_PART II._
_Remarks upon the foregoing Observations._
Having given my Observations of these Colours, before I make use of them
to unfold the Causes of the Colours of natural Bodies, it is convenient
that by the simplest of them, such as are the 2d, 3d, 4th, 9th, 12th,
18th, 20th, and 24th, I first explain the more compounded. And first to
shew how the Colours in the fourth and eighteenth Observations are
produced, let there be taken in any Right Line from the Point Y, [in
_Fig._ 6.] the Lengths YA, YB, YC, YD, YE, YF, YG, YH, in proportion to
one another, as the Cube-Roots of the Squares of the Numbers, 1/2, 9/16,
3/5, 2/3, 3/4, 5/6, 8/9, 1, whereby the Lengths of a Musical Chord to
sound all the Notes in an eighth are represented; that is, in the
Proportion of the Numbers 6300, 6814, 7114, 7631, 8255, 8855, 9243,
10000. And at the Points A, B, C, D, E, F, G, H, let Perpendiculars
A[Greek: a], B[Greek: b], &c. be erected, by whose Intervals the Extent
of the several Colours set underneath against them, is to be
represented. Then divide the Line _A[Greek: a]_ in such Proportion as
the Numbers 1, 2, 3, 5, 6, 7, 9, 10, 11, &c. set at the Points of
Division denote. And through those Divisions from Y draw Lines 1I, 2K,
3L, 5M, 6N, 7O, &c.
Now, if A2 be supposed to represent the Thickness of any thin
transparent Body, at which the outmost Violet is most copiously
reflected in the first Ring, or Series of Colours, then by the 13th
Observation, HK will represent its Thickness, at which the utmost Red is
most copiously reflected in the same Series. Also by the 5th and 16th
Observations, A6 and HN will denote the Thicknesses at which those
extreme Colours are most copiously reflected in the second Series, and
A10 and HQ the Thicknesses at which they are most copiously reflected in
the third Series, and so on. And the Thickness at which any of the
intermediate Colours are reflected most copiously, will, according to
the 14th Observation, be defined by the distance of the Line AH from the
intermediate parts of the Lines 2K, 6N, 10Q, &c. against which the Names
of those Colours are written below.
[Illustration: FIG. 6.]
But farther, to define the Latitude of these Colours in each Ring or
Series, let A1 design the least thickness, and A3 the greatest
thickness, at which the extreme violet in the first Series is reflected,
and let HI, and HL, design the like limits for the extreme red, and let
the intermediate Colours be limited by the intermediate parts of the
Lines 1I, and 3L, against which the Names of those Colours are written,
and so on: But yet with this caution, that the Reflexions be supposed
strongest at the intermediate Spaces, 2K, 6N, 10Q, &c. and from thence
to decrease gradually towards these limits, 1I, 3L, 5M, 7O, &c. on
either side; where you must not conceive them to be precisely limited,
but to decay indefinitely. And whereas I have assign'd the same Latitude
to every Series, I did it, because although the Colours in the first
Series seem to be a little broader than the rest, by reason of a
stronger Reflexion there, yet that inequality is so insensible as
scarcely to be determin'd by Observation.
Now according to this Description, conceiving that the Rays originally
of several Colours are by turns reflected at the Spaces 1I, L3, 5M, O7,
9PR11, &c. and transmitted at the Spaces AHI1, 3LM5, 7OP9, &c. it is
easy to know what Colour must in the open Air be exhibited at any
thickness of a transparent thin Body. For if a Ruler be applied parallel
to AH, at that distance from it by which the thickness of the Body is
represented, the alternate Spaces 1IL3, 5MO7, &c. which it crosseth will
denote the reflected original Colours, of which the Colour exhibited in
the open Air is compounded. Thus if the constitution of the green in the
third Series of Colours be desired, apply the Ruler as you see at
[Greek: prsph], and by its passing through some of the blue at [Greek:
p] and yellow at [Greek: s], as well as through the green at [Greek: r],
you may conclude that the green exhibited at that thickness of the Body
is principally constituted of original green, but not without a mixture
of some blue and yellow.
By this means you may know how the Colours from the center of the Rings
outward ought to succeed in order as they were described in the 4th and
18th Observations. For if you move the Ruler gradually from AH through
all distances, having pass'd over the first Space which denotes little
or no Reflexion to be made by thinnest Substances, it will first arrive
at 1 the violet, and then very quickly at the blue and green, which
together with that violet compound blue, and then at the yellow and red,
by whose farther addition that blue is converted into whiteness, which
whiteness continues during the transit of the edge of the Ruler from I
to 3, and after that by the successive deficience of its component
Colours, turns first to compound yellow, and then to red, and last of
all the red ceaseth at L. Then begin the Colours of the second Series,
which succeed in order during the transit of the edge of the Ruler from
5 to O, and are more lively than before, because more expanded and
severed. And for the same reason instead of the former white there
intercedes between the blue and yellow a mixture of orange, yellow,
green, blue and indigo, all which together ought to exhibit a dilute and
imperfect green. So the Colours of the third Series all succeed in
order; first, the violet, which a little interferes with the red of the
second order, and is thereby inclined to a reddish purple; then the blue
and green, which are less mix'd with other Colours, and consequently
more lively than before, especially the green: Then follows the yellow,
some of which towards the green is distinct and good, but that part of
it towards the succeeding red, as also that red is mix'd with the violet
and blue of the fourth Series, whereby various degrees of red very much
inclining to purple are compounded. This violet and blue, which should
succeed this red, being mixed with, and hidden in it, there succeeds a
green. And this at first is much inclined to blue, but soon becomes a
good green, the only unmix'd and lively Colour in this fourth Series.
For as it verges towards the yellow, it begins to interfere with the
Colours of the fifth Series, by whose mixture the succeeding yellow and
red are very much diluted and made dirty, especially the yellow, which
being the weaker Colour is scarce able to shew it self. After this the
several Series interfere more and more, and their Colours become more
and more intermix'd, till after three or four more revolutions (in which
the red and blue predominate by turns) all sorts of Colours are in all
places pretty equally blended, and compound an even whiteness.
And since by the 15th Observation the Rays endued with one Colour are
transmitted, where those of another Colour are reflected, the reason of
the Colours made by the transmitted Light in the 9th and 20th
Observations is from hence evident.
If not only the Order and Species of these Colours, but also the precise
thickness of the Plate, or thin Body at which they are exhibited, be
desired in parts of an Inch, that may be also obtained by assistance of
the 6th or 16th Observations. For according to those Observations the
thickness of the thinned Air, which between two Glasses exhibited the
most luminous parts of the first six Rings were 1/178000, 3/178000,
5/178000, 7/178000, 9/178000, 11/178000 parts of an Inch. Suppose the
Light reflected most copiously at these thicknesses be the bright
citrine yellow, or confine of yellow and orange, and these thicknesses
will be F[Greek: l], F[Greek: m], F[Greek: u], F[Greek: x], F[Greek: o],
F[Greek: t]. And this being known, it is easy to determine what
thickness of Air is represented by G[Greek: ph], or by any other
distance of the Ruler from AH.
But farther, since by the 10th Observation the thickness of Air was to
the thickness of Water, which between the same Glasses exhibited the
same Colour, as 4 to 3, and by the 21st Observation the Colours of thin
Bodies are not varied by varying the ambient Medium; the thickness of a
Bubble of Water, exhibiting any Colour, will be 3/4 of the thickness of
Air producing the same Colour. And so according to the same 10th and
21st Observations, the thickness of a Plate of Glass, whose Refraction
of the mean refrangible Ray, is measured by the proportion of the Sines
31 to 20, may be 20/31 of the thickness of Air producing the same
Colours; and the like of other Mediums. I do not affirm, that this
proportion of 20 to 31, holds in all the Rays; for the Sines of other
sorts of Rays have other Proportions. But the differences of those
Proportions are so little that I do not here consider them. On these
Grounds I have composed the following Table, wherein the thickness of
Air, Water, and Glass, at which each Colour is most intense and
specifick, is expressed in parts of an Inch divided into ten hundred
thousand equal parts.
Now if this Table be compared with the 6th Scheme, you will there see
the constitution of each Colour, as to its Ingredients, or the original
Colours of which it is compounded, and thence be enabled to judge of its
Intenseness or Imperfection; which may suffice in explication of the 4th
and 18th Observations, unless it be farther desired to delineate the
manner how the Colours appear, when the two Object-glasses are laid upon
one another. To do which, let there be described a large Arc of a
Circle, and a streight Line which may touch that Arc, and parallel to
that Tangent several occult Lines, at such distances from it, as the
Numbers set against the several Colours in the Table denote. For the
Arc, and its Tangent, will represent the Superficies of the Glasses
terminating the interjacent Air; and the places where the occult Lines
cut the Arc will show at what distances from the center, or Point of
contact, each Colour is reflected.
_The thickness of colour'd Plates and Particles of_
_____________|_______________
/ \
Air. Water. Glass.
|---------+----------+----------+
{Very black | 1/2 | 3/8 | 10/31 |
{Black | 1 | 3/4 | 20/31 |
{Beginning of | | | |
{ Black | 2 | 1-1/2 | 1-2/7 |
Their Colours of the {Blue | 2-2/5 | 1-4/5 | 1-11/22 |
first Order, {White | 5-1/4 | 3-7/8 | 3-2/5 |
{Yellow | 7-1/9 | 5-1/3 | 4-3/5 |
{Orange | 8 | 6 | 5-1/6 |
{Red | 9 | 6-3/4 | 5-4/5 |
|---------+----------+----------|
{Violet | 11-1/6 | 8-3/8 | 7-1/5 |
{Indigo | 12-5/6 | 9-5/8 | 8-2/11 |
{Blue | 14 | 10-1/2 | 9 |
{Green | 15-1/8 | 11-2/3 | 9-5/7 |
Of the second order, {Yellow | 16-2/7 | 12-1/5 | 10-2/5 |
{Orange | 17-2/9 | 13 | 11-1/9 |
{Bright red | 18-1/3 | 13-3/4 | 11-5/6 |
{Scarlet | 19-2/3 | 14-3/4 | 12-2/3 |
|---------+----------+----------|
{Purple | 21 | 15-3/4 | 13-11/20 |
{Indigo | 22-1/10 | 16-4/7 | 14-1/4 |
{Blue | 23-2/5 | 17-11/20 | 15-1/10 |
Of the third Order, {Green | 25-1/5 | 18-9/10 | 16-1/4 |
{Yellow | 27-1/7 | 20-1/3 | 17-1/2 |
{Red | 29 | 21-3/4 | 18-5/7 |
{Bluish red | 32 | 24 | 20-2/3 |
|---------+----------+----------|
{Bluish green | 34 | 25-1/2 | 22 |
{Green | 35-2/7 | 26-1/2 | 22-3/4 |
Of the fourth Order, {Yellowish green | 36 | 27 | 23-2/9 |
{Red | 40-1/3 | 30-1/4 | 26 |
|---------+----------+----------|
{Greenish blue | 46 | 34-1/2 | 29-2/3 |
Of the fifth Order, {Red | 52-1/2 | 39-3/8 | 34 |
|---------+----------+----------|
{Greenish blue | 58-3/4 | 44 | 38 |
Of the sixth Order, {Red | 65 | 48-3/4 | 42 |
|---------+----------+----------|
Of the seventh Order, {Greenish blue | 71 | 53-1/4 | 45-4/5 |
{Ruddy White | 77 | 57-3/4 | 49-2/3 |
|---------+----------+----------|
There are also other Uses of this Table: For by its assistance the
thickness of the Bubble in the 19th Observation was determin'd by the
Colours which it exhibited. And so the bigness of the parts of natural
Bodies may be conjectured by their Colours, as shall be hereafter shewn.
Also, if two or more very thin Plates be laid one upon another, so as to
compose one Plate equalling them all in thickness, the resulting Colour
may be hereby determin'd. For instance, Mr. _Hook_ observed, as is
mentioned in his _Micrographia_, that a faint yellow Plate of _Muscovy_
Glass laid upon a blue one, constituted a very deep purple. The yellow
of the first Order is a faint one, and the thickness of the Plate
exhibiting it, according to the Table is 4-3/5, to which add 9, the
thickness exhibiting blue of the second Order, and the Sum will be
13-3/5, which is the thickness exhibiting the purple of the third Order.
To explain, in the next place, the circumstances of the 2d and 3d
Observations; that is, how the Rings of the Colours may (by turning the
Prisms about their common Axis the contrary way to that expressed in
those Observations) be converted into white and black Rings, and
afterwards into Rings of Colours again, the Colours of each Ring lying
now in an inverted order; it must be remember'd, that those Rings of
Colours are dilated by the obliquation of the Rays to the Air which
intercedes the Glasses, and that according to the Table in the 7th
Observation, their Dilatation or Increase of their Diameter is most
manifest and speedy when they are obliquest. Now the Rays of yellow
being more refracted by the first Superficies of the said Air than those
of red, are thereby made more oblique to the second Superficies, at
which they are reflected to produce the colour'd Rings, and consequently
the yellow Circle in each Ring will be more dilated than the red; and
the Excess of its Dilatation will be so much the greater, by how much
the greater is the obliquity of the Rays, until at last it become of
equal extent with the red of the same Ring. And for the same reason the
green, blue and violet, will be also so much dilated by the still
greater obliquity of their Rays, as to become all very nearly of equal
extent with the red, that is, equally distant from the center of the
Rings. And then all the Colours of the same Ring must be co-incident,
and by their mixture exhibit a white Ring. And these white Rings must
have black and dark Rings between them, because they do not spread and
interfere with one another, as before. And for that reason also they
must become distincter, and visible to far greater numbers. But yet the
violet being obliquest will be something more dilated, in proportion to
its extent, than the other Colours, and so very apt to appear at the
exterior Verges of the white.
Afterwards, by a greater obliquity of the Rays, the violet and blue
become more sensibly dilated than the red and yellow, and so being
farther removed from the center of the Rings, the Colours must emerge
out of the white in an order contrary to that which they had before; the
violet and blue at the exterior Limbs of each Ring, and the red and
yellow at the interior. And the violet, by reason of the greatest
obliquity of its Rays, being in proportion most of all expanded, will
soonest appear at the exterior Limb of each white Ring, and become more
conspicuous than the rest. And the several Series of Colours belonging
to the several Rings, will, by their unfolding and spreading, begin
again to interfere, and thereby render the Rings less distinct, and not
visible to so great numbers.
If instead of the Prisms the Object-glasses be made use of, the Rings
which they exhibit become not white and distinct by the obliquity of the
Eye, by reason that the Rays in their passage through that Air which
intercedes the Glasses are very nearly parallel to those Lines in which
they were first incident on the Glasses, and consequently the Rays
endued with several Colours are not inclined one more than another to
that Air, as it happens in the Prisms.
There is yet another circumstance of these Experiments to be consider'd,
and that is why the black and white Rings which when view'd at a
distance appear distinct, should not only become confused by viewing
them near at hand, but also yield a violet Colour at both the edges of
every white Ring. And the reason is, that the Rays which enter the Eye
at several parts of the Pupil, have several Obliquities to the Glasses,
and those which are most oblique, if consider'd apart, would represent
the Rings bigger than those which are the least oblique. Whence the
breadth of the Perimeter of every white Ring is expanded outwards by the
obliquest Rays, and inwards by the least oblique. And this Expansion is
so much the greater by how much the greater is the difference of the
Obliquity; that is, by how much the Pupil is wider, or the Eye nearer to
the Glasses. And the breadth of the violet must be most expanded,
because the Rays apt to excite a Sensation of that Colour are most
oblique to a second or farther Superficies of the thinn'd Air at which
they are reflected, and have also the greatest variation of Obliquity,
which makes that Colour soonest emerge out of the edges of the white.
And as the breadth of every Ring is thus augmented, the dark Intervals
must be diminish'd, until the neighbouring Rings become continuous, and
are blended, the exterior first, and then those nearer the center; so
that they can no longer be distinguish'd apart, but seem to constitute
an even and uniform whiteness.
Among all the Observations there is none accompanied with so odd
circumstances as the twenty-fourth. Of those the principal are, that in
thin Plates, which to the naked Eye seem of an even and uniform
transparent whiteness, without any terminations of Shadows, the
Refraction of a Prism should make Rings of Colours appear, whereas it
usually makes Objects appear colour'd only there where they are
terminated with Shadows, or have parts unequally luminous; and that it
should make those Rings exceedingly distinct and white, although it
usually renders Objects confused and coloured. The Cause of these things
you will understand by considering, that all the Rings of Colours are
really in the Plate, when view'd with the naked Eye, although by reason
of the great breadth of their Circumferences they so much interfere and
are blended together, that they seem to constitute an uniform whiteness.
But when the Rays pass through the Prism to the Eye, the Orbits of the
several Colours in every Ring are refracted, some more than others,
according to their degrees of Refrangibility: By which means the Colours
on one side of the Ring (that is in the circumference on one side of its
center), become more unfolded and dilated, and those on the other side
more complicated and contracted. And where by a due Refraction they are
so much contracted, that the several Rings become narrower than to
interfere with one another, they must appear distinct, and also white,
if the constituent Colours be so much contracted as to be wholly
co-incident. But on the other side, where the Orbit of every Ring is
made broader by the farther unfolding of its Colours, it must interfere
more with other Rings than before, and so become less distinct.
[Illustration: FIG. 7.]
To explain this a little farther, suppose the concentrick Circles AV,
and BX, [in _Fig._ 7.] represent the red and violet of any Order, which,
together with the intermediate Colours, constitute any one of these
Rings. Now these being view'd through a Prism, the violet Circle BX,
will, by a greater Refraction, be farther translated from its place than
the red AV, and so approach nearer to it on that side of the Circles,
towards which the Refractions are made. For instance, if the red be
translated to _av_, the violet may be translated to _bx_, so as to
approach nearer to it at _x_ than before; and if the red be farther
translated to av, the violet may be so much farther translated to bx as
to convene with it at x; and if the red be yet farther translated to
[Greek: aY], the violet may be still so much farther translated to
[Greek: bx] as to pass beyond it at [Greek: x], and convene with it at
_e_ and _f_. And this being understood not only of the red and violet,
but of all the other intermediate Colours, and also of every revolution
of those Colours, you will easily perceive how those of the same
revolution or order, by their nearness at _xv_ and [Greek: Yx], and
their coincidence at xv, _e_ and _f_, ought to constitute pretty
distinct Arcs of Circles, especially at xv, or at _e_ and _f_; and that
they will appear severally at _x_[Greek: u] and at xv exhibit whiteness
by their coincidence, and again appear severally at [Greek: Yx], but yet
in a contrary order to that which they had before, and still retain
beyond _e_ and _f_. But on the other side, at _ab_, ab, or [Greek: ab],
these Colours must become much more confused by being dilated and spread
so as to interfere with those of other Orders. And the same confusion
will happen at [Greek: Ux] between _e_ and _f_, if the Refraction be
very great, or the Prism very distant from the Object-glasses: In which
case no parts of the Rings will be seen, save only two little Arcs at
_e_ and _f_, whose distance from one another will be augmented by
removing the Prism still farther from the Object-glasses: And these
little Arcs must be distinctest and whitest at their middle, and at
their ends, where they begin to grow confused, they must be colour'd.
And the Colours at one end of every Arc must be in a contrary order to
those at the other end, by reason that they cross in the intermediate
white; namely, their ends, which verge towards [Greek: Ux], will be red
and yellow on that side next the center, and blue and violet on the
other side. But their other ends which verge from [Greek: Ux], will on
the contrary be blue and violet on that side towards the center, and on
the other side red and yellow.
Now as all these things follow from the properties of Light by a
mathematical way of reasoning, so the truth of them may be manifested by
Experiments. For in a dark Room, by viewing these Rings through a Prism,
by reflexion of the several prismatick Colours, which an assistant
causes to move to and fro upon a Wall or Paper from whence they are
reflected, whilst the Spectator's Eye, the Prism, and the
Object-glasses, (as in the 13th Observation,) are placed steady; the
Position of the Circles made successively by the several Colours, will
be found such, in respect of one another, as I have described in the
Figures _abxv_, or abxv, or _[Greek: abxU]_. And by the same method the
truth of the Explications of other Observations may be examined.
By what hath been said, the like Phaenomena of Water and thin Plates of
Glass may be understood. But in small fragments of those Plates there is
this farther observable, that where they lie flat upon a Table, and are
turned about their centers whilst they are view'd through a Prism, they
will in some postures exhibit Waves of various Colours; and some of them
exhibit these Waves in one or two Positions only, but the most of them
do in all Positions exhibit them, and make them for the most part appear
almost all over the Plates. The reason is, that the Superficies of such
Plates are not even, but have many Cavities and Swellings, which, how
shallow soever, do a little vary the thickness of the Plate. For at the
several sides of those Cavities, for the Reasons newly described, there
ought to be produced Waves in several postures of the Prism. Now though
it be but some very small and narrower parts of the Glass, by which
these Waves for the most part are caused, yet they may seem to extend
themselves over the whole Glass, because from the narrowest of those
parts there are Colours of several Orders, that is, of several Rings,
confusedly reflected, which by Refraction of the Prism are unfolded,
separated, and, according to their degrees of Refraction, dispersed to
several places, so as to constitute so many several Waves, as there were
divers orders of Colours promiscuously reflected from that part of the
Glass.
These are the principal Phaenomena of thin Plates or Bubbles, whose
Explications depend on the properties of Light, which I have heretofore
deliver'd. And these you see do necessarily follow from them, and agree
with them, even to their very least circumstances; and not only so, but
do very much tend to their proof. Thus, by the 24th Observation it
appears, that the Rays of several Colours, made as well by thin Plates
or Bubbles, as by Refractions of a Prism, have several degrees of
Refrangibility; whereby those of each order, which at the reflexion from
the Plate or Bubble are intermix'd with those of other orders, are
separated from them by Refraction, and associated together so as to
become visible by themselves like Arcs of Circles. For if the Rays were
all alike refrangible, 'tis impossible that the whiteness, which to the
naked Sense appears uniform, should by Refraction have its parts
transposed and ranged into those black and white Arcs.
It appears also that the unequal Refractions of difform Rays proceed not
from any contingent irregularities; such as are Veins, an uneven Polish,
or fortuitous Position of the Pores of Glass; unequal and casual Motions
in the Air or AEther, the spreading, breaking, or dividing the same Ray
into many diverging parts; or the like. For, admitting any such
irregularities, it would be impossible for Refractions to render those
Rings so very distinct, and well defined, as they do in the 24th
Observation. It is necessary therefore that every Ray have its proper
and constant degree of Refrangibility connate with it, according to
which its refraction is ever justly and regularly perform'd; and that
several Rays have several of those degrees.
And what is said of their Refrangibility may be also understood of their
Reflexibility, that is, of their Dispositions to be reflected, some at a
greater, and others at a less thickness of thin Plates or Bubbles;
namely, that those Dispositions are also connate with the Rays, and
immutable; as may appear by the 13th, 14th, and 15th Observations,
compared with the fourth and eighteenth.
By the Precedent Observations it appears also, that whiteness is a
dissimilar mixture of all Colours, and that Light is a mixture of Rays
endued with all those Colours. For, considering the multitude of the
Rings of Colours in the 3d, 12th, and 24th Observations, it is manifest,
that although in the 4th and 18th Observations there appear no more than
eight or nine of those Rings, yet there are really a far greater number,
which so much interfere and mingle with one another, as after those
eight or nine revolutions to dilute one another wholly, and constitute
an even and sensibly uniform whiteness. And consequently that whiteness
must be allow'd a mixture of all Colours, and the Light which conveys it
to the Eye must be a mixture of Rays endued with all those Colours.
But farther; by the 24th Observation it appears, that there is a
constant relation between Colours and Refrangibility; the most
refrangible Rays being violet, the least refrangible red, and those of
intermediate Colours having proportionably intermediate degrees of
Refrangibility. And by the 13th, 14th, and 15th Observations, compared
with the 4th or 18th there appears to be the same constant relation
between Colour and Reflexibility; the violet being in like circumstances
reflected at least thicknesses of any thin Plate or Bubble, the red at
greatest thicknesses, and the intermediate Colours at intermediate
thicknesses. Whence it follows, that the colorifick Dispositions of
Rays are also connate with them, and immutable; and by consequence, that
all the Productions and Appearances of Colours in the World are derived,
not from any physical Change caused in Light by Refraction or Reflexion,
but only from the various Mixtures or Separations of Rays, by virtue of
their different Refrangibility or Reflexibility. And in this respect the
Science of Colours becomes a Speculation as truly mathematical as any
other part of Opticks. I mean, so far as they depend on the Nature of
Light, and are not produced or alter'd by the Power of Imagination, or
by striking or pressing the Eye.