
  4613  would have caused, and it exhibited the same Colours. But it was not
  4614  air, for where any Bubbles of Air were in the Water they would not
  4615  vanish. The Reflexion must have rather been caused by a subtiler Medium,
  4616  which could recede through the Glasses at the creeping in of the Water.
  4618  _Obs._ 12. These Observations were made in the open Air. But farther to
  4619  examine the Effects of colour'd Light falling on the Glasses, I darken'd
  4620  the Room, and view'd them by Reflexion of the Colours of a Prism cast on
  4621  a Sheet of white Paper, my Eye being so placed that I could see the
  4622  colour'd Paper by Reflexion in the Glasses, as in a Looking-glass. And
  4623  by this means the Rings became distincter and visible to a far greater
  4624  number than in the open Air. I have sometimes seen more than twenty of
  4625  them, whereas in the open Air I could not discern above eight or nine.
  4627  [Illustration: FIG. 3.]
  4629  _Obs._ 13. Appointing an Assistant to move the Prism to and fro about
  4630  its Axis, that all the Colours might successively fall on that part of
  4631  the Paper which I saw by Reflexion from that part of the Glasses, where
  4632  the Circles appear'd, so that all the Colours might be successively
  4633  reflected from the Circles to my Eye, whilst I held it immovable, I
  4634  found the Circles which the red Light made to be manifestly bigger than
  4635  those which were made by the blue and violet. And it was very pleasant
  4636  to see them gradually swell or contract accordingly as the Colour of the
  4637  Light was changed. The Interval of the Glasses at any of the Rings when
  4638  they were made by the utmost red Light, was to their Interval at the
  4639  same Ring when made by the utmost violet, greater than as 3 to 2, and
  4640  less than as 13 to 8. By the most of my Observations it was as 14 to 9.
  4641  And this Proportion seem'd very nearly the same in all Obliquities of my
  4642  Eye; unless when two Prisms were made use of instead of the
  4643  Object-glasses. For then at a certain great obliquity of my Eye, the
  4644  Rings made by the several Colours seem'd equal, and at a greater
  4645  obliquity those made by the violet would be greater than the same Rings
  4646  made by the red: the Refraction of the Prism in this case causing the
  4647  most refrangible Rays to fall more obliquely on that plate of the Air
  4648  than the least refrangible ones. Thus the Experiment succeeded in the
  4649  colour'd Light, which was sufficiently strong and copious to make the
  4650  Rings sensible. And thence it may be gather'd, that if the most
  4651  refrangible and least refrangible Rays had been copious enough to make
  4652  the Rings sensible without the mixture of other Rays, the Proportion
  4653  which here was 14 to 9 would have been a little greater, suppose 14-1/4
  4654  or 14-1/3 to 9.
  4656  _Obs._ 14. Whilst the Prism was turn'd about its Axis with an uniform
  4657  Motion, to make all the several Colours fall successively upon the
  4658  Object-glasses, and thereby to make the Rings contract and dilate: The
  4659  Contraction or Dilatation of each Ring thus made by the variation of its
  4660  Colour was swiftest in the red, and slowest in the violet, and in the
  4661  intermediate Colours it had intermediate degrees of Celerity. Comparing
  4662  the quantity of Contraction and Dilatation made by all the degrees of
  4663  each Colour, I found that it was greatest in the red; less in the
  4664  yellow, still less in the blue, and least in the violet. And to make as
  4665  just an Estimation as I could of the Proportions of their Contractions
  4666  or Dilatations, I observ'd that the whole Contraction or Dilatation of
  4667  the Diameter of any Ring made by all the degrees of red, was to that of
  4668  the Diameter of the same Ring made by all the degrees of violet, as
  4669  about four to three, or five to four, and that when the Light was of the
  4670  middle Colour between yellow and green, the Diameter of the Ring was
  4671  very nearly an arithmetical Mean between the greatest Diameter of the
  4672  same Ring made by the outmost red, and the least Diameter thereof made
  4673  by the outmost violet: Contrary to what happens in the Colours of the
  4674  oblong Spectrum made by the Refraction of a Prism, where the red is most
  4675  contracted, the violet most expanded, and in the midst of all the
  4676  Colours is the Confine of green and blue. And hence I seem to collect
  4677  that the thicknesses of the Air between the Glasses there, where the
  4678  Ring is successively made by the limits of the five principal Colours
  4679  (red, yellow, green, blue, violet) in order (that is, by the extreme
  4680  red, by the limit of red and yellow in the middle of the orange, by the
  4681  limit of yellow and green, by the limit of green and blue, by the limit
  4682  of blue and violet in the middle of the indigo, and by the extreme
  4683  violet) are to one another very nearly as the sixth lengths of a Chord
  4684  which found the Notes in a sixth Major, _sol_, _la_, _mi_, _fa_, _sol_,
  4685  _la_. But it agrees something better with the Observation to say, that
  4686  the thicknesses of the Air between the Glasses there, where the Rings
  4687  are successively made by the limits of the seven Colours, red, orange,
  4688  yellow, green, blue, indigo, violet in order, are to one another as the
  4689  Cube Roots of the Squares of the eight lengths of a Chord, which found
  4690  the Notes in an eighth, _sol_, _la_, _fa_, _sol_, _la_, _mi_, _fa_,
  4691  _sol_; that is, as the Cube Roots of the Squares of the Numbers, 1, 8/9,
  4692  5/6, 3/4, 2/3, 3/5, 9/16, 1/2.
  4694  _Obs._ 15. These Rings were not of various Colours like those made in
  4695  the open Air, but appeared all over of that prismatick Colour only with
  4696  which they were illuminated. And by projecting the prismatick Colours
  4697  immediately upon the Glasses, I found that the Light which fell on the
  4698  dark Spaces which were between the Colour'd Rings was transmitted
  4699  through the Glasses without any variation of Colour. For on a white
  4700  Paper placed behind, it would paint Rings of the same Colour with those
  4701  which were reflected, and of the bigness of their immediate Spaces. And
  4702  from thence the origin of these Rings is manifest; namely, that the Air
  4703  between the Glasses, according to its various thickness, is disposed in
  4704  some places to reflect, and in others to transmit the Light of any one
  4705  Colour (as you may see represented in the fourth Figure) and in the same
  4706  place to reflect that of one Colour where it transmits that of another.
  4708  [Illustration: FIG. 4.]
  4710  _Obs._ 16. The Squares of the Diameters of these Rings made by any
  4711  prismatick Colour were in arithmetical Progression, as in the fifth
  4712  Observation. And the Diameter of the sixth Circle, when made by the
  4713  citrine yellow, and viewed almost perpendicularly was about 58/100 parts
  4714  of an Inch, or a little less, agreeable to the sixth Observation.
  4716  The precedent Observations were made with a rarer thin Medium,
  4717  terminated by a denser, such as was Air or Water compress'd between two
  4718  Glasses. In those that follow are set down the Appearances of a denser
  4719  Medium thin'd within a rarer, such as are Plates of Muscovy Glass,
  4720  Bubbles of Water, and some other thin Substances terminated on all sides
  4721  with air.
  4723  _Obs._ 17. If a Bubble be blown with Water first made tenacious by
  4724  dissolving a little Soap in it, 'tis a common Observation, that after a
  4725  while it will appear tinged with a great variety of Colours. To defend
  4726  these Bubbles from being agitated by the external Air (whereby their
  4727  Colours are irregularly moved one among another, so that no accurate
  4728  Observation can be made of them,) as soon as I had blown any of them I
  4729  cover'd it with a clear Glass, and by that means its Colours emerged in
  4730  a very regular order, like so many concentrick Rings encompassing the
  4731  top of the Bubble. And as the Bubble grew thinner by the continual
  4732  subsiding of the Water, these Rings dilated slowly and overspread the
  4733  whole Bubble, descending in order to the bottom of it, where they
  4734  vanish'd successively. In the mean while, after all the Colours were
  4735  emerged at the top, there grew in the center of the Rings a small round
  4736  black Spot, like that in the first Observation, which continually
  4737  dilated it self till it became sometimes more than 1/2 or 3/4 of an Inch
  4738  in breadth before the Bubble broke. At first I thought there had been no
  4739  Light reflected from the Water in that place, but observing it more
  4740  curiously, I saw within it several smaller round Spots, which appeared
  4741  much blacker and darker than the rest, whereby I knew that there was
  4742  some Reflexion at the other places which were not so dark as those
  4743  Spots. And by farther Tryal I found that I could see the Images of some
  4744  things (as of a Candle or the Sun) very faintly reflected, not only from
  4745  the great black Spot, but also from the little darker Spots which were
  4746  within it.
  4748  Besides the aforesaid colour'd Rings there would often appear small
  4749  Spots of Colours, ascending and descending up and down the sides of the
  4750  Bubble, by reason of some Inequalities in the subsiding of the Water.
  4751  And sometimes small black Spots generated at the sides would ascend up
  4752  to the larger black Spot at the top of the Bubble, and unite with it.
  4754  _Obs._ 18. Because the Colours of these Bubbles were more extended and
  4755  lively than those of the Air thinn'd between two Glasses, and so more
  4756  easy to be distinguish'd, I shall here give you a farther description of
  4757  their order, as they were observ'd in viewing them by Reflexion of the
  4758  Skies when of a white Colour, whilst a black substance was placed
  4759  behind the Bubble. And they were these, red, blue; red, blue; red, blue;
  4760  red, green; red, yellow, green, blue, purple; red, yellow, green, blue,
  4761  violet; red, yellow, white, blue, black.
  4763  The three first Successions of red and blue were very dilute and dirty,
  4764  especially the first, where the red seem'd in a manner to be white.
  4765  Among these there was scarce any other Colour sensible besides red and
  4766  blue, only the blues (and principally the second blue) inclined a little
  4767  to green.
  4769  The fourth red was also dilute and dirty, but not so much as the former
  4770  three; after that succeeded little or no yellow, but a copious green,
  4771  which at first inclined a little to yellow, and then became a pretty
  4772  brisk and good willow green, and afterwards changed to a bluish Colour;
  4773  but there succeeded neither blue nor violet.
  4775  The fifth red at first inclined very much to purple, and afterwards
  4776  became more bright and brisk, but yet not very pure. This was succeeded
  4777  with a very bright and intense yellow, which was but little in quantity,
  4778  and soon chang'd to green: But that green was copious and something more
  4779  pure, deep and lively, than the former green. After that follow'd an
  4780  excellent blue of a bright Sky-colour, and then a purple, which was less
  4781  in quantity than the blue, and much inclined to red.
  4783  The sixth red was at first of a very fair and lively scarlet, and soon
  4784  after of a brighter Colour, being very pure and brisk, and the best of
  4785  all the reds. Then after a lively orange follow'd an intense bright and
  4786  copious yellow, which was also the best of all the yellows, and this
  4787  changed first to a greenish yellow, and then to a greenish blue; but the
  4788  green between the yellow and the blue, was very little and dilute,
  4789  seeming rather a greenish white than a green. The blue which succeeded
  4790  became very good, and of a very bright Sky-colour, but yet something
  4791  inferior to the former blue; and the violet was intense and deep with
  4792  little or no redness in it. And less in quantity than the blue.
  4794  In the last red appeared a tincture of scarlet next to violet, which
  4795  soon changed to a brighter Colour, inclining to an orange; and the
  4796  yellow which follow'd was at first pretty good and lively, but
  4797  afterwards it grew more dilute until by degrees it ended in perfect
  4798  whiteness. And this whiteness, if the Water was very tenacious and
  4799  well-temper'd, would slowly spread and dilate it self over the greater
  4800  part of the Bubble; continually growing paler at the top, where at
  4801  length it would crack in many places, and those cracks, as they dilated,
  4802  would appear of a pretty good, but yet obscure and dark Sky-colour; the
  4803  white between the blue Spots diminishing, until it resembled the Threds
  4804  of an irregular Net-work, and soon after vanish'd, and left all the
  4805  upper part of the Bubble of the said dark blue Colour. And this Colour,
  4806  after the aforesaid manner, dilated it self downwards, until sometimes
  4807  it hath overspread the whole Bubble. In the mean while at the top, which
  4808  was of a darker blue than the bottom, and appear'd also full of many
  4809  round blue Spots, something darker than the rest, there would emerge
  4810  one or more very black Spots, and within those, other Spots of an
  4811  intenser blackness, which I mention'd in the former Observation; and
  4812  these continually dilated themselves until the Bubble broke.
  4814  If the Water was not very tenacious, the black Spots would break forth
  4815  in the white, without any sensible intervention of the blue. And
  4816  sometimes they would break forth within the precedent yellow, or red, or
  4817  perhaps within the blue of the second order, before the intermediate
  4818  Colours had time to display themselves.
  4820  By this description you may perceive how great an affinity these Colours
  4821  have with those of Air described in the fourth Observation, although set
  4822  down in a contrary order, by reason that they begin to appear when the
  4823  Bubble is thickest, and are most conveniently reckon'd from the lowest
  4824  and thickest part of the Bubble upwards.
  4826  _Obs._ 19. Viewing in several oblique Positions of my Eye the Rings of
  4827  Colours emerging on the top of the Bubble, I found that they were
  4828  sensibly dilated by increasing the obliquity, but yet not so much by far
  4829  as those made by thinn'd Air in the seventh Observation. For there they
  4830  were dilated so much as, when view'd most obliquely, to arrive at a part
  4831  of the Plate more than twelve times thicker than that where they
  4832  appear'd when viewed perpendicularly; whereas in this case the thickness
  4833  of the Water, at which they arrived when viewed most obliquely, was to
  4834  that thickness which exhibited them by perpendicular Rays, something
  4835  less than as 8 to 5. By the best of my Observations it was between 15
  4836  and 15-1/2 to 10; an increase about 24 times less than in the other
  4837  case.
  4839  Sometimes the Bubble would become of an uniform thickness all over,
  4840  except at the top of it near the black Spot, as I knew, because it would
  4841  exhibit the same appearance of Colours in all Positions of the Eye. And
  4842  then the Colours which were seen at its apparent circumference by the
  4843  obliquest Rays, would be different from those that were seen in other
  4844  places, by Rays less oblique to it. And divers Spectators might see the
  4845  same part of it of differing Colours, by viewing it at very differing
  4846  Obliquities. Now observing how much the Colours at the same places of
  4847  the Bubble, or at divers places of equal thickness, were varied by the
  4848  several Obliquities of the Rays; by the assistance of the 4th, 14th,
  4849  16th and 18th Observations, as they are hereafter explain'd, I collect
  4850  the thickness of the Water requisite to exhibit any one and the same
  4851  Colour, at several Obliquities, to be very nearly in the Proportion
  4852  expressed in this Table.
  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  -----------------+------------------+----------------
  4875  In the two first Columns are express'd the Obliquities of the Rays to
  4876  the Superficies of the Water, that is, their Angles of Incidence and
  4877  Refraction. Where I suppose, that the Sines which measure them are in
  4878  round Numbers, as 3 to 4, though probably the Dissolution of Soap in the
  4879  Water, may a little alter its refractive Virtue. In the third Column,
  4880  the Thickness of the Bubble, at which any one Colour is exhibited in
  4881  those several Obliquities, is express'd in Parts, of which ten
  4882  constitute its Thickness when the Rays are perpendicular. And the Rule
  4883  found by the seventh Observation agrees well with these Measures, if
  4884  duly apply'd; namely, that the Thickness of a Plate of Water requisite
  4885  to exhibit one and the same Colour at several Obliquities of the Eye, is
  4886  proportional to the Secant of an Angle, whose Sine is the first of an
  4887  hundred and six arithmetical mean Proportionals between the Sines of
  4888  Incidence and Refraction counted from the lesser Sine, that is, from the
  4889  Sine of Refraction when the Refraction is made out of Air into Water,
  4890  otherwise from the Sine of Incidence.
  4892  I have sometimes observ'd, that the Colours which arise on polish'd
  4893  Steel by heating it, or on Bell-metal, and some other metalline
  4894  Substances, when melted and pour'd on the Ground, where they may cool in
  4895  the open Air, have, like the Colours of Water-bubbles, been a little
  4896  changed by viewing them at divers Obliquities, and particularly that a
  4897  deep blue, or violet, when view'd very obliquely, hath been changed to a
  4898  deep red. But the Changes of these Colours are not so great and
  4899  sensible as of those made by Water. For the Scoria, or vitrified Part of
  4900  the Metal, which most Metals when heated or melted do continually
  4901  protrude, and send out to their Surface, and which by covering the
  4902  Metals in form of a thin glassy Skin, causes these Colours, is much
  4903  denser than Water; and I find that the Change made by the Obliquation of
  4904  the Eye is least in Colours of the densest thin Substances.
  4906  _Obs._ 20. As in the ninth Observation, so here, the Bubble, by
  4907  transmitted Light, appear'd of a contrary Colour to that, which it
  4908  exhibited by Reflexion. Thus when the Bubble being look'd on by the
  4909  Light of the Clouds reflected from it, seemed red at its apparent
  4910  Circumference, if the Clouds at the same time, or immediately after,
  4911  were view'd through it, the Colour at its Circumference would be blue.
  4912  And, on the contrary, when by reflected Light it appeared blue, it would
  4913  appear red by transmitted Light.
  4915  _Obs._ 21. By wetting very thin Plates of _Muscovy_ Glass, whose
  4916  thinness made the like Colours appear, the Colours became more faint and
  4917  languid, especially by wetting the Plates on that side opposite to the
  4918  Eye: But I could not perceive any variation of their Species. So then
  4919  the thickness of a Plate requisite to produce any Colour, depends only
  4920  on the density of the Plate, and not on that of the ambient Medium. And
  4921  hence, by the 10th and 16th Observations, may be known the thickness
  4922  which Bubbles of Water, or Plates of _Muscovy_ Glass, or other
  4923  Substances, have at any Colour produced by them.
  4925  _Obs._ 22. A thin transparent Body, which is denser than its ambient
  4926  Medium, exhibits more brisk and vivid Colours than that which is so much
  4927  rarer; as I have particularly observed in the Air and Glass. For blowing
  4928  Glass very thin at a Lamp Furnace, those Plates encompassed with Air did
  4929  exhibit Colours much more vivid than those of Air made thin between two
  4930  Glasses.
  4932  _Obs._ 23. Comparing the quantity of Light reflected from the several
  4933  Rings, I found that it was most copious from the first or inmost, and in
  4934  the exterior Rings became gradually less and less. Also the whiteness of
  4935  the first Ring was stronger than that reflected from those parts of the
  4936  thin Medium or Plate which were without the Rings; as I could manifestly
  4937  perceive by viewing at a distance the Rings made by the two
  4938  Object-glasses; or by comparing two Bubbles of Water blown at distant
  4939  Times, in the first of which the Whiteness appear'd, which succeeded all
  4940  the Colours, and in the other, the Whiteness which preceded them all.
  4942  _Obs._ 24. When the two Object-glasses were lay'd upon one another, so
  4943  as to make the Rings of the Colours appear, though with my naked Eye I
  4944  could not discern above eight or nine of those Rings, yet by viewing
  4945  them through a Prism I have seen a far greater Multitude, insomuch that
  4946  I could number more than forty, besides many others, that were so very
  4947  small and close together, that I could not keep my Eye steady on them
  4948  severally so as to number them, but by their Extent I have sometimes
  4949  estimated them to be more than an hundred. And I believe the Experiment
  4950  may be improved to the Discovery of far greater Numbers. For they seem
  4951  to be really unlimited, though visible only so far as they can be
  4952  separated by the Refraction of the Prism, as I shall hereafter explain.
  4954  [Illustration: FIG. 5.]
  4956  But it was but one side of these Rings, namely, that towards which the
  4957  Refraction was made, which by that Refraction was render'd distinct, and
  4958  the other side became more confused than when view'd by the naked Eye,
  4959  insomuch that there I could not discern above one or two, and sometimes
  4960  none of those Rings, of which I could discern eight or nine with my
  4961  naked Eye. And their Segments or Arcs, which on the other side appear'd
  4962  so numerous, for the most part exceeded not the third Part of a Circle.
  4963  If the Refraction was very great, or the Prism very distant from the
  4964  Object-glasses, the middle Part of those Arcs became also confused, so
  4965  as to disappear and constitute an even Whiteness, whilst on either side
  4966  their Ends, as also the whole Arcs farthest from the Center, became
  4967  distincter than before, appearing in the Form as you see them design'd
  4968  in the fifth Figure.
  4970  The Arcs, where they seem'd distinctest, were only white and black
  4971  successively, without any other Colours intermix'd. But in other Places
  4972  there appeared Colours, whose Order was inverted by the refraction in
  4973  such manner, that if I first held the Prism very near the
  4974  Object-glasses, and then gradually removed it farther off towards my
  4975  Eye, the Colours of the 2d, 3d, 4th, and following Rings, shrunk towards
  4976  the white that emerged between them, until they wholly vanish'd into it
  4977  at the middle of the Arcs, and afterwards emerged again in a contrary
  4978  Order. But at the Ends of the Arcs they retain'd their Order unchanged.
  4980  I have sometimes so lay'd one Object-glass upon the other, that to the
  4981  naked Eye they have all over seem'd uniformly white, without the least
  4982  Appearance of any of the colour'd Rings; and yet by viewing them through
  4983  a Prism, great Multitudes of those Rings have discover'd themselves. And
  4984  in like manner Plates of _Muscovy_ Glass, and Bubbles of Glass blown at
  4985  a Lamp-Furnace, which were not so thin as to exhibit any Colours to the
  4986  naked Eye, have through the Prism exhibited a great Variety of them
  4987  ranged irregularly up and down in the Form of Waves. And so Bubbles of
  4988  Water, before they began to exhibit their Colours to the naked Eye of a
  4989  Bystander, have appeared through a Prism, girded about with many
  4990  parallel and horizontal Rings; to produce which Effect, it was necessary
  4991  to hold the Prism parallel, or very nearly parallel to the Horizon, and
  4992  to dispose it so that the Rays might be refracted upwards.
  4997  THE
  5001  OF
  5003  OPTICKS
  5006  _PART II._
  5008  _Remarks upon the foregoing Observations._
  5011  Having given my Observations of these Colours, before I make use of them
  5012  to unfold the Causes of the Colours of natural Bodies, it is convenient
  5013  that by the simplest of them, such as are the 2d, 3d, 4th, 9th, 12th,
  5014  18th, 20th, and 24th, I first explain the more compounded. And first to
  5015  shew how the Colours in the fourth and eighteenth Observations are
  5016  produced, let there be taken in any Right Line from the Point Y, [in
  5017  _Fig._ 6.] the Lengths YA, YB, YC, YD, YE, YF, YG, YH, in proportion to
  5018  one another, as the Cube-Roots of the Squares of the Numbers, 1/2, 9/16,
  5019  3/5, 2/3, 3/4, 5/6, 8/9, 1, whereby the Lengths of a Musical Chord to
  5020  sound all the Notes in an eighth are represented; that is, in the
  5021  Proportion of the Numbers 6300, 6814, 7114, 7631, 8255, 8855, 9243,
  5022  10000. And at the Points A, B, C, D, E, F, G, H, let Perpendiculars
  5023  A[Greek: a], B[Greek: b], &c. be erected, by whose Intervals the Extent
  5024  of the several Colours set underneath against them, is to be
  5025  represented. Then divide the Line _A[Greek: a]_ in such Proportion as
  5026  the Numbers 1, 2, 3, 5, 6, 7, 9, 10, 11, &c. set at the Points of
  5027  Division denote. And through those Divisions from Y draw Lines 1I, 2K,
  5028  3L, 5M, 6N, 7O, &c.
  5030  Now, if A2 be supposed to represent the Thickness of any thin
  5031  transparent Body, at which the outmost Violet is most copiously
  5032  reflected in the first Ring, or Series of Colours, then by the 13th
  5033  Observation, HK will represent its Thickness, at which the utmost Red is
  5034  most copiously reflected in the same Series. Also by the 5th and 16th
  5035  Observations, A6 and HN will denote the Thicknesses at which those
  5036  extreme Colours are most copiously reflected in the second Series, and
  5037  A10 and HQ the Thicknesses at which they are most copiously reflected in
  5038  the third Series, and so on. And the Thickness at which any of the
  5039  intermediate Colours are reflected most copiously, will, according to
  5040  the 14th Observation, be defined by the distance of the Line AH from the
  5041  intermediate parts of the Lines 2K, 6N, 10Q, &c. against which the Names
  5042  of those Colours are written below.
  5044  [Illustration: FIG. 6.]
  5046  But farther, to define the Latitude of these Colours in each Ring or
  5047  Series, let A1 design the least thickness, and A3 the greatest
  5048  thickness, at which the extreme violet in the first Series is reflected,
  5049  and let HI, and HL, design the like limits for the extreme red, and let
  5050  the intermediate Colours be limited by the intermediate parts of the
  5051  Lines 1I, and 3L, against which the Names of those Colours are written,
  5052  and so on: But yet with this caution, that the Reflexions be supposed
  5053  strongest at the intermediate Spaces, 2K, 6N, 10Q, &c. and from thence
  5054  to decrease gradually towards these limits, 1I, 3L, 5M, 7O, &c. on
  5055  either side; where you must not conceive them to be precisely limited,
  5056  but to decay indefinitely. And whereas I have assign'd the same Latitude
  5057  to every Series, I did it, because although the Colours in the first
  5058  Series seem to be a little broader than the rest, by reason of a
  5059  stronger Reflexion there, yet that inequality is so insensible as
  5060  scarcely to be determin'd by Observation.
  5062  Now according to this Description, conceiving that the Rays originally
  5063  of several Colours are by turns reflected at the Spaces 1I, L3, 5M, O7,
  5064  9PR11, &c. and transmitted at the Spaces AHI1, 3LM5, 7OP9, &c. it is
  5065  easy to know what Colour must in the open Air be exhibited at any
  5066  thickness of a transparent thin Body. For if a Ruler be applied parallel
  5067  to AH, at that distance from it by which the thickness of the Body is
  5068  represented, the alternate Spaces 1IL3, 5MO7, &c. which it crosseth will
  5069  denote the reflected original Colours, of which the Colour exhibited in
  5070  the open Air is compounded. Thus if the constitution of the green in the
  5071  third Series of Colours be desired, apply the Ruler as you see at
  5072  [Greek: prsph], and by its passing through some of the blue at [Greek:
  5073  p] and yellow at [Greek: s], as well as through the green at [Greek: r],
  5074  you may conclude that the green exhibited at that thickness of the Body
  5075  is principally constituted of original green, but not without a mixture
  5076  of some blue and yellow.
  5078  By this means you may know how the Colours from the center of the Rings
  5079  outward ought to succeed in order as they were described in the 4th and
  5080  18th Observations. For if you move the Ruler gradually from AH through
  5081  all distances, having pass'd over the first Space which denotes little
  5082  or no Reflexion to be made by thinnest Substances, it will first arrive
  5083  at 1 the violet, and then very quickly at the blue and green, which
  5084  together with that violet compound blue, and then at the yellow and red,
  5085  by whose farther addition that blue is converted into whiteness, which
  5086  whiteness continues during the transit of the edge of the Ruler from I
  5087  to 3, and after that by the successive deficience of its component
  5088  Colours, turns first to compound yellow, and then to red, and last of
  5089  all the red ceaseth at L. Then begin the Colours of the second Series,
  5090  which succeed in order during the transit of the edge of the Ruler from
  5091  5 to O, and are more lively than before, because more expanded and
  5092  severed. And for the same reason instead of the former white there
  5093  intercedes between the blue and yellow a mixture of orange, yellow,
  5094  green, blue and indigo, all which together ought to exhibit a dilute and
  5095  imperfect green. So the Colours of the third Series all succeed in
  5096  order; first, the violet, which a little interferes with the red of the
  5097  second order, and is thereby inclined to a reddish purple; then the blue
  5098  and green, which are less mix'd with other Colours, and consequently
  5099  more lively than before, especially the green: Then follows the yellow,
  5100  some of which towards the green is distinct and good, but that part of
  5101  it towards the succeeding red, as also that red is mix'd with the violet
  5102  and blue of the fourth Series, whereby various degrees of red very much
  5103  inclining to purple are compounded. This violet and blue, which should
  5104  succeed this red, being mixed with, and hidden in it, there succeeds a
  5105  green. And this at first is much inclined to blue, but soon becomes a
  5106  good green, the only unmix'd and lively Colour in this fourth Series.
  5107  For as it verges towards the yellow, it begins to interfere with the
  5108  Colours of the fifth Series, by whose mixture the succeeding yellow and
  5109  red are very much diluted and made dirty, especially the yellow, which
  5110  being the weaker Colour is scarce able to shew it self. After this the
  5111  several Series interfere more and more, and their Colours become more
  5112  and more intermix'd, till after three or four more revolutions (in which
  5113  the red and blue predominate by turns) all sorts of Colours are in all
  5114  places pretty equally blended, and compound an even whiteness.
  5116  And since by the 15th Observation the Rays endued with one Colour are
  5117  transmitted, where those of another Colour are reflected, the reason of
  5118  the Colours made by the transmitted Light in the 9th and 20th
  5119  Observations is from hence evident.
  5121  If not only the Order and Species of these Colours, but also the precise
  5122  thickness of the Plate, or thin Body at which they are exhibited, be
  5123  desired in parts of an Inch, that may be also obtained by assistance of
  5124  the 6th or 16th Observations. For according to those Observations the
  5125  thickness of the thinned Air, which between two Glasses exhibited the
  5126  most luminous parts of the first six Rings were 1/178000, 3/178000,
  5127  5/178000, 7/178000, 9/178000, 11/178000 parts of an Inch. Suppose the
  5128  Light reflected most copiously at these thicknesses be the bright
  5129  citrine yellow, or confine of yellow and orange, and these thicknesses
  5130  will be F[Greek: l], F[Greek: m], F[Greek: u], F[Greek: x], F[Greek: o],
  5131  F[Greek: t]. And this being known, it is easy to determine what
  5132  thickness of Air is represented by G[Greek: ph], or by any other
  5133  distance of the Ruler from AH.
  5135  But farther, since by the 10th Observation the thickness of Air was to
  5136  the thickness of Water, which between the same Glasses exhibited the
  5137  same Colour, as 4 to 3, and by the 21st Observation the Colours of thin
  5138  Bodies are not varied by varying the ambient Medium; the thickness of a
  5139  Bubble of Water, exhibiting any Colour, will be 3/4 of the thickness of
  5140  Air producing the same Colour. And so according to the same 10th and
  5141  21st Observations, the thickness of a Plate of Glass, whose Refraction
  5142  of the mean refrangible Ray, is measured by the proportion of the Sines
  5143  31 to 20, may be 20/31 of the thickness of Air producing the same
  5144  Colours; and the like of other Mediums. I do not affirm, that this
  5145  proportion of 20 to 31, holds in all the Rays; for the Sines of other
  5146  sorts of Rays have other Proportions. But the differences of those
  5147  Proportions are so little that I do not here consider them. On these
  5148  Grounds I have composed the following Table, wherein the thickness of
  5149  Air, Water, and Glass, at which each Colour is most intense and
  5150  specifick, is expressed in parts of an Inch divided into ten hundred
  5151  thousand equal parts.
  5153  Now if this Table be compared with the 6th Scheme, you will there see
  5154  the constitution of each Colour, as to its Ingredients, or the original
  5155  Colours of which it is compounded, and thence be enabled to judge of its
  5156  Intenseness or Imperfection; which may suffice in explication of the 4th
  5157  and 18th Observations, unless it be farther desired to delineate the
  5158  manner how the Colours appear, when the two Object-glasses are laid upon
  5159  one another. To do which, let there be described a large Arc of a
  5160  Circle, and a streight Line which may touch that Arc, and parallel to
  5161  that Tangent several occult Lines, at such distances from it, as the
  5162  Numbers set against the several Colours in the Table denote. For the
  5163  Arc, and its Tangent, will represent the Superficies of the Glasses
  5164  terminating the interjacent Air; and the places where the occult Lines
  5165  cut the Arc will show at what distances from the center, or Point of
  5166  contact, each Colour is reflected.
  5168  _The thickness of colour'd Plates and Particles of_
  5169                                            _____________|_______________
  5170                                           /                             \
  5171                                              Air.      Water.     Glass.
  5172                                          |---------+----------+----------+
  5173                         {Very black      |    1/2  |    3/8   |  10/31   |
  5174                         {Black           |  1      |    3/4   |  20/31   |
  5175                         {Beginning of    |         |          |          |
  5176                         {  Black         |  2      |  1-1/2   |  1-2/7   |
  5177  Their Colours of the   {Blue            |  2-2/5  |  1-4/5   |  1-11/22 |
  5178  first Order,           {White           |  5-1/4  |  3-7/8   |  3-2/5   |
  5179                         {Yellow          |  7-1/9  |  5-1/3   |  4-3/5   |
  5180                         {Orange          |  8      |  6       |  5-1/6   |
  5181                         {Red             |  9      |  6-3/4   |  5-4/5   |
  5182                                          |---------+----------+----------|
  5183                         {Violet          | 11-1/6  |  8-3/8   |  7-1/5   |
  5184                         {Indigo          | 12-5/6  |  9-5/8   |  8-2/11  |
  5185                         {Blue            | 14      |  10-1/2  |  9       |
  5186                         {Green           | 15-1/8  | 11-2/3   |  9-5/7   |
  5187  Of the second order,   {Yellow          | 16-2/7  | 12-1/5   | 10-2/5   |
  5188                         {Orange          | 17-2/9  | 13       | 11-1/9   |
  5189                         {Bright red      | 18-1/3  | 13-3/4   | 11-5/6   |
  5190                         {Scarlet         | 19-2/3  | 14-3/4   | 12-2/3   |
  5191                                          |---------+----------+----------|
  5192                         {Purple          | 21      | 15-3/4   | 13-11/20 |
  5193                         {Indigo          | 22-1/10 | 16-4/7   | 14-1/4   |
  5194                         {Blue            | 23-2/5  | 17-11/20 | 15-1/10  |
  5195  Of the third Order,    {Green           | 25-1/5  | 18-9/10  | 16-1/4   |
  5196                         {Yellow          | 27-1/7  | 20-1/3   | 17-1/2   |
  5197                         {Red             | 29      | 21-3/4   | 18-5/7   |
  5198                         {Bluish red      | 32      | 24       | 20-2/3   |
  5199                                          |---------+----------+----------|
  5200                         {Bluish green    | 34      | 25-1/2   | 22       |
  5201                         {Green           | 35-2/7  | 26-1/2   | 22-3/4   |
  5202  Of the fourth Order,   {Yellowish green | 36      | 27       | 23-2/9   |
  5203                         {Red             | 40-1/3  | 30-1/4   | 26       |
  5204                                          |---------+----------+----------|
  5205                         {Greenish blue   | 46      | 34-1/2   | 29-2/3   |
  5206  Of the fifth Order,    {Red             | 52-1/2  | 39-3/8   | 34       |
  5207                                          |---------+----------+----------|
  5208                         {Greenish blue   | 58-3/4  | 44       | 38       |
  5209  Of the sixth Order,    {Red             | 65      | 48-3/4   | 42       |
  5210                                          |---------+----------+----------|
  5211  Of the seventh Order,  {Greenish blue   | 71      | 53-1/4   | 45-4/5   |
  5212                         {Ruddy White     | 77      | 57-3/4   | 49-2/3   |
  5213                                          |---------+----------+----------|
  5215  There are also other Uses of this Table: For by its assistance the
  5216  thickness of the Bubble in the 19th Observation was determin'd by the
  5217  Colours which it exhibited. And so the bigness of the parts of natural
  5218  Bodies may be conjectured by their Colours, as shall be hereafter shewn.
  5219  Also, if two or more very thin Plates be laid one upon another, so as to
  5220  compose one Plate equalling them all in thickness, the resulting Colour
  5221  may be hereby determin'd. For instance, Mr. _Hook_ observed, as is
  5222  mentioned in his _Micrographia_, that a faint yellow Plate of _Muscovy_
  5223  Glass laid upon a blue one, constituted a very deep purple. The yellow
  5224  of the first Order is a faint one, and the thickness of the Plate
  5225  exhibiting it, according to the Table is 4-3/5, to which add 9, the
  5226  thickness exhibiting blue of the second Order, and the Sum will be
  5227  13-3/5, which is the thickness exhibiting the purple of the third Order.
  5229  To explain, in the next place, the circumstances of the 2d and 3d
  5230  Observations; that is, how the Rings of the Colours may (by turning the
  5231  Prisms about their common Axis the contrary way to that expressed in
  5232  those Observations) be converted into white and black Rings, and
  5233  afterwards into Rings of Colours again, the Colours of each Ring lying
  5234  now in an inverted order; it must be remember'd, that those Rings of
  5235  Colours are dilated by the obliquation of the Rays to the Air which
  5236  intercedes the Glasses, and that according to the Table in the 7th
  5237  Observation, their Dilatation or Increase of their Diameter is most
  5238  manifest and speedy when they are obliquest. Now the Rays of yellow
  5239  being more refracted by the first Superficies of the said Air than those
  5240  of red, are thereby made more oblique to the second Superficies, at
  5241  which they are reflected to produce the colour'd Rings, and consequently
  5242  the yellow Circle in each Ring will be more dilated than the red; and
  5243  the Excess of its Dilatation will be so much the greater, by how much
  5244  the greater is the obliquity of the Rays, until at last it become of
  5245  equal extent with the red of the same Ring. And for the same reason the
  5246  green, blue and violet, will be also so much dilated by the still
  5247  greater obliquity of their Rays, as to become all very nearly of equal
  5248  extent with the red, that is, equally distant from the center of the
  5249  Rings. And then all the Colours of the same Ring must be co-incident,
  5250  and by their mixture exhibit a white Ring. And these white Rings must
  5251  have black and dark Rings between them, because they do not spread and
  5252  interfere with one another, as before. And for that reason also they
  5253  must become distincter, and visible to far greater numbers. But yet the
  5254  violet being obliquest will be something more dilated, in proportion to
  5255  its extent, than the other Colours, and so very apt to appear at the
  5256  exterior Verges of the white.
  5258  Afterwards, by a greater obliquity of the Rays, the violet and blue
  5259  become more sensibly dilated than the red and yellow, and so being
  5260  farther removed from the center of the Rings, the Colours must emerge
  5261  out of the white in an order contrary to that which they had before; the
  5262  violet and blue at the exterior Limbs of each Ring, and the red and
  5263  yellow at the interior. And the violet, by reason of the greatest
  5264  obliquity of its Rays, being in proportion most of all expanded, will
  5265  soonest appear at the exterior Limb of each white Ring, and become more
  5266  conspicuous than the rest. And the several Series of Colours belonging
  5267  to the several Rings, will, by their unfolding and spreading, begin
  5268  again to interfere, and thereby render the Rings less distinct, and not
  5269  visible to so great numbers.
  5271  If instead of the Prisms the Object-glasses be made use of, the Rings
  5272  which they exhibit become not white and distinct by the obliquity of the
  5273  Eye, by reason that the Rays in their passage through that Air which
  5274  intercedes the Glasses are very nearly parallel to those Lines in which
  5275  they were first incident on the Glasses, and consequently the Rays
  5276  endued with several Colours are not inclined one more than another to
  5277  that Air, as it happens in the Prisms.
  5279  There is yet another circumstance of these Experiments to be consider'd,
  5280  and that is why the black and white Rings which when view'd at a
  5281  distance appear distinct, should not only become confused by viewing
  5282  them near at hand, but also yield a violet Colour at both the edges of
  5283  every white Ring. And the reason is, that the Rays which enter the Eye
  5284  at several parts of the Pupil, have several Obliquities to the Glasses,
  5285  and those which are most oblique, if consider'd apart, would represent
  5286  the Rings bigger than those which are the least oblique. Whence the
  5287  breadth of the Perimeter of every white Ring is expanded outwards by the
  5288  obliquest Rays, and inwards by the least oblique. And this Expansion is
  5289  so much the greater by how much the greater is the difference of the
  5290  Obliquity; that is, by how much the Pupil is wider, or the Eye nearer to
  5291  the Glasses. And the breadth of the violet must be most expanded,
  5292  because the Rays apt to excite a Sensation of that Colour are most
  5293  oblique to a second or farther Superficies of the thinn'd Air at which
  5294  they are reflected, and have also the greatest variation of Obliquity,
  5295  which makes that Colour soonest emerge out of the edges of the white.
  5296  And as the breadth of every Ring is thus augmented, the dark Intervals
  5297  must be diminish'd, until the neighbouring Rings become continuous, and
  5298  are blended, the exterior first, and then those nearer the center; so
  5299  that they can no longer be distinguish'd apart, but seem to constitute
  5300  an even and uniform whiteness.
  5302  Among all the Observations there is none accompanied with so odd
  5303  circumstances as the twenty-fourth. Of those the principal are, that in
  5304  thin Plates, which to the naked Eye seem of an even and uniform
  5305  transparent whiteness, without any terminations of Shadows, the
  5306  Refraction of a Prism should make Rings of Colours appear, whereas it
  5307  usually makes Objects appear colour'd only there where they are
  5308  terminated with Shadows, or have parts unequally luminous; and that it
  5309  should make those Rings exceedingly distinct and white, although it
  5310  usually renders Objects confused and coloured. The Cause of these things
  5311  you will understand by considering, that all the Rings of Colours are
  5312  really in the Plate, when view'd with the naked Eye, although by reason
  5313  of the great breadth of their Circumferences they so much interfere and
  5314  are blended together, that they seem to constitute an uniform whiteness.
  5315  But when the Rays pass through the Prism to the Eye, the Orbits of the
  5316  several Colours in every Ring are refracted, some more than others,
  5317  according to their degrees of Refrangibility: By which means the Colours
  5318  on one side of the Ring (that is in the circumference on one side of its
  5319  center), become more unfolded and dilated, and those on the other side
  5320  more complicated and contracted. And where by a due Refraction they are
  5321  so much contracted, that the several Rings become narrower than to
  5322  interfere with one another, they must appear distinct, and also white,
  5323  if the constituent Colours be so much contracted as to be wholly
  5324  co-incident. But on the other side, where the Orbit of every Ring is
  5325  made broader by the farther unfolding of its Colours, it must interfere
  5326  more with other Rings than before, and so become less distinct.
  5328  [Illustration: FIG. 7.]
  5330  To explain this a little farther, suppose the concentrick Circles AV,
  5331  and BX, [in _Fig._ 7.] represent the red and violet of any Order, which,
  5332  together with the intermediate Colours, constitute any one of these
  5333  Rings. Now these being view'd through a Prism, the violet Circle BX,
  5334  will, by a greater Refraction, be farther translated from its place than
  5335  the red AV, and so approach nearer to it on that side of the Circles,
  5336  towards which the Refractions are made. For instance, if the red be
  5337  translated to _av_, the violet may be translated to _bx_, so as to
  5338  approach nearer to it at _x_ than before; and if the red be farther
  5339  translated to av, the violet may be so much farther translated to bx as
  5340  to convene with it at x; and if the red be yet farther translated to
  5341  [Greek: aY], the violet may be still so much farther translated to
  5342  [Greek: bx] as to pass beyond it at [Greek: x], and convene with it at
  5343  _e_ and _f_. And this being understood not only of the red and violet,
  5344  but of all the other intermediate Colours, and also of every revolution
  5345  of those Colours, you will easily perceive how those of the same
  5346  revolution or order, by their nearness at _xv_ and [Greek: Yx], and
  5347  their coincidence at xv, _e_ and _f_, ought to constitute pretty
  5348  distinct Arcs of Circles, especially at xv, or at _e_ and _f_; and that
  5349  they will appear severally at _x_[Greek: u] and at xv exhibit whiteness
  5350  by their coincidence, and again appear severally at [Greek: Yx], but yet
  5351  in a contrary order to that which they had before, and still retain
  5352  beyond _e_ and _f_. But on the other side, at _ab_, ab, or [Greek: ab],
  5353  these Colours must become much more confused by being dilated and spread
  5354  so as to interfere with those of other Orders. And the same confusion
  5355  will happen at [Greek: Ux] between _e_ and _f_, if the Refraction be
  5356  very great, or the Prism very distant from the Object-glasses: In which
  5357  case no parts of the Rings will be seen, save only two little Arcs at
  5358  _e_ and _f_, whose distance from one another will be augmented by
  5359  removing the Prism still farther from the Object-glasses: And these
  5360  little Arcs must be distinctest and whitest at their middle, and at
  5361  their ends, where they begin to grow confused, they must be colour'd.
  5362  And the Colours at one end of every Arc must be in a contrary order to
  5363  those at the other end, by reason that they cross in the intermediate
  5364  white; namely, their ends, which verge towards [Greek: Ux], will be red
  5365  and yellow on that side next the center, and blue and violet on the
  5366  other side. But their other ends which verge from [Greek: Ux], will on
  5367  the contrary be blue and violet on that side towards the center, and on
  5368  the other side red and yellow.
  5370  Now as all these things follow from the properties of Light by a
  5371  mathematical way of reasoning, so the truth of them may be manifested by
  5372  Experiments. For in a dark Room, by viewing these Rings through a Prism,
  5373  by reflexion of the several prismatick Colours, which an assistant
  5374  causes to move to and fro upon a Wall or Paper from whence they are
  5375  reflected, whilst the Spectator's Eye, the Prism, and the
  5376  Object-glasses, (as in the 13th Observation,) are placed steady; the
  5377  Position of the Circles made successively by the several Colours, will
  5378  be found such, in respect of one another, as I have described in the
  5379  Figures _abxv_, or abxv, or _[Greek: abxU]_. And by the same method the
  5380  truth of the Explications of other Observations may be examined.
  5382  By what hath been said, the like Phænomena of Water and thin Plates of
  5383  Glass may be understood. But in small fragments of those Plates there is
  5384  this farther observable, that where they lie flat upon a Table, and are
  5385  turned about their centers whilst they are view'd through a Prism, they
  5386  will in some postures exhibit Waves of various Colours; and some of them
  5387  exhibit these Waves in one or two Positions only, but the most of them
  5388  do in all Positions exhibit them, and make them for the most part appear
  5389  almost all over the Plates. The reason is, that the Superficies of such
  5390  Plates are not even, but have many Cavities and Swellings, which, how
  5391  shallow soever, do a little vary the thickness of the Plate. For at the
  5392  several sides of those Cavities, for the Reasons newly described, there
  5393  ought to be produced Waves in several postures of the Prism. Now though
  5394  it be but some very small and narrower parts of the Glass, by which
  5395  these Waves for the most part are caused, yet they may seem to extend
  5396  themselves over the whole Glass, because from the narrowest of those
  5397  parts there are Colours of several Orders, that is, of several Rings,
  5398  confusedly reflected, which by Refraction of the Prism are unfolded,
  5399  separated, and, according to their degrees of Refraction, dispersed to
  5400  several places, so as to constitute so many several Waves, as there were
  5401  divers orders of Colours promiscuously reflected from that part of the
  5402  Glass.
  5404  These are the principal Phænomena of thin Plates or Bubbles, whose
  5405  Explications depend on the properties of Light, which I have heretofore
  5406  deliver'd. And these you see do necessarily follow from them, and agree
  5407  with them, even to their very least circumstances; and not only so, but
  5408  do very much tend to their proof. Thus, by the 24th Observation it
  5409  appears, that the Rays of several Colours, made as well by thin Plates
  5410  or Bubbles, as by Refractions of a Prism, have several degrees of
  5411  Refrangibility; whereby those of each order, which at the reflexion from
  5412  the Plate or Bubble are intermix'd with those of other orders, are
  5413  separated from them by Refraction, and associated together so as to
  5414  become visible by themselves like Arcs of Circles. For if the Rays were
  5415  all alike refrangible, 'tis impossible that the whiteness, which to the
  5416  naked Sense appears uniform, should by Refraction have its parts
  5417  transposed and ranged into those black and white Arcs.
  5419  It appears also that the unequal Refractions of difform Rays proceed not
  5420  from any contingent irregularities; such as are Veins, an uneven Polish,
  5421  or fortuitous Position of the Pores of Glass; unequal and casual Motions
  5422  in the Air or Æther, the spreading, breaking, or dividing the same Ray
  5423  into many diverging parts; or the like. For, admitting any such
  5424  irregularities, it would be impossible for Refractions to render those
  5425  Rings so very distinct, and well defined, as they do in the 24th
  5426  Observation. It is necessary therefore that every Ray have its proper
  5427  and constant degree of Refrangibility connate with it, according to
  5428  which its refraction is ever justly and regularly perform'd; and that
  5429  several Rays have several of those degrees.
  5431  And what is said of their Refrangibility may be also understood of their
  5432  Reflexibility, that is, of their Dispositions to be reflected, some at a
  5433  greater, and others at a less thickness of thin Plates or Bubbles;
  5434  namely, that those Dispositions are also connate with the Rays, and
  5435  immutable; as may appear by the 13th, 14th, and 15th Observations,
  5436  compared with the fourth and eighteenth.
  5438  By the Precedent Observations it appears also, that whiteness is a
  5439  dissimilar mixture of all Colours, and that Light is a mixture of Rays
  5440  endued with all those Colours. For, considering the multitude of the
  5441  Rings of Colours in the 3d, 12th, and 24th Observations, it is manifest,
  5442  that although in the 4th and 18th Observations there appear no more than
  5443  eight or nine of those Rings, yet there are really a far greater number,
  5444  which so much interfere and mingle with one another, as after those
  5445  eight or nine revolutions to dilute one another wholly, and constitute
  5446  an even and sensibly uniform whiteness. And consequently that whiteness
  5447  must be allow'd a mixture of all Colours, and the Light which conveys it
  5448  to the Eye must be a mixture of Rays endued with all those Colours.
  5450  But farther; by the 24th Observation it appears, that there is a
  5451  constant relation between Colours and Refrangibility; the most
  5452  refrangible Rays being violet, the least refrangible red, and those of
  5453  intermediate Colours having proportionably intermediate degrees of
  5454  Refrangibility. And by the 13th, 14th, and 15th Observations, compared
  5455  with the 4th or 18th there appears to be the same constant relation
  5456  between Colour and Reflexibility; the violet being in like circumstances
  5457  reflected at least thicknesses of any thin Plate or Bubble, the red at
  5458  greatest thicknesses, and the intermediate Colours at intermediate
  5459  thicknesses. Whence it follows, that the colorifick Dispositions of
  5460  Rays are also connate with them, and immutable; and by consequence, that
  5461  all the Productions and Appearances of Colours in the World are derived,
  5462  not from any physical Change caused in Light by Refraction or Reflexion,
  5463  but only from the various Mixtures or Separations of Rays, by virtue of
  5464  their different Refrangibility or Reflexibility. And in this respect the
  5465  Science of Colours becomes a Speculation as truly mathematical as any
  5466  other part of Opticks. I mean, so far as they depend on the Nature of
  5467  Light, and are not produced or alter'd by the Power of Imagination, or
  5468  by striking or pressing the Eye.
  5473  THE
  5477  OF
  5479  OPTICKS
  5482  _PART III._
  5484  _Of the permanent Colours of natural Bodies, and the Analogy between
  5485  them and the Colours of thin transparent Plates._
  5487  I am now come to another part of this Design, which is to consider how
  5488  the Phænomena of thin transparent Plates stand related to those of all
  5489  other natural Bodies. Of these Bodies I have already told you that they
  5490  appear of divers Colours, accordingly as they are disposed to reflect
  5491  most copiously the Rays originally endued with those Colours. But their
  5492  Constitutions, whereby they reflect some Rays more copiously than
  5493  others, remain to be discover'd; and these I shall endeavour to manifest
  5494  in the following Propositions.
  5497  PROP. I.
  5499  _Those Superficies of transparent Bodies reflect the greatest quantity
  5500  of Light, which have the greatest refracting Power; that is, which
  5501  intercede Mediums that differ most in their refractive Densities. And in
  5502  the Confines of equally refracting Mediums there is no Reflexion._
  5504  The Analogy between Reflexion and Refraction will appear by considering,
  5505  that when Light passeth obliquely out of one Medium into another which
  5506  refracts from the perpendicular, the greater is the difference of their
  5507  refractive Density, the less Obliquity of Incidence is requisite to
  5508  cause a total Reflexion. For as the Sines are which measure the
  5509  Refraction, so is the Sine of Incidence at which the total Reflexion
  5510  begins, to the Radius of the Circle; and consequently that Angle of
  5511  Incidence is least where there is the greatest difference of the Sines.
  5512  Thus in the passing of Light out of Water into Air, where the Refraction
  5513  is measured by the Ratio of the Sines 3 to 4, the total Reflexion begins
  5514  when the Angle of Incidence is about 48 Degrees 35 Minutes. In passing
  5515  out of Glass into Air, where the Refraction is measured by the Ratio of
  5516  the Sines 20 to 31, the total Reflexion begins when the Angle of
  5517  Incidence is 40 Degrees 10 Minutes; and so in passing out of Crystal, or
  5518  more strongly refracting Mediums into Air, there is still a less
  5519  obliquity requisite to cause a total reflexion. Superficies therefore
  5520  which refract most do soonest reflect all the Light which is incident on
  5521  them, and so must be allowed most strongly reflexive.
  5523  But the truth of this Proposition will farther appear by observing, that
  5524  in the Superficies interceding two transparent Mediums, (such as are
  5525  Air, Water, Oil, common Glass, Crystal, metalline Glasses, Island
  5526  Glasses, white transparent Arsenick, Diamonds, &c.) the Reflexion is
  5527  stronger or weaker accordingly, as the Superficies hath a greater or
  5528  less refracting Power. For in the Confine of Air and Sal-gem 'tis
  5529  stronger than in the Confine of Air and Water, and still stronger in the
  5530  Confine of Air and common Glass or Crystal, and stronger in the Confine
  5531  of Air and a Diamond. If any of these, and such like transparent Solids,
  5532  be immerged in Water, its Reflexion becomes, much weaker than before;
  5533  and still weaker if they be immerged in the more strongly refracting
  5534  Liquors of well rectified Oil of Vitriol or Spirit of Turpentine. If
  5535  Water be distinguish'd into two parts by any imaginary Surface, the
  5536  Reflexion in the Confine of those two parts is none at all. In the
  5537  Confine of Water and Ice 'tis very little; in that of Water and Oil 'tis
  5538  something greater; in that of Water and Sal-gem still greater; and in
  5539  that of Water and Glass, or Crystal or other denser Substances still
  5540  greater, accordingly as those Mediums differ more or less in their
  5541  refracting Powers. Hence in the Confine of common Glass and Crystal,
  5542  there ought to be a weak Reflexion, and a stronger Reflexion in the
  5543  Confine of common and metalline Glass; though I have not yet tried
  5544  this. But in the Confine of two Glasses of equal density, there is not
  5545  any sensible Reflexion; as was shewn in the first Observation. And the
  5546  same may be understood of the Superficies interceding two Crystals, or
  5547  two Liquors, or any other Substances in which no Refraction is caused.
  5548  So then the reason why uniform pellucid Mediums (such as Water, Glass,
  5549  or Crystal,) have no sensible Reflexion but in their external
  5550  Superficies, where they are adjacent to other Mediums of a different
  5551  density, is because all their contiguous parts have one and the same
  5552  degree of density.
  5555  PROP. II.
  5557  _The least parts of almost all natural Bodies are in some measure
  5558  transparent: And the Opacity of those Bodies ariseth from the multitude
  5559  of Reflexions caused in their internal Parts._
  5561  That this is so has been observed by others, and will easily be granted
  5562  by them that have been conversant with Microscopes. And it may be also
  5563  tried by applying any substance to a hole through which some Light is
  5564  immitted into a dark Room. For how opake soever that Substance may seem
  5565  in the open Air, it will by that means appear very manifestly
  5566  transparent, if it be of a sufficient thinness. Only white metalline
  5567  Bodies must be excepted, which by reason of their excessive density seem
  5568  to reflect almost all the Light incident on their first Superficies;
  5569  unless by solution in Menstruums they be reduced into very small
  5570  Particles, and then they become transparent.
  5573  PROP. III.
  5575  _Between the parts of opake and colour'd Bodies are many Spaces, either
  5576  empty, or replenish'd with Mediums of other Densities; as Water between
  5577  the tinging Corpuscles wherewith any Liquor is impregnated, Air between
  5578  the aqueous Globules that constitute Clouds or Mists; and for the most
  5579  part Spaces void of both Air and Water, but yet perhaps not wholly void
  5580  of all Substance, between the parts of hard Bodies._
  5582  The truth of this is evinced by the two precedent Propositions: For by
  5583  the second Proposition there are many Reflexions made by the internal
  5584  parts of Bodies, which, by the first Proposition, would not happen if
  5585  the parts of those Bodies were continued without any such Interstices
  5586  between them; because Reflexions are caused only in Superficies, which
  5587  intercede Mediums of a differing density, by _Prop._ 1.
  5589  But farther, that this discontinuity of parts is the principal Cause of
  5590  the opacity of Bodies, will appear by considering, that opake Substances
  5591  become transparent by filling their Pores with any Substance of equal or
  5592  almost equal density with their parts. Thus Paper dipped in Water or
  5593  Oil, the _Oculus Mundi_ Stone steep'd in Water, Linnen Cloth oiled or
  5594  varnish'd, and many other Substances soaked in such Liquors as will
  5595  intimately pervade their little Pores, become by that means more
  5596  transparent than otherwise; so, on the contrary, the most transparent
  5597  Substances, may, by evacuating their Pores, or separating their parts,
  5598  be render'd sufficiently opake; as Salts or wet Paper, or the _Oculus
  5599  Mundi_ Stone by being dried, Horn by being scraped, Glass by being
  5600  reduced to Powder, or otherwise flawed; Turpentine by being stirred
  5601  about with Water till they mix imperfectly, and Water by being form'd
  5602  into many small Bubbles, either alone in the form of Froth, or by
  5603  shaking it together with Oil of Turpentine, or Oil Olive, or with some
  5604  other convenient Liquor, with which it will not perfectly incorporate.
  5605  And to the increase of the opacity of these Bodies, it conduces
  5606  something, that by the 23d Observation the Reflexions of very thin
  5607  transparent Substances are considerably stronger than those made by the
  5608  same Substances of a greater thickness.
  5611  PROP. IV.
  5613  _The Parts of Bodies and their Interstices must not be less than of some
  5614  definite bigness, to render them opake and colour'd._
  5616  For the opakest Bodies, if their parts be subtilly divided, (as Metals,
  5617  by being dissolved in acid Menstruums, &c.) become perfectly
  5618  transparent. And you may also remember, that in the eighth Observation
  5619  there was no sensible reflexion at the Superficies of the
  5620  Object-glasses, where they were very near one another, though they did
  5621  not absolutely touch. And in the 17th Observation the Reflexion of the
  5622  Water-bubble where it became thinnest was almost insensible, so as to
  5623  cause very black Spots to appear on the top of the Bubble, by the want
  5624  of reflected Light.
  5626  On these grounds I perceive it is that Water, Salt, Glass, Stones, and
  5627  such like Substances, are transparent. For, upon divers Considerations,
  5628  they seem to be as full of Pores or Interstices between their parts as
  5629  other Bodies are, but yet their Parts and Interstices to be too small to
  5630  cause Reflexions in their common Surfaces.
  5633  PROP. V.
  5635  _The transparent parts of Bodies, according to their several sizes,
  5636  reflect Rays of one Colour, and transmit those of another, on the same
  5637  grounds that thin Plates or Bubbles do reflect or transmit those Rays.
  5638  And this I take to be the ground of all their Colours._
  5640  For if a thinn'd or plated Body, which being of an even thickness,
  5641  appears all over of one uniform Colour, should be slit into Threads, or
  5642  broken into Fragments, of the same thickness with the Plate; I see no
  5643  reason why every Thread or Fragment should not keep its Colour, and by
  5644  consequence why a heap of those Threads or Fragments should not
  5645  constitute a Mass or Powder of the same Colour, which the Plate
  5646  exhibited before it was broken. And the parts of all natural Bodies
  5647  being like so many Fragments of a Plate, must on the same grounds
  5648  exhibit the same Colours.
  5650  Now, that they do so will appear by the affinity of their Properties.
  5651  The finely colour'd Feathers of some Birds, and particularly those of
  5652  Peacocks Tails, do, in the very same part of the Feather, appear of
  5653  several Colours in several Positions of the Eye, after the very same
  5654  manner that thin Plates were found to do in the 7th and 19th
  5655  Observations, and therefore their Colours arise from the thinness of the
  5656  transparent parts of the Feathers; that is, from the slenderness of the
  5657  very fine Hairs, or _Capillamenta_, which grow out of the sides of the
  5658  grosser lateral Branches or Fibres of those Feathers. And to the same
  5659  purpose it is, that the Webs of some Spiders, by being spun very fine,
  5660  have appeared colour'd, as some have observ'd, and that the colour'd
  5661  Fibres of some Silks, by varying the Position of the Eye, do vary their
  5662  Colour. Also the Colours of Silks, Cloths, and other Substances, which
  5663  Water or Oil can intimately penetrate, become more faint and obscure by
  5664  being immerged in those Liquors, and recover their Vigor again by being
  5665  dried; much after the manner declared of thin Bodies in the 10th and
  5666  21st Observations. Leaf-Gold, some sorts of painted Glass, the Infusion
  5667  of _Lignum Nephriticum_, and some other Substances, reflect one Colour,
  5668  and transmit another; like thin Bodies in the 9th and 20th Observations.
  5669  And some of those colour'd Powders which Painters use, may have their
  5670  Colours a little changed, by being very elaborately and finely ground.
  5671  Where I see not what can be justly pretended for those changes, besides
  5672  the breaking of their parts into less parts by that contrition, after
  5673  the same manner that the Colour of a thin Plate is changed by varying
  5674  its thickness. For which reason also it is that the colour'd Flowers of
  5675  Plants and Vegetables, by being bruised, usually become more transparent
  5676  than before, or at least in some degree or other change their Colours.
  5677  Nor is it much less to my purpose, that, by mixing divers Liquors, very
  5678  odd and remarkable Productions and Changes of Colours may be effected,
  5679  of which no cause can be more obvious and rational than that the saline
  5680  Corpuscles of one Liquor do variously act upon or unite with the tinging
  5681  Corpuscles of another, so as to make them swell, or shrink, (whereby not
  5682  only their bulk but their density also may be changed,) or to divide
  5683  them into smaller Corpuscles, (whereby a colour'd Liquor may become
  5684  transparent,) or to make many of them associate into one cluster,
  5685  whereby two transparent Liquors may compose a colour'd one. For we see
  5686  how apt those saline Menstruums are to penetrate and dissolve Substances
  5687  to which they are applied, and some of them to precipitate what others
  5688  dissolve. In like manner, if we consider the various Phænomena of the
  5689  Atmosphere, we may observe, that when Vapours are first raised, they
  5690  hinder not the transparency of the Air, being divided into parts too
  5691  small to cause any Reflexion in their Superficies. But when in order to
  5692  compose drops of Rain they begin to coalesce and constitute Globules of
  5693  all intermediate sizes, those Globules, when they become of convenient
  5694  size to reflect some Colours and transmit others, may constitute Clouds
  5695  of various Colours according to their sizes. And I see not what can be
  5696  rationally conceived in so transparent a Substance as Water for the
  5697  production of these Colours, besides the various sizes of its fluid and
  5698  globular Parcels.
  5701  PROP. VI.
  5703  _The parts of Bodies on which their Colours depend, are denser than the
  5704  Medium which pervades their Interstices._
  5706  This will appear by considering, that the Colour of a Body depends not
  5707  only on the Rays which are incident perpendicularly on its parts, but on
  5708  those also which are incident at all other Angles. And that according to
  5709  the 7th Observation, a very little variation of obliquity will change
  5710  the reflected Colour, where the thin Body or small Particles is rarer
  5711  than the ambient Medium, insomuch that such a small Particle will at
  5712  diversly oblique Incidences reflect all sorts of Colours, in so great a
  5713  variety that the Colour resulting from them all, confusedly reflected
  5714  from a heap of such Particles, must rather be a white or grey than any
  5715  other Colour, or at best it must be but a very imperfect and dirty
  5716  Colour. Whereas if the thin Body or small Particle be much denser than
  5717  the ambient Medium, the Colours, according to the 19th Observation, are
  5718  so little changed by the variation of obliquity, that the Rays which
  5719  are reflected least obliquely may predominate over the rest, so much as
  5720  to cause a heap of such Particles to appear very intensely of their
  5721  Colour.
  5723  It conduces also something to the confirmation of this Proposition,
  5724  that, according to the 22d Observation, the Colours exhibited by the
  5725  denser thin Body within the rarer, are more brisk than those exhibited
  5726  by the rarer within the denser.
  5729  PROP. VII.
  5731  _The bigness of the component parts of natural Bodies may be conjectured
  5732  by their Colours._
  5734  For since the parts of these Bodies, by _Prop._ 5. do most probably
  5735  exhibit the same Colours with a Plate of equal thickness, provided they
  5736  have the same refractive density; and since their parts seem for the
  5737  most part to have much the same density with Water or Glass, as by many
  5738  circumstances is obvious to collect; to determine the sizes of those
  5739  parts, you need only have recourse to the precedent Tables, in which the
  5740  thickness of Water or Glass exhibiting any Colour is expressed. Thus if
  5741  it be desired to know the diameter of a Corpuscle, which being of equal
  5742  density with Glass shall reflect green of the third Order; the Number
  5743  16-1/4 shews it to be (16-1/4)/10000 parts of an Inch.
  5745  The greatest difficulty is here to know of what Order the Colour of any
  5746  Body is. And for this end we must have recourse to the 4th and 18th
  5747  Observations; from whence may be collected these particulars.
  5749  _Scarlets_, and other _reds_, _oranges_, and _yellows_, if they be pure
  5750  and intense, are most probably of the second order. Those of the first
  5751  and third order also may be pretty good; only the yellow of the first
  5752  order is faint, and the orange and red of the third Order have a great
  5753  Mixture of violet and blue.
  5755  There may be good _Greens_ of the fourth Order, but the purest are of
  5756  the third. And of this Order the green of all Vegetables seems to be,
  5757  partly by reason of the Intenseness of their Colours, and partly because
  5758  when they wither some of them turn to a greenish yellow, and others to a
  5759  more perfect yellow or orange, or perhaps to red, passing first through
  5760  all the aforesaid intermediate Colours. Which Changes seem to be
  5761  effected by the exhaling of the Moisture which may leave the tinging
  5762  Corpuscles more dense, and something augmented by the Accretion of the
  5763  oily and earthy Part of that Moisture. Now the green, without doubt, is
  5764  of the same Order with those Colours into which it changeth, because the
  5765  Changes are gradual, and those Colours, though usually not very full,
  5766  yet are often too full and lively to be of the fourth Order.
  5768  _Blues_ and _Purples_ may be either of the second or third Order, but
  5769  the best are of the third. Thus the Colour of Violets seems to be of
  5770  that Order, because their Syrup by acid Liquors turns red, and by
  5771  urinous and alcalizate turns green. For since it is of the Nature of
  5772  Acids to dissolve or attenuate, and of Alcalies to precipitate or
  5773  incrassate, if the Purple Colour of the Syrup was of the second Order,
  5774  an acid Liquor by attenuating its tinging Corpuscles would change it to
  5775  a red of the first Order, and an Alcali by incrassating them would
  5776  change it to a green of the second Order; which red and green,
  5777  especially the green, seem too imperfect to be the Colours produced by
  5778  these Changes. But if the said Purple be supposed of the third Order,
  5779  its Change to red of the second, and green of the third, may without any
  5780  Inconvenience be allow'd.
  5782  If there be found any Body of a deeper and less reddish Purple than that
  5783  of the Violets, its Colour most probably is of the second Order. But yet
  5784  there being no Body commonly known whose Colour is constantly more deep
  5785  than theirs, I have made use of their Name to denote the deepest and
  5786  least reddish Purples, such as manifestly transcend their Colour in
  5787  purity.
  5789  The _blue_ of the first Order, though very faint and little, may
  5790  possibly be the Colour of some Substances; and particularly the azure
  5791  Colour of the Skies seems to be of this Order. For all Vapours when they
  5792  begin to condense and coalesce into small Parcels, become first of that
  5793  Bigness, whereby such an Azure must be reflected before they can
  5794  constitute Clouds of other Colours. And so this being the first Colour
  5795  which Vapours begin to reflect, it ought to be the Colour of the finest
  5796  and most transparent Skies, in which Vapours are not arrived to that
  5797  Grossness requisite to reflect other Colours, as we find it is by
  5798  Experience.
  5800  _Whiteness_, if most intense and luminous, is that of the first Order,
  5801  if less strong and luminous, a Mixture of the Colours of several Orders.
  5802  Of this last kind is the Whiteness of Froth, Paper, Linnen, and most
  5803  white Substances; of the former I reckon that of white Metals to be. For
  5804  whilst the densest of Metals, Gold, if foliated, is transparent, and all
  5805  Metals become transparent if dissolved in Menstruums or vitrified, the
  5806  Opacity of white Metals ariseth not from their Density alone. They being
  5807  less dense than Gold would be more transparent than it, did not some
  5808  other Cause concur with their Density to make them opake. And this Cause
  5809  I take to be such a Bigness of their Particles as fits them to reflect
  5810  the white of the first order. For, if they be of other Thicknesses they
  5811  may reflect other Colours, as is manifest by the Colours which appear
  5812  upon hot Steel in tempering it, and sometimes upon the Surface of melted
  5813  Metals in the Skin or Scoria which arises upon them in their cooling.
  5814  And as the white of the first order is the strongest which can be made
  5815  by Plates of transparent Substances, so it ought to be stronger in the
  5816  denser Substances of Metals than in the rarer of Air, Water, and Glass.
  5817  Nor do I see but that metallick Substances of such a Thickness as may
  5818  fit them to reflect the white of the first order, may, by reason of
  5819  their great Density (according to the Tenor of the first of these
  5820  Propositions) reflect all the Light incident upon them, and so be as
  5821  opake and splendent as it's possible for any Body to be. Gold, or Copper
  5822  mix'd with less than half their Weight of Silver, or Tin, or Regulus of
  5823  Antimony, in fusion, or amalgamed with a very little Mercury, become
  5824  white; which shews both that the Particles of white Metals have much
  5825  more Superficies, and so are smaller, than those of Gold and Copper, and
  5826  also that they are so opake as not to suffer the Particles of Gold or
  5827  Copper to shine through them. Now it is scarce to be doubted but that
  5828  the Colours of Gold and Copper are of the second and third order, and
  5829  therefore the Particles of white Metals cannot be much bigger than is
  5830  requisite to make them reflect the white of the first order. The
  5831  Volatility of Mercury argues that they are not much bigger, nor may they
  5832  be much less, lest they lose their Opacity, and become either
  5833  transparent as they do when attenuated by Vitrification, or by Solution
  5834  in Menstruums, or black as they do when ground smaller, by rubbing
  5835  Silver, or Tin, or Lead, upon other Substances to draw black Lines. The
  5836  first and only Colour which white Metals take by grinding their
  5837  Particles smaller, is black, and therefore their white ought to be that
  5838  which borders upon the black Spot in the Center of the Rings of Colours,
  5839  that is, the white of the first order. But, if you would hence gather
  5840  the Bigness of metallick Particles, you must allow for their Density.
  5841  For were Mercury transparent, its Density is such that the Sine of
  5842  Incidence upon it (by my Computation) would be to the Sine of its
  5843  Refraction, as 71 to 20, or 7 to 2. And therefore the Thickness of its
  5844  Particles, that they may exhibit the same Colours with those of Bubbles
  5845  of Water, ought to be less than the Thickness of the Skin of those
  5846  Bubbles in the Proportion of 2 to 7. Whence it's possible, that the
  5847  Particles of Mercury may be as little as the Particles of some
  5848  transparent and volatile Fluids, and yet reflect the white of the first
  5849  order.
  5851  Lastly, for the production of _black_, the Corpuscles must be less than
  5852  any of those which exhibit Colours. For at all greater sizes there is
  5853  too much Light reflected to constitute this Colour. But if they be
  5854  supposed a little less than is requisite to reflect the white and very
  5855  faint blue of the first order, they will, according to the 4th, 8th,
  5856  17th and 18th Observations, reflect so very little Light as to appear
  5857  intensely black, and yet may perhaps variously refract it to and fro
  5858  within themselves so long, until it happen to be stifled and lost, by
  5859  which means they will appear black in all positions of the Eye without
  5860  any transparency. And from hence may be understood why Fire, and the
  5861  more subtile dissolver Putrefaction, by dividing the Particles of
  5862  Substances, turn them to black, why small quantities of black Substances
  5863  impart their Colour very freely and intensely to other Substances to
  5864  which they are applied; the minute Particles of these, by reason of
  5865  their very great number, easily overspreading the gross Particles of
  5866  others; why Glass ground very elaborately with Sand on a Copper Plate,
  5867  'till it be well polish'd, makes the Sand, together with what is worn
  5868  off from the Glass and Copper, become very black: why black Substances
  5869  do soonest of all others become hot in the Sun's Light and burn, (which
  5870  Effect may proceed partly from the multitude of Refractions in a little
  5871  room, and partly from the easy Commotion of so very small Corpuscles;)
  5872  and why blacks are usually a little inclined to a bluish Colour. For
  5873  that they are so may be seen by illuminating white Paper by Light
  5874  reflected from black Substances. For the Paper will usually appear of a
  5875  bluish white; and the reason is, that black borders in the obscure blue
  5876  of the order described in the 18th Observation, and therefore reflects
  5877  more Rays of that Colour than of any other.
  5879  In these Descriptions I have been the more particular, because it is not
  5880  impossible but that Microscopes may at length be improved to the
  5881  discovery of the Particles of Bodies on which their Colours depend, if
  5882  they are not already in some measure arrived to that degree of
  5883  perfection. For if those Instruments are or can be so far improved as
  5884  with sufficient distinctness to represent Objects five or six hundred
  5885  times bigger than at a Foot distance they appear to our naked Eyes, I
  5886  should hope that we might be able to discover some of the greatest of
  5887  those Corpuscles. And by one that would magnify three or four thousand
  5888  times perhaps they might all be discover'd, but those which produce
  5889  blackness. In the mean while I see nothing material in this Discourse
  5890  that may rationally be doubted of, excepting this Position: That
  5891  transparent Corpuscles of the same thickness and density with a Plate,
  5892  do exhibit the same Colour. And this I would have understood not without
  5893  some Latitude, as well because those Corpuscles may be of irregular
  5894  Figures, and many Rays must be obliquely incident on them, and so have
  5895  a shorter way through them than the length of their Diameters, as
  5896  because the straitness of the Medium put in on all sides within such
  5897  Corpuscles may a little alter its Motions or other qualities on which
  5898  the Reflexion depends. But yet I cannot much suspect the last, because I
  5899  have observed of some small Plates of Muscovy Glass which were of an
  5900  even thickness, that through a Microscope they have appeared of the same
  5901  Colour at their edges and corners where the included Medium was
  5902  terminated, which they appeared of in other places. However it will add
  5903  much to our Satisfaction, if those Corpuscles can be discover'd with
  5904  Microscopes; which if we shall at length attain to, I fear it will be
  5905  the utmost improvement of this Sense. For it seems impossible to see the
  5906  more secret and noble Works of Nature within the Corpuscles by reason of
  5907  their transparency.
  5910  PROP. VIII.
  5912  _The Cause of Reflexion is not the impinging of Light on the solid or
  5913  impervious parts of Bodies, as is commonly believed._
  5915  This will appear by the following Considerations. First, That in the
  5916  passage of Light out of Glass into Air there is a Reflexion as strong as
  5917  in its passage out of Air into Glass, or rather a little stronger, and
  5918  by many degrees stronger than in its passage out of Glass into Water.
  5919  And it seems not probable that Air should have more strongly reflecting
  5920  parts than Water or Glass. But if that should possibly be supposed, yet
  5921  it will avail nothing; for the Reflexion is as strong or stronger when
  5922  the Air is drawn away from the Glass, (suppose by the Air-Pump invented
  5923  by _Otto Gueriet_, and improved and made useful by Mr. _Boyle_) as when
  5924  it is adjacent to it. Secondly, If Light in its passage out of Glass
  5925  into Air be incident more obliquely than at an Angle of 40 or 41 Degrees
  5926  it is wholly reflected, if less obliquely it is in great measure
  5927  transmitted. Now it is not to be imagined that Light at one degree of
  5928  obliquity should meet with Pores enough in the Air to transmit the
  5929  greater part of it, and at another degree of obliquity should meet with
  5930  nothing but parts to reflect it wholly, especially considering that in
  5931  its passage out of Air into Glass, how oblique soever be its Incidence,
  5932  it finds Pores enough in the Glass to transmit a great part of it. If
  5933  any Man suppose that it is not reflected by the Air, but by the outmost
  5934  superficial parts of the Glass, there is still the same difficulty:
  5935  Besides, that such a Supposition is unintelligible, and will also appear
  5936  to be false by applying Water behind some part of the Glass instead of
  5937  Air. For so in a convenient obliquity of the Rays, suppose of 45 or 46
  5938  Degrees, at which they are all reflected where the Air is adjacent to
  5939  the Glass, they shall be in great measure transmitted where the Water is
  5940  adjacent to it; which argues, that their Reflexion or Transmission
  5941  depends on the constitution of the Air and Water behind the Glass, and
  5942  not on the striking of the Rays upon the parts of the Glass. Thirdly,
  5943  If the Colours made by a Prism placed at the entrance of a Beam of Light
  5944  into a darken'd Room be successively cast on a second Prism placed at a
  5945  greater distance from the former, in such manner that they are all alike
  5946  incident upon it, the second Prism may be so inclined to the incident
  5947  Rays, that those which are of a blue Colour shall be all reflected by
  5948  it, and yet those of a red Colour pretty copiously transmitted. Now if
  5949  the Reflexion be caused by the parts of Air or Glass, I would ask, why
  5950  at the same Obliquity of Incidence the blue should wholly impinge on
  5951  those parts, so as to be all reflected, and yet the red find Pores
  5952  enough to be in a great measure transmitted. Fourthly, Where two Glasses
  5953  touch one another, there is no sensible Reflexion, as was declared in
  5954  the first Observation; and yet I see no reason why the Rays should not
  5955  impinge on the parts of Glass, as much when contiguous to other Glass as
  5956  when contiguous to Air. Fifthly, When the top of a Water-Bubble (in the
  5957  17th Observation,) by the continual subsiding and exhaling of the Water
  5958  grew very thin, there was such a little and almost insensible quantity
  5959  of Light reflected from it, that it appeared intensely black; whereas
  5960  round about that black Spot, where the Water was thicker, the Reflexion
  5961  was so strong as to make the Water seem very white. Nor is it only at
  5962  the least thickness of thin Plates or Bubbles, that there is no manifest
  5963  Reflexion, but at many other thicknesses continually greater and
  5964  greater. For in the 15th Observation the Rays of the same Colour were by
  5965  turns transmitted at one thickness, and reflected at another thickness,
  5966  for an indeterminate number of Successions. And yet in the Superficies
  5967  of the thinned Body, where it is of any one thickness, there are as many
  5968  parts for the Rays to impinge on, as where it is of any other thickness.
  5969  Sixthly, If Reflexion were caused by the parts of reflecting Bodies, it
  5970  would be impossible for thin Plates or Bubbles, at one and the same
  5971  place, to reflect the Rays of one Colour, and transmit those of another,
  5972  as they do according to the 13th and 15th Observations. For it is not to
  5973  be imagined that at one place the Rays which, for instance, exhibit a
  5974  blue Colour, should have the fortune to dash upon the parts, and those
  5975  which exhibit a red to hit upon the Pores of the Body; and then at
  5976  another place, where the Body is either a little thicker or a little
  5977  thinner, that on the contrary the blue should hit upon its pores, and
  5978  the red upon its parts. Lastly, Were the Rays of Light reflected by
  5979  impinging on the solid parts of Bodies, their Reflexions from polish'd
  5980  Bodies could not be so regular as they are. For in polishing Glass with
  5981  Sand, Putty, or Tripoly, it is not to be imagined that those Substances
  5982  can, by grating and fretting the Glass, bring all its least Particles to
  5983  an accurate Polish; so that all their Surfaces shall be truly plain or
  5984  truly spherical, and look all the same way, so as together to compose
  5985  one even Surface. The smaller the Particles of those Substances are, the
  5986  smaller will be the Scratches by which they continually fret and wear
  5987  away the Glass until it be polish'd; but be they never so small they can
  5988  wear away the Glass no otherwise than by grating and scratching it, and
  5989  breaking the Protuberances; and therefore polish it no otherwise than by
  5990  bringing its roughness to a very fine Grain, so that the Scratches and
  5991  Frettings of the Surface become too small to be visible. And therefore
  5992  if Light were reflected by impinging upon the solid parts of the Glass,
  5993  it would be scatter'd as much by the most polish'd Glass as by the
  5994  roughest. So then it remains a Problem, how Glass polish'd by fretting
  5995  Substances can reflect Light so regularly as it does. And this Problem
  5996  is scarce otherwise to be solved, than by saying, that the Reflexion of
  5997  a Ray is effected, not by a single point of the reflecting Body, but by
  5998  some power of the Body which is evenly diffused all over its Surface,
  5999  and by which it acts upon the Ray without immediate Contact. For that
  6000  the parts of Bodies do act upon Light at a distance shall be shewn
  6001  hereafter.
  6003  Now if Light be reflected, not by impinging on the solid parts of
  6004  Bodies, but by some other principle; it's probable that as many of its
  6005  Rays as impinge on the solid parts of Bodies are not reflected but
  6006  stifled and lost in the Bodies. For otherwise we must allow two sorts of
  6007  Reflexions. Should all the Rays be reflected which impinge on the
  6008  internal parts of clear Water or Crystal, those Substances would rather
  6009  have a cloudy Colour than a clear Transparency. To make Bodies look
  6010  black, it's necessary that many Rays be stopp'd, retained, and lost in
  6011  them; and it seems not probable that any Rays can be stopp'd and
  6012  stifled in them which do not impinge on their parts.
  6014  And hence we may understand that Bodies are much more rare and porous
  6015  than is commonly believed. Water is nineteen times lighter, and by
  6016  consequence nineteen times rarer than Gold; and Gold is so rare as very
  6017  readily and without the least opposition to transmit the magnetick
  6018  Effluvia, and easily to admit Quicksilver into its Pores, and to let
  6019  Water pass through it. For a concave Sphere of Gold filled with Water,
  6020  and solder'd up, has, upon pressing the Sphere with great force, let the
  6021  Water squeeze through it, and stand all over its outside in multitudes
  6022  of small Drops, like Dew, without bursting or cracking the Body of the
  6023  Gold, as I have been inform'd by an Eye witness. From all which we may
  6024  conclude, that Gold has more Pores than solid parts, and by consequence
  6025  that Water has above forty times more Pores than Parts. And he that
  6026  shall find out an Hypothesis, by which Water may be so rare, and yet not
  6027  be capable of compression by force, may doubtless by the same Hypothesis
  6028  make Gold, and Water, and all other Bodies, as much rarer as he pleases;
  6029  so that Light may find a ready passage through transparent Substances.
  6031  The Magnet acts upon Iron through all dense Bodies not magnetick nor red
  6032  hot, without any diminution of its Virtue; as for instance, through
  6033  Gold, Silver, Lead, Glass, Water. The gravitating Power of the Sun is
  6034  transmitted through the vast Bodies of the Planets without any
  6035  diminution, so as to act upon all their parts to their very centers
  6036  with the same Force and according to the same Laws, as if the part upon
  6037  which it acts were not surrounded with the Body of the Planet, The Rays
  6038  of Light, whether they be very small Bodies projected, or only Motion or
  6039  Force propagated, are moved in right Lines; and whenever a Ray of Light
  6040  is by any Obstacle turned out of its rectilinear way, it will never
  6041  return into the same rectilinear way, unless perhaps by very great
  6042  accident. And yet Light is transmitted through pellucid solid Bodies in
  6043  right Lines to very great distances. How Bodies can have a sufficient
  6044  quantity of Pores for producing these Effects is very difficult to
  6045  conceive, but perhaps not altogether impossible. For the Colours of
  6046  Bodies arise from the Magnitudes of the Particles which reflect them, as
  6047  was explained above. Now if we conceive these Particles of Bodies to be
  6048  so disposed amongst themselves, that the Intervals or empty Spaces
  6049  between them may be equal in magnitude to them all; and that these
  6050  Particles may be composed of other Particles much smaller, which have as
  6051  much empty Space between them as equals all the Magnitudes of these
  6052  smaller Particles: And that in like manner these smaller Particles are
  6053  again composed of others much smaller, all which together are equal to
  6054  all the Pores or empty Spaces between them; and so on perpetually till
  6055  you come to solid Particles, such as have no Pores or empty Spaces
  6056  within them: And if in any gross Body there be, for instance, three such
  6057  degrees of Particles, the least of which are solid; this Body will have
  6058  seven times more Pores than solid Parts. But if there be four such
  6059  degrees of Particles, the least of which are solid, the Body will have
  6060  fifteen times more Pores than solid Parts. If there be five degrees, the
  6061  Body will have one and thirty times more Pores than solid Parts. If six
  6062  degrees, the Body will have sixty and three times more Pores than solid
  6063  Parts. And so on perpetually. And there are other ways of conceiving how
  6064  Bodies may be exceeding porous. But what is really their inward Frame is
  6065  not yet known to us.
  6068  PROP. IX.
  6070  _Bodies reflect and refract Light by one and the same power, variously
  6071  exercised in various Circumstances._
  6073  This appears by several Considerations. First, Because when Light goes
  6074  out of Glass into Air, as obliquely as it can possibly do. If its
  6075  Incidence be made still more oblique, it becomes totally reflected. For
  6076  the power of the Glass after it has refracted the Light as obliquely as
  6077  is possible, if the Incidence be still made more oblique, becomes too
  6078  strong to let any of its Rays go through, and by consequence causes
  6079  total Reflexions. Secondly, Because Light is alternately reflected and
  6080  transmitted by thin Plates of Glass for many Successions, accordingly as
  6081  the thickness of the Plate increases in an arithmetical Progression. For
  6082  here the thickness of the Glass determines whether that Power by which
  6083  Glass acts upon Light shall cause it to be reflected, or suffer it to
  6084  be transmitted. And, Thirdly, because those Surfaces of transparent
  6085  Bodies which have the greatest refracting power, reflect the greatest
  6086  quantity of Light, as was shewn in the first Proposition.
  6089  PROP. X.
  6091  _If Light be swifter in Bodies than in Vacuo, in the proportion of the
  6092  Sines which measure the Refraction of the Bodies, the Forces of the
  6093  Bodies to reflect and refract Light, are very nearly proportional to the
  6094  densities of the same Bodies; excepting that unctuous and sulphureous
  6095  Bodies refract more than others of this same density._
  6097  [Illustration: FIG. 8.]
  6099  Let AB represent the refracting plane Surface of any Body, and IC a Ray
  6100  incident very obliquely upon the Body in C, so that the Angle ACI may be
  6101  infinitely little, and let CR be the refracted Ray. From a given Point B
  6102  perpendicular to the refracting Surface erect BR meeting with the
  6103  refracting Ray CR in R, and if CR represent the Motion of the refracted
  6104  Ray, and this Motion be distinguish'd into two Motions CB and BR,
  6105  whereof CB is parallel to the refracting Plane, and BR perpendicular to
  6106  it: CB shall represent the Motion of the incident Ray, and BR the
  6107  Motion generated by the Refraction, as Opticians have of late explain'd.
  6109  Now if any Body or Thing, in moving through any Space of a given breadth
  6110  terminated on both sides by two parallel Planes, be urged forward in all
  6111  parts of that Space by Forces tending directly forwards towards the last
  6112  Plane, and before its Incidence on the first Plane, had no Motion
  6113  towards it, or but an infinitely little one; and if the Forces in all
  6114  parts of that Space, between the Planes, be at equal distances from the
  6115  Planes equal to one another, but at several distances be bigger or less
  6116  in any given Proportion, the Motion generated by the Forces in the whole
  6117  passage of the Body or thing through that Space shall be in a
  6118  subduplicate Proportion of the Forces, as Mathematicians will easily
  6119  understand. And therefore, if the Space of activity of the refracting
  6120  Superficies of the Body be consider'd as such a Space, the Motion of the
  6121  Ray generated by the refracting Force of the Body, during its passage
  6122  through that Space, that is, the Motion BR, must be in subduplicate
  6123  Proportion of that refracting Force. I say therefore, that the Square of
  6124  the Line BR, and by consequence the refracting Force of the Body, is
  6125  very nearly as the density of the same Body. For this will appear by the
  6126  following Table, wherein the Proportion of the Sines which measure the
  6127  Refractions of several Bodies, the Square of BR, supposing CB an unite,
  6128  the Densities of the Bodies estimated by their Specifick Gravities, and
  6129  their Refractive Power in respect of their Densities are set down in
  6130  several Columns.
  6132  ---------------------+----------------+----------------+----------+-----------
  6133                       |                |                |          |
  6134                       |                | The Square     | The      | The
  6135                       |                | of BR, to      | density  | refractive
  6136                       | The Proportion | which the      | and      | Power of
  6137                       | of the Sines of| refracting     | specifick| the Body
  6138                       | Incidence and  | force of the   | gravity  | in respect
  6139     The refracting    | Refraction of  | Body is        | of the   | of its
  6140        Bodies.        | yellow Light.  | proportionate. | Body.    | density.
  6141  ---------------------+----------------+----------------+----------+-----------
  6142  A Pseudo-Topazius,   |                |                |          |
  6143    being a natural,   |                |                |          |
  6144    pellucid, brittle, |   23 to   14   |    1'699       |  4'27    |   3979
  6145    hairy Stone, of a  |                |                |          |
  6146    yellow Colour.     |                |                |          |
  6147  Air.                 | 3201 to 3200   |    0'000625    |  0'0012  |   5208
  6148  Glass of Antimony.   |   17 to    9   |    2'568       |  5'28    |   4864
  6149  A Selenitis.         |   61 to   41   |    1'213       |  2'252   |   5386
  6150  Glass vulgar.        |   31 to   20   |    1'4025      |  2'58    |   5436
  6151  Crystal of the Rock. |   25 to   16   |    1'445       |  2'65    |   5450
  6152  Island Crystal.      |    5 to    3   |    1'778       |  2'72    |   6536
  6153  Sal Gemmæ.           |   17 to   11   |    1'388       |  2'143   |   6477
  6154  Alume.               |   35 to   24   |    1'1267      |  1'714   |   6570
  6155  Borax.               |   22 to   15   |    1'1511      |  1'714   |   6716
  6156  Niter.               |   32 to   21   |    1'345       |  1'9     |   7079
  6157  Dantzick Vitriol.    |  303 to  200   |    1'295       |  1'715   |   7551
  6158  Oil of Vitriol.      |   10 to    7   |    1'041       |  1'7     |   6124
  6159  Rain Water.          |  529 to  396   |    0'7845      |  1'      |   7845
  6160  Gum Arabick.         |   31 to   21   |    1'179       |  1'375   |   8574
  6161  Spirit of Wine well  |                |                |          |
  6162    rectified.         |  100 to   73   |    0'8765      |  0'866   |  10121
  6163  Camphire.            |    3 to    2   |    1'25        |  0'996   |  12551
  6164  Oil Olive.           |   22 to   15   |    1'1511      |  0'913   |  12607
  6165  Linseed Oil.         |   40 to   27   |    1'1948      |  0'932   |  12819
  6166  Spirit of Turpentine.|   25 to   17   |    1'1626      |  0'874   |  13222
  6167  Amber.               |   14 to    9   |    1'42        |  1'04    |  13654
  6168  A Diamond.           |  100 to   41   |    4'949       |  3'4     |  14556
  6169  ---------------------+----------------+----------------+----------+-----------
  6171  The Refraction of the Air in this Table is determin'd by that of the
  6172  Atmosphere observed by Astronomers. For, if Light pass through many
  6173  refracting Substances or Mediums gradually denser and denser, and
  6174  terminated with parallel Surfaces, the Sum of all the Refractions will
  6175  be equal to the single Refraction which it would have suffer'd in
  6176  passing immediately out of the first Medium into the last. And this
  6177  holds true, though the Number of the refracting Substances be increased
  6178  to Infinity, and the Distances from one another as much decreased, so
  6179  that the Light may be refracted in every Point of its Passage, and by
  6180  continual Refractions bent into a Curve-Line. And therefore the whole
  6181  Refraction of Light in passing through the Atmosphere from the highest
  6182  and rarest Part thereof down to the lowest and densest Part, must be
  6183  equal to the Refraction which it would suffer in passing at like
  6184  Obliquity out of a Vacuum immediately into Air of equal Density with
  6185  that in the lowest Part of the Atmosphere.
  6187  Now, although a Pseudo-Topaz, a Selenitis, Rock Crystal, Island Crystal,
  6188  Vulgar Glass (that is, Sand melted together) and Glass of Antimony,
  6189  which are terrestrial stony alcalizate Concretes, and Air which probably
  6190  arises from such Substances by Fermentation, be Substances very
  6191  differing from one another in Density, yet by this Table, they have
  6192  their refractive Powers almost in the same Proportion to one another as
  6193  their Densities are, excepting that the Refraction of that strange
  6194  Substance, Island Crystal is a little bigger than the rest. And
  6195  particularly Air, which is 3500 Times rarer than the Pseudo-Topaz, and
  6196  4400 Times rarer than Glass of Antimony, and 2000 Times rarer than the
  6197  Selenitis, Glass vulgar, or Crystal of the Rock, has notwithstanding its
  6198  rarity the same refractive Power in respect of its Density which those
  6199  very dense Substances have in respect of theirs, excepting so far as
  6200  those differ from one another.
  6202  Again, the Refraction of Camphire, Oil Olive, Linseed Oil, Spirit of
  6203  Turpentine and Amber, which are fat sulphureous unctuous Bodies, and a
  6204  Diamond, which probably is an unctuous Substance coagulated, have their
  6205  refractive Powers in Proportion to one another as their Densities
  6206  without any considerable Variation. But the refractive Powers of these
  6207  unctuous Substances are two or three Times greater in respect of their
  6208  Densities than the refractive Powers of the former Substances in respect
  6209  of theirs.
  6211  Water has a refractive Power in a middle degree between those two sorts
  6212  of Substances, and probably is of a middle nature. For out of it grow
  6213  all vegetable and animal Substances, which consist as well of
  6214  sulphureous fat and inflamable Parts, as of earthy lean and alcalizate
  6215  ones.
  6217  Salts and Vitriols have refractive Powers in a middle degree between
  6218  those of earthy Substances and Water, and accordingly are composed of
  6219  those two sorts of Substances. For by distillation and rectification of
  6220  their Spirits a great Part of them goes into Water, and a great Part
  6221  remains behind in the form of a dry fix'd Earth capable of
  6222  Vitrification.
  6224  Spirit of Wine has a refractive Power in a middle degree between those
  6225  of Water and oily Substances, and accordingly seems to be composed of
  6226  both, united by Fermentation; the Water, by means of some saline Spirits
  6227  with which 'tis impregnated, dissolving the Oil, and volatizing it by
  6228  the Action. For Spirit of Wine is inflamable by means of its oily Parts,
  6229  and being distilled often from Salt of Tartar, grow by every
  6230  distillation more and more aqueous and phlegmatick. And Chymists
  6231  observe, that Vegetables (as Lavender, Rue, Marjoram, &c.) distilled
  6232  _per se_, before fermentation yield Oils without any burning Spirits,
  6233  but after fermentation yield ardent Spirits without Oils: Which shews,
  6234  that their Oil is by fermentation converted into Spirit. They find also,
  6235  that if Oils be poured in a small quantity upon fermentating Vegetables,
  6236  they distil over after fermentation in the form of Spirits.
  6238  So then, by the foregoing Table, all Bodies seem to have their
  6239  refractive Powers proportional to their Densities, (or very nearly;)
  6240  excepting so far as they partake more or less of sulphureous oily
  6241  Particles, and thereby have their refractive Power made greater or less.
  6242  Whence it seems rational to attribute the refractive Power of all Bodies
  6243  chiefly, if not wholly, to the sulphureous Parts with which they abound.
  6244  For it's probable that all Bodies abound more or less with Sulphurs. And
  6245  as Light congregated by a Burning-glass acts most upon sulphureous
  6246  Bodies, to turn them into Fire and Flame; so, since all Action is
  6247  mutual, Sulphurs ought to act most upon Light. For that the action
  6248  between Light and Bodies is mutual, may appear from this Consideration;
  6249  That the densest Bodies which refract and reflect Light most strongly,
  6250  grow hottest in the Summer Sun, by the action of the refracted or
  6251  reflected Light.
  6253  I have hitherto explain'd the power of Bodies to reflect and refract,
  6254  and shew'd, that thin transparent Plates, Fibres, and Particles, do,
  6255  according to their several thicknesses and densities, reflect several
  6256  sorts of Rays, and thereby appear of several Colours; and by consequence
  6257  that nothing more is requisite for producing all the Colours of natural
  6258  Bodies, than the several sizes and densities of their transparent
  6259  Particles. But whence it is that these Plates, Fibres, and Particles,
  6260  do, according to their several thicknesses and densities, reflect
  6261  several sorts of Rays, I have not yet explain'd. To give some insight
  6262  into this matter, and make way for understanding the next part of this
  6263  Book, I shall conclude this part with a few more Propositions. Those
  6264  which preceded respect the nature of Bodies, these the nature of Light:
  6265  For both must be understood, before the reason of their Actions upon one
  6266  another can be known. And because the last Proposition depended upon the
  6267  velocity of Light, I will begin with a Proposition of that kind.
  6270  PROP. XI.
  6272  _Light is propagated from luminous Bodies in time, and spends about
  6273  seven or eight Minutes of an Hour in passing from the Sun to the Earth._
  6275  This was observed first by _Roemer_, and then by others, by means of the
  6276  Eclipses of the Satellites of _Jupiter_. For these Eclipses, when the
  6277  Earth is between the Sun and _Jupiter_, happen about seven or eight
  6278  Minutes sooner than they ought to do by the Tables, and when the Earth
  6279  is beyond the Sun they happen about seven or eight Minutes later than
  6280  they ought to do; the reason being, that the Light of the Satellites has
  6281  farther to go in the latter case than in the former by the Diameter of
  6282  the Earth's Orbit. Some inequalities of time may arise from the
  6283  Excentricities of the Orbs of the Satellites; but those cannot answer in
  6284  all the Satellites, and at all times to the Position and Distance of the
  6285  Earth from the Sun. The mean motions of _Jupiter_'s Satellites is also
  6286  swifter in his descent from his Aphelium to his Perihelium, than in his
  6287  ascent in the other half of his Orb. But this inequality has no respect
  6288  to the position of the Earth, and in the three interior Satellites is
  6289  insensible, as I find by computation from the Theory of their Gravity.
  6292  PROP. XII.
  6294  _Every Ray of Light in its passage through any refracting Surface is put
  6295  into a certain transient Constitution or State, which in the progress of
  6296  the Ray returns at equal Intervals, and disposes the Ray at every return
  6297  to be easily transmitted through the next refracting Surface, and
  6298  between the returns to be easily reflected by it._
  6300  This is manifest by the 5th, 9th, 12th, and 15th Observations. For by
  6301  those Observations it appears, that one and the same sort of Rays at
  6302  equal Angles of Incidence on any thin transparent Plate, is alternately
  6303  reflected and transmitted for many Successions accordingly as the
  6304  thickness of the Plate increases in arithmetical Progression of the
  6305  Numbers, 0, 1, 2, 3, 4, 5, 6, 7, 8, &c. so that if the first Reflexion
  6306  (that which makes the first or innermost of the Rings of Colours there
  6307  described) be made at the thickness 1, the Rays shall be transmitted at
  6308  the thicknesses 0, 2, 4, 6, 8, 10, 12, &c. and thereby make the central
  6309  Spot and Rings of Light, which appear by transmission, and be reflected
  6310  at the thickness 1, 3, 5, 7, 9, 11, &c. and thereby make the Rings which
  6311  appear by Reflexion. And this alternate Reflexion and Transmission, as I
  6312  gather by the 24th Observation, continues for above an hundred
  6313  vicissitudes, and by the Observations in the next part of this Book, for
  6314  many thousands, being propagated from one Surface of a Glass Plate to
  6315  the other, though the thickness of the Plate be a quarter of an Inch or
  6316  above: So that this alternation seems to be propagated from every
  6317  refracting Surface to all distances without end or limitation.
  6319  This alternate Reflexion and Refraction depends on both the Surfaces of
  6320  every thin Plate, because it depends on their distance. By the 21st
  6321  Observation, if either Surface of a thin Plate of _Muscovy_ Glass be
  6322  wetted, the Colours caused by the alternate Reflexion and Refraction
  6323  grow faint, and therefore it depends on them both.
  6325  It is therefore perform'd at the second Surface; for if it were
  6326  perform'd at the first, before the Rays arrive at the second, it would
  6327  not depend on the second.
  6329  It is also influenced by some action or disposition, propagated from the
  6330  first to the second, because otherwise at the second it would not depend
  6331  on the first. And this action or disposition, in its propagation,
  6332  intermits and returns by equal Intervals, because in all its progress it
  6333  inclines the Ray at one distance from the first Surface to be reflected
  6334  by the second, at another to be transmitted by it, and that by equal
  6335  Intervals for innumerable vicissitudes. And because the Ray is disposed
  6336  to Reflexion at the distances 1, 3, 5, 7, 9, &c. and to Transmission at
  6337  the distances 0, 2, 4, 6, 8, 10, &c. (for its transmission through the
  6338  first Surface, is at the distance 0, and it is transmitted through both
  6339  together, if their distance be infinitely little or much less than 1)
  6340  the disposition to be transmitted at the distances 2, 4, 6, 8, 10, &c.
  6341  is to be accounted a return of the same disposition which the Ray first
  6342  had at the distance 0, that is at its transmission through the first
  6343  refracting Surface. All which is the thing I would prove.
  6345  What kind of action or disposition this is; Whether it consists in a
  6346  circulating or a vibrating motion of the Ray, or of the Medium, or
  6347  something else, I do not here enquire. Those that are averse from
  6348  assenting to any new Discoveries, but such as they can explain by an
  6349  Hypothesis, may for the present suppose, that as Stones by falling upon
  6350  Water put the Water into an undulating Motion, and all Bodies by
  6351  percussion excite vibrations in the Air; so the Rays of Light, by
  6352  impinging on any refracting or reflecting Surface, excite vibrations in
  6353  the refracting or reflecting Medium or Substance, and by exciting them
  6354  agitate the solid parts of the refracting or reflecting Body, and by
  6355  agitating them cause the Body to grow warm or hot; that the vibrations
  6356  thus excited are propagated in the refracting or reflecting Medium or
  6357  Substance, much after the manner that vibrations are propagated in the
  6358  Air for causing Sound, and move faster than the Rays so as to overtake
  6359  them; and that when any Ray is in that part of the vibration which
  6360  conspires with its Motion, it easily breaks through a refracting
  6361  Surface, but when it is in the contrary part of the vibration which
  6362  impedes its Motion, it is easily reflected; and, by consequence, that
  6363  every Ray is successively disposed to be easily reflected, or easily
  6364  transmitted, by every vibration which overtakes it. But whether this
  6365  Hypothesis be true or false I do not here consider. I content my self
  6366  with the bare Discovery, that the Rays of Light are by some cause or
  6367  other alternately disposed to be reflected or refracted for many
  6368  vicissitudes.
  6373  _The returns of the disposition of any Ray to be reflected I will call
  6374  its_ Fits of easy Reflexion, _and those of its disposition to be
  6375  transmitted its_ Fits of easy Transmission, _and the space it passes
  6376  between every return and the next return, the_ Interval of its Fits.
  6379  PROP. XIII.
  6381  _The reason why the Surfaces of all thick transparent Bodies reflect
  6382  part of the Light incident on them, and refract the rest, is, that some
  6383  Rays at their Incidence are in Fits of easy Reflexion, and others in
  6384  Fits of easy Transmission._
  6386  This may be gather'd from the 24th Observation, where the Light
  6387  reflected by thin Plates of Air and Glass, which to the naked Eye
  6388  appear'd evenly white all over the Plate, did through a Prism appear
  6389  waved with many Successions of Light and Darkness made by alternate Fits
  6390  of easy Reflexion and easy Transmission, the Prism severing and
  6391  distinguishing the Waves of which the white reflected Light was
  6392  composed, as was explain'd above.
  6394  And hence Light is in Fits of easy Reflexion and easy Transmission,
  6395  before its Incidence on transparent Bodies. And probably it is put into
  6396  such fits at its first emission from luminous Bodies, and continues in
  6397  them during all its progress. For these Fits are of a lasting nature, as
  6398  will appear by the next part of this Book.
  6400  In this Proposition I suppose the transparent Bodies to be thick;
  6401  because if the thickness of the Body be much less than the Interval of
  6402  the Fits of easy Reflexion and Transmission of the Rays, the Body loseth
  6403  its reflecting power. For if the Rays, which at their entering into the
  6404  Body are put into Fits of easy Transmission, arrive at the farthest
  6405  Surface of the Body before they be out of those Fits, they must be
  6406  transmitted. And this is the reason why Bubbles of Water lose their
  6407  reflecting power when they grow very thin; and why all opake Bodies,
  6408  when reduced into very small parts, become transparent.
  6411  PROP. XIV.
  6413  _Those Surfaces of transparent Bodies, which if the Ray be in a Fit of
  6414  Refraction do refract it most strongly, if the Ray be in a Fit of
  6415  Reflexion do reflect it most easily._
  6417  For we shewed above, in _Prop._ 8. that the cause of Reflexion is not
  6418  the impinging of Light on the solid impervious parts of Bodies, but some
  6419  other power by which those solid parts act on Light at a distance. We
  6420  shewed also in _Prop._ 9. that Bodies reflect and refract Light by one
  6421  and the same power, variously exercised in various circumstances; and in
  6422  _Prop._ 1. that the most strongly refracting Surfaces reflect the most
  6423  Light: All which compared together evince and rarify both this and the
  6424  last Proposition.
  6427  PROP. XV.
  6429  _In any one and the same sort of Rays, emerging in any Angle out of any
  6430  refracting Surface into one and the same Medium, the Interval of the
  6431  following Fits of easy Reflexion and Transmission are either accurately
  6432  or very nearly, as the Rectangle of the Secant of the Angle of
  6433  Refraction, and of the Secant of another Angle, whose Sine is the first
  6434  of 106 arithmetical mean Proportionals, between the Sines of Incidence
  6435  and Refraction, counted from the Sine of Refraction._
  6437  This is manifest by the 7th and 19th Observations.
  6440  PROP. XVI.
  6442  _In several sorts of Rays emerging in equal Angles out of any refracting
  6443  Surface into the same Medium, the Intervals of the following Fits of
  6444  easy Reflexion and easy Transmission are either accurately, or very
  6445  nearly, as the Cube-Roots of the Squares of the lengths of a Chord,
  6446  which found the Notes in an Eight_, sol, la, fa, sol, la, mi, fa, sol,
  6447  _with all their intermediate degrees answering to the Colours of those
  6448  Rays, according to the Analogy described in the seventh Experiment of
  6449  the second Part of the first Book._
  6451  This is manifest by the 13th and 14th Observations.
  6454  PROP. XVII.
  6456  _If Rays of any sort pass perpendicularly into several Mediums, the
  6457  Intervals of the Fits of easy Reflexion and Transmission in any one
  6458  Medium, are to those Intervals in any other, as the Sine of Incidence to
  6459  the Sine of Refraction, when the Rays pass out of the first of those two
  6460  Mediums into the second._
  6462  This is manifest by the 10th Observation.
  6465  PROP. XVIII.
  6467  _If the Rays which paint the Colour in the Confine of yellow and orange
  6468  pass perpendicularly out of any Medium into Air, the Intervals of their
  6469  Fits of easy Reflexion are the 1/89000th part of an Inch. And of the
  6470  same length are the Intervals of their Fits of easy Transmission._
  6472  This is manifest by the 6th Observation. From these Propositions it is
  6473  easy to collect the Intervals of the Fits of easy Reflexion and easy
  6474  Transmission of any sort of Rays refracted in any angle into any Medium;
  6475  and thence to know, whether the Rays shall be reflected or transmitted
  6476  at their subsequent Incidence upon any other pellucid Medium. Which
  6477  thing, being useful for understanding the next part of this Book, was
  6478  here to be set down. And for the same reason I add the two following
  6479  Propositions.
  6482  PROP. XIX.
  6484  _If any sort of Rays falling on the polite Surface of any pellucid
  6485  Medium be reflected back, the Fits of easy Reflexion, which they have at
  6486  the point of Reflexion, shall still continue to return; and the Returns
  6487  shall be at distances from the point of Reflexion in the arithmetical
  6488  progression of the Numbers 2, 4, 6, 8, 10, 12, &c. and between these
  6489  Fits the Rays shall be in Fits of easy Transmission._
  6491  For since the Fits of easy Reflexion and easy Transmission are of a
  6492  returning nature, there is no reason why these Fits, which continued
  6493  till the Ray arrived at the reflecting Medium, and there inclined the
  6494  Ray to Reflexion, should there cease. And if the Ray at the point of
  6495  Reflexion was in a Fit of easy Reflexion, the progression of the
  6496  distances of these Fits from that point must begin from 0, and so be of
  6497  the Numbers 0, 2, 4, 6, 8, &c. And therefore the progression of the
  6498  distances of the intermediate Fits of easy Transmission, reckon'd from
  6499  the same point, must be in the progression of the odd Numbers 1, 3, 5,
  6500  7, 9, &c. contrary to what happens when the Fits are propagated from
  6501  points of Refraction.
  6504  PROP. XX.
  6506  _The Intervals of the Fits of easy Reflexion and easy Transmission,
  6507  propagated from points of Reflexion into any Medium, are equal to the
  6508  Intervals of the like Fits, which the same Rays would have, if refracted
  6509  into the same Medium in Angles of Refraction equal to their Angles of
  6510  Reflexion._
  6512  For when Light is reflected by the second Surface of thin Plates, it
  6513  goes out afterwards freely at the first Surface to make the Rings of
  6514  Colours which appear by Reflexion; and, by the freedom of its egress,
  6515  makes the Colours of these Rings more vivid and strong than those which
  6516  appear on the other side of the Plates by the transmitted Light. The
  6517  reflected Rays are therefore in Fits of easy Transmission at their
  6518  egress; which would not always happen, if the Intervals of the Fits
  6519  within the Plate after Reflexion were not equal, both in length and
  6520  number, to their Intervals before it. And this confirms also the
  6521  proportions set down in the former Proposition. For if the Rays both in
  6522  going in and out at the first Surface be in Fits of easy Transmission,
  6523  and the Intervals and Numbers of those Fits between the first and second
  6524  Surface, before and after Reflexion, be equal, the distances of the Fits
  6525  of easy Transmission from either Surface, must be in the same
  6526  progression after Reflexion as before; that is, from the first Surface
  6527  which transmitted them in the progression of the even Numbers 0, 2, 4,
  6528  6, 8, &c. and from the second which reflected them, in that of the odd
  6529  Numbers 1, 3, 5, 7, &c. But these two Propositions will become much more
  6530  evident by the Observations in the following part of this Book.
  6535  THE
  6539  OF
  6541  OPTICKS
  6544  _PART IV._
  6546  _Observations concerning the Reflexions and Colours of thick transparent
  6547  polish'd Plates._
  6549  There is no Glass or Speculum how well soever polished, but, besides the
  6550  Light which it refracts or reflects regularly, scatters every way
  6551  irregularly a faint Light, by means of which the polish'd Surface, when
  6552  illuminated in a dark room by a beam of the Sun's Light, may be easily
  6553  seen in all positions of the Eye. There are certain Phænomena of this
  6554  scatter'd Light, which when I first observed them, seem'd very strange
  6555  and surprizing to me. My Observations were as follows.
  6557  _Obs._ 1. The Sun shining into my darken'd Chamber through a hole one
  6558  third of an Inch wide, I let the intromitted beam of Light fall
  6559  perpendicularly upon a Glass Speculum ground concave on one side and
  6560  convex on the other, to a Sphere of five Feet and eleven Inches Radius,
  6561  and Quick-silver'd over on the convex side. And holding a white opake
  6562  Chart, or a Quire of Paper at the center of the Spheres to which the
  6563  Speculum was ground, that is, at the distance of about five Feet and
  6564  eleven Inches from the Speculum, in such manner, that the beam of Light
  6565  might pass through a little hole made in the middle of the Chart to the
  6566  Speculum, and thence be reflected back to the same hole: I observed upon
  6567  the Chart four or five concentric Irises or Rings of Colours, like
  6568  Rain-bows, encompassing the hole much after the manner that those, which
  6569  in the fourth and following Observations of the first part of this Book
  6570  appear'd between the Object-glasses, encompassed the black Spot, but yet
  6571  larger and fainter than those. These Rings as they grew larger and
  6572  larger became diluter and fainter, so that the fifth was scarce visible.
  6573  Yet sometimes, when the Sun shone very clear, there appear'd faint
  6574  Lineaments of a sixth and seventh. If the distance of the Chart from the
  6575  Speculum was much greater or much less than that of six Feet, the Rings
  6576  became dilute and vanish'd. And if the distance of the Speculum from the
  6577  Window was much greater than that of six Feet, the reflected beam of
  6578  Light would be so broad at the distance of six Feet from the Speculum
  6579  where the Rings appear'd, as to obscure one or two of the innermost
  6580  Rings. And therefore I usually placed the Speculum at about six Feet
  6581  from the Window; so that its Focus might there fall in with the center
  6582  of its concavity at the Rings upon the Chart. And this Posture is always
  6583  to be understood in the following Observations where no other is
  6584  express'd.
  6586  _Obs._ 2. The Colours of these Rain-bows succeeded one another from the
  6587  center outwards, in the same form and order with those which were made
  6588  in the ninth Observation of the first Part of this Book by Light not
  6589  reflected, but transmitted through the two Object-glasses. For, first,
  6590  there was in their common center a white round Spot of faint Light,
  6591  something broader than the reflected beam of Light, which beam sometimes
  6592  fell upon the middle of the Spot, and sometimes by a little inclination
  6593  of the Speculum receded from the middle, and left the Spot white to the
  6594  center.
  6596  This white Spot was immediately encompassed with a dark grey or russet,
  6597  and that dark grey with the Colours of the first Iris; which Colours on
  6598  the inside next the dark grey were a little violet and indigo, and next
  6599  to that a blue, which on the outside grew pale, and then succeeded a
  6600  little greenish yellow, and after that a brighter yellow, and then on
  6601  the outward edge of the Iris a red which on the outside inclined to
  6602  purple.
  6604  This Iris was immediately encompassed with a second, whose Colours were
  6605  in order from the inside outwards, purple, blue, green, yellow, light
  6606  red, a red mix'd with purple.
  6608  Then immediately follow'd the Colours of the third Iris, which were in
  6609  order outwards a green inclining to purple, a good green, and a red more
  6610  bright than that of the former Iris.
  6612  The fourth and fifth Iris seem'd of a bluish green within, and red
  6613  without, but so faintly that it was difficult to discern the Colours.
  6615  _Obs._ 3. Measuring the Diameters of these Rings upon the Chart as
  6616  accurately as I could, I found them also in the same proportion to one
  6617  another with the Rings made by Light transmitted through the two
  6618  Object-glasses. For the Diameters of the four first of the bright Rings
  6619  measured between the brightest parts of their Orbits, at the distance of
  6620  six Feet from the Speculum were 1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches,
  6621  whose Squares are in arithmetical progression of the numbers 1, 2, 3, 4.
  6622  If the white circular Spot in the middle be reckon'd amongst the Rings,
  6623  and its central Light, where it seems to be most luminous, be put
  6624  equipollent to an infinitely little Ring; the Squares of the Diameters
  6625  of the Rings will be in the progression 0, 1, 2, 3, 4, &c. I measured
  6626  also the Diameters of the dark Circles between these luminous ones, and
  6627  found their Squares in the progression of the numbers 1/2, 1-1/2, 2-1/2,
  6628  3-1/2, &c. the Diameters of the first four at the distance of six Feet
  6629  from the Speculum, being 1-3/16, 2-1/16, 2-2/3, 3-3/20 Inches. If the
  6630  distance of the Chart from the Speculum was increased or diminished, the
  6631  Diameters of the Circles were increased or diminished proportionally.
  6633  _Obs._ 4. By the analogy between these Rings and those described in the
  6634  Observations of the first Part of this Book, I suspected that there
  6635  were many more of them which spread into one another, and by interfering
  6636  mix'd their Colours, and diluted one another so that they could not be
  6637  seen apart. I viewed them therefore through a Prism, as I did those in
  6638  the 24th Observation of the first Part of this Book. And when the Prism
  6639  was so placed as by refracting the Light of their mix'd Colours to
  6640  separate them, and distinguish the Rings from one another, as it did
  6641  those in that Observation, I could then see them distincter than before,
  6642  and easily number eight or nine of them, and sometimes twelve or
  6643  thirteen. And had not their Light been so very faint, I question not but
  6644  that I might have seen many more.
  6646  _Obs._ 5. Placing a Prism at the Window to refract the intromitted beam
  6647  of Light, and cast the oblong Spectrum of Colours on the Speculum: I
  6648  covered the Speculum with a black Paper which had in the middle of it a
  6649  hole to let any one of the Colours pass through to the Speculum, whilst
  6650  the rest were intercepted by the Paper. And now I found Rings of that
  6651  Colour only which fell upon the Speculum. If the Speculum was
  6652  illuminated with red, the Rings were totally red with dark Intervals, if
  6653  with blue they were totally blue, and so of the other Colours. And when
  6654  they were illuminated with any one Colour, the Squares of their
  6655  Diameters measured between their most luminous Parts, were in the
  6656  arithmetical Progression of the Numbers, 0, 1, 2, 3, 4 and the Squares
  6657  of the Diameters of their dark Intervals in the Progression of the
  6658  intermediate Numbers 1/2, 1-1/2, 2-1/2, 3-1/2. But if the Colour was
  6659  varied, they varied their Magnitude. In the red they were largest, in
  6660  the indigo and violet least, and in the intermediate Colours yellow,
  6661  green, and blue, they were of several intermediate Bignesses answering
  6662  to the Colour, that is, greater in yellow than in green, and greater in
  6663  green than in blue. And hence I knew, that when the Speculum was
  6664  illuminated with white Light, the red and yellow on the outside of the
  6665  Rings were produced by the least refrangible Rays, and the blue and
  6666  violet by the most refrangible, and that the Colours of each Ring spread
  6667  into the Colours of the neighbouring Rings on either side, after the
  6668  manner explain'd in the first and second Part of this Book, and by
  6669  mixing diluted one another so that they could not be distinguish'd,
  6670  unless near the Center where they were least mix'd. For in this
  6671  Observation I could see the Rings more distinctly, and to a greater
  6672  Number than before, being able in the yellow Light to number eight or
  6673  nine of them, besides a faint shadow of a tenth. To satisfy my self how
  6674  much the Colours of the several Rings spread into one another, I
  6675  measured the Diameters of the second and third Rings, and found them
  6676  when made by the Confine of the red and orange to be to the same
  6677  Diameters when made by the Confine of blue and indigo, as 9 to 8, or
  6678  thereabouts. For it was hard to determine this Proportion accurately.
  6679  Also the Circles made successively by the red, yellow, and green,
  6680  differ'd more from one another than those made successively by the
  6681  green, blue, and indigo. For the Circle made by the violet was too dark
  6682  to be seen. To carry on the Computation, let us therefore suppose that
  6683  the Differences of the Diameters of the Circles made by the outmost red,
  6684  the Confine of red and orange, the Confine of orange and yellow, the
  6685  Confine of yellow and green, the Confine of green and blue, the Confine
  6686  of blue and indigo, the Confine of indigo and violet, and outmost
  6687  violet, are in proportion as the Differences of the Lengths of a
  6688  Monochord which sound the Tones in an Eight; _sol_, _la_, _fa_, _sol_,
  6689  _la_, _mi_, _fa_, _sol_, that is, as the Numbers 1/9, 1/18, 1/12, 1/12,
  6690  2/27, 1/27, 1/18. And if the Diameter of the Circle made by the Confine
  6691  of red and orange be 9A, and that of the Circle made by the Confine of
  6692  blue and indigo be 8A as above; their difference 9A-8A will be to the
  6693  difference of the Diameters of the Circles made by the outmost red, and
  6694  by the Confine of red and orange, as 1/18 + 1/12 + 1/12 + 2/27 to 1/9,
  6695  that is as 8/27 to 1/9, or 8 to 3, and to the difference of the Circles
  6696  made by the outmost violet, and by the Confine of blue and indigo, as
  6697  1/18 + 1/12 + 1/12 + 2/27 to 1/27 + 1/18, that is, as 8/27 to 5/54, or
  6698  as 16 to 5. And therefore these differences will be 3/8A and 5/16A. Add
  6699  the first to 9A and subduct the last from 8A, and you will have the
  6700  Diameters of the Circles made by the least and most refrangible Rays
  6701  75/8A and ((61-1/2)/8)A. These diameters are therefore to one another as
  6702  75 to 61-1/2 or 50 to 41, and their Squares as 2500 to 1681, that is, as
  6703  3 to 2 very nearly. Which proportion differs not much from the
  6704  proportion of the Diameters of the Circles made by the outmost red and
  6705  outmost violet, in the 13th Observation of the first part of this Book.
  6707  _Obs._ 6. Placing my Eye where these Rings appear'd plainest, I saw the
  6708  Speculum tinged all over with Waves of Colours, (red, yellow, green,
  6709  blue;) like those which in the Observations of the first part of this
  6710  Book appeared between the Object-glasses, and upon Bubbles of Water, but
  6711  much larger. And after the manner of those, they were of various
  6712  magnitudes in various Positions of the Eye, swelling and shrinking as I
  6713  moved my Eye this way and that way. They were formed like Arcs of
  6714  concentrick Circles, as those were; and when my Eye was over against the
  6715  center of the concavity of the Speculum, (that is, 5 Feet and 10 Inches
  6716  distant from the Speculum,) their common center was in a right Line with
  6717  that center of concavity, and with the hole in the Window. But in other
  6718  postures of my Eye their center had other positions. They appear'd by
  6719  the Light of the Clouds propagated to the Speculum through the hole in
  6720  the Window; and when the Sun shone through that hole upon the Speculum,
  6721  his Light upon it was of the Colour of the Ring whereon it fell, but by
  6722  its splendor obscured the Rings made by the Light of the Clouds, unless
  6723  when the Speculum was removed to a great distance from the Window, so
  6724  that his Light upon it might be broad and faint. By varying the position
  6725  of my Eye, and moving it nearer to or farther from the direct beam of
  6726  the Sun's Light, the Colour of the Sun's reflected Light constantly
  6727  varied upon the Speculum, as it did upon my Eye, the same Colour always
  6728  appearing to a Bystander upon my Eye which to me appear'd upon the
  6729  Speculum. And thence I knew that the Rings of Colours upon the Chart
  6730  were made by these reflected Colours, propagated thither from the
  6731  Speculum in several Angles, and that their production depended not upon
  6732  the termination of Light and Shadow.
  6734  _Obs._ 7. By the Analogy of all these Phænomena with those of the like
  6735  Rings of Colours described in the first part of this Book, it seemed to
  6736  me that these Colours were produced by this thick Plate of Glass, much
  6737  after the manner that those were produced by very thin Plates. For, upon
  6738  trial, I found that if the Quick-silver were rubb'd off from the
  6739  backside of the Speculum, the Glass alone would cause the same Rings of
  6740  Colours, but much more faint than before; and therefore the Phænomenon
  6741  depends not upon the Quick-silver, unless so far as the Quick-silver by
  6742  increasing the Reflexion of the backside of the Glass increases the
  6743  Light of the Rings of Colours. I found also that a Speculum of Metal
  6744  without Glass made some Years since for optical uses, and very well
  6745  wrought, produced none of those Rings; and thence I understood that
  6746  these Rings arise not from one specular Surface alone, but depend upon
  6747  the two Surfaces of the Plate of Glass whereof the Speculum was made,
  6748  and upon the thickness of the Glass between them. For as in the 7th and
  6749  19th Observations of the first part of this Book a thin Plate of Air,
  6750  Water, or Glass of an even thickness appeared of one Colour when the
  6751  Rays were perpendicular to it, of another when they were a little
  6752  oblique, of another when more oblique, of another when still more
  6753  oblique, and so on; so here, in the sixth Observation, the Light which
  6754  emerged out of the Glass in several Obliquities, made the Glass appear
  6755  of several Colours, and being propagated in those Obliquities to the
  6756  Chart, there painted Rings of those Colours. And as the reason why a
  6757  thin Plate appeared of several Colours in several Obliquities of the
  6758  Rays, was, that the Rays of one and the same sort are reflected by the
  6759  thin Plate at one obliquity and transmitted at another, and those of
  6760  other sorts transmitted where these are reflected, and reflected where
  6761  these are transmitted: So the reason why the thick Plate of Glass
  6762  whereof the Speculum was made did appear of various Colours in various
  6763  Obliquities, and in those Obliquities propagated those Colours to the
  6764  Chart, was, that the Rays of one and the same sort did at one Obliquity
  6765  emerge out of the Glass, at another did not emerge, but were reflected
  6766  back towards the Quick-silver by the hither Surface of the Glass, and
  6767  accordingly as the Obliquity became greater and greater, emerged and
  6768  were reflected alternately for many Successions; and that in one and the
  6769  same Obliquity the Rays of one sort were reflected, and those of another
  6770  transmitted. This is manifest by the fifth Observation of this part of
  6771  this Book. For in that Observation, when the Speculum was illuminated by
  6772  any one of the prismatick Colours, that Light made many Rings of the
  6773  same Colour upon the Chart with dark Intervals, and therefore at its
  6774  emergence out of the Speculum was alternately transmitted and not
  6775  transmitted from the Speculum to the Chart for many Successions,
  6776  according to the various Obliquities of its Emergence. And when the
  6777  Colour cast on the Speculum by the Prism was varied, the Rings became of
  6778  the Colour cast on it, and varied their bigness with their Colour, and
  6779  therefore the Light was now alternately transmitted and not transmitted
  6780  from the Speculum to the Chart at other Obliquities than before. It
  6781  seemed to me therefore that these Rings were of one and the same
  6782  original with those of thin Plates, but yet with this difference, that
  6783  those of thin Plates are made by the alternate Reflexions and
  6784  Transmissions of the Rays at the second Surface of the Plate, after one
  6785  passage through it; but here the Rays go twice through the Plate before
  6786  they are alternately reflected and transmitted. First, they go through
  6787  it from the first Surface to the Quick-silver, and then return through
  6788  it from the Quick-silver to the first Surface, and there are either
  6789  transmitted to the Chart or reflected back to the Quick-silver,
  6790  accordingly as they are in their Fits of easy Reflexion or Transmission
  6791  when they arrive at that Surface. For the Intervals of the Fits of the
  6792  Rays which fall perpendicularly on the Speculum, and are reflected back
  6793  in the same perpendicular Lines, by reason of the equality of these
  6794  Angles and Lines, are of the same length and number within the Glass
  6795  after Reflexion as before, by the 19th Proposition of the third part of
  6796  this Book. And therefore since all the Rays that enter through the
  6797  first Surface are in their Fits of easy Transmission at their entrance,
  6798  and as many of these as are reflected by the second are in their Fits of
  6799  easy Reflexion there, all these must be again in their Fits of easy
  6800  Transmission at their return to the first, and by consequence there go
  6801  out of the Glass to the Chart, and form upon it the white Spot of Light
  6802  in the center of the Rings. For the reason holds good in all sorts of
  6803  Rays, and therefore all sorts must go out promiscuously to that Spot,
  6804  and by their mixture cause it to be white. But the Intervals of the Fits
  6805  of those Rays which are reflected more obliquely than they enter, must
  6806  be greater after Reflexion than before, by the 15th and 20th
  6807  Propositions. And thence it may happen that the Rays at their return to
  6808  the first Surface, may in certain Obliquities be in Fits of easy
  6809  Reflexion, and return back to the Quick-silver, and in other
  6810  intermediate Obliquities be again in Fits of easy Transmission, and so
  6811  go out to the Chart, and paint on it the Rings of Colours about the
  6812  white Spot. And because the Intervals of the Fits at equal obliquities
  6813  are greater and fewer in the less refrangible Rays, and less and more
  6814  numerous in the more refrangible, therefore the less refrangible at
  6815  equal obliquities shall make fewer Rings than the more refrangible, and
  6816  the Rings made by those shall be larger than the like number of Rings
  6817  made by these; that is, the red Rings shall be larger than the yellow,
  6818  the yellow than the green, the green than the blue, and the blue than
  6819  the violet, as they were really found to be in the fifth Observation.
  6820  And therefore the first Ring of all Colours encompassing the white Spot
  6821  of Light shall be red without any violet within, and yellow, and green,
  6822  and blue in the middle, as it was found in the second Observation; and
  6823  these Colours in the second Ring, and those that follow, shall be more
  6824  expanded, till they spread into one another, and blend one another by
  6825  interfering.
  6827  These seem to be the reasons of these Rings in general; and this put me
  6828  upon observing the thickness of the Glass, and considering whether the
  6829  dimensions and proportions of the Rings may be truly derived from it by
  6830  computation.
  6832  _Obs._ 8. I measured therefore the thickness of this concavo-convex
  6833  Plate of Glass, and found it every where 1/4 of an Inch precisely. Now,
  6834  by the sixth Observation of the first Part of this Book, a thin Plate of
  6835  Air transmits the brightest Light of the first Ring, that is, the bright
  6836  yellow, when its thickness is the 1/89000th part of an Inch; and by the
  6837  tenth Observation of the same Part, a thin Plate of Glass transmits the
  6838  same Light of the same Ring, when its thickness is less in proportion of
  6839  the Sine of Refraction to the Sine of Incidence, that is, when its
  6840  thickness is the 11/1513000th or 1/137545th part of an Inch, supposing
  6841  the Sines are as 11 to 17. And if this thickness be doubled, it
  6842  transmits the same bright Light of the second Ring; if tripled, it
  6843  transmits that of the third, and so on; the bright yellow Light in all
  6844  these cases being in its Fits of Transmission. And therefore if its
  6845  thickness be multiplied 34386 times, so as to become 1/4 of an Inch, it
  6846  transmits the same bright Light of the 34386th Ring. Suppose this be the
  6847  bright yellow Light transmitted perpendicularly from the reflecting
  6848  convex side of the Glass through the concave side to the white Spot in
  6849  the center of the Rings of Colours on the Chart: And by a Rule in the
  6850  7th and 19th Observations in the first Part of this Book, and by the
  6851  15th and 20th Propositions of the third Part of this Book, if the Rays
  6852  be made oblique to the Glass, the thickness of the Glass requisite to
  6853  transmit the same bright Light of the same Ring in any obliquity, is to
  6854  this thickness of 1/4 of an Inch, as the Secant of a certain Angle to
  6855  the Radius, the Sine of which Angle is the first of an hundred and six
  6856  arithmetical Means between the Sines of Incidence and Refraction,
  6857  counted from the Sine of Incidence when the Refraction is made out of
  6858  any plated Body into any Medium encompassing it; that is, in this case,
  6859  out of Glass into Air. Now if the thickness of the Glass be increased by
  6860  degrees, so as to bear to its first thickness, (_viz._ that of a quarter
  6861  of an Inch,) the Proportions which 34386 (the number of Fits of the
  6862  perpendicular Rays in going through the Glass towards the white Spot in
  6863  the center of the Rings,) hath to 34385, 34384, 34383, and 34382, (the
  6864  numbers of the Fits of the oblique Rays in going through the Glass
  6865  towards the first, second, third, and fourth Rings of Colours,) and if
  6866  the first thickness be divided into 100000000 equal parts, the increased
  6867  thicknesses will be 100002908, 100005816, 100008725, and 100011633, and
  6868  the Angles of which these thicknesses are Secants will be 26´ 13´´, 37´
  6869  5´´, 45´ 6´´, and 52´ 26´´, the Radius being 100000000; and the Sines of
  6870  these Angles are 762, 1079, 1321, and 1525, and the proportional Sines
  6871  of Refraction 1172, 1659, 2031, and 2345, the Radius being 100000. For
  6872  since the Sines of Incidence out of Glass into Air are to the Sines of
  6873  Refraction as 11 to 17, and to the above-mentioned Secants as 11 to the
  6874  first of 106 arithmetical Means between 11 and 17, that is, as 11 to
  6875  11-6/106, those Secants will be to the Sines of Refraction as 11-6/106,
  6876  to 17, and by this Analogy will give these Sines. So then, if the
  6877  obliquities of the Rays to the concave Surface of the Glass be such that
  6878  the Sines of their Refraction in passing out of the Glass through that
  6879  Surface into the Air be 1172, 1659, 2031, 2345, the bright Light of the
  6880  34386th Ring shall emerge at the thicknesses of the Glass, which are to
  6881  1/4 of an Inch as 34386 to 34385, 34384, 34383, 34382, respectively. And
  6882  therefore, if the thickness in all these Cases be 1/4 of an Inch (as it
  6883  is in the Glass of which the Speculum was made) the bright Light of the
  6884  34385th Ring shall emerge where the Sine of Refraction is 1172, and that
  6885  of the 34384th, 34383th, and 34382th Ring where the Sine is 1659, 2031,
  6886  and 2345 respectively. And in these Angles of Refraction the Light of
  6887  these Rings shall be propagated from the Speculum to the Chart, and
  6888  there paint Rings about the white central round Spot of Light which we
  6889  said was the Light of the 34386th Ring. And the Semidiameters of these
  6890  Rings shall subtend the Angles of Refraction made at the
  6891  Concave-Surface of the Speculum, and by consequence their Diameters
  6892  shall be to the distance of the Chart from the Speculum as those Sines
  6893  of Refraction doubled are to the Radius, that is, as 1172, 1659, 2031,
  6894  and 2345, doubled are to 100000. And therefore, if the distance of the
  6895  Chart from the Concave-Surface of the Speculum be six Feet (as it was in
  6896  the third of these Observations) the Diameters of the Rings of this
  6897  bright yellow Light upon the Chart shall be 1'688, 2'389, 2'925, 3'375
  6898  Inches: For these Diameters are to six Feet, as the above-mention'd
  6899  Sines doubled are to the Radius. Now, these Diameters of the bright
  6900  yellow Rings, thus found by Computation are the very same with those
  6901  found in the third of these Observations by measuring them, _viz._ with
  6902  1-11/16, 2-3/8, 2-11/12, and 3-3/8 Inches, and therefore the Theory of
  6903  deriving these Rings from the thickness of the Plate of Glass of which
  6904  the Speculum was made, and from the Obliquity of the emerging Rays
  6905  agrees with the Observation. In this Computation I have equalled the
  6906  Diameters of the bright Rings made by Light of all Colours, to the
  6907  Diameters of the Rings made by the bright yellow. For this yellow makes
  6908  the brightest Part of the Rings of all Colours. If you desire the
  6909  Diameters of the Rings made by the Light of any other unmix'd Colour,
  6910  you may find them readily by putting them to the Diameters of the bright
  6911  yellow ones in a subduplicate Proportion of the Intervals of the Fits of
  6912  the Rays of those Colours when equally inclined to the refracting or
  6913  reflecting Surface which caused those Fits, that is, by putting the
  6914  Diameters of the Rings made by the Rays in the Extremities and Limits of
  6915  the seven Colours, red, orange, yellow, green, blue, indigo, violet,
  6916  proportional to the Cube-roots of the Numbers, 1, 8/9, 5/6, 3/4, 2/3,
  6917  3/5, 9/16, 1/2, which express the Lengths of a Monochord sounding the
  6918  Notes in an Eighth: For by this means the Diameters of the Rings of
  6919  these Colours will be found pretty nearly in the same Proportion to one
  6920  another, which they ought to have by the fifth of these Observations.
  6922  And thus I satisfy'd my self, that these Rings were of the same kind and
  6923  Original with those of thin Plates, and by consequence that the Fits or
  6924  alternate Dispositions of the Rays to be reflected and transmitted are
  6925  propagated to great distances from every reflecting and refracting
  6926  Surface. But yet to put the matter out of doubt, I added the following
  6927  Observation.
  6929  _Obs._ 9. If these Rings thus depend on the thickness of the Plate of
  6930  Glass, their Diameters at equal distances from several Speculums made of
  6931  such concavo-convex Plates of Glass as are ground on the same Sphere,
  6932  ought to be reciprocally in a subduplicate Proportion of the thicknesses
  6933  of the Plates of Glass. And if this Proportion be found true by
  6934  experience it will amount to a demonstration that these Rings (like
  6935  those formed in thin Plates) do depend on the thickness of the Glass. I
  6936  procured therefore another concavo-convex Plate of Glass ground on both
  6937  sides to the same Sphere with the former Plate. Its thickness was 5/62
  6938  Parts of an Inch; and the Diameters of the three first bright Rings
  6939  measured between the brightest Parts of their Orbits at the distance of
  6940  six Feet from the Glass were 3·4-1/6·5-1/8· Inches. Now, the thickness
  6941  of the other Glass being 1/4 of an Inch was to the thickness of this
  6942  Glass as 1/4 to 5/62, that is as 31 to 10, or 310000000 to 100000000,
  6943  and the Roots of these Numbers are 17607 and 10000, and in the
  6944  Proportion of the first of these Roots to the second are the Diameters
  6945  of the bright Rings made in this Observation by the thinner Glass,
  6946  3·4-1/6·5-1/8, to the Diameters of the same Rings made in the third of
  6947  these Observations by the thicker Glass 1-11/16, 2-3/8. 2-11/12, that
  6948  is, the Diameters of the Rings are reciprocally in a subduplicate
  6949  Proportion of the thicknesses of the Plates of Glass.
  6951  So then in Plates of Glass which are alike concave on one side, and
  6952  alike convex on the other side, and alike quick-silver'd on the convex
  6953  sides, and differ in nothing but their thickness, the Diameters of the
  6954  Rings are reciprocally in a subduplicate Proportion of the thicknesses
  6955  of the Plates. And this shews sufficiently that the Rings depend on both
  6956  the Surfaces of the Glass. They depend on the convex Surface, because
  6957  they are more luminous when that Surface is quick-silver'd over than
  6958  when it is without Quick-silver. They depend also upon the concave
  6959  Surface, because without that Surface a Speculum makes them not. They
  6960  depend on both Surfaces, and on the distances between them, because
  6961  their bigness is varied by varying only that distance. And this
  6962  dependence is of the same kind with that which the Colours of thin
  6963  Plates have on the distance of the Surfaces of those Plates, because the
  6964  bigness of the Rings, and their Proportion to one another, and the
  6965  variation of their bigness arising from the variation of the thickness
  6966  of the Glass, and the Orders of their Colours, is such as ought to
  6967  result from the Propositions in the end of the third Part of this Book,
  6968  derived from the Phænomena of the Colours of thin Plates set down in the
  6969  first Part.
  6971  There are yet other Phænomena of these Rings of Colours, but such as
  6972  follow from the same Propositions, and therefore confirm both the Truth
  6973  of those Propositions, and the Analogy between these Rings and the Rings
  6974  of Colours made by very thin Plates. I shall subjoin some of them.
  6976  _Obs._ 10. When the beam of the Sun's Light was reflected back from the
  6977  Speculum not directly to the hole in the Window, but to a place a little
  6978  distant from it, the common center of that Spot, and of all the Rings of
  6979  Colours fell in the middle way between the beam of the incident Light,
  6980  and the beam of the reflected Light, and by consequence in the center of
  6981  the spherical concavity of the Speculum, whenever the Chart on which the
  6982  Rings of Colours fell was placed at that center. And as the beam of
  6983  reflected Light by inclining the Speculum receded more and more from the
  6984  beam of incident Light and from the common center of the colour'd Rings
  6985  between them, those Rings grew bigger and bigger, and so also did the
  6986  white round Spot, and new Rings of Colours emerged successively out of
  6987  their common center, and the white Spot became a white Ring
  6988  encompassing them; and the incident and reflected beams of Light always
  6989  fell upon the opposite parts of this white Ring, illuminating its
  6990  Perimeter like two mock Suns in the opposite parts of an Iris. So then
  6991  the Diameter of this Ring, measured from the middle of its Light on one
  6992  side to the middle of its Light on the other side, was always equal to
  6993  the distance between the middle of the incident beam of Light, and the
  6994  middle of the reflected beam measured at the Chart on which the Rings
  6995  appeared: And the Rays which form'd this Ring were reflected by the
  6996  Speculum in Angles equal to their Angles of Incidence, and by
  6997  consequence to their Angles of Refraction at their entrance into the
  6998  Glass, but yet their Angles of Reflexion were not in the same Planes
  6999  with their Angles of Incidence.
  7001  _Obs._ 11. The Colours of the new Rings were in a contrary order to
  7002  those of the former, and arose after this manner. The white round Spot
  7003  of Light in the middle of the Rings continued white to the center till
  7004  the distance of the incident and reflected beams at the Chart was about
  7005  7/8 parts of an Inch, and then it began to grow dark in the middle. And
  7006  when that distance was about 1-3/16 of an Inch, the white Spot was
  7007  become a Ring encompassing a dark round Spot which in the middle
  7008  inclined to violet and indigo. And the luminous Rings encompassing it
  7009  were grown equal to those dark ones which in the four first Observations
  7010  encompassed them, that is to say, the white Spot was grown a white Ring
  7011  equal to the first of those dark Rings, and the first of those luminous
  7012  Rings was now grown equal to the second of those dark ones, and the
  7013  second of those luminous ones to the third of those dark ones, and so
  7014  on. For the Diameters of the luminous Rings were now 1-3/16, 2-1/16,
  7015  2-2/3, 3-3/20, &c. Inches.
  7017  When the distance between the incident and reflected beams of Light
  7018  became a little bigger, there emerged out of the middle of the dark Spot
  7019  after the indigo a blue, and then out of that blue a pale green, and
  7020  soon after a yellow and red. And when the Colour at the center was
  7021  brightest, being between yellow and red, the bright Rings were grown
  7022  equal to those Rings which in the four first Observations next
  7023  encompassed them; that is to say, the white Spot in the middle of those
  7024  Rings was now become a white Ring equal to the first of those bright
  7025  Rings, and the first of those bright ones was now become equal to the
  7026  second of those, and so on. For the Diameters of the white Ring, and of
  7027  the other luminous Rings encompassing it, were now 1-11/16, 2-3/8,
  7028  2-11/12, 3-3/8, &c. or thereabouts.
  7030  When the distance of the two beams of Light at the Chart was a little
  7031  more increased, there emerged out of the middle in order after the red,
  7032  a purple, a blue, a green, a yellow, and a red inclining much to purple,
  7033  and when the Colour was brightest being between yellow and red, the
  7034  former indigo, blue, green, yellow and red, were become an Iris or Ring
  7035  of Colours equal to the first of those luminous Rings which appeared in
  7036  the four first Observations, and the white Ring which was now become
  7037  the second of the luminous Rings was grown equal to the second of those,
  7038  and the first of those which was now become the third Ring was become
  7039  equal to the third of those, and so on. For their Diameters were
  7040  1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches, the distance of the two beams of
  7041  Light, and the Diameter of the white Ring being 2-3/8 Inches.
  7043  When these two beams became more distant there emerged out of the middle
  7044  of the purplish red, first a darker round Spot, and then out of the
  7045  middle of that Spot a brighter. And now the former Colours (purple,
  7046  blue, green, yellow, and purplish red) were become a Ring equal to the
  7047  first of the bright Rings mentioned in the four first Observations, and
  7048  the Rings about this Ring were grown equal to the Rings about that
  7049  respectively; the distance between the two beams of Light and the
  7050  Diameter of the white Ring (which was now become the third Ring) being
  7051  about 3 Inches.
  7053  The Colours of the Rings in the middle began now to grow very dilute,
  7054  and if the distance between the two Beams was increased half an Inch, or
  7055  an Inch more, they vanish'd whilst the white Ring, with one or two of
  7056  the Rings next it on either side, continued still visible. But if the
  7057  distance of the two beams of Light was still more increased, these also
  7058  vanished: For the Light which coming from several parts of the hole in
  7059  the Window fell upon the Speculum in several Angles of Incidence, made
  7060  Rings of several bignesses, which diluted and blotted out one another,
  7061  as I knew by intercepting some part of that Light. For if I intercepted
  7062  that part which was nearest to the Axis of the Speculum the Rings would
  7063  be less, if the other part which was remotest from it they would be
  7064  bigger.
  7066  _Obs._ 12. When the Colours of the Prism were cast successively on the
  7067  Speculum, that Ring which in the two last Observations was white, was of
  7068  the same bigness in all the Colours, but the Rings without it were
  7069  greater in the green than in the blue, and still greater in the yellow,
  7070  and greatest in the red. And, on the contrary, the Rings within that
  7071  white Circle were less in the green than in the blue, and still less in
  7072  the yellow, and least in the red. For the Angles of Reflexion of those
  7073  Rays which made this Ring, being equal to their Angles of Incidence, the
  7074  Fits of every reflected Ray within the Glass after Reflexion are equal
  7075  in length and number to the Fits of the same Ray within the Glass before
  7076  its Incidence on the reflecting Surface. And therefore since all the
  7077  Rays of all sorts at their entrance into the Glass were in a Fit of
  7078  Transmission, they were also in a Fit of Transmission at their returning
  7079  to the same Surface after Reflexion; and by consequence were
  7080  transmitted, and went out to the white Ring on the Chart. This is the
  7081  reason why that Ring was of the same bigness in all the Colours, and why
  7082  in a mixture of all it appears white. But in Rays which are reflected in
  7083  other Angles, the Intervals of the Fits of the least refrangible being
  7084  greatest, make the Rings of their Colour in their progress from this
  7085  white Ring, either outwards or inwards, increase or decrease by the
  7086  greatest steps; so that the Rings of this Colour without are greatest,
  7087  and within least. And this is the reason why in the last Observation,
  7088  when the Speculum was illuminated with white Light, the exterior Rings
  7089  made by all Colours appeared red without and blue within, and the
  7090  interior blue without and red within.
  7092  These are the Phænomena of thick convexo-concave Plates of Glass, which
  7093  are every where of the same thickness. There are yet other Phænomena
  7094  when these Plates are a little thicker on one side than on the other,
  7095  and others when the Plates are more or less concave than convex, or
  7096  plano-convex, or double-convex. For in all these cases the Plates make
  7097  Rings of Colours, but after various manners; all which, so far as I have
  7098  yet observed, follow from the Propositions in the end of the third part
  7099  of this Book, and so conspire to confirm the truth of those
  7100  Propositions. But the Phænomena are too various, and the Calculations
  7101  whereby they follow from those Propositions too intricate to be here
  7102  prosecuted. I content my self with having prosecuted this kind of
  7103  Phænomena so far as to discover their Cause, and by discovering it to
  7104  ratify the Propositions in the third Part of this Book.
  7106  _Obs._ 13. As Light reflected by a Lens quick-silver'd on the backside
  7107  makes the Rings of Colours above described, so it ought to make the like
  7108  Rings of Colours in passing through a drop of Water. At the first
  7109  Reflexion of the Rays within the drop, some Colours ought to be
  7110  transmitted, as in the case of a Lens, and others to be reflected back
  7111  to the Eye. For instance, if the Diameter of a small drop or globule of
  7112  Water be about the 500th part of an Inch, so that a red-making Ray in
  7113  passing through the middle of this globule has 250 Fits of easy
  7114  Transmission within the globule, and that all the red-making Rays which
  7115  are at a certain distance from this middle Ray round about it have 249
  7116  Fits within the globule, and all the like Rays at a certain farther
  7117  distance round about it have 248 Fits, and all those at a certain
  7118  farther distance 247 Fits, and so on; these concentrick Circles of Rays
  7119  after their transmission, falling on a white Paper, will make
  7120  concentrick Rings of red upon the Paper, supposing the Light which
  7121  passes through one single globule, strong enough to be sensible. And, in
  7122  like manner, the Rays of other Colours will make Rings of other Colours.
  7123  Suppose now that in a fair Day the Sun shines through a thin Cloud of
  7124  such globules of Water or Hail, and that the globules are all of the
  7125  same bigness; and the Sun seen through this Cloud shall appear
  7126  encompassed with the like concentrick Rings of Colours, and the Diameter
  7127  of the first Ring of red shall be 7-1/4 Degrees, that of the second
  7128  10-1/4 Degrees, that of the third 12 Degrees 33 Minutes. And accordingly
  7129  as the Globules of Water are bigger or less, the Rings shall be less or
  7130  bigger. This is the Theory, and Experience answers it. For in _June_
  7131  1692, I saw by reflexion in a Vessel of stagnating Water three Halos,
  7132  Crowns, or Rings of Colours about the Sun, like three little Rain-bows,
  7133  concentrick to his Body. The Colours of the first or innermost Crown
  7134  were blue next the Sun, red without, and white in the middle between the
  7135  blue and red. Those of the second Crown were purple and blue within, and
  7136  pale red without, and green in the middle. And those of the third were
  7137  pale blue within, and pale red without; these Crowns enclosed one
  7138  another immediately, so that their Colours proceeded in this continual
  7139  order from the Sun outward: blue, white, red; purple, blue, green, pale
  7140  yellow and red; pale blue, pale red. The Diameter of the second Crown
  7141  measured from the middle of the yellow and red on one side of the Sun,
  7142  to the middle of the same Colour on the other side was 9-1/3 Degrees, or
  7143  thereabouts. The Diameters of the first and third I had not time to
  7144  measure, but that of the first seemed to be about five or six Degrees,
  7145  and that of the third about twelve. The like Crowns appear sometimes
  7146  about the Moon; for in the beginning of the Year 1664, _Febr._ 19th at
  7147  Night, I saw two such Crowns about her. The Diameter of the first or
  7148  innermost was about three Degrees, and that of the second about five
  7149  Degrees and an half. Next about the Moon was a Circle of white, and next
  7150  about that the inner Crown, which was of a bluish green within next the
  7151  white, and of a yellow and red without, and next about these Colours
  7152  were blue and green on the inside of the outward Crown, and red on the
  7153  outside of it. At the same time there appear'd a Halo about 22 Degrees
  7154  35´ distant from the center of the Moon. It was elliptical, and its long
  7155  Diameter was perpendicular to the Horizon, verging below farthest from
  7156  the Moon. I am told that the Moon has sometimes three or more
  7157  concentrick Crowns of Colours encompassing one another next about her
  7158  Body. The more equal the globules of Water or Ice are to one another,
  7159  the more Crowns of Colours will appear, and the Colours will be the more
  7160  lively. The Halo at the distance of 22-1/2 Degrees from the Moon is of
  7161  another sort. By its being oval and remoter from the Moon below than
  7162  above, I conclude, that it was made by Refraction in some sort of Hail
  7163  or Snow floating in the Air in an horizontal posture, the refracting
  7164  Angle being about 58 or 60 Degrees.
  7169  THE
  7171  THIRD BOOK
  7173  OF
  7175  OPTICKS
  7178  _PART I._
  7180  _Observations concerning the Inflexions of the Rays of Light, and the
  7181  Colours made thereby._
  7183  Grimaldo has inform'd us, that if a beam of the Sun's Light be let into
  7184  a dark Room through a very small hole, the Shadows of things in this
  7185  Light will be larger than they ought to be if the Rays went on by the
  7186  Bodies in straight Lines, and that these Shadows have three parallel
  7187  Fringes, Bands or Ranks of colour'd Light adjacent to them. But if the
  7188  Hole be enlarged the Fringes grow broad and run into one another, so
  7189  that they cannot be distinguish'd. These broad Shadows and Fringes have
  7190  been reckon'd by some to proceed from the ordinary refraction of the
  7191  Air, but without due examination of the Matter. For the circumstances of
  7192  the Phænomenon, so far as I have observed them, are as follows.
  7194  _Obs._ 1. I made in a piece of Lead a small Hole with a Pin, whose
  7195  breadth was the 42d part of an Inch. For 21 of those Pins laid together
  7196  took up the breadth of half an Inch. Through this Hole I let into my
  7197  darken'd Chamber a beam of the Sun's Light, and found that the Shadows
  7198  of Hairs, Thred, Pins, Straws, and such like slender Substances placed
  7199  in this beam of Light, were considerably broader than they ought to be,
  7200  if the Rays of Light passed on by these Bodies in right Lines. And
  7201  particularly a Hair of a Man's Head, whose breadth was but the 280th
  7202  part of an Inch, being held in this Light, at the distance of about
  7203  twelve Feet from the Hole, did cast a Shadow which at the distance of
  7204  four Inches from the Hair was the sixtieth part of an Inch broad, that
  7205  is, above four times broader than the Hair, and at the distance of two
  7206  Feet from the Hair was about the eight and twentieth part of an Inch
  7207  broad, that is, ten times broader than the Hair, and at the distance of
  7208  ten Feet was the eighth part of an Inch broad, that is 35 times broader.
  7210  Nor is it material whether the Hair be encompassed with Air, or with any
  7211  other pellucid Substance. For I wetted a polish'd Plate of Glass, and
  7212  laid the Hair in the Water upon the Glass, and then laying another
  7213  polish'd Plate of Glass upon it, so that the Water might fill up the
  7214  space between the Glasses, I held them in the aforesaid beam of Light,
  7215  so that the Light might pass through them perpendicularly, and the
  7216  Shadow of the Hair was at the same distances as big as before. The
  7217  Shadows of Scratches made in polish'd Plates of Glass were also much
  7218  broader than they ought to be, and the Veins in polish'd Plates of Glass
  7219  did also cast the like broad Shadows. And therefore the great breadth of
  7220  these Shadows proceeds from some other cause than the Refraction of the
  7221  Air.
  7223  Let the Circle X [in _Fig._ 1.] represent the middle of the Hair; ADG,
  7224  BEH, CFI, three Rays passing by one side of the Hair at several
  7225  distances; KNQ, LOR, MPS, three other Rays passing by the other side of
  7226  the Hair at the like distances; D, E, F, and N, O, P, the places where
  7227  the Rays are bent in their passage by the Hair; G, H, I, and Q, R, S,
  7228  the places where the Rays fall on a Paper GQ; IS the breadth of the
  7229  Shadow of the Hair cast on the Paper, and TI, VS, two Rays passing to
  7230  the Points I and S without bending when the Hair is taken away. And it's
  7231  manifest that all the Light between these two Rays TI and VS is bent in
  7232  passing by the Hair, and turned aside from the Shadow IS, because if any
  7233  part of this Light were not bent it would fall on the Paper within the
  7234  Shadow, and there illuminate the Paper, contrary to experience. And
  7235  because when the Paper is at a great distance from the Hair, the Shadow
  7236  is broad, and therefore the Rays TI and VS are at a great distance from
  7237  one another, it follows that the Hair acts upon the Rays of Light at a
  7238  good distance in their passing by it. But the Action is strongest on the
  7239  Rays which pass by at least distances, and grows weaker and weaker
  7240  accordingly as the Rays pass by at distances greater and greater, as is
  7241  represented in the Scheme: For thence it comes to pass, that the Shadow
  7242  of the Hair is much broader in proportion to the distance of the Paper
  7243  from the Hair, when the Paper is nearer the Hair, than when it is at a
  7244  great distance from it.
  7246  _Obs._ 2. The Shadows of all Bodies (Metals, Stones, Glass, Wood, Horn,
  7247  Ice, &c.) in this Light were border'd with three Parallel Fringes or
  7248  Bands of colour'd Light, whereof that which was contiguous to the Shadow
  7249  was broadest and most luminous, and that which was remotest from it was
  7250  narrowest, and so faint, as not easily to be visible. It was difficult
  7251  to distinguish the Colours, unless when the Light fell very obliquely
  7252  upon a smooth Paper, or some other smooth white Body, so as to make them
  7253  appear much broader than they would otherwise do. And then the Colours
  7254  were plainly visible in this Order: The first or innermost Fringe was
  7255  violet and deep blue next the Shadow, and then light blue, green, and
  7256  yellow in the middle, and red without. The second Fringe was almost
  7257  contiguous to the first, and the third to the second, and both were blue
  7258  within, and yellow and red without, but their Colours were very faint,
  7259  especially those of the third. The Colours therefore proceeded in this
  7260  order from the Shadow; violet, indigo, pale blue, green, yellow, red;
  7261  blue, yellow, red; pale blue, pale yellow and red. The Shadows made by
  7262  Scratches and Bubbles in polish'd Plates of Glass were border'd with the
  7263  like Fringes of colour'd Light. And if Plates of Looking-glass sloop'd
  7264  off near the edges with a Diamond-cut, be held in the same beam of
  7265  Light, the Light which passes through the parallel Planes of the Glass
  7266  will be border'd with the like Fringes of Colours where those Planes
  7267  meet with the Diamond-cut, and by this means there will sometimes appear
  7268  four or five Fringes of Colours. Let AB, CD [in _Fig._ 2.] represent the
  7269  parallel Planes of a Looking-glass, and BD the Plane of the Diamond-cut,
  7270  making at B a very obtuse Angle with the Plane AB. And let all the Light
  7271  between the Rays ENI and FBM pass directly through the parallel Planes
  7272  of the Glass, and fall upon the Paper between I and M, and all the Light
  7273  between the Rays GO and HD be refracted by the oblique Plane of the
  7274  Diamond-cut BD, and fall upon the Paper between K and L; and the Light
  7275  which passes directly through the parallel Planes of the Glass, and
  7276  falls upon the Paper between I and M, will be border'd with three or
  7277  more Fringes at M.
  7279  [Illustration: FIG. 1.]
  7281  [Illustration: FIG. 2.]
  7283  So by looking on the Sun through a Feather or black Ribband held close
  7284  to the Eye, several Rain-bows will appear; the Shadows which the Fibres
  7285  or Threds cast on the _Tunica Retina_, being border'd with the like
  7286  Fringes of Colours.
  7288  _Obs._ 3. When the Hair was twelve Feet distant from this Hole, and its
  7289  Shadow fell obliquely upon a flat white Scale of Inches and Parts of an
  7290  Inch placed half a Foot beyond it, and also when the Shadow fell
  7291  perpendicularly upon the same Scale placed nine Feet beyond it; I
  7292  measured the breadth of the Shadow and Fringes as accurately as I could,
  7293  and found them in Parts of an Inch as follows.
  7295  -------------------------------------------+-----------+--------
  7296                                             |  half a   | Nine
  7297                        At the Distance of   |   Foot    |  Feet
  7298  -------------------------------------------+-----------+--------
  7299  The breadth of the Shadow                  |   1/54    |  1/9
  7300  -------------------------------------------+-----------+--------
  7301  The breadth between the Middles of the     |   1/38    |
  7302    brightest Light of the innermost Fringes |    or     |
  7303    on either side the Shadow                |   1/39    |  7/50
  7304  -------------------------------------------+-----------+--------
  7305  The breadth between the Middles of the     |           |
  7306    brightest Light of the middlemost Fringes|           |
  7307    on either side the Shadow                | 1/23-1/2  |  4/17
  7308  -------------------------------------------+-----------+--------
  7309  The breadth between the Middles of the     |  1/18     |
  7310    brightest Light of the outmost Fringes   |   or      |
  7311    on either side the Shadow                | 1/18-1/2  |  3/10
  7312  -------------------------------------------+-----------+--------
  7313  The distance between the Middles of the    |           |
  7314    brightest Light of the first and second  |           |
  7315    Fringes                                  |  1/120    |  1/21
  7316  -------------------------------------------+-----------+--------
  7317  The distance between the Middles of the    |           |
  7318    brightest Light of the second and third  |           |
  7319    Fringes                                  |  1/170    |  1/31
  7320  -------------------------------------------+-----------+--------
  7321  The breadth of the luminous Part (green,   |           |
  7322    white, yellow, and red) of the first     |           |
  7323    Fringe                                   |  1/170    |  1/32
  7324  -------------------------------------------+-----------+--------
  7325  The breadth of the darker Space between    |           |
  7326    the first and second Fringes             |  1/240    |  1/45
  7327  -------------------------------------------+-----------+--------
  7328  The breadth of the luminous Part of the    |           |
  7329    second Fringe                            |  1/290    |  1/55
  7330  -------------------------------------------+-----------+--------
  7331  The breadth of the darker Space between    |           |
  7332    the second and third Fringes             |  1/340    |  1/63
  7333  -------------------------------------------+-----------+--------
  7335  These Measures I took by letting the Shadow of the Hair, at half a Foot
  7336  distance, fall so obliquely on the Scale, as to appear twelve times
  7337  broader than when it fell perpendicularly on it at the same distance,
  7338  and setting down in this Table the twelfth part of the Measures I then
  7339  took.
  7341  _Obs._ 4. When the Shadow and Fringes were cast obliquely upon a smooth
  7342  white Body, and that Body was removed farther and farther from the Hair,
  7343  the first Fringe began to appear and look brighter than the rest of the
  7344  Light at the distance of less than a quarter of an Inch from the Hair,
  7345  and the dark Line or Shadow between that and the second Fringe began to
  7346  appear at a less distance from the Hair than that of the third part of
  7347  an Inch. The second Fringe began to appear at a distance from the Hair
  7348  of less than half an Inch, and the Shadow between that and the third
  7349  Fringe at a distance less than an inch, and the third Fringe at a
  7350  distance less than three Inches. At greater distances they became much
  7351  more sensible, but kept very nearly the same proportion of their
  7352  breadths and intervals which they had at their first appearing. For the
  7353  distance between the middle of the first, and middle of the second
  7354  Fringe, was to the distance between the middle of the second and middle
  7355  of the third Fringe, as three to two, or ten to seven. And the last of
  7356  these two distances was equal to the breadth of the bright Light or
  7357  luminous part of the first Fringe. And this breadth was to the breadth
  7358  of the bright Light of the second Fringe as seven to four, and to the
  7359  dark Interval of the first and second Fringe as three to two, and to
  7360  the like dark Interval between the second and third as two to one. For
  7361  the breadths of the Fringes seem'd to be in the progression of the
  7362  Numbers 1, sqrt(1/3), sqrt(1/5), and their Intervals to be in the
  7363  same progression with them; that is, the Fringes and their Intervals
  7364  together to be in the continual progression of the Numbers 1,
  7365  sqrt(1/2), sqrt(1/3), sqrt(1/4), sqrt(1/5), or thereabouts. And
  7366  these Proportions held the same very nearly at all distances from the
  7367  Hair; the dark Intervals of the Fringes being as broad in proportion to
  7368  the breadth of the Fringes at their first appearance as afterwards at
  7369  great distances from the Hair, though not so dark and distinct.
  7371  _Obs._ 5. The Sun shining into my darken'd Chamber through a hole a
  7372  quarter of an Inch broad, I placed at the distance of two or three Feet
  7373  from the Hole a Sheet of Pasteboard, which was black'd all over on both
  7374  sides, and in the middle of it had a hole about three quarters of an
  7375  Inch square for the Light to pass through. And behind the hole I
  7376  fasten'd to the Pasteboard with Pitch the blade of a sharp Knife, to
  7377  intercept some part of the Light which passed through the hole. The
  7378  Planes of the Pasteboard and blade of the Knife were parallel to one
  7379  another, and perpendicular to the Rays. And when they were so placed
  7380  that none of the Sun's Light fell on the Pasteboard, but all of it
  7381  passed through the hole to the Knife, and there part of it fell upon the
  7382  blade of the Knife, and part of it passed by its edge; I let this part
  7383  of the Light which passed by, fall on a white Paper two or three Feet
  7384  beyond the Knife, and there saw two streams of faint Light shoot out
  7385  both ways from the beam of Light into the shadow, like the Tails of
  7386  Comets. But because the Sun's direct Light by its brightness upon the
  7387  Paper obscured these faint streams, so that I could scarce see them, I
  7388  made a little hole in the midst of the Paper for that Light to pass
  7389  through and fall on a black Cloth behind it; and then I saw the two
  7390  streams plainly. They were like one another, and pretty nearly equal in
  7391  length, and breadth, and quantity of Light. Their Light at that end next
  7392  the Sun's direct Light was pretty strong for the space of about a
  7393  quarter of an Inch, or half an Inch, and in all its progress from that
  7394  direct Light decreased gradually till it became insensible. The whole
  7395  length of either of these streams measured upon the paper at the
  7396  distance of three Feet from the Knife was about six or eight Inches; so
  7397  that it subtended an Angle at the edge of the Knife of about 10 or 12,
  7398  or at most 14 Degrees. Yet sometimes I thought I saw it shoot three or
  7399  four Degrees farther, but with a Light so very faint that I could scarce
  7400  perceive it, and suspected it might (in some measure at least) arise
  7401  from some other cause than the two streams did. For placing my Eye in
  7402  that Light beyond the end of that stream which was behind the Knife, and
  7403  looking towards the Knife, I could see a line of Light upon its edge,
  7404  and that not only when my Eye was in the line of the Streams, but also
  7405  when it was without that line either towards the point of the Knife, or
  7406  towards the handle. This line of Light appear'd contiguous to the edge
  7407  of the Knife, and was narrower than the Light of the innermost Fringe,
  7408  and narrowest when my Eye was farthest from the direct Light, and
  7409  therefore seem'd to pass between the Light of that Fringe and the edge
  7410  of the Knife, and that which passed nearest the edge to be most bent,
  7411  though not all of it.
  7413  _Obs._ 6. I placed another Knife by this, so that their edges might be
  7414  parallel, and look towards one another, and that the beam of Light might
  7415  fall upon both the Knives, and some part of it pass between their edges.
  7416  And when the distance of their edges was about the 400th part of an
  7417  Inch, the stream parted in the middle, and left a Shadow between the two
  7418  parts. This Shadow was so black and dark that all the Light which passed
  7419  between the Knives seem'd to be bent, and turn'd aside to the one hand
  7420  or to the other. And as the Knives still approach'd one another the
  7421  Shadow grew broader, and the streams shorter at their inward ends which
  7422  were next the Shadow, until upon the contact of the Knives the whole
  7423  Light vanish'd, leaving its place to the Shadow.
  7425  And hence I gather that the Light which is least bent, and goes to the
  7426  inward ends of the streams, passes by the edges of the Knives at the
  7427  greatest distance, and this distance when the Shadow begins to appear
  7428  between the streams, is about the 800th part of an Inch. And the Light
  7429  which passes by the edges of the Knives at distances still less and
  7430  less, is more and more bent, and goes to those parts of the streams
  7431  which are farther and farther from the direct Light; because when the
  7432  Knives approach one another till they touch, those parts of the streams
  7433  vanish last which are farthest from the direct Light.
  7435  _Obs._ 7. In the fifth Observation the Fringes did not appear, but by
  7436  reason of the breadth of the hole in the Window became so broad as to
  7437  run into one another, and by joining, to make one continued Light in the
  7438  beginning of the streams. But in the sixth, as the Knives approached one
  7439  another, a little before the Shadow appeared between the two streams,
  7440  the Fringes began to appear on the inner ends of the Streams on either
  7441  side of the direct Light; three on one side made by the edge of one
  7442  Knife, and three on the other side made by the edge of the other Knife.
  7443  They were distinctest when the Knives were placed at the greatest
  7444  distance from the hole in the Window, and still became more distinct by
  7445  making the hole less, insomuch that I could sometimes see a faint
  7446  lineament of a fourth Fringe beyond the three above mention'd. And as
  7447  the Knives continually approach'd one another, the Fringes grew
  7448  distincter and larger, until they vanish'd. The outmost Fringe vanish'd
  7449  first, and the middlemost next, and the innermost last. And after they
  7450  were all vanish'd, and the line of Light which was in the middle between
  7451  them was grown very broad, enlarging it self on both sides into the
  7452  streams of Light described in the fifth Observation, the above-mention'd
  7453  Shadow began to appear in the middle of this line, and divide it along
  7454  the middle into two lines of Light, and increased until the whole Light
  7455  vanish'd. This enlargement of the Fringes was so great that the Rays
  7456  which go to the innermost Fringe seem'd to be bent above twenty times
  7457  more when this Fringe was ready to vanish, than when one of the Knives
  7458  was taken away.
  7460  And from this and the former Observation compared, I gather, that the
  7461  Light of the first Fringe passed by the edge of the Knife at a distance
  7462  greater than the 800th part of an Inch, and the Light of the second
  7463  Fringe passed by the edge of the Knife at a greater distance than the
  7464  Light of the first Fringe did, and that of the third at a greater
  7465  distance than that of the second, and that of the streams of Light
  7466  described in the fifth and sixth Observations passed by the edges of the
  7467  Knives at less distances than that of any of the Fringes.
  7469  _Obs._ 8. I caused the edges of two Knives to be ground truly strait,
  7470  and pricking their points into a Board so that their edges might look
  7471  towards one another, and meeting near their points contain a rectilinear
  7472  Angle, I fasten'd their Handles together with Pitch to make this Angle
  7473  invariable. The distance of the edges of the Knives from one another at
  7474  the distance of four Inches from the angular Point, where the edges of
  7475  the Knives met, was the eighth part of an Inch; and therefore the Angle
  7476  contain'd by the edges was about one Degree 54: The Knives thus fix'd
  7477  together I placed in a beam of the Sun's Light, let into my darken'd
  7478  Chamber through a Hole the 42d Part of an Inch wide, at the distance of
  7479  10 or 15 Feet from the Hole, and let the Light which passed between
  7480  their edges fall very obliquely upon a smooth white Ruler at the
  7481  distance of half an Inch, or an Inch from the Knives, and there saw the
  7482  Fringes by the two edges of the Knives run along the edges of the
  7483  Shadows of the Knives in Lines parallel to those edges without growing
  7484  sensibly broader, till they met in Angles equal to the Angle contained
  7485  by the edges of the Knives, and where they met and joined they ended
  7486  without crossing one another. But if the Ruler was held at a much
  7487  greater distance from the Knives, the Fringes where they were farther
  7488  from the Place of their Meeting, were a little narrower, and became
  7489  something broader and broader as they approach'd nearer and nearer to
  7490  one another, and after they met they cross'd one another, and then
  7491  became much broader than before.
  7493  Whence I gather that the distances at which the Fringes pass by the
  7494  Knives are not increased nor alter'd by the approach of the Knives, but
  7495  the Angles in which the Rays are there bent are much increased by that
  7496  approach; and that the Knife which is nearest any Ray determines which
  7497  way the Ray shall be bent, and the other Knife increases the bent.
  7499  _Obs._ 9. When the Rays fell very obliquely upon the Ruler at the
  7500  distance of the third Part of an Inch from the Knives, the dark Line
  7501  between the first and second Fringe of the Shadow of one Knife, and the
  7502  dark Line between the first and second Fringe of the Shadow of the other
  7503  knife met with one another, at the distance of the fifth Part of an Inch
  7504  from the end of the Light which passed between the Knives at the
  7505  concourse of their edges. And therefore the distance of the edges of the
  7506  Knives at the meeting of these dark Lines was the 160th Part of an Inch.
  7507  For as four Inches to the eighth Part of an Inch, so is any Length of
  7508  the edges of the Knives measured from the point of their concourse to
  7509  the distance of the edges of the Knives at the end of that Length, and
  7510  so is the fifth Part of an Inch to the 160th Part. So then the dark
  7511  Lines above-mention'd meet in the middle of the Light which passes
  7512  between the Knives where they are distant the 160th Part of an Inch, and
  7513  the one half of that Light passes by the edge of one Knife at a distance
  7514  not greater than the 320th Part of an Inch, and falling upon the Paper
  7515  makes the Fringes of the Shadow of that Knife, and the other half passes
  7516  by the edge of the other Knife, at a distance not greater than the 320th
  7517  Part of an Inch, and falling upon the Paper makes the Fringes of the
  7518  Shadow of the other Knife. But if the Paper be held at a distance from
  7519  the Knives greater than the third Part of an Inch, the dark Lines
  7520  above-mention'd meet at a greater distance than the fifth Part of an
  7521  Inch from the end of the Light which passed between the Knives at the
  7522  concourse of their edges; and therefore the Light which falls upon the
  7523  Paper where those dark Lines meet passes between the Knives where the
  7524  edges are distant above the 160th part of an Inch.
  7526  For at another time, when the two Knives were distant eight Feet and
  7527  five Inches from the little hole in the Window, made with a small Pin as
  7528  above, the Light which fell upon the Paper where the aforesaid dark
  7529  lines met, passed between the Knives, where the distance between their
  7530  edges was as in the following Table, when the distance of the Paper from
  7531  the Knives was also as follows.
  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  _____________________________|______________________________
  7546  And hence I gather, that the Light which makes the Fringes upon the
  7547  Paper is not the same Light at all distances of the Paper from the
  7548  Knives, but when the Paper is held near the Knives, the Fringes are made
  7549  by Light which passes by the edges of the Knives at a less distance, and
  7550  is more bent than when the Paper is held at a greater distance from the
  7551  Knives.
  7553  [Illustration: FIG. 3.]
  7555  _Obs._ 10. When the Fringes of the Shadows of the Knives fell
  7556  perpendicularly upon a Paper at a great distance from the Knives, they
  7557  were in the form of Hyperbola's, and their Dimensions were as follows.
  7558  Let CA, CB [in _Fig._ 3.] represent Lines drawn upon the Paper parallel
  7559  to the edges of the Knives, and between which all the Light would fall,
  7560  if it passed between the edges of the Knives without inflexion; DE a
  7561  Right Line drawn through C making the Angles ACD, BCE, equal to one
  7562  another, and terminating all the Light which falls upon the Paper from
  7563  the point where the edges of the Knives meet; _eis_, _fkt_, and _glv_,
  7564  three hyperbolical Lines representing the Terminus of the Shadow of one
  7565  of the Knives, the dark Line between the first and second Fringes of
  7566  that Shadow, and the dark Line between the second and third Fringes of
  7567  the same Shadow; _xip_, _ykq_, and _zlr_, three other hyperbolical Lines
  7568  representing the Terminus of the Shadow of the other Knife, the dark
  7569  Line between the first and second Fringes of that Shadow, and the dark
  7570  line between the second and third Fringes of the same Shadow. And
  7571  conceive that these three Hyperbola's are like and equal to the former
  7572  three, and cross them in the points _i_, _k_, and _l_, and that the
  7573  Shadows of the Knives are terminated and distinguish'd from the first
  7574  luminous Fringes by the lines _eis_ and _xip_, until the meeting and
  7575  crossing of the Fringes, and then those lines cross the Fringes in the
  7576  form of dark lines, terminating the first luminous Fringes within side,
  7577  and distinguishing them from another Light which begins to appear at
  7578  _i_, and illuminates all the triangular space _ip_DE_s_ comprehended by
  7579  these dark lines, and the right line DE. Of these Hyperbola's one
  7580  Asymptote is the line DE, and their other Asymptotes are parallel to the
  7581  lines CA and CB. Let _rv_ represent a line drawn any where upon the
  7582  Paper parallel to the Asymptote DE, and let this line cross the right
  7583  lines AC in _m_, and BC in _n_, and the six dark hyperbolical lines in
  7584  _p_, _q_, _r_; _s_, _t_, _v_; and by measuring the distances _ps_, _qt_,
  7585  _rv_, and thence collecting the lengths of the Ordinates _np_, _nq_,
  7586  _nr_ or _ms_, _mt_, _mv_, and doing this at several distances of the
  7587  line _rv_ from the Asymptote DD, you may find as many points of these
  7588  Hyperbola's as you please, and thereby know that these curve lines are
  7589  Hyperbola's differing little from the conical Hyperbola. And by
  7590  measuring the lines C_i_, C_k_, C_l_, you may find other points of these
  7591  Curves.
  7593  For instance; when the Knives were distant from the hole in the Window
  7594  ten Feet, and the Paper from the Knives nine Feet, and the Angle
  7595  contained by the edges of the Knives to which the Angle ACB is equal,
  7596  was subtended by a Chord which was to the Radius as 1 to 32, and the
  7597  distance of the line _rv_ from the Asymptote DE was half an Inch: I
  7598  measured the lines _ps_, _qt_, _rv_, and found them 0'35, 0'65, 0'98
  7599  Inches respectively; and by adding to their halfs the line 1/2 _mn_,
  7600  (which here was the 128th part of an Inch, or 0'0078 Inches,) the Sums
  7601  _np_, _nq_, _nr_, were 0'1828, 0'3328, 0'4978 Inches. I measured also
  7602  the distances of the brightest parts of the Fringes which run between
  7603  _pq_ and _st_, _qr_ and _tv_, and next beyond _r_ and _v_, and found
  7604  them 0'5, 0'8, and 1'17 Inches.
  7606  _Obs._ 11. The Sun shining into my darken'd Room through a small round
  7607  hole made in a Plate of Lead with a slender Pin, as above; I placed at
  7608  the hole a Prism to refract the Light, and form on the opposite Wall the
  7609  Spectrum of Colours, described in the third Experiment of the first
  7610  Book. And then I found that the Shadows of all Bodies held in the
  7611  colour'd Light between the Prism and the Wall, were border'd with
  7612  Fringes of the Colour of that Light in which they were held. In the full
  7613  red Light they were totally red without any sensible blue or violet, and
  7614  in the deep blue Light they were totally blue without any sensible red
  7615  or yellow; and so in the green Light they were totally green, excepting
  7616  a little yellow and blue, which were mixed in the green Light of the
  7617  Prism. And comparing the Fringes made in the several colour'd Lights, I
  7618  found that those made in the red Light were largest, those made in the
  7619  violet were least, and those made in the green were of a middle bigness.
  7620  For the Fringes with which the Shadow of a Man's Hair were bordered,
  7621  being measured cross the Shadow at the distance of six Inches from the
  7622  Hair, the distance between the middle and most luminous part of the
  7623  first or innermost Fringe on one side of the Shadow, and that of the
  7624  like Fringe on the other side of the Shadow, was in the full red Light
  7625  1/37-1/4 of an Inch, and in the full violet 7/46. And the like distance
  7626  between the middle and most luminous parts of the second Fringes on
  7627  either side the Shadow was in the full red Light 1/22, and in the violet
  7628  1/27 of an Inch. And these distances of the Fringes held the same
  7629  proportion at all distances from the Hair without any sensible
  7630  variation.
  7632  So then the Rays which made these Fringes in the red Light passed by the
  7633  Hair at a greater distance than those did which made the like Fringes in
  7634  the violet; and therefore the Hair in causing these Fringes acted alike
  7635  upon the red Light or least refrangible Rays at a greater distance, and
  7636  upon the violet or most refrangible Rays at a less distance, and by
  7637  those actions disposed the red Light into Larger Fringes, and the violet
  7638  into smaller, and the Lights of intermediate Colours into Fringes of
  7639  intermediate bignesses without changing the Colour of any sort of Light.
  7641  When therefore the Hair in the first and second of these Observations
  7642  was held in the white beam of the Sun's Light, and cast a Shadow which
  7643  was border'd with three Fringes of coloured Light, those Colours arose
  7644  not from any new modifications impress'd upon the Rays of Light by the
  7645  Hair, but only from the various inflexions whereby the several Sorts of
  7646  Rays were separated from one another, which before separation, by the
  7647  mixture of all their Colours, composed the white beam of the Sun's
  7648  Light, but whenever separated compose Lights of the several Colours
  7649  which they are originally disposed to exhibit. In this 11th Observation,
  7650  where the Colours are separated before the Light passes by the Hair, the
  7651  least refrangible Rays, which when separated from the rest make red,
  7652  were inflected at a greater distance from the Hair, so as to make three
  7653  red Fringes at a greater distance from the middle of the Shadow of the
  7654  Hair; and the most refrangible Rays which when separated make violet,
  7655  were inflected at a less distance from the Hair, so as to make three
  7656  violet Fringes at a less distance from the middle of the Shadow of the
  7657  Hair. And other Rays of intermediate degrees of Refrangibility were
  7658  inflected at intermediate distances from the Hair, so as to make Fringes
  7659  of intermediate Colours at intermediate distances from the middle of the
  7660  Shadow of the Hair. And in the second Observation, where all the Colours
  7661  are mix'd in the white Light which passes by the Hair, these Colours are
  7662  separated by the various inflexions of the Rays, and the Fringes which
  7663  they make appear all together, and the innermost Fringes being
  7664  contiguous make one broad Fringe composed of all the Colours in due
  7665  order, the violet lying on the inside of the Fringe next the Shadow, the
  7666  red on the outside farthest from the Shadow, and the blue, green, and
  7667  yellow, in the middle. And, in like manner, the middlemost Fringes of
  7668  all the Colours lying in order, and being contiguous, make another broad
  7669  Fringe composed of all the Colours; and the outmost Fringes of all the
  7670  Colours lying in order, and being contiguous, make a third broad Fringe
  7671  composed of all the Colours. These are the three Fringes of colour'd
  7672  Light with which the Shadows of all Bodies are border'd in the second
  7673  Observation.
  7675  When I made the foregoing Observations, I design'd to repeat most of
  7676  them with more care and exactness, and to make some new ones for
  7677  determining the manner how the Rays of Light are bent in their passage
  7678  by Bodies, for making the Fringes of Colours with the dark lines between
  7679  them. But I was then interrupted, and cannot now think of taking these
  7680  things into farther Consideration. And since I have not finish'd this
  7681  part of my Design, I shall conclude with proposing only some Queries, in
  7682  order to a farther search to be made by others.
  7684  _Query_ 1. Do not Bodies act upon Light at a distance, and by their
  7685  action bend its Rays; and is not this action (_cæteris paribus_)
  7686  strongest at the least distance?
  7688  _Qu._ 2. Do not the Rays which differ in Refrangibility differ also in
  7689  Flexibity; and are they not by their different Inflexions separated from
  7690  one another, so as after separation to make the Colours in the three
  7691  Fringes above described? And after what manner are they inflected to
  7692  make those Fringes?
  7694  _Qu._ 3. Are not the Rays of Light in passing by the edges and sides of
  7695  Bodies, bent several times backwards and forwards, with a motion like
  7696  that of an Eel? And do not the three Fringes of colour'd Light
  7697  above-mention'd arise from three such bendings?
  7699  _Qu._ 4. Do not the Rays of Light which fall upon Bodies, and are
  7700  reflected or refracted, begin to bend before they arrive at the Bodies;
  7701  and are they not reflected, refracted, and inflected, by one and the
  7702  same Principle, acting variously in various Circumstances?
  7704  _Qu._ 5. Do not Bodies and Light act mutually upon one another; that is
  7705  to say, Bodies upon Light in emitting, reflecting, refracting and
  7706  inflecting it, and Light upon Bodies for heating them, and putting their
  7707  parts into a vibrating motion wherein heat consists?
  7709  _Qu._ 6. Do not black Bodies conceive heat more easily from Light than
  7710  those of other Colours do, by reason that the Light falling on them is
  7711  not reflected outwards, but enters the Bodies, and is often reflected
  7712  and refracted within them, until it be stifled and lost?
  7714  _Qu._ 7. Is not the strength and vigor of the action between Light and
  7715  sulphureous Bodies observed above, one reason why sulphureous Bodies
  7716  take fire more readily, and burn more vehemently than other Bodies do?
  7718  _Qu._ 8. Do not all fix'd Bodies, when heated beyond a certain degree,
  7719  emit Light and shine; and is not this Emission perform'd by the
  7720  vibrating motions of their parts? And do not all Bodies which abound
  7721  with terrestrial parts, and especially with sulphureous ones, emit Light
  7722  as often as those parts are sufficiently agitated; whether that
  7723  agitation be made by Heat, or by Friction, or Percussion, or
  7724  Putrefaction, or by any vital Motion, or any other Cause? As for
  7725  instance; Sea-Water in a raging Storm; Quick-silver agitated in _vacuo_;
  7726  the Back of a Cat, or Neck of a Horse, obliquely struck or rubbed in a
  7727  dark place; Wood, Flesh and Fish while they putrefy; Vapours arising
  7728  from putrefy'd Waters, usually call'd _Ignes Fatui_; Stacks of moist Hay
  7729  or Corn growing hot by fermentation; Glow-worms and the Eyes of some
  7730  Animals by vital Motions; the vulgar _Phosphorus_ agitated by the
  7731  attrition of any Body, or by the acid Particles of the Air; Amber and
  7732  some Diamonds by striking, pressing or rubbing them; Scrapings of Steel
  7733  struck off with a Flint; Iron hammer'd very nimbly till it become so hot
  7734  as to kindle Sulphur thrown upon it; the Axletrees of Chariots taking
  7735  fire by the rapid rotation of the Wheels; and some Liquors mix'd with
  7736  one another whose Particles come together with an Impetus, as Oil of
  7737  Vitriol distilled from its weight of Nitre, and then mix'd with twice
  7738  its weight of Oil of Anniseeds. So also a Globe of Glass about 8 or 10
  7739  Inches in diameter, being put into a Frame where it may be swiftly
  7740  turn'd round its Axis, will in turning shine where it rubs against the
  7741  palm of ones Hand apply'd to it: And if at the same time a piece of
  7742  white Paper or white Cloth, or the end of ones Finger be held at the
  7743  distance of about a quarter of an Inch or half an Inch from that part of
  7744  the Glass where it is most in motion, the electrick Vapour which is
  7745  excited by the friction of the Glass against the Hand, will by dashing
  7746  against the white Paper, Cloth or Finger, be put into such an agitation
  7747  as to emit Light, and make the white Paper, Cloth or Finger, appear
  7748  lucid like a Glowworm; and in rushing out of the Glass will sometimes
  7749  push against the finger so as to be felt. And the same things have been
  7750  found by rubbing a long and large Cylinder or Glass or Amber with a
  7751  Paper held in ones hand, and continuing the friction till the Glass grew
  7752  warm.
  7754  _Qu._ 9. Is not Fire a Body heated so hot as to emit Light copiously?
  7755  For what else is a red hot Iron than Fire? And what else is a burning
  7756  Coal than red hot Wood?
  7758  _Qu._ 10. Is not Flame a Vapour, Fume or Exhalation heated red hot, that
  7759  is, so hot as to shine? For Bodies do not flame without emitting a
  7760  copious Fume, and this Fume burns in the Flame. The _Ignis Fatuus_ is a
  7761  Vapour shining without heat, and is there not the same difference
  7762  between this Vapour and Flame, as between rotten Wood shining without
  7763  heat and burning Coals of Fire? In distilling hot Spirits, if the Head
  7764  of the Still be taken off, the Vapour which ascends out of the Still
  7765  will take fire at the Flame of a Candle, and turn into Flame, and the
  7766  Flame will run along the Vapour from the Candle to the Still. Some
  7767  Bodies heated by Motion, or Fermentation, if the heat grow intense, fume
  7768  copiously, and if the heat be great enough the Fumes will shine and
  7769  become Flame. Metals in fusion do not flame for want of a copious Fume,
  7770  except Spelter, which fumes copiously, and thereby flames. All flaming
  7771  Bodies, as Oil, Tallow, Wax, Wood, fossil Coals, Pitch, Sulphur, by
  7772  flaming waste and vanish into burning Smoke, which Smoke, if the Flame
  7773  be put out, is very thick and visible, and sometimes smells strongly,
  7774  but in the Flame loses its smell by burning, and according to the nature
  7775  of the Smoke the Flame is of several Colours, as that of Sulphur blue,
  7776  that of Copper open'd with sublimate green, that of Tallow yellow, that
  7777  of Camphire white. Smoke passing through Flame cannot but grow red hot,
  7778  and red hot Smoke can have no other appearance than that of Flame. When
  7779  Gun-powder takes fire, it goes away into Flaming Smoke. For the Charcoal
  7780  and Sulphur easily take fire, and set fire to the Nitre, and the Spirit
  7781  of the Nitre being thereby rarified into Vapour, rushes out with
  7782  Explosion much after the manner that the Vapour of Water rushes out of
  7783  an Æolipile; the Sulphur also being volatile is converted into Vapour,
  7784  and augments the Explosion. And the acid Vapour of the Sulphur (namely
  7785  that which distils under a Bell into Oil of Sulphur,) entring violently
  7786  into the fix'd Body of the Nitre, sets loose the Spirit of the Nitre,
  7787  and excites a great Fermentation, whereby the Heat is farther augmented,
  7788  and the fix'd Body of the Nitre is also rarified into Fume, and the
  7789  Explosion is thereby made more vehement and quick. For if Salt of Tartar
  7790  be mix'd with Gun-powder, and that Mixture be warm'd till it takes fire,
  7791  the Explosion will be more violent and quick than that of Gun-powder
  7792  alone; which cannot proceed from any other cause than the action of the
  7793  Vapour of the Gun-powder upon the Salt of Tartar, whereby that Salt is
  7794  rarified. The Explosion of Gun-powder arises therefore from the violent
  7795  action whereby all the Mixture being quickly and vehemently heated, is
  7796  rarified and converted into Fume and Vapour: which Vapour, by the
  7797  violence of that action, becoming so hot as to shine, appears in the
  7798  form of Flame.
  7800  _Qu._ 11. Do not great Bodies conserve their heat the longest, their
  7801  parts heating one another, and may not great dense and fix'd Bodies,
  7802  when heated beyond a certain degree, emit Light so copiously, as by the
  7803  Emission and Re-action of its Light, and the Reflexions and Refractions
  7804  of its Rays within its Pores to grow still hotter, till it comes to a
  7805  certain period of heat, such as is that of the Sun? And are not the Sun
  7806  and fix'd Stars great Earths vehemently hot, whose heat is conserved by
  7807  the greatness of the Bodies, and the mutual Action and Reaction between
  7808  them, and the Light which they emit, and whose parts are kept from
  7809  fuming away, not only by their fixity, but also by the vast weight and
  7810  density of the Atmospheres incumbent upon them; and very strongly
  7811  compressing them, and condensing the Vapours and Exhalations which arise
  7812  from them? For if Water be made warm in any pellucid Vessel emptied of
  7813  Air, that Water in the _Vacuum_ will bubble and boil as vehemently as it
  7814  would in the open Air in a Vessel set upon the Fire till it conceives a
  7815  much greater heat. For the weight of the incumbent Atmosphere keeps down
  7816  the Vapours, and hinders the Water from boiling, until it grow much
  7817  hotter than is requisite to make it boil _in vacuo_. Also a mixture of
  7818  Tin and Lead being put upon a red hot Iron _in vacuo_ emits a Fume and
  7819  Flame, but the same Mixture in the open Air, by reason of the incumbent
  7820  Atmosphere, does not so much as emit any Fume which can be perceived by
  7821  Sight. In like manner the great weight of the Atmosphere which lies upon
  7822  the Globe of the Sun may hinder Bodies there from rising up and going
  7823  away from the Sun in the form of Vapours and Fumes, unless by means of a
  7824  far greater heat than that which on the Surface of our Earth would very
  7825  easily turn them into Vapours and Fumes. And the same great weight may
  7826  condense those Vapours and Exhalations as soon as they shall at any time
  7827  begin to ascend from the Sun, and make them presently fall back again
  7828  into him, and by that action increase his Heat much after the manner
  7829  that in our Earth the Air increases the Heat of a culinary Fire. And the
  7830  same weight may hinder the Globe of the Sun from being diminish'd,
  7831  unless by the Emission of Light, and a very small quantity of Vapours
  7832  and Exhalations.
  7834  _Qu._ 12. Do not the Rays of Light in falling upon the bottom of the Eye
  7835  excite Vibrations in the _Tunica Retina_? Which Vibrations, being
  7836  propagated along the solid Fibres of the optick Nerves into the Brain,
  7837  cause the Sense of seeing. For because dense Bodies conserve their Heat
  7838  a long time, and the densest Bodies conserve their Heat the longest, the
  7839  Vibrations of their parts are of a lasting nature, and therefore may be
  7840  propagated along solid Fibres of uniform dense Matter to a great
  7841  distance, for conveying into the Brain the impressions made upon all the
  7842  Organs of Sense. For that Motion which can continue long in one and the
  7843  same part of a Body, can be propagated a long way from one part to
  7844  another, supposing the Body homogeneal, so that the Motion may not be
  7845  reflected, refracted, interrupted or disorder'd by any unevenness of the
  7846  Body.
  7848  _Qu._ 13. Do not several sorts of Rays make Vibrations of several
  7849  bignesses, which according to their bignesses excite Sensations of
  7850  several Colours, much after the manner that the Vibrations of the Air,
  7851  according to their several bignesses excite Sensations of several
  7852  Sounds? And particularly do not the most refrangible Rays excite the
  7853  shortest Vibrations for making a Sensation of deep violet, the least
  7854  refrangible the largest for making a Sensation of deep red, and the
  7855  several intermediate sorts of Rays, Vibrations of several intermediate
  7856  bignesses to make Sensations of the several intermediate Colours?
  7858  _Qu._ 14. May not the harmony and discord of Colours arise from the
  7859  proportions of the Vibrations propagated through the Fibres of the
  7860  optick Nerves into the Brain, as the harmony and discord of Sounds arise
  7861  from the proportions of the Vibrations of the Air? For some Colours, if
  7862  they be view'd together, are agreeable to one another, as those of Gold
  7863  and Indigo, and others disagree.
  7865  _Qu._ 15. Are not the Species of Objects seen with both Eyes united
  7866  where the optick Nerves meet before they come into the Brain, the Fibres
  7867  on the right side of both Nerves uniting there, and after union going
  7868  thence into the Brain in the Nerve which is on the right side of the
  7869  Head, and the Fibres on the left side of both Nerves uniting in the same
  7870  place, and after union going into the Brain in the Nerve which is on the
  7871  left side of the Head, and these two Nerves meeting in the Brain in such
  7872  a manner that their Fibres make but one entire Species or Picture, half
  7873  of which on the right side of the Sensorium comes from the right side of
  7874  both Eyes through the right side of both optick Nerves to the place
  7875  where the Nerves meet, and from thence on the right side of the Head
  7876  into the Brain, and the other half on the left side of the Sensorium
  7877  comes in like manner from the left side of both Eyes. For the optick
  7878  Nerves of such Animals as look the same way with both Eyes (as of Men,
  7879  Dogs, Sheep, Oxen, &c.) meet before they come into the Brain, but the
  7880  optick Nerves of such Animals as do not look the same way with both Eyes
  7881  (as of Fishes, and of the Chameleon,) do not meet, if I am rightly
  7882  inform'd.
  7884  _Qu._ 16. When a Man in the dark presses either corner of his Eye with
  7885  his Finger, and turns his Eye away from his Finger, he will see a Circle
  7886  of Colours like those in the Feather of a Peacock's Tail. If the Eye and
  7887  the Finger remain quiet these Colours vanish in a second Minute of Time,
  7888  but if the Finger be moved with a quavering Motion they appear again. Do
  7889  not these Colours arise from such Motions excited in the bottom of the
  7890  Eye by the Pressure and Motion of the Finger, as, at other times are
  7891  excited there by Light for causing Vision? And do not the Motions once
  7892  excited continue about a Second of Time before they cease? And when a
  7893  Man by a stroke upon his Eye sees a flash of Light, are not the like
  7894  Motions excited in the _Retina_ by the stroke? And when a Coal of Fire
  7895  moved nimbly in the circumference of a Circle, makes the whole
  7896  circumference appear like a Circle of Fire; is it not because the
  7897  Motions excited in the bottom of the Eye by the Rays of Light are of a
  7898  lasting nature, and continue till the Coal of Fire in going round
  7899  returns to its former place? And considering the lastingness of the
  7900  Motions excited in the bottom of the Eye by Light, are they not of a
  7901  vibrating nature?
  7903  _Qu._ 17. If a stone be thrown into stagnating Water, the Waves excited
  7904  thereby continue some time to arise in the place where the Stone fell
  7905  into the Water, and are propagated from thence in concentrick Circles
  7906  upon the Surface of the Water to great distances. And the Vibrations or
  7907  Tremors excited in the Air by percussion, continue a little time to move
  7908  from the place of percussion in concentrick Spheres to great distances.
  7909  And in like manner, when a Ray of Light falls upon the Surface of any
  7910  pellucid Body, and is there refracted or reflected, may not Waves of
  7911  Vibrations, or Tremors, be thereby excited in the refracting or
  7912  reflecting Medium at the point of Incidence, and continue to arise
  7913  there, and to be propagated from thence as long as they continue to
  7914  arise and be propagated, when they are excited in the bottom of the Eye
  7915  by the Pressure or Motion of the Finger, or by the Light which comes
  7916  from the Coal of Fire in the Experiments above-mention'd? and are not
  7917  these Vibrations propagated from the point of Incidence to great
  7918  distances? And do they not overtake the Rays of Light, and by overtaking
  7919  them successively, do they not put them into the Fits of easy Reflexion
  7920  and easy Transmission described above? For if the Rays endeavour to
  7921  recede from the densest part of the Vibration, they may be alternately
  7922  accelerated and retarded by the Vibrations overtaking them.
  7924  _Qu._ 18. If in two large tall cylindrical Vessels of Glass inverted,
  7925  two little Thermometers be suspended so as not to touch the Vessels, and
  7926  the Air be drawn out of one of these Vessels, and these Vessels thus
  7927  prepared be carried out of a cold place into a warm one; the Thermometer
  7928  _in vacuo_ will grow warm as much, and almost as soon as the Thermometer
  7929  which is not _in vacuo_. And when the Vessels are carried back into the
  7930  cold place, the Thermometer _in vacuo_ will grow cold almost as soon as
  7931  the other Thermometer. Is not the Heat of the warm Room convey'd through
  7932  the _Vacuum_ by the Vibrations of a much subtiler Medium than Air, which
  7933  after the Air was drawn out remained in the _Vacuum_? And is not this
  7934  Medium the same with that Medium by which Light is refracted and
  7935  reflected, and by whose Vibrations Light communicates Heat to Bodies,
  7936  and is put into Fits of easy Reflexion and easy Transmission? And do not
  7937  the Vibrations of this Medium in hot Bodies contribute to the
  7938  intenseness and duration of their Heat? And do not hot Bodies
  7939  communicate their Heat to contiguous cold ones, by the Vibrations of
  7940  this Medium propagated from them into the cold ones? And is not this
  7941  Medium exceedingly more rare and subtile than the Air, and exceedingly
  7942  more elastick and active? And doth it not readily pervade all Bodies?
  7943  And is it not (by its elastick force) expanded through all the Heavens?
  7945  _Qu._ 19. Doth not the Refraction of Light proceed from the different
  7946  density of this Æthereal Medium in different places, the Light receding
  7947  always from the denser parts of the Medium? And is not the density
  7948  thereof greater in free and open Spaces void of Air and other grosser
  7949  Bodies, than within the Pores of Water, Glass, Crystal, Gems, and other
  7950  compact Bodies? For when Light passes through Glass or Crystal, and
  7951  falling very obliquely upon the farther Surface thereof is totally
  7952  reflected, the total Reflexion ought to proceed rather from the density
  7953  and vigour of the Medium without and beyond the Glass, than from the
  7954  rarity and weakness thereof.
  7956  _Qu._ 20. Doth not this Æthereal Medium in passing out of Water, Glass,
  7957  Crystal, and other compact and dense Bodies into empty Spaces, grow
  7958  denser and denser by degrees, and by that means refract the Rays of
  7959  Light not in a point, but by bending them gradually in curve Lines? And
  7960  doth not the gradual condensation of this Medium extend to some distance
  7961  from the Bodies, and thereby cause the Inflexions of the Rays of Light,
  7962  which pass by the edges of dense Bodies, at some distance from the
  7963  Bodies?
  7965  _Qu._ 21. Is not this Medium much rarer within the dense Bodies of the
  7966  Sun, Stars, Planets and Comets, than in the empty celestial Spaces
  7967  between them? And in passing from them to great distances, doth it not
  7968  grow denser and denser perpetually, and thereby cause the gravity of
  7969  those great Bodies towards one another, and of their parts towards the
  7970  Bodies; every Body endeavouring to go from the denser parts of the
  7971  Medium towards the rarer? For if this Medium be rarer within the Sun's
  7972  Body than at its Surface, and rarer there than at the hundredth part of
  7973  an Inch from its Body, and rarer there than at the fiftieth part of an
  7974  Inch from its Body, and rarer there than at the Orb of _Saturn_; I see
  7975  no reason why the Increase of density should stop any where, and not
  7976  rather be continued through all distances from the Sun to _Saturn_, and
  7977  beyond. And though this Increase of density may at great distances be
  7978  exceeding slow, yet if the elastick force of this Medium be exceeding
  7979  great, it may suffice to impel Bodies from the denser parts of the
  7980  Medium towards the rarer, with all that power which we call Gravity. And
  7981  that the elastick force of this Medium is exceeding great, may be
  7982  gather'd from the swiftness of its Vibrations. Sounds move about 1140
  7983  _English_ Feet in a second Minute of Time, and in seven or eight Minutes
  7984  of Time they move about one hundred _English_ Miles. Light moves from
  7985  the Sun to us in about seven or eight Minutes of Time, which distance is
  7986  about 70,000,000 _English_ Miles, supposing the horizontal Parallax of
  7987  the Sun to be about 12´´. And the Vibrations or Pulses of this Medium,
  7988  that they may cause the alternate Fits of easy Transmission and easy
  7989  Reflexion, must be swifter than Light, and by consequence above 700,000
  7990  times swifter than Sounds. And therefore the elastick force of this
  7991  Medium, in proportion to its density, must be above 700000 x 700000
  7992  (that is, above 490,000,000,000) times greater than the elastick force
  7993  of the Air is in proportion to its density. For the Velocities of the
  7994  Pulses of elastick Mediums are in a subduplicate _Ratio_ of the
  7995  Elasticities and the Rarities of the Mediums taken together.
  7997  As Attraction is stronger in small Magnets than in great ones in
  7998  proportion to their Bulk, and Gravity is greater in the Surfaces of
  7999  small Planets than in those of great ones in proportion to their bulk,
  8000  and small Bodies are agitated much more by electric attraction than
  8001  great ones; so the smallness of the Rays of Light may contribute very
  8002  much to the power of the Agent by which they are refracted. And so if
  8003  any one should suppose that _Æther_ (like our Air) may contain Particles
  8004  which endeavour to recede from one another (for I do not know what this
  8005  _Æther_ is) and that its Particles are exceedingly smaller than those of
  8006  Air, or even than those of Light: The exceeding smallness of its
  8007  Particles may contribute to the greatness of the force by which those
  8008  Particles may recede from one another, and thereby make that Medium
  8009  exceedingly more rare and elastick than Air, and by consequence
  8010  exceedingly less able to resist the motions of Projectiles, and
  8011  exceedingly more able to press upon gross Bodies, by endeavouring to
  8012  expand it self.
  8014  _Qu._ 22. May not Planets and Comets, and all gross Bodies, perform
  8015  their Motions more freely, and with less resistance in this Æthereal
  8016  Medium than in any Fluid, which fills all Space adequately without
  8017  leaving any Pores, and by consequence is much denser than Quick-silver
  8018  or Gold? And may not its resistance be so small, as to be
  8019  inconsiderable? For instance; If this _Æther_ (for so I will call it)
  8020  should be supposed 700000 times more elastick than our Air, and above
  8021  700000 times more rare; its resistance would be above 600,000,000 times
  8022  less than that of Water. And so small a resistance would scarce make any
  8023  sensible alteration in the Motions of the Planets in ten thousand
  8024  Years. If any one would ask how a Medium can be so rare, let him tell me
  8025  how the Air, in the upper parts of the Atmosphere, can be above an
  8026  hundred thousand thousand times rarer than Gold. Let him also tell me,
  8027  how an electrick Body can by Friction emit an Exhalation so rare and
  8028  subtile, and yet so potent, as by its Emission to cause no sensible
  8029  Diminution of the weight of the electrick Body, and to be expanded
  8030  through a Sphere, whose Diameter is above two Feet, and yet to be able
  8031  to agitate and carry up Leaf Copper, or Leaf Gold, at the distance of
  8032  above a Foot from the electrick Body? And how the Effluvia of a Magnet
  8033  can be so rare and subtile, as to pass through a Plate of Glass without
  8034  any Resistance or Diminution of their Force, and yet so potent as to
  8035  turn a magnetick Needle beyond the Glass?
  8037  _Qu._ 23. Is not Vision perform'd chiefly by the Vibrations of this
  8038  Medium, excited in the bottom of the Eye by the Rays of Light, and
  8039  propagated through the solid, pellucid and uniform Capillamenta of the
  8040  optick Nerves into the place of Sensation? And is not Hearing perform'd
  8041  by the Vibrations either of this or some other Medium, excited in the
  8042  auditory Nerves by the Tremors of the Air, and propagated through the
  8043  solid, pellucid and uniform Capillamenta of those Nerves into the place
  8044  of Sensation? And so of the other Senses.
  8046  _Qu._ 24. Is not Animal Motion perform'd by the Vibrations of this
  8047  Medium, excited in the Brain by the power of the Will, and propagated
  8048  from thence through the solid, pellucid and uniform Capillamenta of the
  8049  Nerves into the Muscles, for contracting and dilating them? I suppose
  8050  that the Capillamenta of the Nerves are each of them solid and uniform,
  8051  that the vibrating Motion of the Æthereal Medium may be propagated along
  8052  them from one end to the other uniformly, and without interruption: For
  8053  Obstructions in the Nerves create Palsies. And that they may be
  8054  sufficiently uniform, I suppose them to be pellucid when view'd singly,
  8055  tho' the Reflexions in their cylindrical Surfaces may make the whole
  8056  Nerve (composed of many Capillamenta) appear opake and white. For
  8057  opacity arises from reflecting Surfaces, such as may disturb and
  8058  interrupt the Motions of this Medium.
  8060  [Sidenote: _See the following Scheme, p. 356._]
  8062  _Qu._ 25. Are there not other original Properties of the Rays of Light,
  8063  besides those already described? An instance of another original
  8064  Property we have in the Refraction of Island Crystal, described first by
  8065  _Erasmus Bartholine_, and afterwards more exactly by _Hugenius_, in his
  8066  Book _De la Lumiere_. This Crystal is a pellucid fissile Stone, clear as
  8067  Water or Crystal of the Rock, and without Colour; enduring a red Heat
  8068  without losing its transparency, and in a very strong Heat calcining
  8069  without Fusion. Steep'd a Day or two in Water, it loses its natural
  8070  Polish. Being rubb'd on Cloth, it attracts pieces of Straws and other
  8071  light things, like Ambar or Glass; and with _Aqua fortis_ it makes an
  8072  Ebullition. It seems to be a sort of Talk, and is found in form of an
  8073  oblique Parallelopiped, with six parallelogram Sides and eight solid
  8074  Angles. The obtuse Angles of the Parallelograms are each of them 101
  8075  Degrees and 52 Minutes; the acute ones 78 Degrees and 8 Minutes. Two of
  8076  the solid Angles opposite to one another, as C and E, are compassed each
  8077  of them with three of these obtuse Angles, and each of the other six
  8078  with one obtuse and two acute ones. It cleaves easily in planes parallel
  8079  to any of its Sides, and not in any other Planes. It cleaves with a
  8080  glossy polite Surface not perfectly plane, but with some little
  8081  unevenness. It is easily scratch'd, and by reason of its softness it
  8082  takes a Polish very difficultly. It polishes better upon polish'd
  8083  Looking-glass than upon Metal, and perhaps better upon Pitch, Leather or
  8084  Parchment. Afterwards it must be rubb'd with a little Oil or white of an
  8085  Egg, to fill up its Scratches; whereby it will become very transparent
  8086  and polite. But for several Experiments, it is not necessary to polish
  8087  it. If a piece of this crystalline Stone be laid upon a Book, every
  8088  Letter of the Book seen through it will appear double, by means of a
  8089  double Refraction. And if any beam of Light falls either
  8090  perpendicularly, or in any oblique Angle upon any Surface of this
  8091  Crystal, it becomes divided into two beams by means of the same double
  8092  Refraction. Which beams are of the same Colour with the incident beam of
  8093  Light, and seem equal to one another in the quantity of their Light, or
  8094  very nearly equal. One of these Refractions is perform'd by the usual
  8095  Rule of Opticks, the Sine of Incidence out of Air into this Crystal
  8096  being to the Sine of Refraction, as five to three. The other
  8097  Refraction, which may be called the unusual Refraction, is perform'd by
  8098  the following Rule.
  8100  [Illustration: FIG. 4.]
  8102  Let ADBC represent the refracting Surface of the Crystal, C the biggest
  8103  solid Angle at that Surface, GEHF the opposite Surface, and CK a
  8104  perpendicular on that Surface. This perpendicular makes with the edge of
  8105  the Crystal CF, an Angle of 19 Degr. 3'. Join KF, and in it take KL, so
  8106  that the Angle KCL be 6 Degr. 40'. and the Angle LCF 12 Degr. 23'. And
  8107  if ST represent any beam of Light incident at T in any Angle upon the
  8108  refracting Surface ADBC, let TV be the refracted beam determin'd by the
  8109  given Portion of the Sines 5 to 3, according to the usual Rule of
  8110  Opticks. Draw VX parallel and equal to KL. Draw it the same way from V
  8111  in which L lieth from K; and joining TX, this line TX shall be the other
  8112  refracted beam carried from T to X, by the unusual Refraction.
  8114  If therefore the incident beam ST be perpendicular to the refracting
  8115  Surface, the two beams TV and TX, into which it shall become divided,
  8116  shall be parallel to the lines CK and CL; one of those beams going
  8117  through the Crystal perpendicularly, as it ought to do by the usual Laws
  8118  of Opticks, and the other TX by an unusual Refraction diverging from the
  8119  perpendicular, and making with it an Angle VTX of about 6-2/3 Degrees,
  8120  as is found by Experience. And hence, the Plane VTX, and such like
  8121  Planes which are parallel to the Plane CFK, may be called the Planes of
  8122  perpendicular Refraction. And the Coast towards which the lines KL and
  8123  VX are drawn, may be call'd the Coast of unusual Refraction.
  8125  In like manner Crystal of the Rock has a double Refraction: But the
  8126  difference of the two Refractions is not so great and manifest as in
  8127  Island Crystal.
  8129  When the beam ST incident on Island Crystal is divided into two beams TV
  8130  and TX, and these two beams arrive at the farther Surface of the Glass;
  8131  the beam TV, which was refracted at the first Surface after the usual
  8132  manner, shall be again refracted entirely after the usual manner at the
  8133  second Surface; and the beam TX, which was refracted after the unusual
  8134  manner in the first Surface, shall be again refracted entirely after the
  8135  unusual manner in the second Surface; so that both these beams shall
  8136  emerge out of the second Surface in lines parallel to the first incident
  8137  beam ST.
  8139  And if two pieces of Island Crystal be placed one after another, in such
  8140  manner that all the Surfaces of the latter be parallel to all the
  8141  corresponding Surfaces of the former: The Rays which are refracted after
  8142  the usual manner in the first Surface of the first Crystal, shall be
  8143  refracted after the usual manner in all the following Surfaces; and the
  8144  Rays which are refracted after the unusual manner in the first Surface,
  8145  shall be refracted after the unusual manner in all the following
  8146  Surfaces. And the same thing happens, though the Surfaces of the
  8147  Crystals be any ways inclined to one another, provided that their Planes
  8148  of perpendicular Refraction be parallel to one another.
  8150  And therefore there is an original difference in the Rays of Light, by
  8151  means of which some Rays are in this Experiment constantly refracted
  8152  after the usual manner, and others constantly after the unusual manner:
  8153  For if the difference be not original, but arises from new Modifications
  8154  impress'd on the Rays at their first Refraction, it would be alter'd by
  8155  new Modifications in the three following Refractions; whereas it suffers
  8156  no alteration, but is constant, and has the same effect upon the Rays in
  8157  all the Refractions. The unusual Refraction is therefore perform'd by an
  8158  original property of the Rays. And it remains to be enquired, whether
  8159  the Rays have not more original Properties than are yet discover'd.
  8161  _Qu._ 26. Have not the Rays of Light several sides, endued with several
  8162  original Properties? For if the Planes of perpendicular Refraction of
  8163  the second Crystal be at right Angles with the Planes of perpendicular
  8164  Refraction of the first Crystal, the Rays which are refracted after the
  8165  usual manner in passing through the first Crystal, will be all of them
  8166  refracted after the unusual manner in passing through the second
  8167  Crystal; and the Rays which are refracted after the unusual manner in
  8168  passing through the first Crystal, will be all of them refracted after
  8169  the usual manner in passing through the second Crystal. And therefore
  8170  there are not two sorts of Rays differing in their nature from one
  8171  another, one of which is constantly and in all Positions refracted after
  8172  the usual manner, and the other constantly and in all Positions after
  8173  the unusual manner. The difference between the two sorts of Rays in the
  8174  Experiment mention'd in the 25th Question, was only in the Positions of
  8175  the Sides of the Rays to the Planes of perpendicular Refraction. For one
  8176  and the same Ray is here refracted sometimes after the usual, and
  8177  sometimes after the unusual manner, according to the Position which its
  8178  Sides have to the Crystals. If the Sides of the Ray are posited the same
  8179  way to both Crystals, it is refracted after the same manner in them
  8180  both: But if that side of the Ray which looks towards the Coast of the
  8181  unusual Refraction of the first Crystal, be 90 Degrees from that side of
  8182  the same Ray which looks toward the Coast of the unusual Refraction of
  8183  the second Crystal, (which may be effected by varying the Position of
  8184  the second Crystal to the first, and by consequence to the Rays of
  8185  Light,) the Ray shall be refracted after several manners in the several
  8186  Crystals. There is nothing more required to determine whether the Rays
  8187  of Light which fall upon the second Crystal shall be refracted after
  8188  the usual or after the unusual manner, but to turn about this Crystal,
  8189  so that the Coast of this Crystal's unusual Refraction may be on this or
  8190  on that side of the Ray. And therefore every Ray may be consider'd as
  8191  having four Sides or Quarters, two of which opposite to one another
  8192  incline the Ray to be refracted after the unusual manner, as often as
  8193  either of them are turn'd towards the Coast of unusual Refraction; and
  8194  the other two, whenever either of them are turn'd towards the Coast of
  8195  unusual Refraction, do not incline it to be otherwise refracted than
  8196  after the usual manner. The two first may therefore be call'd the Sides
  8197  of unusual Refraction. And since these Dispositions were in the Rays
  8198  before their Incidence on the second, third, and fourth Surfaces of the
  8199  two Crystals, and suffered no alteration (so far as appears,) by the
  8200  Refraction of the Rays in their passage through those Surfaces, and the
  8201  Rays were refracted by the same Laws in all the four Surfaces; it
  8202  appears that those Dispositions were in the Rays originally, and
  8203  suffer'd no alteration by the first Refraction, and that by means of
  8204  those Dispositions the Rays were refracted at their Incidence on the
  8205  first Surface of the first Crystal, some of them after the usual, and
  8206  some of them after the unusual manner, accordingly as their Sides of
  8207  unusual Refraction were then turn'd towards the Coast of the unusual
  8208  Refraction of that Crystal, or sideways from it.
  8210  Every Ray of Light has therefore two opposite Sides, originally endued
  8211  with a Property on which the unusual Refraction depends, and the other
  8212  two opposite Sides not endued with that Property. And it remains to be
  8213  enquired, whether there are not more Properties of Light by which the
  8214  Sides of the Rays differ, and are distinguished from one another.
  8216  In explaining the difference of the Sides of the Rays above mention'd, I
  8217  have supposed that the Rays fall perpendicularly on the first Crystal.
  8218  But if they fall obliquely on it, the Success is the same. Those Rays
  8219  which are refracted after the usual manner in the first Crystal, will be
  8220  refracted after the unusual manner in the second Crystal, supposing the
  8221  Planes of perpendicular Refraction to be at right Angles with one
  8222  another, as above; and on the contrary.
  8224  If the Planes of the perpendicular Refraction of the two Crystals be
  8225  neither parallel nor perpendicular to one another, but contain an acute
  8226  Angle: The two beams of Light which emerge out of the first Crystal,
  8227  will be each of them divided into two more at their Incidence on the
  8228  second Crystal. For in this case the Rays in each of the two beams will
  8229  some of them have their Sides of unusual Refraction, and some of them
  8230  their other Sides turn'd towards the Coast of the unusual Refraction of
  8231  the second Crystal.
  8233  _Qu._ 27. Are not all Hypotheses erroneous which have hitherto been
  8234  invented for explaining the Phænomena of Light, by new Modifications of
  8235  the Rays? For those Phænomena depend not upon new Modifications, as has
  8236  been supposed, but upon the original and unchangeable Properties of the
  8237  Rays.
  8239  _Qu._ 28. Are not all Hypotheses erroneous, in which Light is supposed
  8240  to consist in Pression or Motion, propagated through a fluid Medium? For
  8241  in all these Hypotheses the Phænomena of Light have been hitherto
  8242  explain'd by supposing that they arise from new Modifications of the
  8243  Rays; which is an erroneous Supposition.
  8245  If Light consisted only in Pression propagated without actual Motion, it
  8246  would not be able to agitate and heat the Bodies which refract and
  8247  reflect it. If it consisted in Motion propagated to all distances in an
  8248  instant, it would require an infinite force every moment, in every
  8249  shining Particle, to generate that Motion. And if it consisted in
  8250  Pression or Motion, propagated either in an instant or in time, it would
  8251  bend into the Shadow. For Pression or Motion cannot be propagated in a
  8252  Fluid in right Lines, beyond an Obstacle which stops part of the Motion,
  8253  but will bend and spread every way into the quiescent Medium which lies
  8254  beyond the Obstacle. Gravity tends downwards, but the Pressure of Water
  8255  arising from Gravity tends every way with equal Force, and is propagated
  8256  as readily, and with as much force sideways as downwards, and through
  8257  crooked passages as through strait ones. The Waves on the Surface of
  8258  stagnating Water, passing by the sides of a broad Obstacle which stops
  8259  part of them, bend afterwards and dilate themselves gradually into the
  8260  quiet Water behind the Obstacle. The Waves, Pulses or Vibrations of the
  8261  Air, wherein Sounds consist, bend manifestly, though not so much as the
  8262  Waves of Water. For a Bell or a Cannon may be heard beyond a Hill which
  8263  intercepts the sight of the sounding Body, and Sounds are propagated as
  8264  readily through crooked Pipes as through streight ones. But Light is
  8265  never known to follow crooked Passages nor to bend into the Shadow. For
  8266  the fix'd Stars by the Interposition of any of the Planets cease to be
  8267  seen. And so do the Parts of the Sun by the Interposition of the Moon,
  8268  _Mercury_ or _Venus_. The Rays which pass very near to the edges of any
  8269  Body, are bent a little by the action of the Body, as we shew'd above;
  8270  but this bending is not towards but from the Shadow, and is perform'd
  8271  only in the passage of the Ray by the Body, and at a very small distance
  8272  from it. So soon as the Ray is past the Body, it goes right on.
  8274  [Sidenote: _Mais pour dire comment cela se fait, je n'ay rien trove
  8275  jusqu' ici qui me satisfasse._ C. H. de la lumiere, c. 5, p. 91.]
  8277  To explain the unusual Refraction of Island Crystal by Pression or
  8278  Motion propagated, has not hitherto been attempted (to my knowledge)
  8279  except by _Huygens_, who for that end supposed two several vibrating
  8280  Mediums within that Crystal. But when he tried the Refractions in two
  8281  successive pieces of that Crystal, and found them such as is mention'd
  8282  above; he confessed himself at a loss for explaining them. For Pressions
  8283  or Motions, propagated from a shining Body through an uniform Medium,
  8284  must be on all sides alike; whereas by those Experiments it appears,
  8285  that the Rays of Light have different Properties in their different
  8286  Sides. He suspected that the Pulses of _Æther_ in passing through the
  8287  first Crystal might receive certain new Modifications, which might
  8288  determine them to be propagated in this or that Medium within the
  8289  second Crystal, according to the Position of that Crystal. But what
  8290  Modifications those might be he could not say, nor think of any thing
  8291  satisfactory in that Point. And if he had known that the unusual
  8292  Refraction depends not on new Modifications, but on the original and
  8293  unchangeable Dispositions of the Rays, he would have found it as
  8294  difficult to explain how those Dispositions which he supposed to be
  8295  impress'd on the Rays by the first Crystal, could be in them before
  8296  their Incidence on that Crystal, and in general, how all Rays emitted by
  8297  shining Bodies, can have those Dispositions in them from the beginning.
  8298  To me, at least, this seems inexplicable, if Light be nothing else than
  8299  Pression or Motion propagated through _Æther_.
  8301  And it is as difficult to explain by these Hypotheses, how Rays can be
  8302  alternately in Fits of easy Reflexion and easy Transmission; unless
  8303  perhaps one might suppose that there are in all Space two Æthereal
  8304  vibrating Mediums, and that the Vibrations of one of them constitute
  8305  Light, and the Vibrations of the other are swifter, and as often as they
  8306  overtake the Vibrations of the first, put them into those Fits. But how
  8307  two _Æthers_ can be diffused through all Space, one of which acts upon
  8308  the other, and by consequence is re-acted upon, without retarding,
  8309  shattering, dispersing and confounding one anothers Motions, is
  8310  inconceivable. And against filling the Heavens with fluid Mediums,
  8311  unless they be exceeding rare, a great Objection arises from the regular
  8312  and very lasting Motions of the Planets and Comets in all manner of
  8313  Courses through the Heavens. For thence it is manifest, that the Heavens
  8314  are void of all sensible Resistance, and by consequence of all sensible
  8315  Matter.
  8317  For the resisting Power of fluid Mediums arises partly from the
  8318  Attrition of the Parts of the Medium, and partly from the _Vis inertiæ_
  8319  of the Matter. That part of the Resistance of a spherical Body which
  8320  arises from the Attrition of the Parts of the Medium is very nearly as
  8321  the Diameter, or, at the most, as the _Factum_ of the Diameter, and the
  8322  Velocity of the spherical Body together. And that part of the Resistance
  8323  which arises from the _Vis inertiæ_ of the Matter, is as the Square of
  8324  that _Factum_. And by this difference the two sorts of Resistance may be
  8325  distinguish'd from one another in any Medium; and these being
  8326  distinguish'd, it will be found that almost all the Resistance of Bodies
  8327  of a competent Magnitude moving in Air, Water, Quick-silver, and such
  8328  like Fluids with a competent Velocity, arises from the _Vis inertiæ_ of
  8329  the Parts of the Fluid.
  8331  Now that part of the resisting Power of any Medium which arises from the
  8332  Tenacity, Friction or Attrition of the Parts of the Medium, may be
  8333  diminish'd by dividing the Matter into smaller Parts, and making the
  8334  Parts more smooth and slippery: But that part of the Resistance which
  8335  arises from the _Vis inertiæ_, is proportional to the Density of the
  8336  Matter, and cannot be diminish'd by dividing the Matter into smaller
  8337  Parts, nor by any other means than by decreasing the Density of the
  8338  Medium. And for these Reasons the Density of fluid Mediums is very
  8339  nearly proportional to their Resistance. Liquors which differ not much
  8340  in Density, as Water, Spirit of Wine, Spirit of Turpentine, hot Oil,
  8341  differ not much in Resistance. Water is thirteen or fourteen times
  8342  lighter than Quick-silver and by consequence thirteen or fourteen times
  8343  rarer, and its Resistance is less than that of Quick-silver in the same
  8344  Proportion, or thereabouts, as I have found by Experiments made with
  8345  Pendulums. The open Air in which we breathe is eight or nine hundred
  8346  times lighter than Water, and by consequence eight or nine hundred times
  8347  rarer, and accordingly its Resistance is less than that of Water in the
  8348  same Proportion, or thereabouts; as I have also found by Experiments
  8349  made with Pendulums. And in thinner Air the Resistance is still less,
  8350  and at length, by ratifying the Air, becomes insensible. For small
  8351  Feathers falling in the open Air meet with great Resistance, but in a
  8352  tall Glass well emptied of Air, they fall as fast as Lead or Gold, as I
  8353  have seen tried several times. Whence the Resistance seems still to
  8354  decrease in proportion to the Density of the Fluid. For I do not find by
  8355  any Experiments, that Bodies moving in Quick-silver, Water or Air, meet
  8356  with any other sensible Resistance than what arises from the Density and
  8357  Tenacity of those sensible Fluids, as they would do if the Pores of
  8358  those Fluids, and all other Spaces, were filled with a dense and
  8359  subtile Fluid. Now if the Resistance in a Vessel well emptied of Air,
  8360  was but an hundred times less than in the open Air, it would be about a
  8361  million of times less than in Quick-silver. But it seems to be much less
  8362  in such a Vessel, and still much less in the Heavens, at the height of
  8363  three or four hundred Miles from the Earth, or above. For Mr. _Boyle_
  8364  has shew'd that Air may be rarified above ten thousand times in Vessels
  8365  of Glass; and the Heavens are much emptier of Air than any _Vacuum_ we
  8366  can make below. For since the Air is compress'd by the Weight of the
  8367  incumbent Atmosphere, and the Density of Air is proportional to the
  8368  Force compressing it, it follows by Computation, that at the height of
  8369  about seven and a half _English_ Miles from the Earth, the Air is four
  8370  times rarer than at the Surface of the Earth; and at the height of 15
  8371  Miles it is sixteen times rarer than that at the Surface of the Earth;
  8372  and at the height of 22-1/2, 30, or 38 Miles, it is respectively 64,
  8373  256, or 1024 times rarer, or thereabouts; and at the height of 76, 152,
  8374  228 Miles, it is about 1000000, 1000000000000, or 1000000000000000000
  8375  times rarer; and so on.
  8377  Heat promotes Fluidity very much by diminishing the Tenacity of Bodies.
  8378  It makes many Bodies fluid which are not fluid in cold, and increases
  8379  the Fluidity of tenacious Liquids, as of Oil, Balsam, and Honey, and
  8380  thereby decreases their Resistance. But it decreases not the Resistance
  8381  of Water considerably, as it would do if any considerable part of the
  8382  Resistance of Water arose from the Attrition or Tenacity of its Parts.
  8383  And therefore the Resistance of Water arises principally and almost
  8384  entirely from the _Vis inertiæ_ of its Matter; and by consequence, if
  8385  the Heavens were as dense as Water, they would not have much less
  8386  Resistance than Water; if as dense as Quick-silver, they would not have
  8387  much less Resistance than Quick-silver; if absolutely dense, or full of
  8388  Matter without any _Vacuum_, let the Matter be never so subtil and
  8389  fluid, they would have a greater Resistance than Quick-silver. A solid
  8390  Globe in such a Medium would lose above half its Motion in moving three
  8391  times the length of its Diameter, and a Globe not solid (such as are the
  8392  Planets,) would be retarded sooner. And therefore to make way for the
  8393  regular and lasting Motions of the Planets and Comets, it's necessary to
  8394  empty the Heavens of all Matter, except perhaps some very thin Vapours,
  8395  Steams, or Effluvia, arising from the Atmospheres of the Earth, Planets,
  8396  and Comets, and from such an exceedingly rare Æthereal Medium as we
  8397  described above. A dense Fluid can be of no use for explaining the
  8398  Phænomena of Nature, the Motions of the Planets and Comets being better
  8399  explain'd without it. It serves only to disturb and retard the Motions
  8400  of those great Bodies, and make the Frame of Nature languish: And in the
  8401  Pores of Bodies, it serves only to stop the vibrating Motions of their
  8402  Parts, wherein their Heat and Activity consists. And as it is of no use,
  8403  and hinders the Operations of Nature, and makes her languish, so there
  8404  is no evidence for its Existence, and therefore it ought to be rejected.
  8405  And if it be rejected, the Hypotheses that Light consists in Pression
  8406  or Motion, propagated through such a Medium, are rejected with it.
  8408  And for rejecting such a Medium, we have the Authority of those the
  8409  oldest and most celebrated Philosophers of _Greece_ and _Phoenicia_,
  8410  who made a _Vacuum_, and Atoms, and the Gravity of Atoms, the first
  8411  Principles of their Philosophy; tacitly attributing Gravity to some
  8412  other Cause than dense Matter. Later Philosophers banish the
  8413  Consideration of such a Cause out of natural Philosophy, feigning
  8414  Hypotheses for explaining all things mechanically, and referring other
  8415  Causes to Metaphysicks: Whereas the main Business of natural Philosophy
  8416  is to argue from Phænomena without feigning Hypotheses, and to deduce
  8417  Causes from Effects, till we come to the very first Cause, which
  8418  certainly is not mechanical; and not only to unfold the Mechanism of the
  8419  World, but chiefly to resolve these and such like Questions. What is
  8420  there in places almost empty of Matter, and whence is it that the Sun
  8421  and Planets gravitate towards one another, without dense Matter between
  8422  them? Whence is it that Nature doth nothing in vain; and whence arises
  8423  all that Order and Beauty which we see in the World? To what end are
  8424  Comets, and whence is it that Planets move all one and the same way in
  8425  Orbs concentrick, while Comets move all manner of ways in Orbs very
  8426  excentrick; and what hinders the fix'd Stars from falling upon one
  8427  another? How came the Bodies of Animals to be contrived with so much
  8428  Art, and for what ends were their several Parts? Was the Eye contrived
  8429  without Skill in Opticks, and the Ear without Knowledge of Sounds? How
  8430  do the Motions of the Body follow from the Will, and whence is the
  8431  Instinct in Animals? Is not the Sensory of Animals that place to which
  8432  the sensitive Substance is present, and into which the sensible Species
  8433  of Things are carried through the Nerves and Brain, that there they may
  8434  be perceived by their immediate presence to that Substance? And these
  8435  things being rightly dispatch'd, does it not appear from Phænomena that
  8436  there is a Being incorporeal, living, intelligent, omnipresent, who in
  8437  infinite Space, as it were in his Sensory, sees the things themselves
  8438  intimately, and throughly perceives them, and comprehends them wholly by
  8439  their immediate presence to himself: Of which things the Images only
  8440  carried through the Organs of Sense into our little Sensoriums, are
  8441  there seen and beheld by that which in us perceives and thinks. And
  8442  though every true Step made in this Philosophy brings us not immediately
  8443  to the Knowledge of the first Cause, yet it brings us nearer to it, and
  8444  on that account is to be highly valued.
  8446  _Qu._ 29. Are not the Rays of Light very small Bodies emitted from
  8447  shining Substances? For such Bodies will pass through uniform Mediums in
  8448  right Lines without bending into the Shadow, which is the Nature of the
  8449  Rays of Light. They will also be capable of several Properties, and be
  8450  able to conserve their Properties unchanged in passing through several
  8451  Mediums, which is another Condition of the Rays of Light. Pellucid
  8452  Substances act upon the Rays of Light at a distance in refracting,
  8453  reflecting, and inflecting them, and the Rays mutually agitate the Parts
  8454  of those Substances at a distance for heating them; and this Action and
  8455  Re-action at a distance very much resembles an attractive Force between
  8456  Bodies. If Refraction be perform'd by Attraction of the Rays, the Sines
  8457  of Incidence must be to the Sines of Refraction in a given Proportion,
  8458  as we shew'd in our Principles of Philosophy: And this Rule is true by
  8459  Experience. The Rays of Light in going out of Glass into a _Vacuum_, are
  8460  bent towards the Glass; and if they fall too obliquely on the _Vacuum_,
  8461  they are bent backwards into the Glass, and totally reflected; and this
  8462  Reflexion cannot be ascribed to the Resistance of an absolute _Vacuum_,
  8463  but must be caused by the Power of the Glass attracting the Rays at
  8464  their going out of it into the _Vacuum_, and bringing them back. For if
  8465  the farther Surface of the Glass be moisten'd with Water or clear Oil,
  8466  or liquid and clear Honey, the Rays which would otherwise be reflected
  8467  will go into the Water, Oil, or Honey; and therefore are not reflected
  8468  before they arrive at the farther Surface of the Glass, and begin to go
  8469  out of it. If they go out of it into the Water, Oil, or Honey, they go
  8470  on, because the Attraction of the Glass is almost balanced and rendered
  8471  ineffectual by the contrary Attraction of the Liquor. But if they go out
  8472  of it into a _Vacuum_ which has no Attraction to balance that of the
  8473  Glass, the Attraction of the Glass either bends and refracts them, or
  8474  brings them back and reflects them. And this is still more evident by
  8475  laying together two Prisms of Glass, or two Object-glasses of very long
  8476  Telescopes, the one plane, the other a little convex, and so compressing
  8477  them that they do not fully touch, nor are too far asunder. For the
  8478  Light which falls upon the farther Surface of the first Glass where the
  8479  Interval between the Glasses is not above the ten hundred thousandth
  8480  Part of an Inch, will go through that Surface, and through the Air or
  8481  _Vacuum_ between the Glasses, and enter into the second Glass, as was
  8482  explain'd in the first, fourth, and eighth Observations of the first
  8483  Part of the second Book. But, if the second Glass be taken away, the
  8484  Light which goes out of the second Surface of the first Glass into the
  8485  Air or _Vacuum_, will not go on forwards, but turns back into the first
  8486  Glass, and is reflected; and therefore it is drawn back by the Power of
  8487  the first Glass, there being nothing else to turn it back. Nothing more
  8488  is requisite for producing all the variety of Colours, and degrees of
  8489  Refrangibility, than that the Rays of Light be Bodies of different
  8490  Sizes, the least of which may take violet the weakest and darkest of the
  8491  Colours, and be more easily diverted by refracting Surfaces from the
  8492  right Course; and the rest as they are bigger and bigger, may make the
  8493  stronger and more lucid Colours, blue, green, yellow, and red, and be
  8494  more and more difficultly diverted. Nothing more is requisite for
  8495  putting the Rays of Light into Fits of easy Reflexion and easy
  8496  Transmission, than that they be small Bodies which by their attractive
  8497  Powers, or some other Force, stir up Vibrations in what they act upon,
  8498  which Vibrations being swifter than the Rays, overtake them
  8499  successively, and agitate them so as by turns to increase and decrease
  8500  their Velocities, and thereby put them into those Fits. And lastly, the
  8501  unusual Refraction of Island-Crystal looks very much as if it were
  8502  perform'd by some kind of attractive virtue lodged in certain Sides both
  8503  of the Rays, and of the Particles of the Crystal. For were it not for
  8504  some kind of Disposition or Virtue lodged in some Sides of the Particles
  8505  of the Crystal, and not in their other Sides, and which inclines and
  8506  bends the Rays towards the Coast of unusual Refraction, the Rays which
  8507  fall perpendicularly on the Crystal, would not be refracted towards that
  8508  Coast rather than towards any other Coast, both at their Incidence and
  8509  at their Emergence, so as to emerge perpendicularly by a contrary
  8510  Situation of the Coast of unusual Refraction at the second Surface; the
  8511  Crystal acting upon the Rays after they have pass'd through it, and are
  8512  emerging into the Air; or, if you please, into a _Vacuum_. And since the
  8513  Crystal by this Disposition or Virtue does not act upon the Rays, unless
  8514  when one of their Sides of unusual Refraction looks towards that Coast,
  8515  this argues a Virtue or Disposition in those Sides of the Rays, which
  8516  answers to, and sympathizes with that Virtue or Disposition of the
  8517  Crystal, as the Poles of two Magnets answer to one another. And as
  8518  Magnetism may be intended and remitted, and is found only in the Magnet
  8519  and in Iron: So this Virtue of refracting the perpendicular Rays is
  8520  greater in Island-Crystal, less in Crystal of the Rock, and is not yet
  8521  found in other Bodies. I do not say that this Virtue is magnetical: It
  8522  seems to be of another kind. I only say, that whatever it be, it's
  8523  difficult to conceive how the Rays of Light, unless they be Bodies, can
  8524  have a permanent Virtue in two of their Sides which is not in their
  8525  other Sides, and this without any regard to their Position to the Space
  8526  or Medium through which they pass.
  8528  What I mean in this Question by a _Vacuum_, and by the Attractions of
  8529  the Rays of Light towards Glass or Crystal, may be understood by what
  8530  was said in the 18th, 19th, and 20th Questions.
  8532  _Quest._ 30. Are not gross Bodies and Light convertible into one
  8533  another, and may not Bodies receive much of their Activity from the
  8534  Particles of Light which enter their Composition? For all fix'd Bodies
  8535  being heated emit Light so long as they continue sufficiently hot, and
  8536  Light mutually stops in Bodies as often as its Rays strike upon their
  8537  Parts, as we shew'd above. I know no Body less apt to shine than Water;
  8538  and yet Water by frequent Distillations changes into fix'd Earth, as Mr.
  8539  _Boyle_ has try'd; and then this Earth being enabled to endure a
  8540  sufficient Heat, shines by Heat like other Bodies.
  8542  The changing of Bodies into Light, and Light into Bodies, is very
  8543  conformable to the Course of Nature, which seems delighted with
  8544  Transmutations. Water, which is a very fluid tasteless Salt, she changes
  8545  by Heat into Vapour, which is a sort of Air, and by Cold into Ice, which
  8546  is a hard, pellucid, brittle, fusible Stone; and this Stone returns into
  8547  Water by Heat, and Vapour returns into Water by Cold. Earth by Heat
  8548  becomes Fire, and by Cold returns into Earth. Dense Bodies by
  8549  Fermentation rarify into several sorts of Air, and this Air by
  8550  Fermentation, and sometimes without it, returns into dense Bodies.
  8551  Mercury appears sometimes in the form of a fluid Metal, sometimes in the
  8552  form of a hard brittle Metal, sometimes in the form of a corrosive
  8553  pellucid Salt call'd Sublimate, sometimes in the form of a tasteless,
  8554  pellucid, volatile white Earth, call'd _Mercurius Dulcis_; or in that of
  8555  a red opake volatile Earth, call'd Cinnaber; or in that of a red or
  8556  white Precipitate, or in that of a fluid Salt; and in Distillation it
  8557  turns into Vapour, and being agitated _in Vacuo_, it shines like Fire.
  8558  And after all these Changes it returns again into its first form of
  8559  Mercury. Eggs grow from insensible Magnitudes, and change into Animals;
  8560  Tadpoles into Frogs; and Worms into Flies. All Birds, Beasts and Fishes,
  8561  Insects, Trees, and other Vegetables, with their several Parts, grow out
  8562  of Water and watry Tinctures and Salts, and by Putrefaction return again
  8563  into watry Substances. And Water standing a few Days in the open Air,
  8564  yields a Tincture, which (like that of Malt) by standing longer yields a
  8565  Sediment and a Spirit, but before Putrefaction is fit Nourishment for
  8566  Animals and Vegetables. And among such various and strange
  8567  Transmutations, why may not Nature change Bodies into Light, and Light
  8568  into Bodies?
  8570  _Quest._ 31. Have not the small Particles of Bodies certain Powers,
  8571  Virtues, or Forces, by which they act at a distance, not only upon the
  8572  Rays of Light for reflecting, refracting, and inflecting them, but also
  8573  upon one another for producing a great Part of the Phænomena of Nature?
  8574  For it's well known, that Bodies act one upon another by the Attractions
  8575  of Gravity, Magnetism, and Electricity; and these Instances shew the
  8576  Tenor and Course of Nature, and make it not improbable but that there
  8577  may be more attractive Powers than these. For Nature is very consonant
  8578  and conformable to her self. How these Attractions may be perform'd, I
  8579  do not here consider. What I call Attraction may be perform'd by
  8580  impulse, or by some other means unknown to me. I use that Word here to
  8581  signify only in general any Force by which Bodies tend towards one
  8582  another, whatsoever be the Cause. For we must learn from the Phænomena
  8583  of Nature what Bodies attract one another, and what are the Laws and
  8584  Properties of the Attraction, before we enquire the Cause by which the
  8585  Attraction is perform'd. The Attractions of Gravity, Magnetism, and
  8586  Electricity, reach to very sensible distances, and so have been observed
  8587  by vulgar Eyes, and there may be others which reach to so small
  8588  distances as hitherto escape Observation; and perhaps electrical
  8589  Attraction may reach to such small distances, even without being excited
  8590  by Friction.
  8592  For when Salt of Tartar runs _per Deliquium_, is not this done by an
  8593  Attraction between the Particles of the Salt of Tartar, and the
  8594  Particles of the Water which float in the Air in the form of Vapours?
  8595  And why does not common Salt, or Salt-petre, or Vitriol, run _per
  8596  Deliquium_, but for want of such an Attraction? Or why does not Salt of
  8597  Tartar draw more Water out of the Air than in a certain Proportion to
  8598  its quantity, but for want of an attractive Force after it is satiated
  8599  with Water? And whence is it but from this attractive Power that Water
  8600  which alone distils with a gentle luke-warm Heat, will not distil from
  8601  Salt of Tartar without a great Heat? And is it not from the like
  8602  attractive Power between the Particles of Oil of Vitriol and the
  8603  Particles of Water, that Oil of Vitriol draws to it a good quantity of
  8604  Water out of the Air, and after it is satiated draws no more, and in
  8605  Distillation lets go the Water very difficultly? And when Water and Oil
  8606  of Vitriol poured successively into the same Vessel grow very hot in the
  8607  mixing, does not this Heat argue a great Motion in the Parts of the
  8608  Liquors? And does not this Motion argue, that the Parts of the two
  8609  Liquors in mixing coalesce with Violence, and by consequence rush
  8610  towards one another with an accelerated Motion? And when _Aqua fortis_,
  8611  or Spirit of Vitriol poured upon Filings of Iron dissolves the Filings
  8612  with a great Heat and Ebullition, is not this Heat and Ebullition
  8613  effected by a violent Motion of the Parts, and does not that Motion
  8614  argue that the acid Parts of the Liquor rush towards the Parts of the
  8615  Metal with violence, and run forcibly into its Pores till they get
  8616  between its outmost Particles, and the main Mass of the Metal, and
  8617  surrounding those Particles loosen them from the main Mass, and set them
  8618  at liberty to float off into the Water? And when the acid Particles,
  8619  which alone would distil with an easy Heat, will not separate from the
  8620  Particles of the Metal without a very violent Heat, does not this
  8621  confirm the Attraction between them?
  8623  When Spirit of Vitriol poured upon common Salt or Salt-petre makes an
  8624  Ebullition with the Salt, and unites with it, and in Distillation the
  8625  Spirit of the common Salt or Salt-petre comes over much easier than it
  8626  would do before, and the acid part of the Spirit of Vitriol stays
  8627  behind; does not this argue that the fix'd Alcaly of the Salt attracts
  8628  the acid Spirit of the Vitriol more strongly than its own Spirit, and
  8629  not being able to hold them both, lets go its own? And when Oil of
  8630  Vitriol is drawn off from its weight of Nitre, and from both the
  8631  Ingredients a compound Spirit of Nitre is distilled, and two parts of
  8632  this Spirit are poured on one part of Oil of Cloves or Carraway Seeds,
  8633  or of any ponderous Oil of vegetable or animal Substances, or Oil of
  8634  Turpentine thicken'd with a little Balsam of Sulphur, and the Liquors
  8635  grow so very hot in mixing, as presently to send up a burning Flame;
  8636  does not this very great and sudden Heat argue that the two Liquors mix
  8637  with violence, and that their Parts in mixing run towards one another
  8638  with an accelerated Motion, and clash with the greatest Force? And is it
  8639  not for the same reason that well rectified Spirit of Wine poured on the
  8640  same compound Spirit flashes; and that the _Pulvis fulminans_, composed
  8641  of Sulphur, Nitre, and Salt of Tartar, goes off with a more sudden and
  8642  violent Explosion than Gun-powder, the acid Spirits of the Sulphur and
  8643  Nitre rushing towards one another, and towards the Salt of Tartar, with
  8644  so great a violence, as by the shock to turn the whole at once into
  8645  Vapour and Flame? Where the Dissolution is slow, it makes a slow
  8646  Ebullition and a gentle Heat; and where it is quicker, it makes a
  8647  greater Ebullition with more heat; and where it is done at once, the
  8648  Ebullition is contracted into a sudden Blast or violent Explosion, with
  8649  a heat equal to that of Fire and Flame. So when a Drachm of the
  8650  above-mention'd compound Spirit of Nitre was poured upon half a Drachm
  8651  of Oil of Carraway Seeds _in vacuo_, the Mixture immediately made a
  8652  flash like Gun-powder, and burst the exhausted Receiver, which was a
  8653  Glass six Inches wide, and eight Inches deep. And even the gross Body of
  8654  Sulphur powder'd, and with an equal weight of Iron Filings and a little
  8655  Water made into Paste, acts upon the Iron, and in five or six hours
  8656  grows too hot to be touch'd, and emits a Flame. And by these Experiments
  8657  compared with the great quantity of Sulphur with which the Earth
  8658  abounds, and the warmth of the interior Parts of the Earth, and hot
  8659  Springs, and burning Mountains, and with Damps, mineral Coruscations,
  8660  Earthquakes, hot suffocating Exhalations, Hurricanes, and Spouts; we may
  8661  learn that sulphureous Steams abound in the Bowels of the Earth and
  8662  ferment with Minerals, and sometimes take fire with a sudden Coruscation
  8663  and Explosion; and if pent up in subterraneous Caverns, burst the
  8664  Caverns with a great shaking of the Earth, as in springing of a Mine.
  8665  And then the Vapour generated by the Explosion, expiring through the
  8666  Pores of the Earth, feels hot and suffocates, and makes Tempests and
  8667  Hurricanes, and sometimes causes the Land to slide, or the Sea to boil,
  8668  and carries up the Water thereof in Drops, which by their weight fall
  8669  down again in Spouts. Also some sulphureous Steams, at all times when
  8670  the Earth is dry, ascending into the Air, ferment there with nitrous
  8671  Acids, and sometimes taking fire cause Lightning and Thunder, and fiery
  8672  Meteors. For the Air abounds with acid Vapours fit to promote
  8673  Fermentations, as appears by the rusting of Iron and Copper in it, the
  8674  kindling of Fire by blowing, and the beating of the Heart by means of
  8675  Respiration. Now the above-mention'd Motions are so great and violent as
  8676  to shew that in Fermentations the Particles of Bodies which almost rest,
  8677  are put into new Motions by a very potent Principle, which acts upon
  8678  them only when they approach one another, and causes them to meet and
  8679  clash with great violence, and grow hot with the motion, and dash one
  8680  another into pieces, and vanish into Air, and Vapour, and Flame.
  8682  When Salt of Tartar _per deliquium_, being poured into the Solution of
  8683  any Metal, precipitates the Metal and makes it fall down to the bottom
  8684  of the Liquor in the form of Mud: Does not this argue that the acid
  8685  Particles are attracted more strongly by the Salt of Tartar than by the
  8686  Metal, and by the stronger Attraction go from the Metal to the Salt of
  8687  Tartar? And so when a Solution of Iron in _Aqua fortis_ dissolves the
  8688  _Lapis Calaminaris_, and lets go the Iron, or a Solution of Copper
  8689  dissolves Iron immersed in it and lets go the Copper, or a Solution of
  8690  Silver dissolves Copper and lets go the Silver, or a Solution of Mercury
  8691  in _Aqua fortis_ being poured upon Iron, Copper, Tin, or Lead, dissolves
  8692  the Metal and lets go the Mercury; does not this argue that the acid
  8693  Particles of the _Aqua fortis_ are attracted more strongly by the _Lapis
  8694  Calaminaris_ than by Iron, and more strongly by Iron than by Copper, and
  8695  more strongly by Copper than by Silver, and more strongly by Iron,
  8696  Copper, Tin, and Lead, than by Mercury? And is it not for the same
  8697  reason that Iron requires more _Aqua fortis_ to dissolve it than Copper,
  8698  and Copper more than the other Metals; and that of all Metals, Iron is
  8699  dissolved most easily, and is most apt to rust; and next after Iron,
  8700  Copper?
  8702  When Oil of Vitriol is mix'd with a little Water, or is run _per
  8703  deliquium_, and in Distillation the Water ascends difficultly, and
  8704  brings over with it some part of the Oil of Vitriol in the form of
  8705  Spirit of Vitriol, and this Spirit being poured upon Iron, Copper, or
  8706  Salt of Tartar, unites with the Body and lets go the Water; doth not
  8707  this shew that the acid Spirit is attracted by the Water, and more
  8708  attracted by the fix'd Body than by the Water, and therefore lets go the
  8709  Water to close with the fix'd Body? And is it not for the same reason
  8710  that the Water and acid Spirits which are mix'd together in Vinegar,
  8711  _Aqua fortis_, and Spirit of Salt, cohere and rise together in
  8712  Distillation; but if the _Menstruum_ be poured on Salt of Tartar, or on
  8713  Lead, or Iron, or any fix'd Body which it can dissolve, the Acid by a
  8714  stronger Attraction adheres to the Body, and lets go the Water? And is
  8715  it not also from a mutual Attraction that the Spirits of Soot and
  8716  Sea-Salt unite and compose the Particles of Sal-armoniac, which are less
  8717  volatile than before, because grosser and freer from Water; and that the
  8718  Particles of Sal-armoniac in Sublimation carry up the Particles of
  8719  Antimony, which will not sublime alone; and that the Particles of
  8720  Mercury uniting with the acid Particles of Spirit of Salt compose
  8721  Mercury sublimate, and with the Particles of Sulphur, compose Cinnaber;
  8722  and that the Particles of Spirit of Wine and Spirit of Urine well
  8723  rectified unite, and letting go the Water which dissolved them, compose
  8724  a consistent Body; and that in subliming Cinnaber from Salt of Tartar,
  8725  or from quick Lime, the Sulphur by a stronger Attraction of the Salt or
  8726  Lime lets go the Mercury, and stays with the fix'd Body; and that when
  8727  Mercury sublimate is sublimed from Antimony, or from Regulus of
  8728  Antimony, the Spirit of Salt lets go the Mercury, and unites with the
  8729  antimonial metal which attracts it more strongly, and stays with it till
  8730  the Heat be great enough to make them both ascend together, and then
  8731  carries up the Metal with it in the form of a very fusible Salt, called
  8732  Butter of Antimony, although the Spirit of Salt alone be almost as
  8733  volatile as Water, and the Antimony alone as fix'd as Lead?
  8735  When _Aqua fortis_ dissolves Silver and not Gold, and _Aqua regia_
  8736  dissolves Gold and not Silver, may it not be said that _Aqua fortis_ is
  8737  subtil enough to penetrate Gold as well as Silver, but wants the
  8738  attractive Force to give it Entrance; and that _Aqua regia_ is subtil
  8739  enough to penetrate Silver as well as Gold, but wants the attractive
  8740  Force to give it Entrance? For _Aqua regia_ is nothing else than _Aqua
  8741  fortis_ mix'd with some Spirit of Salt, or with Sal-armoniac; and even
  8742  common Salt dissolved in _Aqua fortis_, enables the _Menstruum_ to
  8743  dissolve Gold, though the Salt be a gross Body. When therefore Spirit of
  8744  Salt precipitates Silver out of _Aqua fortis_, is it not done by
  8745  attracting and mixing with the _Aqua fortis_, and not attracting, or
  8746  perhaps repelling Silver? And when Water precipitates Antimony out of
  8747  the Sublimate of Antimony and Sal-armoniac, or out of Butter of
  8748  Antimony, is it not done by its dissolving, mixing with, and weakening
  8749  the Sal-armoniac or Spirit of Salt, and its not attracting, or perhaps
  8750  repelling the Antimony? And is it not for want of an attractive virtue
  8751  between the Parts of Water and Oil, of Quick-silver and Antimony, of
  8752  Lead and Iron, that these Substances do not mix; and by a weak
  8753  Attraction, that Quick-silver and Copper mix difficultly; and from a
  8754  strong one, that Quick-silver and Tin, Antimony and Iron, Water and
  8755  Salts, mix readily? And in general, is it not from the same Principle
  8756  that Heat congregates homogeneal Bodies, and separates heterogeneal
  8757  ones?
  8759  When Arsenick with Soap gives a Regulus, and with Mercury sublimate a
  8760  volatile fusible Salt, like Butter of Antimony, doth not this shew that
  8761  Arsenick, which is a Substance totally volatile, is compounded of fix'd
  8762  and volatile Parts, strongly cohering by a mutual Attraction, so that
  8763  the volatile will not ascend without carrying up the fixed? And so, when
  8764  an equal weight of Spirit of Wine and Oil of Vitriol are digested
  8765  together, and in Distillation yield two fragrant and volatile Spirits
  8766  which will not mix with one another, and a fix'd black Earth remains
  8767  behind; doth not this shew that Oil of Vitriol is composed of volatile
  8768  and fix'd Parts strongly united by Attraction, so as to ascend together
  8769  in form of a volatile, acid, fluid Salt, until the Spirit of Wine
  8770  attracts and separates the volatile Parts from the fixed? And therefore,
  8771  since Oil of Sulphur _per Campanam_ is of the same Nature with Oil of
  8772  Vitriol, may it not be inferred, that Sulphur is also a mixture of
  8773  volatile and fix'd Parts so strongly cohering by Attraction, as to
  8774  ascend together in Sublimation. By dissolving Flowers of Sulphur in Oil
  8775  of Turpentine, and distilling the Solution, it is found that Sulphur is
  8776  composed of an inflamable thick Oil or fat Bitumen, an acid Salt, a very
  8777  fix'd Earth, and a little Metal. The three first were found not much
  8778  unequal to one another, the fourth in so small a quantity as scarce to
  8779  be worth considering. The acid Salt dissolved in Water, is the same with
  8780  Oil of Sulphur _per Campanam_, and abounding much in the Bowels of the
  8781  Earth, and particularly in Markasites, unites it self to the other
  8782  Ingredients of the Markasite, which are, Bitumen, Iron, Copper, and
  8783  Earth, and with them compounds Allum, Vitriol, and Sulphur. With the
  8784  Earth alone it compounds Allum; with the Metal alone, or Metal and
  8785  Earth together, it compounds Vitriol; and with the Bitumen and Earth it
  8786  compounds Sulphur. Whence it comes to pass that Markasites abound with
  8787  those three Minerals. And is it not from the mutual Attraction of the
  8788  Ingredients that they stick together for compounding these Minerals, and
  8789  that the Bitumen carries up the other Ingredients of the Sulphur, which
  8790  without it would not sublime? And the same Question may be put
  8791  concerning all, or almost all the gross Bodies in Nature. For all the
  8792  Parts of Animals and Vegetables are composed of Substances volatile and
  8793  fix'd, fluid and solid, as appears by their Analysis; and so are Salts
  8794  and Minerals, so far as Chymists have been hitherto able to examine
  8795  their Composition.
  8797  When Mercury sublimate is re-sublimed with fresh Mercury, and becomes
  8798  _Mercurius Dulcis_, which is a white tasteless Earth scarce dissolvable
  8799  in Water, and _Mercurius Dulcis_ re-sublimed with Spirit of Salt returns
  8800  into Mercury sublimate; and when Metals corroded with a little acid turn
  8801  into rust, which is an Earth tasteless and indissolvable in Water, and
  8802  this Earth imbibed with more acid becomes a metallick Salt; and when
  8803  some Stones, as Spar of Lead, dissolved in proper _Menstruums_ become
  8804  Salts; do not these things shew that Salts are dry Earth and watry Acid
  8805  united by Attraction, and that the Earth will not become a Salt without
  8806  so much acid as makes it dissolvable in Water? Do not the sharp and
  8807  pungent Tastes of Acids arise from the strong Attraction whereby the
  8808  acid Particles rush upon and agitate the Particles of the Tongue? And
  8809  when Metals are dissolved in acid _Menstruums_, and the Acids in
  8810  conjunction with the Metal act after a different manner, so that the
  8811  Compound has a different Taste much milder than before, and sometimes a
  8812  sweet one; is it not because the Acids adhere to the metallick
  8813  Particles, and thereby lose much of their Activity? And if the Acid be
  8814  in too small a Proportion to make the Compound dissolvable in Water,
  8815  will it not by adhering strongly to the Metal become unactive and lose
  8816  its Taste, and the Compound be a tasteless Earth? For such things as are
  8817  not dissolvable by the Moisture of the Tongue, act not upon the Taste.
  8819  As Gravity makes the Sea flow round the denser and weightier Parts of
  8820  the Globe of the Earth, so the Attraction may make the watry Acid flow
  8821  round the denser and compacter Particles of Earth for composing the
  8822  Particles of Salt. For otherwise the Acid would not do the Office of a
  8823  Medium between the Earth and common Water, for making Salts dissolvable
  8824  in the Water; nor would Salt of Tartar readily draw off the Acid from
  8825  dissolved Metals, nor Metals the Acid from Mercury. Now, as in the great
  8826  Globe of the Earth and Sea, the densest Bodies by their Gravity sink
  8827  down in Water, and always endeavour to go towards the Center of the
  8828  Globe; so in Particles of Salt, the densest Matter may always endeavour
  8829  to approach the Center of the Particle: So that a Particle of Salt may
  8830  be compared to a Chaos; being dense, hard, dry, and earthy in the
  8831  Center; and rare, soft, moist, and watry in the Circumference. And
  8832  hence it seems to be that Salts are of a lasting Nature, being scarce
  8833  destroy'd, unless by drawing away their watry Parts by violence, or by
  8834  letting them soak into the Pores of the central Earth by a gentle Heat
  8835  in Putrefaction, until the Earth be dissolved by the Water, and
  8836  separated into smaller Particles, which by reason of their Smallness
  8837  make the rotten Compound appear of a black Colour. Hence also it may be,
  8838  that the Parts of Animals and Vegetables preserve their several Forms,
  8839  and assimilate their Nourishment; the soft and moist Nourishment easily
  8840  changing its Texture by a gentle Heat and Motion, till it becomes like
  8841  the dense, hard, dry, and durable Earth in the Center of each Particle.
  8842  But when the Nourishment grows unfit to be assimilated, or the central
  8843  Earth grows too feeble to assimilate it, the Motion ends in Confusion,
  8844  Putrefaction, and Death.
  8846  If a very small quantity of any Salt or Vitriol be dissolved in a great
  8847  quantity of Water, the Particles of the Salt or Vitriol will not sink to
  8848  the bottom, though they be heavier in Specie than the Water, but will
  8849  evenly diffuse themselves into all the Water, so as to make it as saline
  8850  at the top as at the bottom. And does not this imply that the Parts of
  8851  the Salt or Vitriol recede from one another, and endeavour to expand
  8852  themselves, and get as far asunder as the quantity of Water in which
  8853  they float, will allow? And does not this Endeavour imply that they have
  8854  a repulsive Force by which they fly from one another, or at least, that
  8855  they attract the Water more strongly than they do one another? For as
  8856  all things ascend in Water which are less attracted than Water, by the
  8857  gravitating Power of the Earth; so all the Particles of Salt which float
  8858  in Water, and are less attracted than Water by any one Particle of Salt,
  8859  must recede from that Particle, and give way to the more attracted
  8860  Water.
  8862  When any saline Liquor is evaporated to a Cuticle and let cool, the Salt
  8863  concretes in regular Figures; which argues, that the Particles of the
  8864  Salt before they concreted, floated in the Liquor at equal distances in
  8865  rank and file, and by consequence that they acted upon one another by
  8866  some Power which at equal distances is equal, at unequal distances
  8867  unequal. For by such a Power they will range themselves uniformly, and
  8868  without it they will float irregularly, and come together as
  8869  irregularly. And since the Particles of Island-Crystal act all the same
  8870  way upon the Rays of Light for causing the unusual Refraction, may it
  8871  not be supposed that in the Formation of this Crystal, the Particles not
  8872  only ranged themselves in rank and file for concreting in regular
  8873  Figures, but also by some kind of polar Virtue turned their homogeneal
  8874  Sides the same way.
  8876  The Parts of all homogeneal hard Bodies which fully touch one another,
  8877  stick together very strongly. And for explaining how this may be, some
  8878  have invented hooked Atoms, which is begging the Question; and others
  8879  tell us that Bodies are glued together by rest, that is, by an occult
  8880  Quality, or rather by nothing; and others, that they stick together by
  8881  conspiring Motions, that is, by relative rest amongst themselves. I had
  8882  rather infer from their Cohesion, that their Particles attract one
  8883  another by some Force, which in immediate Contact is exceeding strong,
  8884  at small distances performs the chymical Operations above-mention'd, and
  8885  reaches not far from the Particles with any sensible Effect.
  8887  All Bodies seem to be composed of hard Particles: For otherwise Fluids
  8888  would not congeal; as Water, Oils, Vinegar, and Spirit or Oil of Vitriol
  8889  do by freezing; Mercury by Fumes of Lead; Spirit of Nitre and Mercury,
  8890  by dissolving the Mercury and evaporating the Flegm; Spirit of Wine and
  8891  Spirit of Urine, by deflegming and mixing them; and Spirit of Urine and
  8892  Spirit of Salt, by subliming them together to make Sal-armoniac. Even
  8893  the Rays of Light seem to be hard Bodies; for otherwise they would not
  8894  retain different Properties in their different Sides. And therefore
  8895  Hardness may be reckon'd the Property of all uncompounded Matter. At
  8896  least, this seems to be as evident as the universal Impenetrability of
  8897  Matter. For all Bodies, so far as Experience reaches, are either hard,
  8898  or may be harden'd; and we have no other Evidence of universal
  8899  Impenetrability, besides a large Experience without an experimental
  8900  Exception. Now if compound Bodies are so very hard as we find some of
  8901  them to be, and yet are very porous, and consist of Parts which are only
  8902  laid together; the simple Particles which are void of Pores, and were
  8903  never yet divided, must be much harder. For such hard Particles being
  8904  heaped up together, can scarce touch one another in more than a few
  8905  Points, and therefore must be separable by much less Force than is
  8906  requisite to break a solid Particle, whose Parts touch in all the Space
  8907  between them, without any Pores or Interstices to weaken their Cohesion.
  8908  And how such very hard Particles which are only laid together and touch
  8909  only in a few Points, can stick together, and that so firmly as they do,
  8910  without the assistance of something which causes them to be attracted or
  8911  press'd towards one another, is very difficult to conceive.
  8913  The same thing I infer also from the cohering of two polish'd Marbles
  8914  _in vacuo_, and from the standing of Quick-silver in the Barometer at
  8915  the height of 50, 60 or 70 Inches, or above, when ever it is well-purged
  8916  of Air and carefully poured in, so that its Parts be every where
  8917  contiguous both to one another and to the Glass. The Atmosphere by its
  8918  weight presses the Quick-silver into the Glass, to the height of 29 or
  8919  30 Inches. And some other Agent raises it higher, not by pressing it
  8920  into the Glass, but by making its Parts stick to the Glass, and to one
  8921  another. For upon any discontinuation of Parts, made either by Bubbles
  8922  or by shaking the Glass, the whole Mercury falls down to the height of
  8923  29 or 30 Inches.
  8925  And of the same kind with these Experiments are those that follow. If
  8926  two plane polish'd Plates of Glass (suppose two pieces of a polish'd
  8927  Looking-glass) be laid together, so that their sides be parallel and at
  8928  a very small distance from one another, and then their lower edges be
  8929  dipped into Water, the Water will rise up between them. And the less
  8930  the distance of the Glasses is, the greater will be the height to which
  8931  the Water will rise. If the distance be about the hundredth part of an
  8932  Inch, the Water will rise to the height of about an Inch; and if the
  8933  distance be greater or less in any Proportion, the height will be
  8934  reciprocally proportional to the distance very nearly. For the
  8935  attractive Force of the Glasses is the same, whether the distance
  8936  between them be greater or less; and the weight of the Water drawn up is
  8937  the same, if the height of it be reciprocally proportional to the
  8938  distance of the Glasses. And in like manner, Water ascends between two
  8939  Marbles polish'd plane, when their polish'd sides are parallel, and at a
  8940  very little distance from one another, And if slender Pipes of Glass be
  8941  dipped at one end into stagnating Water, the Water will rise up within
  8942  the Pipe, and the height to which it rises will be reciprocally
  8943  proportional to the Diameter of the Cavity of the Pipe, and will equal
  8944  the height to which it rises between two Planes of Glass, if the
  8945  Semi-diameter of the Cavity of the Pipe be equal to the distance between
  8946  the Planes, or thereabouts. And these Experiments succeed after the same
  8947  manner _in vacuo_ as in the open Air, (as hath been tried before the
  8948  Royal Society,) and therefore are not influenced by the Weight or
  8949  Pressure of the Atmosphere.
  8951  And if a large Pipe of Glass be filled with sifted Ashes well pressed
  8952  together in the Glass, and one end of the Pipe be dipped into stagnating
  8953  Water, the Water will rise up slowly in the Ashes, so as in the space
  8954  of a Week or Fortnight to reach up within the Glass, to the height of 30
  8955  or 40 Inches above the stagnating Water. And the Water rises up to this
  8956  height by the Action only of those Particles of the Ashes which are upon
  8957  the Surface of the elevated Water; the Particles which are within the
  8958  Water, attracting or repelling it as much downwards as upwards. And
  8959  therefore the Action of the Particles is very strong. But the Particles
  8960  of the Ashes being not so dense and close together as those of Glass,
  8961  their Action is not so strong as that of Glass, which keeps Quick-silver
  8962  suspended to the height of 60 or 70 Inches, and therefore acts with a
  8963  Force which would keep Water suspended to the height of above 60 Feet.
  8965  By the same Principle, a Sponge sucks in Water, and the Glands in the
  8966  Bodies of Animals, according to their several Natures and Dispositions,
  8967  suck in various Juices from the Blood.
  8969  If two plane polish'd Plates of Glass three or four Inches broad, and
  8970  twenty or twenty five long, be laid one of them parallel to the Horizon,
  8971  the other upon the first, so as at one of their ends to touch one
  8972  another, and contain an Angle of about 10 or 15 Minutes, and the same be
  8973  first moisten'd on their inward sides with a clean Cloth dipp'd into Oil
  8974  of Oranges or Spirit of Turpentine, and a Drop or two of the Oil or
  8975  Spirit be let fall upon the lower Glass at the other; so soon as the
  8976  upper Glass is laid down upon the lower, so as to touch it at one end as
  8977  above, and to touch the Drop at the other end, making with the lower
  8978  Glass an Angle of about 10 or 15 Minutes; the Drop will begin to move
  8979  towards the Concourse of the Glasses, and will continue to move with an
  8980  accelerated Motion, till it arrives at that Concourse of the Glasses.
  8981  For the two Glasses attract the Drop, and make it run that way towards
  8982  which the Attractions incline. And if when the Drop is in motion you
  8983  lift up that end of the Glasses where they meet, and towards which the
  8984  Drop moves, the Drop will ascend between the Glasses, and therefore is
  8985  attracted. And as you lift up the Glasses more and more, the Drop will
  8986  ascend slower and slower, and at length rest, being then carried
  8987  downward by its Weight, as much as upwards by the Attraction. And by
  8988  this means you may know the Force by which the Drop is attracted at all
  8989  distances from the Concourse of the Glasses.
  8991  Now by some Experiments of this kind, (made by Mr. _Hauksbee_) it has
  8992  been found that the Attraction is almost reciprocally in a duplicate
  8993  Proportion of the distance of the middle of the Drop from the Concourse
  8994  of the Glasses, _viz._ reciprocally in a simple Proportion, by reason of
  8995  the spreading of the Drop, and its touching each Glass in a larger
  8996  Surface; and again reciprocally in a simple Proportion, by reason of the
  8997  Attractions growing stronger within the same quantity of attracting
  8998  Surface. The Attraction therefore within the same quantity of attracting
  8999  Surface, is reciprocally as the distance between the Glasses. And
  9000  therefore where the distance is exceeding small, the Attraction must be
  9001  exceeding great. By the Table in the second Part of the second Book,
  9002  wherein the thicknesses of colour'd Plates of Water between two Glasses
  9003  are set down, the thickness of the Plate where it appears very black, is
  9004  three eighths of the ten hundred thousandth part of an Inch. And where
  9005  the Oil of Oranges between the Glasses is of this thickness, the
  9006  Attraction collected by the foregoing Rule, seems to be so strong, as
  9007  within a Circle of an Inch in diameter, to suffice to hold up a Weight
  9008  equal to that of a Cylinder of Water of an Inch in diameter, and two or
  9009  three Furlongs in length. And where it is of a less thickness the
  9010  Attraction may be proportionally greater, and continue to increase,
  9011  until the thickness do not exceed that of a single Particle of the Oil.
  9012  There are therefore Agents in Nature able to make the Particles of
  9013  Bodies stick together by very strong Attractions. And it is the Business
  9014  of experimental Philosophy to find them out.
  9016  Now the smallest Particles of Matter may cohere by the strongest
  9017  Attractions, and compose bigger Particles of weaker Virtue; and many of
  9018  these may cohere and compose bigger Particles whose Virtue is still
  9019  weaker, and so on for divers Successions, until the Progression end in
  9020  the biggest Particles on which the Operations in Chymistry, and the
  9021  Colours of natural Bodies depend, and which by cohering compose Bodies
  9022  of a sensible Magnitude. If the Body is compact, and bends or yields
  9023  inward to Pression without any sliding of its Parts, it is hard and
  9024  elastick, returning to its Figure with a Force rising from the mutual
  9025  Attraction of its Parts. If the Parts slide upon one another, the Body
  9026  is malleable or soft. If they slip easily, and are of a fit Size to be
  9027  agitated by Heat, and the Heat is big enough to keep them in Agitation,
  9028  the Body is fluid; and if it be apt to stick to things, it is humid; and
  9029  the Drops of every fluid affect a round Figure by the mutual Attraction
  9030  of their Parts, as the Globe of the Earth and Sea affects a round Figure
  9031  by the mutual Attraction of its Parts by Gravity.
  9033  Since Metals dissolved in Acids attract but a small quantity of the
  9034  Acid, their attractive Force can reach but to a small distance from
  9035  them. And as in Algebra, where affirmative Quantities vanish and cease,
  9036  there negative ones begin; so in Mechanicks, where Attraction ceases,
  9037  there a repulsive Virtue ought to succeed. And that there is such a
  9038  Virtue, seems to follow from the Reflexions and Inflexions of the Rays
  9039  of Light. For the Rays are repelled by Bodies in both these Cases,
  9040  without the immediate Contact of the reflecting or inflecting Body. It
  9041  seems also to follow from the Emission of Light; the Ray so soon as it
  9042  is shaken off from a shining Body by the vibrating Motion of the Parts
  9043  of the Body, and gets beyond the reach of Attraction, being driven away
  9044  with exceeding great Velocity. For that Force which is sufficient to
  9045  turn it back in Reflexion, may be sufficient to emit it. It seems also
  9046  to follow from the Production of Air and Vapour. The Particles when they
  9047  are shaken off from Bodies by Heat or Fermentation, so soon as they are
  9048  beyond the reach of the Attraction of the Body, receding from it, and
  9049  also from one another with great Strength, and keeping at a distance,
  9050  so as sometimes to take up above a Million of Times more space than they
  9051  did before in the form of a dense Body. Which vast Contraction and
  9052  Expansion seems unintelligible, by feigning the Particles of Air to be
  9053  springy and ramous, or rolled up like Hoops, or by any other means than
  9054  a repulsive Power. The Particles of Fluids which do not cohere too
  9055  strongly, and are of such a Smallness as renders them most susceptible
  9056  of those Agitations which keep Liquors in a Fluor, are most easily
  9057  separated and rarified into Vapour, and in the Language of the Chymists,
  9058  they are volatile, rarifying with an easy Heat, and condensing with
  9059  Cold. But those which are grosser, and so less susceptible of Agitation,
  9060  or cohere by a stronger Attraction, are not separated without a stronger
  9061  Heat, or perhaps not without Fermentation. And these last are the Bodies
  9062  which Chymists call fix'd, and being rarified by Fermentation, become
  9063  true permanent Air; those Particles receding from one another with the
  9064  greatest Force, and being most difficultly brought together, which upon
  9065  Contact cohere most strongly. And because the Particles of permanent Air
  9066  are grosser, and arise from denser Substances than those of Vapours,
  9067  thence it is that true Air is more ponderous than Vapour, and that a
  9068  moist Atmosphere is lighter than a dry one, quantity for quantity. From
  9069  the same repelling Power it seems to be that Flies walk upon the Water
  9070  without wetting their Feet; and that the Object-glasses of long
  9071  Telescopes lie upon one another without touching; and that dry Powders
  9072  are difficultly made to touch one another so as to stick together,
  9073  unless by melting them, or wetting them with Water, which by exhaling
  9074  may bring them together; and that two polish'd Marbles, which by
  9075  immediate Contact stick together, are difficultly brought so close
  9076  together as to stick.
  9078  And thus Nature will be very conformable to her self and very simple,
  9079  performing all the great Motions of the heavenly Bodies by the
  9080  Attraction of Gravity which intercedes those Bodies, and almost all the
  9081  small ones of their Particles by some other attractive and repelling
  9082  Powers which intercede the Particles. The _Vis inertiæ_ is a passive
  9083  Principle by which Bodies persist in their Motion or Rest, receive
  9084  Motion in proportion to the Force impressing it, and resist as much as
  9085  they are resisted. By this Principle alone there never could have been
  9086  any Motion in the World. Some other Principle was necessary for putting
  9087  Bodies into Motion; and now they are in Motion, some other Principle is
  9088  necessary for conserving the Motion. For from the various Composition of
  9089  two Motions, 'tis very certain that there is not always the same
  9090  quantity of Motion in the World. For if two Globes joined by a slender
  9091  Rod, revolve about their common Center of Gravity with an uniform
  9092  Motion, while that Center moves on uniformly in a right Line drawn in
  9093  the Plane of their circular Motion; the Sum of the Motions of the two
  9094  Globes, as often as the Globes are in the right Line described by their
  9095  common Center of Gravity, will be bigger than the Sum of their Motions,
  9096  when they are in a Line perpendicular to that right Line. By this
  9097  Instance it appears that Motion may be got or lost. But by reason of the
  9098  Tenacity of Fluids, and Attrition of their Parts, and the Weakness of
  9099  Elasticity in Solids, Motion is much more apt to be lost than got, and
  9100  is always upon the Decay. For Bodies which are either absolutely hard,
  9101  or so soft as to be void of Elasticity, will not rebound from one
  9102  another. Impenetrability makes them only stop. If two equal Bodies meet
  9103  directly _in vacuo_, they will by the Laws of Motion stop where they
  9104  meet, and lose all their Motion, and remain in rest, unless they be
  9105  elastick, and receive new Motion from their Spring. If they have so much
  9106  Elasticity as suffices to make them re-bound with a quarter, or half, or
  9107  three quarters of the Force with which they come together, they will
  9108  lose three quarters, or half, or a quarter of their Motion. And this may
  9109  be try'd, by letting two equal Pendulums fall against one another from
  9110  equal heights. If the Pendulums be of Lead or soft Clay, they will lose
  9111  all or almost all their Motions: If of elastick Bodies they will lose
  9112  all but what they recover from their Elasticity. If it be said, that
  9113  they can lose no Motion but what they communicate to other Bodies, the
  9114  consequence is, that _in vacuo_ they can lose no Motion, but when they
  9115  meet they must go on and penetrate one another's Dimensions. If three
  9116  equal round Vessels be filled, the one with Water, the other with Oil,
  9117  the third with molten Pitch, and the Liquors be stirred about alike to
  9118  give them a vortical Motion; the Pitch by its Tenacity will lose its
  9119  Motion quickly, the Oil being less tenacious will keep it longer, and
  9120  the Water being less tenacious will keep it longest, but yet will lose
  9121  it in a short time. Whence it is easy to understand, that if many
  9122  contiguous Vortices of molten Pitch were each of them as large as those
  9123  which some suppose to revolve about the Sun and fix'd Stars, yet these
  9124  and all their Parts would, by their Tenacity and Stiffness, communicate
  9125  their Motion to one another till they all rested among themselves.
  9126  Vortices of Oil or Water, or some fluider Matter, might continue longer
  9127  in Motion; but unless the Matter were void of all Tenacity and Attrition
  9128  of Parts, and Communication of Motion, (which is not to be supposed,)
  9129  the Motion would constantly decay. Seeing therefore the variety of
  9130  Motion which we find in the World is always decreasing, there is a
  9131  necessity of conserving and recruiting it by active Principles, such as
  9132  are the cause of Gravity, by which Planets and Comets keep their Motions
  9133  in their Orbs, and Bodies acquire great Motion in falling; and the cause
  9134  of Fermentation, by which the Heart and Blood of Animals are kept in
  9135  perpetual Motion and Heat; the inward Parts of the Earth are constantly
  9136  warm'd, and in some places grow very hot; Bodies burn and shine,
  9137  Mountains take fire, the Caverns of the Earth are blown up, and the Sun
  9138  continues violently hot and lucid, and warms all things by his Light.
  9139  For we meet with very little Motion in the World, besides what is owing
  9140  to these active Principles. And if it were not for these Principles, the
  9141  Bodies of the Earth, Planets, Comets, Sun, and all things in them,
  9142  would grow cold and freeze, and become inactive Masses; and all
  9143  Putrefaction, Generation, Vegetation and Life would cease, and the
  9144  Planets and Comets would not remain in their Orbs.
  9146  All these things being consider'd, it seems probable to me, that God in
  9147  the Beginning form'd Matter in solid, massy, hard, impenetrable,
  9148  moveable Particles, of such Sizes and Figures, and with such other
  9149  Properties, and in such Proportion to Space, as most conduced to the End
  9150  for which he form'd them; and that these primitive Particles being
  9151  Solids, are incomparably harder than any porous Bodies compounded of
  9152  them; even so very hard, as never to wear or break in pieces; no
  9153  ordinary Power being able to divide what God himself made one in the
  9154  first Creation. While the Particles continue entire, they may compose
  9155  Bodies of one and the same Nature and Texture in all Ages: But should
  9156  they wear away, or break in pieces, the