_PART IV._
_Observations concerning the Reflexions and Colours of thick transparent
polish'd Plates._
There is no Glass or Speculum how well soever polished, but, besides the
Light which it refracts or reflects regularly, scatters every way
irregularly a faint Light, by means of which the polish'd Surface, when
illuminated in a dark room by a beam of the Sun's Light, may be easily
seen in all positions of the Eye. There are certain Phaenomena of this
scatter'd Light, which when I first observed them, seem'd very strange
and surprizing to me. My Observations were as follows.
_Obs._ 1. The Sun shining into my darken'd Chamber through a hole one
third of an Inch wide, I let the intromitted beam of Light fall
perpendicularly upon a Glass Speculum ground concave on one side and
convex on the other, to a Sphere of five Feet and eleven Inches Radius,
and Quick-silver'd over on the convex side. And holding a white opake
Chart, or a Quire of Paper at the center of the Spheres to which the
Speculum was ground, that is, at the distance of about five Feet and
eleven Inches from the Speculum, in such manner, that the beam of Light
might pass through a little hole made in the middle of the Chart to the
Speculum, and thence be reflected back to the same hole: I observed upon
the Chart four or five concentric Irises or Rings of Colours, like
Rain-bows, encompassing the hole much after the manner that those, which
in the fourth and following Observations of the first part of this Book
appear'd between the Object-glasses, encompassed the black Spot, but yet
larger and fainter than those. These Rings as they grew larger and
larger became diluter and fainter, so that the fifth was scarce visible.
Yet sometimes, when the Sun shone very clear, there appear'd faint
Lineaments of a sixth and seventh. If the distance of the Chart from the
Speculum was much greater or much less than that of six Feet, the Rings
became dilute and vanish'd. And if the distance of the Speculum from the
Window was much greater than that of six Feet, the reflected beam of
Light would be so broad at the distance of six Feet from the Speculum
where the Rings appear'd, as to obscure one or two of the innermost
Rings. And therefore I usually placed the Speculum at about six Feet
from the Window; so that its Focus might there fall in with the center
of its concavity at the Rings upon the Chart. And this Posture is always
to be understood in the following Observations where no other is
express'd.
_Obs._ 2. The Colours of these Rain-bows succeeded one another from the
center outwards, in the same form and order with those which were made
in the ninth Observation of the first Part of this Book by Light not
reflected, but transmitted through the two Object-glasses. For, first,
there was in their common center a white round Spot of faint Light,
something broader than the reflected beam of Light, which beam sometimes
fell upon the middle of the Spot, and sometimes by a little inclination
of the Speculum receded from the middle, and left the Spot white to the
center.
This white Spot was immediately encompassed with a dark grey or russet,
and that dark grey with the Colours of the first Iris; which Colours on
the inside next the dark grey were a little violet and indigo, and next
to that a blue, which on the outside grew pale, and then succeeded a
little greenish yellow, and after that a brighter yellow, and then on
the outward edge of the Iris a red which on the outside inclined to
purple.
This Iris was immediately encompassed with a second, whose Colours were
in order from the inside outwards, purple, blue, green, yellow, light
red, a red mix'd with purple.
Then immediately follow'd the Colours of the third Iris, which were in
order outwards a green inclining to purple, a good green, and a red more
bright than that of the former Iris.
The fourth and fifth Iris seem'd of a bluish green within, and red
without, but so faintly that it was difficult to discern the Colours.
_Obs._ 3. Measuring the Diameters of these Rings upon the Chart as
accurately as I could, I found them also in the same proportion to one
another with the Rings made by Light transmitted through the two
Object-glasses. For the Diameters of the four first of the bright Rings
measured between the brightest parts of their Orbits, at the distance of
six Feet from the Speculum were 1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches,
whose Squares are in arithmetical progression of the numbers 1, 2, 3, 4.
If the white circular Spot in the middle be reckon'd amongst the Rings,
and its central Light, where it seems to be most luminous, be put
equipollent to an infinitely little Ring; the Squares of the Diameters
of the Rings will be in the progression 0, 1, 2, 3, 4, &c. I measured
also the Diameters of the dark Circles between these luminous ones, and
found their Squares in the progression of the numbers 1/2, 1-1/2, 2-1/2,
3-1/2, &c. the Diameters of the first four at the distance of six Feet
from the Speculum, being 1-3/16, 2-1/16, 2-2/3, 3-3/20 Inches. If the
distance of the Chart from the Speculum was increased or diminished, the
Diameters of the Circles were increased or diminished proportionally.
_Obs._ 4. By the analogy between these Rings and those described in the
Observations of the first Part of this Book, I suspected that there
were many more of them which spread into one another, and by interfering
mix'd their Colours, and diluted one another so that they could not be
seen apart. I viewed them therefore through a Prism, as I did those in
the 24th Observation of the first Part of this Book. And when the Prism
was so placed as by refracting the Light of their mix'd Colours to
separate them, and distinguish the Rings from one another, as it did
those in that Observation, I could then see them distincter than before,
and easily number eight or nine of them, and sometimes twelve or
thirteen. And had not their Light been so very faint, I question not but
that I might have seen many more.
_Obs._ 5. Placing a Prism at the Window to refract the intromitted beam
of Light, and cast the oblong Spectrum of Colours on the Speculum: I
covered the Speculum with a black Paper which had in the middle of it a
hole to let any one of the Colours pass through to the Speculum, whilst
the rest were intercepted by the Paper. And now I found Rings of that
Colour only which fell upon the Speculum. If the Speculum was
illuminated with red, the Rings were totally red with dark Intervals, if
with blue they were totally blue, and so of the other Colours. And when
they were illuminated with any one Colour, the Squares of their
Diameters measured between their most luminous Parts, were in the
arithmetical Progression of the Numbers, 0, 1, 2, 3, 4 and the Squares
of the Diameters of their dark Intervals in the Progression of the
intermediate Numbers 1/2, 1-1/2, 2-1/2, 3-1/2. But if the Colour was
varied, they varied their Magnitude. In the red they were largest, in
the indigo and violet least, and in the intermediate Colours yellow,
green, and blue, they were of several intermediate Bignesses answering
to the Colour, that is, greater in yellow than in green, and greater in
green than in blue. And hence I knew, that when the Speculum was
illuminated with white Light, the red and yellow on the outside of the
Rings were produced by the least refrangible Rays, and the blue and
violet by the most refrangible, and that the Colours of each Ring spread
into the Colours of the neighbouring Rings on either side, after the
manner explain'd in the first and second Part of this Book, and by
mixing diluted one another so that they could not be distinguish'd,
unless near the Center where they were least mix'd. For in this
Observation I could see the Rings more distinctly, and to a greater
Number than before, being able in the yellow Light to number eight or
nine of them, besides a faint shadow of a tenth. To satisfy my self how
much the Colours of the several Rings spread into one another, I
measured the Diameters of the second and third Rings, and found them
when made by the Confine of the red and orange to be to the same
Diameters when made by the Confine of blue and indigo, as 9 to 8, or
thereabouts. For it was hard to determine this Proportion accurately.
Also the Circles made successively by the red, yellow, and green,
differ'd more from one another than those made successively by the
green, blue, and indigo. For the Circle made by the violet was too dark
to be seen. To carry on the Computation, let us therefore suppose that
the Differences of the Diameters of the Circles made by the outmost red,
the Confine of red and orange, the Confine of orange and yellow, the
Confine of yellow and green, the Confine of green and blue, the Confine
of blue and indigo, the Confine of indigo and violet, and outmost
violet, are in proportion as the Differences of the Lengths of a
Monochord which sound the Tones in an Eight; _sol_, _la_, _fa_, _sol_,
_la_, _mi_, _fa_, _sol_, that is, as the Numbers 1/9, 1/18, 1/12, 1/12,
2/27, 1/27, 1/18. And if the Diameter of the Circle made by the Confine
of red and orange be 9A, and that of the Circle made by the Confine of
blue and indigo be 8A as above; their difference 9A-8A will be to the
difference of the Diameters of the Circles made by the outmost red, and
by the Confine of red and orange, as 1/18 + 1/12 + 1/12 + 2/27 to 1/9,
that is as 8/27 to 1/9, or 8 to 3, and to the difference of the Circles
made by the outmost violet, and by the Confine of blue and indigo, as
1/18 + 1/12 + 1/12 + 2/27 to 1/27 + 1/18, that is, as 8/27 to 5/54, or
as 16 to 5. And therefore these differences will be 3/8A and 5/16A. Add
the first to 9A and subduct the last from 8A, and you will have the
Diameters of the Circles made by the least and most refrangible Rays
75/8A and ((61-1/2)/8)A. These diameters are therefore to one another as
75 to 61-1/2 or 50 to 41, and their Squares as 2500 to 1681, that is, as
3 to 2 very nearly. Which proportion differs not much from the
proportion of the Diameters of the Circles made by the outmost red and
outmost violet, in the 13th Observation of the first part of this Book.
_Obs._ 6. Placing my Eye where these Rings appear'd plainest, I saw the
Speculum tinged all over with Waves of Colours, (red, yellow, green,
blue;) like those which in the Observations of the first part of this
Book appeared between the Object-glasses, and upon Bubbles of Water, but
much larger. And after the manner of those, they were of various
magnitudes in various Positions of the Eye, swelling and shrinking as I
moved my Eye this way and that way. They were formed like Arcs of
concentrick Circles, as those were; and when my Eye was over against the
center of the concavity of the Speculum, (that is, 5 Feet and 10 Inches
distant from the Speculum,) their common center was in a right Line with
that center of concavity, and with the hole in the Window. But in other
postures of my Eye their center had other positions. They appear'd by
the Light of the Clouds propagated to the Speculum through the hole in
the Window; and when the Sun shone through that hole upon the Speculum,
his Light upon it was of the Colour of the Ring whereon it fell, but by
its splendor obscured the Rings made by the Light of the Clouds, unless
when the Speculum was removed to a great distance from the Window, so
that his Light upon it might be broad and faint. By varying the position
of my Eye, and moving it nearer to or farther from the direct beam of
the Sun's Light, the Colour of the Sun's reflected Light constantly
varied upon the Speculum, as it did upon my Eye, the same Colour always
appearing to a Bystander upon my Eye which to me appear'd upon the
Speculum. And thence I knew that the Rings of Colours upon the Chart
were made by these reflected Colours, propagated thither from the
Speculum in several Angles, and that their production depended not upon
the termination of Light and Shadow.
_Obs._ 7. By the Analogy of all these Phaenomena with those of the like
Rings of Colours described in the first part of this Book, it seemed to
me that these Colours were produced by this thick Plate of Glass, much
after the manner that those were produced by very thin Plates. For, upon
trial, I found that if the Quick-silver were rubb'd off from the
backside of the Speculum, the Glass alone would cause the same Rings of
Colours, but much more faint than before; and therefore the Phaenomenon
depends not upon the Quick-silver, unless so far as the Quick-silver by
increasing the Reflexion of the backside of the Glass increases the
Light of the Rings of Colours. I found also that a Speculum of Metal
without Glass made some Years since for optical uses, and very well
wrought, produced none of those Rings; and thence I understood that
these Rings arise not from one specular Surface alone, but depend upon
the two Surfaces of the Plate of Glass whereof the Speculum was made,
and upon the thickness of the Glass between them. For as in the 7th and
19th Observations of the first part of this Book a thin Plate of Air,
Water, or Glass of an even thickness appeared of one Colour when the
Rays were perpendicular to it, of another when they were a little
oblique, of another when more oblique, of another when still more
oblique, and so on; so here, in the sixth Observation, the Light which
emerged out of the Glass in several Obliquities, made the Glass appear
of several Colours, and being propagated in those Obliquities to the
Chart, there painted Rings of those Colours. And as the reason why a
thin Plate appeared of several Colours in several Obliquities of the
Rays, was, that the Rays of one and the same sort are reflected by the
thin Plate at one obliquity and transmitted at another, and those of
other sorts transmitted where these are reflected, and reflected where
these are transmitted: So the reason why the thick Plate of Glass
whereof the Speculum was made did appear of various Colours in various
Obliquities, and in those Obliquities propagated those Colours to the
Chart, was, that the Rays of one and the same sort did at one Obliquity
emerge out of the Glass, at another did not emerge, but were reflected
back towards the Quick-silver by the hither Surface of the Glass, and
accordingly as the Obliquity became greater and greater, emerged and
were reflected alternately for many Successions; and that in one and the
same Obliquity the Rays of one sort were reflected, and those of another
transmitted. This is manifest by the fifth Observation of this part of
this Book. For in that Observation, when the Speculum was illuminated by
any one of the prismatick Colours, that Light made many Rings of the
same Colour upon the Chart with dark Intervals, and therefore at its
emergence out of the Speculum was alternately transmitted and not
transmitted from the Speculum to the Chart for many Successions,
according to the various Obliquities of its Emergence. And when the
Colour cast on the Speculum by the Prism was varied, the Rings became of
the Colour cast on it, and varied their bigness with their Colour, and
therefore the Light was now alternately transmitted and not transmitted
from the Speculum to the Chart at other Obliquities than before. It
seemed to me therefore that these Rings were of one and the same
original with those of thin Plates, but yet with this difference, that
those of thin Plates are made by the alternate Reflexions and
Transmissions of the Rays at the second Surface of the Plate, after one
passage through it; but here the Rays go twice through the Plate before
they are alternately reflected and transmitted. First, they go through
it from the first Surface to the Quick-silver, and then return through
it from the Quick-silver to the first Surface, and there are either
transmitted to the Chart or reflected back to the Quick-silver,
accordingly as they are in their Fits of easy Reflexion or Transmission
when they arrive at that Surface. For the Intervals of the Fits of the
Rays which fall perpendicularly on the Speculum, and are reflected back
in the same perpendicular Lines, by reason of the equality of these
Angles and Lines, are of the same length and number within the Glass
after Reflexion as before, by the 19th Proposition of the third part of
this Book. And therefore since all the Rays that enter through the
first Surface are in their Fits of easy Transmission at their entrance,
and as many of these as are reflected by the second are in their Fits of
easy Reflexion there, all these must be again in their Fits of easy
Transmission at their return to the first, and by consequence there go
out of the Glass to the Chart, and form upon it the white Spot of Light
in the center of the Rings. For the reason holds good in all sorts of
Rays, and therefore all sorts must go out promiscuously to that Spot,
and by their mixture cause it to be white. But the Intervals of the Fits
of those Rays which are reflected more obliquely than they enter, must
be greater after Reflexion than before, by the 15th and 20th
Propositions. And thence it may happen that the Rays at their return to
the first Surface, may in certain Obliquities be in Fits of easy
Reflexion, and return back to the Quick-silver, and in other
intermediate Obliquities be again in Fits of easy Transmission, and so
go out to the Chart, and paint on it the Rings of Colours about the
white Spot. And because the Intervals of the Fits at equal obliquities
are greater and fewer in the less refrangible Rays, and less and more
numerous in the more refrangible, therefore the less refrangible at
equal obliquities shall make fewer Rings than the more refrangible, and
the Rings made by those shall be larger than the like number of Rings
made by these; that is, the red Rings shall be larger than the yellow,
the yellow than the green, the green than the blue, and the blue than
the violet, as they were really found to be in the fifth Observation.
And therefore the first Ring of all Colours encompassing the white Spot
of Light shall be red without any violet within, and yellow, and green,
and blue in the middle, as it was found in the second Observation; and
these Colours in the second Ring, and those that follow, shall be more
expanded, till they spread into one another, and blend one another by
interfering.
These seem to be the reasons of these Rings in general; and this put me
upon observing the thickness of the Glass, and considering whether the
dimensions and proportions of the Rings may be truly derived from it by
computation.
_Obs._ 8. I measured therefore the thickness of this concavo-convex
Plate of Glass, and found it every where 1/4 of an Inch precisely. Now,
by the sixth Observation of the first Part of this Book, a thin Plate of
Air transmits the brightest Light of the first Ring, that is, the bright
yellow, when its thickness is the 1/89000th part of an Inch; and by the
tenth Observation of the same Part, a thin Plate of Glass transmits the
same Light of the same Ring, when its thickness is less in proportion of
the Sine of Refraction to the Sine of Incidence, that is, when its
thickness is the 11/1513000th or 1/137545th part of an Inch, supposing
the Sines are as 11 to 17. And if this thickness be doubled, it
transmits the same bright Light of the second Ring; if tripled, it
transmits that of the third, and so on; the bright yellow Light in all
these cases being in its Fits of Transmission. And therefore if its
thickness be multiplied 34386 times, so as to become 1/4 of an Inch, it
transmits the same bright Light of the 34386th Ring. Suppose this be the
bright yellow Light transmitted perpendicularly from the reflecting
convex side of the Glass through the concave side to the white Spot in
the center of the Rings of Colours on the Chart: And by a Rule in the
7th and 19th Observations in the first Part of this Book, and by the
15th and 20th Propositions of the third Part of this Book, if the Rays
be made oblique to the Glass, the thickness of the Glass requisite to
transmit the same bright Light of the same Ring in any obliquity, is to
this thickness of 1/4 of an Inch, as the Secant of a certain Angle to
the Radius, the Sine of which Angle is the first of an hundred and six
arithmetical Means between the Sines of Incidence and Refraction,
counted from the Sine of Incidence when the Refraction is made out of
any plated Body into any Medium encompassing it; that is, in this case,
out of Glass into Air. Now if the thickness of the Glass be increased by
degrees, so as to bear to its first thickness, (_viz._ that of a quarter
of an Inch,) the Proportions which 34386 (the number of Fits of the
perpendicular Rays in going through the Glass towards the white Spot in
the center of the Rings,) hath to 34385, 34384, 34383, and 34382, (the
numbers of the Fits of the oblique Rays in going through the Glass
towards the first, second, third, and fourth Rings of Colours,) and if
the first thickness be divided into 100000000 equal parts, the increased
thicknesses will be 100002908, 100005816, 100008725, and 100011633, and
the Angles of which these thicknesses are Secants will be 26' 13'', 37'
5'', 45' 6'', and 52' 26'', the Radius being 100000000; and the Sines of
these Angles are 762, 1079, 1321, and 1525, and the proportional Sines
of Refraction 1172, 1659, 2031, and 2345, the Radius being 100000. For
since the Sines of Incidence out of Glass into Air are to the Sines of
Refraction as 11 to 17, and to the above-mentioned Secants as 11 to the
first of 106 arithmetical Means between 11 and 17, that is, as 11 to
11-6/106, those Secants will be to the Sines of Refraction as 11-6/106,
to 17, and by this Analogy will give these Sines. So then, if the
obliquities of the Rays to the concave Surface of the Glass be such that
the Sines of their Refraction in passing out of the Glass through that
Surface into the Air be 1172, 1659, 2031, 2345, the bright Light of the
34386th Ring shall emerge at the thicknesses of the Glass, which are to
1/4 of an Inch as 34386 to 34385, 34384, 34383, 34382, respectively. And
therefore, if the thickness in all these Cases be 1/4 of an Inch (as it
is in the Glass of which the Speculum was made) the bright Light of the
34385th Ring shall emerge where the Sine of Refraction is 1172, and that
of the 34384th, 34383th, and 34382th Ring where the Sine is 1659, 2031,
and 2345 respectively. And in these Angles of Refraction the Light of
these Rings shall be propagated from the Speculum to the Chart, and
there paint Rings about the white central round Spot of Light which we
said was the Light of the 34386th Ring. And the Semidiameters of these
Rings shall subtend the Angles of Refraction made at the
Concave-Surface of the Speculum, and by consequence their Diameters
shall be to the distance of the Chart from the Speculum as those Sines
of Refraction doubled are to the Radius, that is, as 1172, 1659, 2031,
and 2345, doubled are to 100000. And therefore, if the distance of the
Chart from the Concave-Surface of the Speculum be six Feet (as it was in
the third of these Observations) the Diameters of the Rings of this
bright yellow Light upon the Chart shall be 1'688, 2'389, 2'925, 3'375
Inches: For these Diameters are to six Feet, as the above-mention'd
Sines doubled are to the Radius. Now, these Diameters of the bright
yellow Rings, thus found by Computation are the very same with those
found in the third of these Observations by measuring them, _viz._ with
1-11/16, 2-3/8, 2-11/12, and 3-3/8 Inches, and therefore the Theory of
deriving these Rings from the thickness of the Plate of Glass of which
the Speculum was made, and from the Obliquity of the emerging Rays
agrees with the Observation. In this Computation I have equalled the
Diameters of the bright Rings made by Light of all Colours, to the
Diameters of the Rings made by the bright yellow. For this yellow makes
the brightest Part of the Rings of all Colours. If you desire the
Diameters of the Rings made by the Light of any other unmix'd Colour,
you may find them readily by putting them to the Diameters of the bright
yellow ones in a subduplicate Proportion of the Intervals of the Fits of
the Rays of those Colours when equally inclined to the refracting or
reflecting Surface which caused those Fits, that is, by putting the
Diameters of the Rings made by the Rays in the Extremities and Limits of
the seven Colours, red, orange, yellow, green, blue, indigo, violet,
proportional to the Cube-roots of the Numbers, 1, 8/9, 5/6, 3/4, 2/3,
3/5, 9/16, 1/2, which express the Lengths of a Monochord sounding the
Notes in an Eighth: For by this means the Diameters of the Rings of
these Colours will be found pretty nearly in the same Proportion to one
another, which they ought to have by the fifth of these Observations.
And thus I satisfy'd my self, that these Rings were of the same kind and
Original with those of thin Plates, and by consequence that the Fits or
alternate Dispositions of the Rays to be reflected and transmitted are
propagated to great distances from every reflecting and refracting
Surface. But yet to put the matter out of doubt, I added the following
Observation.
_Obs._ 9. If these Rings thus depend on the thickness of the Plate of
Glass, their Diameters at equal distances from several Speculums made of
such concavo-convex Plates of Glass as are ground on the same Sphere,
ought to be reciprocally in a subduplicate Proportion of the thicknesses
of the Plates of Glass. And if this Proportion be found true by
experience it will amount to a demonstration that these Rings (like
those formed in thin Plates) do depend on the thickness of the Glass. I
procured therefore another concavo-convex Plate of Glass ground on both
sides to the same Sphere with the former Plate. Its thickness was 5/62
Parts of an Inch; and the Diameters of the three first bright Rings
measured between the brightest Parts of their Orbits at the distance of
six Feet from the Glass were 3.4-1/6.5-1/8. Inches. Now, the thickness
of the other Glass being 1/4 of an Inch was to the thickness of this
Glass as 1/4 to 5/62, that is as 31 to 10, or 310000000 to 100000000,
and the Roots of these Numbers are 17607 and 10000, and in the
Proportion of the first of these Roots to the second are the Diameters
of the bright Rings made in this Observation by the thinner Glass,
3.4-1/6.5-1/8, to the Diameters of the same Rings made in the third of
these Observations by the thicker Glass 1-11/16, 2-3/8. 2-11/12, that
is, the Diameters of the Rings are reciprocally in a subduplicate
Proportion of the thicknesses of the Plates of Glass.
So then in Plates of Glass which are alike concave on one side, and
alike convex on the other side, and alike quick-silver'd on the convex
sides, and differ in nothing but their thickness, the Diameters of the
Rings are reciprocally in a subduplicate Proportion of the thicknesses
of the Plates. And this shews sufficiently that the Rings depend on both
the Surfaces of the Glass. They depend on the convex Surface, because
they are more luminous when that Surface is quick-silver'd over than
when it is without Quick-silver. They depend also upon the concave
Surface, because without that Surface a Speculum makes them not. They
depend on both Surfaces, and on the distances between them, because
their bigness is varied by varying only that distance. And this
dependence is of the same kind with that which the Colours of thin
Plates have on the distance of the Surfaces of those Plates, because the
bigness of the Rings, and their Proportion to one another, and the
variation of their bigness arising from the variation of the thickness
of the Glass, and the Orders of their Colours, is such as ought to
result from the Propositions in the end of the third Part of this Book,
derived from the Phaenomena of the Colours of thin Plates set down in the
first Part.
There are yet other Phaenomena of these Rings of Colours, but such as
follow from the same Propositions, and therefore confirm both the Truth
of those Propositions, and the Analogy between these Rings and the Rings
of Colours made by very thin Plates. I shall subjoin some of them.
_Obs._ 10. When the beam of the Sun's Light was reflected back from the
Speculum not directly to the hole in the Window, but to a place a little
distant from it, the common center of that Spot, and of all the Rings of
Colours fell in the middle way between the beam of the incident Light,
and the beam of the reflected Light, and by consequence in the center of
the spherical concavity of the Speculum, whenever the Chart on which the
Rings of Colours fell was placed at that center. And as the beam of
reflected Light by inclining the Speculum receded more and more from the
beam of incident Light and from the common center of the colour'd Rings
between them, those Rings grew bigger and bigger, and so also did the
white round Spot, and new Rings of Colours emerged successively out of
their common center, and the white Spot became a white Ring
encompassing them; and the incident and reflected beams of Light always
fell upon the opposite parts of this white Ring, illuminating its
Perimeter like two mock Suns in the opposite parts of an Iris. So then
the Diameter of this Ring, measured from the middle of its Light on one
side to the middle of its Light on the other side, was always equal to
the distance between the middle of the incident beam of Light, and the
middle of the reflected beam measured at the Chart on which the Rings
appeared: And the Rays which form'd this Ring were reflected by the
Speculum in Angles equal to their Angles of Incidence, and by
consequence to their Angles of Refraction at their entrance into the
Glass, but yet their Angles of Reflexion were not in the same Planes
with their Angles of Incidence.
_Obs._ 11. The Colours of the new Rings were in a contrary order to
those of the former, and arose after this manner. The white round Spot
of Light in the middle of the Rings continued white to the center till
the distance of the incident and reflected beams at the Chart was about
7/8 parts of an Inch, and then it began to grow dark in the middle. And
when that distance was about 1-3/16 of an Inch, the white Spot was
become a Ring encompassing a dark round Spot which in the middle
inclined to violet and indigo. And the luminous Rings encompassing it
were grown equal to those dark ones which in the four first Observations
encompassed them, that is to say, the white Spot was grown a white Ring
equal to the first of those dark Rings, and the first of those luminous
Rings was now grown equal to the second of those dark ones, and the
second of those luminous ones to the third of those dark ones, and so
on. For the Diameters of the luminous Rings were now 1-3/16, 2-1/16,
2-2/3, 3-3/20, &c. Inches.
When the distance between the incident and reflected beams of Light
became a little bigger, there emerged out of the middle of the dark Spot
after the indigo a blue, and then out of that blue a pale green, and
soon after a yellow and red. And when the Colour at the center was
brightest, being between yellow and red, the bright Rings were grown
equal to those Rings which in the four first Observations next
encompassed them; that is to say, the white Spot in the middle of those
Rings was now become a white Ring equal to the first of those bright
Rings, and the first of those bright ones was now become equal to the
second of those, and so on. For the Diameters of the white Ring, and of
the other luminous Rings encompassing it, were now 1-11/16, 2-3/8,
2-11/12, 3-3/8, &c. or thereabouts.
When the distance of the two beams of Light at the Chart was a little
more increased, there emerged out of the middle in order after the red,
a purple, a blue, a green, a yellow, and a red inclining much to purple,
and when the Colour was brightest being between yellow and red, the
former indigo, blue, green, yellow and red, were become an Iris or Ring
of Colours equal to the first of those luminous Rings which appeared in
the four first Observations, and the white Ring which was now become
the second of the luminous Rings was grown equal to the second of those,
and the first of those which was now become the third Ring was become
equal to the third of those, and so on. For their Diameters were
1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches, the distance of the two beams of
Light, and the Diameter of the white Ring being 2-3/8 Inches.
When these two beams became more distant there emerged out of the middle
of the purplish red, first a darker round Spot, and then out of the
middle of that Spot a brighter. And now the former Colours (purple,
blue, green, yellow, and purplish red) were become a Ring equal to the
first of the bright Rings mentioned in the four first Observations, and
the Rings about this Ring were grown equal to the Rings about that
respectively; the distance between the two beams of Light and the
Diameter of the white Ring (which was now become the third Ring) being
about 3 Inches.
The Colours of the Rings in the middle began now to grow very dilute,
and if the distance between the two Beams was increased half an Inch, or
an Inch more, they vanish'd whilst the white Ring, with one or two of
the Rings next it on either side, continued still visible. But if the
distance of the two beams of Light was still more increased, these also
vanished: For the Light which coming from several parts of the hole in
the Window fell upon the Speculum in several Angles of Incidence, made
Rings of several bignesses, which diluted and blotted out one another,
as I knew by intercepting some part of that Light. For if I intercepted
that part which was nearest to the Axis of the Speculum the Rings would
be less, if the other part which was remotest from it they would be
bigger.
_Obs._ 12. When the Colours of the Prism were cast successively on the
Speculum, that Ring which in the two last Observations was white, was of
the same bigness in all the Colours, but the Rings without it were
greater in the green than in the blue, and still greater in the yellow,
and greatest in the red. And, on the contrary, the Rings within that
white Circle were less in the green than in the blue, and still less in
the yellow, and least in the red. For the Angles of Reflexion of those
Rays which made this Ring, being equal to their Angles of Incidence, the
Fits of every reflected Ray within the Glass after Reflexion are equal
in length and number to the Fits of the same Ray within the Glass before
its Incidence on the reflecting Surface. And therefore since all the
Rays of all sorts at their entrance into the Glass were in a Fit of
Transmission, they were also in a Fit of Transmission at their returning
to the same Surface after Reflexion; and by consequence were
transmitted, and went out to the white Ring on the Chart. This is the
reason why that Ring was of the same bigness in all the Colours, and why
in a mixture of all it appears white. But in Rays which are reflected in
other Angles, the Intervals of the Fits of the least refrangible being
greatest, make the Rings of their Colour in their progress from this
white Ring, either outwards or inwards, increase or decrease by the
greatest steps; so that the Rings of this Colour without are greatest,
and within least. And this is the reason why in the last Observation,
when the Speculum was illuminated with white Light, the exterior Rings
made by all Colours appeared red without and blue within, and the
interior blue without and red within.
These are the Phaenomena of thick convexo-concave Plates of Glass, which
are every where of the same thickness. There are yet other Phaenomena
when these Plates are a little thicker on one side than on the other,
and others when the Plates are more or less concave than convex, or
plano-convex, or double-convex. For in all these cases the Plates make
Rings of Colours, but after various manners; all which, so far as I have
yet observed, follow from the Propositions in the end of the third part
of this Book, and so conspire to confirm the truth of those
Propositions. But the Phaenomena are too various, and the Calculations
whereby they follow from those Propositions too intricate to be here
prosecuted. I content my self with having prosecuted this kind of
Phaenomena so far as to discover their Cause, and by discovering it to
ratify the Propositions in the third Part of this Book.
_Obs._ 13. As Light reflected by a Lens quick-silver'd on the backside
makes the Rings of Colours above described, so it ought to make the like
Rings of Colours in passing through a drop of Water. At the first
Reflexion of the Rays within the drop, some Colours ought to be
transmitted, as in the case of a Lens, and others to be reflected back
to the Eye. For instance, if the Diameter of a small drop or globule of
Water be about the 500th part of an Inch, so that a red-making Ray in
passing through the middle of this globule has 250 Fits of easy
Transmission within the globule, and that all the red-making Rays which
are at a certain distance from this middle Ray round about it have 249
Fits within the globule, and all the like Rays at a certain farther
distance round about it have 248 Fits, and all those at a certain
farther distance 247 Fits, and so on; these concentrick Circles of Rays
after their transmission, falling on a white Paper, will make
concentrick Rings of red upon the Paper, supposing the Light which
passes through one single globule, strong enough to be sensible. And, in
like manner, the Rays of other Colours will make Rings of other Colours.
Suppose now that in a fair Day the Sun shines through a thin Cloud of
such globules of Water or Hail, and that the globules are all of the
same bigness; and the Sun seen through this Cloud shall appear
encompassed with the like concentrick Rings of Colours, and the Diameter
of the first Ring of red shall be 7-1/4 Degrees, that of the second
10-1/4 Degrees, that of the third 12 Degrees 33 Minutes. And accordingly
as the Globules of Water are bigger or less, the Rings shall be less or
bigger. This is the Theory, and Experience answers it. For in _June_
1692, I saw by reflexion in a Vessel of stagnating Water three Halos,
Crowns, or Rings of Colours about the Sun, like three little Rain-bows,
concentrick to his Body. The Colours of the first or innermost Crown
were blue next the Sun, red without, and white in the middle between the
blue and red. Those of the second Crown were purple and blue within, and
pale red without, and green in the middle. And those of the third were
pale blue within, and pale red without; these Crowns enclosed one
another immediately, so that their Colours proceeded in this continual
order from the Sun outward: blue, white, red; purple, blue, green, pale
yellow and red; pale blue, pale red. The Diameter of the second Crown
measured from the middle of the yellow and red on one side of the Sun,
to the middle of the same Colour on the other side was 9-1/3 Degrees, or
thereabouts. The Diameters of the first and third I had not time to
measure, but that of the first seemed to be about five or six Degrees,
and that of the third about twelve. The like Crowns appear sometimes
about the Moon; for in the beginning of the Year 1664, _Febr._ 19th at
Night, I saw two such Crowns about her. The Diameter of the first or
innermost was about three Degrees, and that of the second about five
Degrees and an half. Next about the Moon was a Circle of white, and next
about that the inner Crown, which was of a bluish green within next the
white, and of a yellow and red without, and next about these Colours
were blue and green on the inside of the outward Crown, and red on the
outside of it. At the same time there appear'd a Halo about 22 Degrees
35' distant from the center of the Moon. It was elliptical, and its long
Diameter was perpendicular to the Horizon, verging below farthest from
the Moon. I am told that the Moon has sometimes three or more
concentrick Crowns of Colours encompassing one another next about her
Body. The more equal the globules of Water or Ice are to one another,
the more Crowns of Colours will appear, and the Colours will be the more
lively. The Halo at the distance of 22-1/2 Degrees from the Moon is of
another sort. By its being oval and remoter from the Moon below than
above, I conclude, that it was made by Refraction in some sort of Hail
or Snow floating in the Air in an horizontal posture, the refracting
Angle being about 58 or 60 Degrees.