[A] In our Author's _Lectiones Opticae_, Part I. Sect. IV. Prop 29, 30,
there is an elegant Method of determining these _Foci_; not only in
spherical Surfaces, but likewise in any other curved Figure whatever:
And in Prop. 32, 33, the same thing is done for any Ray lying out of the
Axis.
[B] _Ibid._ Prop. 34.
_PROPOSITIONS._
_PROP._ I. THEOR. I.
_Lights which differ in Colour, differ also in Degrees of
Refrangibility._
The PROOF by Experiments.
_Exper._ 1.
I took a black oblong stiff Paper terminated by Parallel Sides, and with
a Perpendicular right Line drawn cross from one Side to the other,
distinguished it into two equal Parts. One of these parts I painted with
a red colour and the other with a blue. The Paper was very black, and
the Colours intense and thickly laid on, that the Phaenomenon might be
more conspicuous. This Paper I view'd through a Prism of solid Glass,
whose two Sides through which the Light passed to the Eye were plane and
well polished, and contained an Angle of about sixty degrees; which
Angle I call the refracting Angle of the Prism. And whilst I view'd it,
I held it and the Prism before a Window in such manner that the Sides of
the Paper were parallel to the Prism, and both those Sides and the Prism
were parallel to the Horizon, and the cross Line was also parallel to
it: and that the Light which fell from the Window upon the Paper made an
Angle with the Paper, equal to that Angle which was made with the same
Paper by the Light reflected from it to the Eye. Beyond the Prism was
the Wall of the Chamber under the Window covered over with black Cloth,
and the Cloth was involved in Darkness that no Light might be reflected
from thence, which in passing by the Edges of the Paper to the Eye,
might mingle itself with the Light of the Paper, and obscure the
Phaenomenon thereof. These things being thus ordered, I found that if the
refracting Angle of the Prism be turned upwards, so that the Paper may
seem to be lifted upwards by the Refraction, its blue half will be
lifted higher by the Refraction than its red half. But if the refracting
Angle of the Prism be turned downward, so that the Paper may seem to be
carried lower by the Refraction, its blue half will be carried something
lower thereby than its red half. Wherefore in both Cases the Light which
comes from the blue half of the Paper through the Prism to the Eye, does
in like Circumstances suffer a greater Refraction than the Light which
comes from the red half, and by consequence is more refrangible.
_Illustration._ In the eleventh Figure, MN represents the Window, and DE
the Paper terminated with parallel Sides DJ and HE, and by the
transverse Line FG distinguished into two halfs, the one DG of an
intensely blue Colour, the other FE of an intensely red. And BAC_cab_
represents the Prism whose refracting Planes AB_ba_ and AC_ca_ meet in
the Edge of the refracting Angle A_a_. This Edge A_a_ being upward, is
parallel both to the Horizon, and to the Parallel-Edges of the Paper DJ
and HE, and the transverse Line FG is perpendicular to the Plane of the
Window. And _de_ represents the Image of the Paper seen by Refraction
upwards in such manner, that the blue half DG is carried higher to _dg_
than the red half FE is to _fe_, and therefore suffers a greater
Refraction. If the Edge of the refracting Angle be turned downward, the
Image of the Paper will be refracted downward; suppose to [Greek: de],
and the blue half will be refracted lower to [Greek: dg] than the red
half is to [Greek: pe].
[Illustration: FIG. 11.]
_Exper._ 2. About the aforesaid Paper, whose two halfs were painted over
with red and blue, and which was stiff like thin Pasteboard, I lapped
several times a slender Thred of very black Silk, in such manner that
the several parts of the Thred might appear upon the Colours like so
many black Lines drawn over them, or like long and slender dark Shadows
cast upon them. I might have drawn black Lines with a Pen, but the
Threds were smaller and better defined. This Paper thus coloured and
lined I set against a Wall perpendicularly to the Horizon, so that one
of the Colours might stand to the Right Hand, and the other to the Left.
Close before the Paper, at the Confine of the Colours below, I placed a
Candle to illuminate the Paper strongly: For the Experiment was tried in
the Night. The Flame of the Candle reached up to the lower edge of the
Paper, or a very little higher. Then at the distance of six Feet, and
one or two Inches from the Paper upon the Floor I erected a Glass Lens
four Inches and a quarter broad, which might collect the Rays coming
from the several Points of the Paper, and make them converge towards so
many other Points at the same distance of six Feet, and one or two
Inches on the other side of the Lens, and so form the Image of the
coloured Paper upon a white Paper placed there, after the same manner
that a Lens at a Hole in a Window casts the Images of Objects abroad
upon a Sheet of white Paper in a dark Room. The aforesaid white Paper,
erected perpendicular to the Horizon, and to the Rays which fell upon it
from the Lens, I moved sometimes towards the Lens, sometimes from it, to
find the Places where the Images of the blue and red Parts of the
coloured Paper appeared most distinct. Those Places I easily knew by the
Images of the black Lines which I had made by winding the Silk about the
Paper. For the Images of those fine and slender Lines (which by reason
of their Blackness were like Shadows on the Colours) were confused and
scarce visible, unless when the Colours on either side of each Line were
terminated most distinctly, Noting therefore, as diligently as I could,
the Places where the Images of the red and blue halfs of the coloured
Paper appeared most distinct, I found that where the red half of the
Paper appeared distinct, the blue half appeared confused, so that the
black Lines drawn upon it could scarce be seen; and on the contrary,
where the blue half appeared most distinct, the red half appeared
confused, so that the black Lines upon it were scarce visible. And
between the two Places where these Images appeared distinct there was
the distance of an Inch and a half; the distance of the white Paper from
the Lens, when the Image of the red half of the coloured Paper appeared
most distinct, being greater by an Inch and an half than the distance of
the same white Paper from the Lens, when the Image of the blue half
appeared most distinct. In like Incidences therefore of the blue and red
upon the Lens, the blue was refracted more by the Lens than the red, so
as to converge sooner by an Inch and a half, and therefore is more
refrangible.
_Illustration._ In the twelfth Figure (p. 27), DE signifies the coloured
Paper, DG the blue half, FE the red half, MN the Lens, HJ the white
Paper in that Place where the red half with its black Lines appeared
distinct, and _hi_ the same Paper in that Place where the blue half
appeared distinct. The Place _hi_ was nearer to the Lens MN than the
Place HJ by an Inch and an half.
_Scholium._ The same Things succeed, notwithstanding that some of the
Circumstances be varied; as in the first Experiment when the Prism and
Paper are any ways inclined to the Horizon, and in both when coloured
Lines are drawn upon very black Paper. But in the Description of these
Experiments, I have set down such Circumstances, by which either the
Phaenomenon might be render'd more conspicuous, or a Novice might more
easily try them, or by which I did try them only. The same Thing, I have
often done in the following Experiments: Concerning all which, this one
Admonition may suffice. Now from these Experiments it follows not, that
all the Light of the blue is more refrangible than all the Light of the
red: For both Lights are mixed of Rays differently refrangible, so that
in the red there are some Rays not less refrangible than those of the
blue, and in the blue there are some Rays not more refrangible than
those of the red: But these Rays, in proportion to the whole Light, are
but few, and serve to diminish the Event of the Experiment, but are not
able to destroy it. For, if the red and blue Colours were more dilute
and weak, the distance of the Images would be less than an Inch and a
half; and if they were more intense and full, that distance would be
greater, as will appear hereafter. These Experiments may suffice for the
Colours of Natural Bodies. For in the Colours made by the Refraction of
Prisms, this Proposition will appear by the Experiments which are now to
follow in the next Proposition.
_PROP._ II. THEOR. II.
_The Light of the Sun consists of Rays differently Refrangible._
The PROOF by Experiments.
[Illustration: FIG. 12.]
[Illustration: FIG. 13.]
_Exper._ 3.
In a very dark Chamber, at a round Hole, about one third Part of an Inch
broad, made in the Shut of a Window, I placed a Glass Prism, whereby the
Beam of the Sun's Light, which came in at that Hole, might be refracted
upwards toward the opposite Wall of the Chamber, and there form a
colour'd Image of the Sun. The Axis of the Prism (that is, the Line
passing through the middle of the Prism from one end of it to the other
end parallel to the edge of the Refracting Angle) was in this and the
following Experiments perpendicular to the incident Rays. About this
Axis I turned the Prism slowly, and saw the refracted Light on the Wall,
or coloured Image of the Sun, first to descend, and then to ascend.
Between the Descent and Ascent, when the Image seemed Stationary, I
stopp'd the Prism, and fix'd it in that Posture, that it should be moved
no more. For in that Posture the Refractions of the Light at the two
Sides of the refracting Angle, that is, at the Entrance of the Rays into
the Prism, and at their going out of it, were equal to one another.[C]
So also in other Experiments, as often as I would have the Refractions
on both sides the Prism to be equal to one another, I noted the Place
where the Image of the Sun formed by the refracted Light stood still
between its two contrary Motions, in the common Period of its Progress
and Regress; and when the Image fell upon that Place, I made fast the
Prism. And in this Posture, as the most convenient, it is to be
understood that all the Prisms are placed in the following Experiments,
unless where some other Posture is described. The Prism therefore being
placed in this Posture, I let the refracted Light fall perpendicularly
upon a Sheet of white Paper at the opposite Wall of the Chamber, and
observed the Figure and Dimensions of the Solar Image formed on the
Paper by that Light. This Image was Oblong and not Oval, but terminated
with two Rectilinear and Parallel Sides, and two Semicircular Ends. On
its Sides it was bounded pretty distinctly, but on its Ends very
confusedly and indistinctly, the Light there decaying and vanishing by
degrees. The Breadth of this Image answered to the Sun's Diameter, and
was about two Inches and the eighth Part of an Inch, including the
Penumbra. For the Image was eighteen Feet and an half distant from the
Prism, and at this distance that Breadth, if diminished by the Diameter
of the Hole in the Window-shut, that is by a quarter of an Inch,
subtended an Angle at the Prism of about half a Degree, which is the
Sun's apparent Diameter. But the Length of the Image was about ten
Inches and a quarter, and the Length of the Rectilinear Sides about
eight Inches; and the refracting Angle of the Prism, whereby so great a
Length was made, was 64 degrees. With a less Angle the Length of the
Image was less, the Breadth remaining the same. If the Prism was turned
about its Axis that way which made the Rays emerge more obliquely out of
the second refracting Surface of the Prism, the Image soon became an
Inch or two longer, or more; and if the Prism was turned about the
contrary way, so as to make the Rays fall more obliquely on the first
refracting Surface, the Image soon became an Inch or two shorter. And
therefore in trying this Experiment, I was as curious as I could be in
placing the Prism by the above-mention'd Rule exactly in such a Posture,
that the Refractions of the Rays at their Emergence out of the Prism
might be equal to that at their Incidence on it. This Prism had some
Veins running along within the Glass from one end to the other, which
scattered some of the Sun's Light irregularly, but had no sensible
Effect in increasing the Length of the coloured Spectrum. For I tried
the same Experiment with other Prisms with the same Success. And
particularly with a Prism which seemed free from such Veins, and whose
refracting Angle was 62-1/2 Degrees, I found the Length of the Image
9-3/4 or 10 Inches at the distance of 18-1/2 Feet from the Prism, the
Breadth of the Hole in the Window-shut being 1/4 of an Inch, as before.
And because it is easy to commit a Mistake in placing the Prism in its
due Posture, I repeated the Experiment four or five Times, and always
found the Length of the Image that which is set down above. With another
Prism of clearer Glass and better Polish, which seemed free from Veins,
and whose refracting Angle was 63-1/2 Degrees, the Length of this Image
at the same distance of 18-1/2 Feet was also about 10 Inches, or 10-1/8.
Beyond these Measures for about a 1/4 or 1/3 of an Inch at either end of
the Spectrum the Light of the Clouds seemed to be a little tinged with
red and violet, but so very faintly, that I suspected that Tincture
might either wholly, or in great Measure arise from some Rays of the
Spectrum scattered irregularly by some Inequalities in the Substance and
Polish of the Glass, and therefore I did not include it in these
Measures. Now the different Magnitude of the hole in the Window-shut,
and different thickness of the Prism where the Rays passed through it,
and different inclinations of the Prism to the Horizon, made no sensible
changes in the length of the Image. Neither did the different matter of
the Prisms make any: for in a Vessel made of polished Plates of Glass
cemented together in the shape of a Prism and filled with Water, there
is the like Success of the Experiment according to the quantity of the
Refraction. It is farther to be observed, that the Rays went on in right
Lines from the Prism to the Image, and therefore at their very going out
of the Prism had all that Inclination to one another from which the
length of the Image proceeded, that is, the Inclination of more than two
degrees and an half. And yet according to the Laws of Opticks vulgarly
received, they could not possibly be so much inclined to one another.[D]
For let EG [_Fig._ 13. (p. 27)] represent the Window-shut, F the hole
made therein through which a beam of the Sun's Light was transmitted
into the darkened Chamber, and ABC a Triangular Imaginary Plane whereby
the Prism is feigned to be cut transversely through the middle of the
Light. Or if you please, let ABC represent the Prism it self, looking
directly towards the Spectator's Eye with its nearer end: And let XY be
the Sun, MN the Paper upon which the Solar Image or Spectrum is cast,
and PT the Image it self whose sides towards _v_ and _w_ are Rectilinear
and Parallel, and ends towards P and T Semicircular. YKHP and XLJT are
two Rays, the first of which comes from the lower part of the Sun to the
higher part of the Image, and is refracted in the Prism at K and H, and
the latter comes from the higher part of the Sun to the lower part of
the Image, and is refracted at L and J. Since the Refractions on both
sides the Prism are equal to one another, that is, the Refraction at K
equal to the Refraction at J, and the Refraction at L equal to the
Refraction at H, so that the Refractions of the incident Rays at K and L
taken together, are equal to the Refractions of the emergent Rays at H
and J taken together: it follows by adding equal things to equal things,
that the Refractions at K and H taken together, are equal to the
Refractions at J and L taken together, and therefore the two Rays being
equally refracted, have the same Inclination to one another after
Refraction which they had before; that is, the Inclination of half a
Degree answering to the Sun's Diameter. For so great was the inclination
of the Rays to one another before Refraction. So then, the length of the
Image PT would by the Rules of Vulgar Opticks subtend an Angle of half a
Degree at the Prism, and by Consequence be equal to the breadth _vw_;
and therefore the Image would be round. Thus it would be were the two
Rays XLJT and YKHP, and all the rest which form the Image P_w_T_v_,
alike refrangible. And therefore seeing by Experience it is found that
the Image is not round, but about five times longer than broad, the Rays
which going to the upper end P of the Image suffer the greatest
Refraction, must be more refrangible than those which go to the lower
end T, unless the Inequality of Refraction be casual.
This Image or Spectrum PT was coloured, being red at its least refracted
end T, and violet at its most refracted end P, and yellow green and
blue in the intermediate Spaces. Which agrees with the first
Proposition, that Lights which differ in Colour, do also differ in
Refrangibility. The length of the Image in the foregoing Experiments, I
measured from the faintest and outmost red at one end, to the faintest
and outmost blue at the other end, excepting only a little Penumbra,
whose breadth scarce exceeded a quarter of an Inch, as was said above.
_Exper._ 4. In the Sun's Beam which was propagated into the Room through
the hole in the Window-shut, at the distance of some Feet from the hole,
I held the Prism in such a Posture, that its Axis might be perpendicular
to that Beam. Then I looked through the Prism upon the hole, and turning
the Prism to and fro about its Axis, to make the Image of the Hole
ascend and descend, when between its two contrary Motions it seemed
Stationary, I stopp'd the Prism, that the Refractions of both sides of
the refracting Angle might be equal to each other, as in the former
Experiment. In this situation of the Prism viewing through it the said
Hole, I observed the length of its refracted Image to be many times
greater than its breadth, and that the most refracted part thereof
appeared violet, the least refracted red, the middle parts blue, green
and yellow in order. The same thing happen'd when I removed the Prism
out of the Sun's Light, and looked through it upon the hole shining by
the Light of the Clouds beyond it. And yet if the Refraction were done
regularly according to one certain Proportion of the Sines of Incidence
and Refraction as is vulgarly supposed, the refracted Image ought to
have appeared round.
So then, by these two Experiments it appears, that in Equal Incidences
there is a considerable inequality of Refractions. But whence this
inequality arises, whether it be that some of the incident Rays are
refracted more, and others less, constantly, or by chance, or that one
and the same Ray is by Refraction disturbed, shatter'd, dilated, and as
it were split and spread into many diverging Rays, as _Grimaldo_
supposes, does not yet appear by these Experiments, but will appear by
those that follow.
_Exper._ 5. Considering therefore, that if in the third Experiment the
Image of the Sun should be drawn out into an oblong Form, either by a
Dilatation of every Ray, or by any other casual inequality of the
Refractions, the same oblong Image would by a second Refraction made
sideways be drawn out as much in breadth by the like Dilatation of the
Rays, or other casual inequality of the Refractions sideways, I tried
what would be the Effects of such a second Refraction. For this end I
ordered all things as in the third Experiment, and then placed a second
Prism immediately after the first in a cross Position to it, that it
might again refract the beam of the Sun's Light which came to it through
the first Prism. In the first Prism this beam was refracted upwards, and
in the second sideways. And I found that by the Refraction of the second
Prism, the breadth of the Image was not increased, but its superior
part, which in the first Prism suffered the greater Refraction, and
appeared violet and blue, did again in the second Prism suffer a greater
Refraction than its inferior part, which appeared red and yellow, and
this without any Dilatation of the Image in breadth.
[Illustration: FIG. 14]
_Illustration._ Let S [_Fig._ 14, 15.] represent the Sun, F the hole in
the Window, ABC the first Prism, DH the second Prism, Y the round Image
of the Sun made by a direct beam of Light when the Prisms are taken
away, PT the oblong Image of the Sun made by that beam passing through
the first Prism alone, when the second Prism is taken away, and _pt_ the
Image made by the cross Refractions of both Prisms together. Now if the
Rays which tend towards the several Points of the round Image Y were
dilated and spread by the Refraction of the first Prism, so that they
should not any longer go in single Lines to single Points, but that
every Ray being split, shattered, and changed from a Linear Ray to a
Superficies of Rays diverging from the Point of Refraction, and lying in
the Plane of the Angles of Incidence and Refraction, they should go in
those Planes to so many Lines reaching almost from one end of the Image
PT to the other, and if that Image should thence become oblong: those
Rays and their several parts tending towards the several Points of the
Image PT ought to be again dilated and spread sideways by the transverse
Refraction of the second Prism, so as to compose a four square Image,
such as is represented at [Greek: pt]. For the better understanding of
which, let the Image PT be distinguished into five equal parts PQK,
KQRL, LRSM, MSVN, NVT. And by the same irregularity that the orbicular
Light Y is by the Refraction of the first Prism dilated and drawn out
into a long Image PT, the Light PQK which takes up a space of the same
length and breadth with the Light Y ought to be by the Refraction of the
second Prism dilated and drawn out into the long Image _[Greek: p]qkp_,
and the Light KQRL into the long Image _kqrl_, and the Lights LRSM,
MSVN, NVT, into so many other long Images _lrsm_, _msvn_, _nvt[Greek:
t]_; and all these long Images would compose the four square Images
_[Greek: pt]_. Thus it ought to be were every Ray dilated by Refraction,
and spread into a triangular Superficies of Rays diverging from the
Point of Refraction. For the second Refraction would spread the Rays one
way as much as the first doth another, and so dilate the Image in
breadth as much as the first doth in length. And the same thing ought to
happen, were some rays casually refracted more than others. But the
Event is otherwise. The Image PT was not made broader by the Refraction
of the second Prism, but only became oblique, as 'tis represented at
_pt_, its upper end P being by the Refraction translated to a greater
distance than its lower end T. So then the Light which went towards the
upper end P of the Image, was (at equal Incidences) more refracted in
the second Prism, than the Light which tended towards the lower end T,
that is the blue and violet, than the red and yellow; and therefore was
more refrangible. The same Light was by the Refraction of the first
Prism translated farther from the place Y to which it tended before
Refraction; and therefore suffered as well in the first Prism as in the
second a greater Refraction than the rest of the Light, and by
consequence was more refrangible than the rest, even before its
incidence on the first Prism.
Sometimes I placed a third Prism after the second, and sometimes also a
fourth after the third, by all which the Image might be often refracted
sideways: but the Rays which were more refracted than the rest in the
first Prism were also more refracted in all the rest, and that without
any Dilatation of the Image sideways: and therefore those Rays for their
constancy of a greater Refraction are deservedly reputed more
refrangible.
[Illustration: FIG. 15]
But that the meaning of this Experiment may more clearly appear, it is
to be considered that the Rays which are equally refrangible do fall
upon a Circle answering to the Sun's Disque. For this was proved in the
third Experiment. By a Circle I understand not here a perfect
geometrical Circle, but any orbicular Figure whose length is equal to
its breadth, and which, as to Sense, may seem circular. Let therefore AG
[in _Fig._ 15.] represent the Circle which all the most refrangible Rays
propagated from the whole Disque of the Sun, would illuminate and paint
upon the opposite Wall if they were alone; EL the Circle which all the
least refrangible Rays would in like manner illuminate and paint if they
were alone; BH, CJ, DK, the Circles which so many intermediate sorts of
Rays would successively paint upon the Wall, if they were singly
propagated from the Sun in successive order, the rest being always
intercepted; and conceive that there are other intermediate Circles
without Number, which innumerable other intermediate sorts of Rays would
successively paint upon the Wall if the Sun should successively emit
every sort apart. And seeing the Sun emits all these sorts at once, they
must all together illuminate and paint innumerable equal Circles, of all
which, being according to their degrees of Refrangibility placed in
order in a continual Series, that oblong Spectrum PT is composed which I
described in the third Experiment. Now if the Sun's circular Image Y [in
_Fig._ 15.] which is made by an unrefracted beam of Light was by any
Dilation of the single Rays, or by any other irregularity in the
Refraction of the first Prism, converted into the oblong Spectrum, PT:
then ought every Circle AG, BH, CJ, &c. in that Spectrum, by the cross
Refraction of the second Prism again dilating or otherwise scattering
the Rays as before, to be in like manner drawn out and transformed into
an oblong Figure, and thereby the breadth of the Image PT would be now
as much augmented as the length of the Image Y was before by the
Refraction of the first Prism; and thus by the Refractions of both
Prisms together would be formed a four square Figure _p[Greek:
p]t[Greek: t]_, as I described above. Wherefore since the breadth of the
Spectrum PT is not increased by the Refraction sideways, it is certain
that the Rays are not split or dilated, or otherways irregularly
scatter'd by that Refraction, but that every Circle is by a regular and
uniform Refraction translated entire into another Place, as the Circle
AG by the greatest Refraction into the place _ag_, the Circle BH by a
less Refraction into the place _bh_, the Circle CJ by a Refraction still
less into the place _ci_, and so of the rest; by which means a new
Spectrum _pt_ inclined to the former PT is in like manner composed of
Circles lying in a right Line; and these Circles must be of the same
bigness with the former, because the breadths of all the Spectrums Y, PT
and _pt_ at equal distances from the Prisms are equal.
I considered farther, that by the breadth of the hole F through which
the Light enters into the dark Chamber, there is a Penumbra made in the
Circuit of the Spectrum Y, and that Penumbra remains in the rectilinear
Sides of the Spectrums PT and _pt_. I placed therefore at that hole a
Lens or Object-glass of a Telescope which might cast the Image of the
Sun distinctly on Y without any Penumbra at all, and found that the
Penumbra of the rectilinear Sides of the oblong Spectrums PT and _pt_
was also thereby taken away, so that those Sides appeared as distinctly
defined as did the Circumference of the first Image Y. Thus it happens
if the Glass of the Prisms be free from Veins, and their sides be
accurately plane and well polished without those numberless Waves or
Curles which usually arise from Sand-holes a little smoothed in
polishing with Putty. If the Glass be only well polished and free from
Veins, and the Sides not accurately plane, but a little Convex or
Concave, as it frequently happens; yet may the three Spectrums Y, PT and
_pt_ want Penumbras, but not in equal distances from the Prisms. Now
from this want of Penumbras, I knew more certainly that every one of the
Circles was refracted according to some most regular, uniform and
constant Law. For if there were any irregularity in the Refraction, the
right Lines AE and GL, which all the Circles in the Spectrum PT do
touch, could not by that Refraction be translated into the Lines _ae_
and _gl_ as distinct and straight as they were before, but there would
arise in those translated Lines some Penumbra or Crookedness or
Undulation, or other sensible Perturbation contrary to what is found by
Experience. Whatsoever Penumbra or Perturbation should be made in the
Circles by the cross Refraction of the second Prism, all that Penumbra
or Perturbation would be conspicuous in the right Lines _ae_ and _gl_
which touch those Circles. And therefore since there is no such Penumbra
or Perturbation in those right Lines, there must be none in the
Circles. Since the distance between those Tangents or breadth of the
Spectrum is not increased by the Refractions, the Diameters of the
Circles are not increased thereby. Since those Tangents continue to be
right Lines, every Circle which in the first Prism is more or less
refracted, is exactly in the same proportion more or less refracted in
the second. And seeing all these things continue to succeed after the
same manner when the Rays are again in a third Prism, and again in a
fourth refracted sideways, it is evident that the Rays of one and the
same Circle, as to their degree of Refrangibility, continue always
uniform and homogeneal to one another, and that those of several Circles
do differ in degree of Refrangibility, and that in some certain and
constant Proportion. Which is the thing I was to prove.
There is yet another Circumstance or two of this Experiment by which it
becomes still more plain and convincing. Let the second Prism DH [in
_Fig._ 16.] be placed not immediately after the first, but at some
distance from it; suppose in the mid-way between it and the Wall on
which the oblong Spectrum PT is cast, so that the Light from the first
Prism may fall upon it in the form of an oblong Spectrum [Greek: pt]
parallel to this second Prism, and be refracted sideways to form the
oblong Spectrum _pt_ upon the Wall. And you will find as before, that
this Spectrum _pt_ is inclined to that Spectrum PT, which the first
Prism forms alone without the second; the blue ends P and _p_ being
farther distant from one another than the red ones T and _t_, and by
consequence that the Rays which go to the blue end [Greek: p] of the
Image [Greek: pt], and which therefore suffer the greatest Refraction in
the first Prism, are again in the second Prism more refracted than the
rest.
[Illustration: FIG. 16.]
[Illustration: FIG. 17.]
The same thing I try'd also by letting the Sun's Light into a dark Room
through two little round holes F and [Greek: ph] [in _Fig._ 17.] made in
the Window, and with two parallel Prisms ABC and [Greek: abg] placed at
those holes (one at each) refracting those two beams of Light to the
opposite Wall of the Chamber, in such manner that the two colour'd
Images PT and MN which they there painted were joined end to end and lay
in one straight Line, the red end T of the one touching the blue end M
of the other. For if these two refracted Beams were again by a third
Prism DH placed cross to the two first, refracted sideways, and the
Spectrums thereby translated to some other part of the Wall of the
Chamber, suppose the Spectrum PT to _pt_ and the Spectrum MN to _mn_,
these translated Spectrums _pt_ and _mn_ would not lie in one straight
Line with their ends contiguous as before, but be broken off from one
another and become parallel, the blue end _m_ of the Image _mn_ being by
a greater Refraction translated farther from its former place MT, than
the red end _t_ of the other Image _pt_ from the same place MT; which
puts the Proposition past Dispute. And this happens whether the third
Prism DH be placed immediately after the two first, or at a great
distance from them, so that the Light refracted in the two first Prisms
be either white and circular, or coloured and oblong when it falls on
the third.
_Exper._ 6. In the middle of two thin Boards I made round holes a third
part of an Inch in diameter, and in the Window-shut a much broader hole
being made to let into my darkned Chamber a large Beam of the Sun's
Light; I placed a Prism behind the Shut in that beam to refract it
towards the opposite Wall, and close behind the Prism I fixed one of the
Boards, in such manner that the middle of the refracted Light might pass
through the hole made in it, and the rest be intercepted by the Board.
Then at the distance of about twelve Feet from the first Board I fixed
the other Board in such manner that the middle of the refracted Light
which came through the hole in the first Board, and fell upon the
opposite Wall, might pass through the hole in this other Board, and the
rest being intercepted by the Board might paint upon it the coloured
Spectrum of the Sun. And close behind this Board I fixed another Prism
to refract the Light which came through the hole. Then I returned
speedily to the first Prism, and by turning it slowly to and fro about
its Axis, I caused the Image which fell upon the second Board to move up
and down upon that Board, that all its parts might successively pass
through the hole in that Board and fall upon the Prism behind it. And in
the mean time, I noted the places on the opposite Wall to which that
Light after its Refraction in the second Prism did pass; and by the
difference of the places I found that the Light which being most
refracted in the first Prism did go to the blue end of the Image, was
again more refracted in the second Prism than the Light which went to
the red end of that Image, which proves as well the first Proposition as
the second. And this happened whether the Axis of the two Prisms were
parallel, or inclined to one another, and to the Horizon in any given
Angles.
_Illustration._ Let F [in _Fig._ 18.] be the wide hole in the
Window-shut, through which the Sun shines upon the first Prism ABC, and
let the refracted Light fall upon the middle of the Board DE, and the
middle part of that Light upon the hole G made in the middle part of
that Board. Let this trajected part of that Light fall again upon the
middle of the second Board _de_, and there paint such an oblong coloured
Image of the Sun as was described in the third Experiment. By turning
the Prism ABC slowly to and fro about its Axis, this Image will be made
to move up and down the Board _de_, and by this means all its parts from
one end to the other may be made to pass successively through the hole
_g_ which is made in the middle of that Board. In the mean while another
Prism _abc_ is to be fixed next after that hole _g_, to refract the
trajected Light a second time. And these things being thus ordered, I
marked the places M and N of the opposite Wall upon which the refracted
Light fell, and found that whilst the two Boards and second Prism
remained unmoved, those places by turning the first Prism about its Axis
were changed perpetually. For when the lower part of the Light which
fell upon the second Board _de_ was cast through the hole _g_, it went
to a lower place M on the Wall and when the higher part of that Light
was cast through the same hole _g_, it went to a higher place N on the
Wall, and when any intermediate part of the Light was cast through that
hole, it went to some place on the Wall between M and N. The unchanged
Position of the holes in the Boards, made the Incidence of the Rays upon
the second Prism to be the same in all cases. And yet in that common
Incidence some of the Rays were more refracted, and others less. And
those were more refracted in this Prism, which by a greater Refraction
in the first Prism were more turned out of the way, and therefore for
their Constancy of being more refracted are deservedly called more
refrangible.
[Illustration: FIG. 18.]
[Illustration: FIG. 20.]
_Exper._ 7. At two holes made near one another in my Window-shut I
placed two Prisms, one at each, which might cast upon the opposite Wall
(after the manner of the third Experiment) two oblong coloured Images of
the Sun. And at a little distance from the Wall I placed a long slender
Paper with straight and parallel edges, and ordered the Prisms and Paper
so, that the red Colour of one Image might fall directly upon one half
of the Paper, and the violet Colour of the other Image upon the other
half of the same Paper; so that the Paper appeared of two Colours, red
and violet, much after the manner of the painted Paper in the first and
second Experiments. Then with a black Cloth I covered the Wall behind
the Paper, that no Light might be reflected from it to disturb the
Experiment, and viewing the Paper through a third Prism held parallel
to it, I saw that half of it which was illuminated by the violet Light
to be divided from the other half by a greater Refraction, especially
when I went a good way off from the Paper. For when I viewed it too near
at hand, the two halfs of the Paper did not appear fully divided from
one another, but seemed contiguous at one of their Angles like the
painted Paper in the first Experiment. Which also happened when the
Paper was too broad.
[Illustration: FIG. 19.]
Sometimes instead of the Paper I used a white Thred, and this appeared
through the Prism divided into two parallel Threds as is represented in
the nineteenth Figure, where DG denotes the Thred illuminated with
violet Light from D to E and with red Light from F to G, and _defg_ are
the parts of the Thred seen by Refraction. If one half of the Thred be
constantly illuminated with red, and the other half be illuminated with
all the Colours successively, (which may be done by causing one of the
Prisms to be turned about its Axis whilst the other remains unmoved)
this other half in viewing the Thred through the Prism, will appear in
a continual right Line with the first half when illuminated with red,
and begin to be a little divided from it when illuminated with Orange,
and remove farther from it when illuminated with yellow, and still
farther when with green, and farther when with blue, and go yet farther
off when illuminated with Indigo, and farthest when with deep violet.
Which plainly shews, that the Lights of several Colours are more and
more refrangible one than another, in this Order of their Colours, red,
orange, yellow, green, blue, indigo, deep violet; and so proves as well
the first Proposition as the second.
I caused also the coloured Spectrums PT [in _Fig._ 17.] and MN made in a
dark Chamber by the Refractions of two Prisms to lie in a Right Line end
to end, as was described above in the fifth Experiment, and viewing them
through a third Prism held parallel to their Length, they appeared no
longer in a Right Line, but became broken from one another, as they are
represented at _pt_ and _mn_, the violet end _m_ of the Spectrum _mn_
being by a greater Refraction translated farther from its former Place
MT than the red end _t_ of the other Spectrum _pt_.
I farther caused those two Spectrums PT [in _Fig._ 20.] and MN to become
co-incident in an inverted Order of their Colours, the red end of each
falling on the violet end of the other, as they are represented in the
oblong Figure PTMN; and then viewing them through a Prism DH held
parallel to their Length, they appeared not co-incident, as when view'd
with the naked Eye, but in the form of two distinct Spectrums _pt_ and
_mn_ crossing one another in the middle after the manner of the Letter
X. Which shews that the red of the one Spectrum and violet of the other,
which were co-incident at PN and MT, being parted from one another by a
greater Refraction of the violet to _p_ and _m_ than of the red to _n_
and _t_, do differ in degrees of Refrangibility.
I illuminated also a little Circular Piece of white Paper all over with
the Lights of both Prisms intermixed, and when it was illuminated with
the red of one Spectrum, and deep violet of the other, so as by the
Mixture of those Colours to appear all over purple, I viewed the Paper,
first at a less distance, and then at a greater, through a third Prism;
and as I went from the Paper, the refracted Image thereof became more
and more divided by the unequal Refraction of the two mixed Colours, and
at length parted into two distinct Images, a red one and a violet one,
whereof the violet was farthest from the Paper, and therefore suffered
the greatest Refraction. And when that Prism at the Window, which cast
the violet on the Paper was taken away, the violet Image disappeared;
but when the other Prism was taken away the red vanished; which shews,
that these two Images were nothing else than the Lights of the two
Prisms, which had been intermixed on the purple Paper, but were parted
again by their unequal Refractions made in the third Prism, through
which the Paper was view'd. This also was observable, that if one of the
Prisms at the Window, suppose that which cast the violet on the Paper,
was turned about its Axis to make all the Colours in this order,
violet, indigo, blue, green, yellow, orange, red, fall successively on
the Paper from that Prism, the violet Image changed Colour accordingly,
turning successively to indigo, blue, green, yellow and red, and in
changing Colour came nearer and nearer to the red Image made by the
other Prism, until when it was also red both Images became fully
co-incident.
I placed also two Paper Circles very near one another, the one in the
red Light of one Prism, and the other in the violet Light of the other.
The Circles were each of them an Inch in diameter, and behind them the
Wall was dark, that the Experiment might not be disturbed by any Light
coming from thence. These Circles thus illuminated, I viewed through a
Prism, so held, that the Refraction might be made towards the red
Circle, and as I went from them they came nearer and nearer together,
and at length became co-incident; and afterwards when I went still
farther off, they parted again in a contrary Order, the violet by a
greater Refraction being carried beyond the red.
_Exper._ 8. In Summer, when the Sun's Light uses to be strongest, I
placed a Prism at the Hole of the Window-shut, as in the third
Experiment, yet so that its Axis might be parallel to the Axis of the
World, and at the opposite Wall in the Sun's refracted Light, I placed
an open Book. Then going six Feet and two Inches from the Book, I placed
there the above-mentioned Lens, by which the Light reflected from the
Book might be made to converge and meet again at the distance of six
Feet and two Inches behind the Lens, and there paint the Species of the
Book upon a Sheet of white Paper much after the manner of the second
Experiment. The Book and Lens being made fast, I noted the Place where
the Paper was, when the Letters of the Book, illuminated by the fullest
red Light of the Solar Image falling upon it, did cast their Species on
that Paper most distinctly: And then I stay'd till by the Motion of the
Sun, and consequent Motion of his Image on the Book, all the Colours
from that red to the middle of the blue pass'd over those Letters; and
when those Letters were illuminated by that blue, I noted again the
Place of the Paper when they cast their Species most distinctly upon it:
And I found that this last Place of the Paper was nearer to the Lens
than its former Place by about two Inches and an half, or two and three
quarters. So much sooner therefore did the Light in the violet end of
the Image by a greater Refraction converge and meet, than the Light in
the red end. But in trying this, the Chamber was as dark as I could make
it. For, if these Colours be diluted and weakned by the Mixture of any
adventitious Light, the distance between the Places of the Paper will
not be so great. This distance in the second Experiment, where the
Colours of natural Bodies were made use of, was but an Inch and an half,
by reason of the Imperfection of those Colours. Here in the Colours of
the Prism, which are manifestly more full, intense, and lively than
those of natural Bodies, the distance is two Inches and three quarters.
And were the Colours still more full, I question not but that the
distance would be considerably greater. For the coloured Light of the
Prism, by the interfering of the Circles described in the second Figure
of the fifth Experiment, and also by the Light of the very bright Clouds
next the Sun's Body intermixing with these Colours, and by the Light
scattered by the Inequalities in the Polish of the Prism, was so very
much compounded, that the Species which those faint and dark Colours,
the indigo and violet, cast upon the Paper were not distinct enough to
be well observed.
_Exper._ 9. A Prism, whose two Angles at its Base were equal to one
another, and half right ones, and the third a right one, I placed in a
Beam of the Sun's Light let into a dark Chamber through a Hole in the
Window-shut, as in the third Experiment. And turning the Prism slowly
about its Axis, until all the Light which went through one of its
Angles, and was refracted by it began to be reflected by its Base, at
which till then it went out of the Glass, I observed that those Rays
which had suffered the greatest Refraction were sooner reflected than
the rest. I conceived therefore, that those Rays of the reflected Light,
which were most refrangible, did first of all by a total Reflexion
become more copious in that Light than the rest, and that afterwards the
rest also, by a total Reflexion, became as copious as these. To try
this, I made the reflected Light pass through another Prism, and being
refracted by it to fall afterwards upon a Sheet of white Paper placed
at some distance behind it, and there by that Refraction to paint the
usual Colours of the Prism. And then causing the first Prism to be
turned about its Axis as above, I observed that when those Rays, which
in this Prism had suffered the greatest Refraction, and appeared of a
blue and violet Colour began to be totally reflected, the blue and
violet Light on the Paper, which was most refracted in the second Prism,
received a sensible Increase above that of the red and yellow, which was
least refracted; and afterwards, when the rest of the Light which was
green, yellow, and red, began to be totally reflected in the first
Prism, the Light of those Colours on the Paper received as great an
Increase as the violet and blue had done before. Whence 'tis manifest,
that the Beam of Light reflected by the Base of the Prism, being
augmented first by the more refrangible Rays, and afterwards by the less
refrangible ones, is compounded of Rays differently refrangible. And
that all such reflected Light is of the same Nature with the Sun's Light
before its Incidence on the Base of the Prism, no Man ever doubted; it
being generally allowed, that Light by such Reflexions suffers no
Alteration in its Modifications and Properties. I do not here take
Notice of any Refractions made in the sides of the first Prism, because
the Light enters it perpendicularly at the first side, and goes out
perpendicularly at the second side, and therefore suffers none. So then,
the Sun's incident Light being of the same Temper and Constitution with
his emergent Light, and the last being compounded of Rays differently
refrangible, the first must be in like manner compounded.
[Illustration: FIG. 21.]
_Illustration._ In the twenty-first Figure, ABC is the first Prism, BC
its Base, B and C its equal Angles at the Base, each of 45 Degrees, A
its rectangular Vertex, FM a beam of the Sun's Light let into a dark
Room through a hole F one third part of an Inch broad, M its Incidence
on the Base of the Prism, MG a less refracted Ray, MH a more refracted
Ray, MN the beam of Light reflected from the Base, VXY the second Prism
by which this beam in passing through it is refracted, N_t_ the less
refracted Light of this beam, and N_p_ the more refracted part thereof.
When the first Prism ABC is turned about its Axis according to the order
of the Letters ABC, the Rays MH emerge more and more obliquely out of
that Prism, and at length after their most oblique Emergence are
reflected towards N, and going on to _p_ do increase the Number of the
Rays N_p_. Afterwards by continuing the Motion of the first Prism, the
Rays MG are also reflected to N and increase the number of the Rays
N_t_. And therefore the Light MN admits into its Composition, first the
more refrangible Rays, and then the less refrangible Rays, and yet after
this Composition is of the same Nature with the Sun's immediate Light
FM, the Reflexion of the specular Base BC causing no Alteration therein.
_Exper._ 10. Two Prisms, which were alike in Shape, I tied so together,
that their Axis and opposite Sides being parallel, they composed a
Parallelopiped. And, the Sun shining into my dark Chamber through a
little hole in the Window-shut, I placed that Parallelopiped in his beam
at some distance from the hole, in such a Posture, that the Axes of the
Prisms might be perpendicular to the incident Rays, and that those Rays
being incident upon the first Side of one Prism, might go on through the
two contiguous Sides of both Prisms, and emerge out of the last Side of
the second Prism. This Side being parallel to the first Side of the
first Prism, caused the emerging Light to be parallel to the incident.
Then, beyond these two Prisms I placed a third, which might refract that
emergent Light, and by that Refraction cast the usual Colours of the
Prism upon the opposite Wall, or upon a sheet of white Paper held at a
convenient Distance behind the Prism for that refracted Light to fall
upon it. After this I turned the Parallelopiped about its Axis, and
found that when the contiguous Sides of the two Prisms became so oblique
to the incident Rays, that those Rays began all of them to be
reflected, those Rays which in the third Prism had suffered the greatest
Refraction, and painted the Paper with violet and blue, were first of
all by a total Reflexion taken out of the transmitted Light, the rest
remaining and on the Paper painting their Colours of green, yellow,
orange and red, as before; and afterwards by continuing the Motion of
the two Prisms, the rest of the Rays also by a total Reflexion vanished
in order, according to their degrees of Refrangibility. The Light
therefore which emerged out of the two Prisms is compounded of Rays
differently refrangible, seeing the more refrangible Rays may be taken
out of it, while the less refrangible remain. But this Light being
trajected only through the parallel Superficies of the two Prisms, if it
suffer'd any change by the Refraction of one Superficies it lost that
Impression by the contrary Refraction of the other Superficies, and so
being restor'd to its pristine Constitution, became of the same Nature
and Condition as at first before its Incidence on those Prisms; and
therefore, before its Incidence, was as much compounded of Rays
differently refrangible, as afterwards.
[Illustration: FIG. 22.]
_Illustration._ In the twenty second Figure ABC and BCD are the two
Prisms tied together in the form of a Parallelopiped, their Sides BC and
CB being contiguous, and their Sides AB and CD parallel. And HJK is the
third Prism, by which the Sun's Light propagated through the hole F into
the dark Chamber, and there passing through those sides of the Prisms
AB, BC, CB and CD, is refracted at O to the white Paper PT, falling
there partly upon P by a greater Refraction, partly upon T by a less
Refraction, and partly upon R and other intermediate places by
intermediate Refractions. By turning the Parallelopiped ACBD about its
Axis, according to the order of the Letters A, C, D, B, at length when
the contiguous Planes BC and CB become sufficiently oblique to the Rays
FM, which are incident upon them at M, there will vanish totally out of
the refracted Light OPT, first of all the most refracted Rays OP, (the
rest OR and OT remaining as before) then the Rays OR and other
intermediate ones, and lastly, the least refracted Rays OT. For when
the Plane BC becomes sufficiently oblique to the Rays incident upon it,
those Rays will begin to be totally reflected by it towards N; and first
the most refrangible Rays will be totally reflected (as was explained in
the preceding Experiment) and by Consequence must first disappear at P,
and afterwards the rest as they are in order totally reflected to N,
they must disappear in the same order at R and T. So then the Rays which
at O suffer the greatest Refraction, may be taken out of the Light MO
whilst the rest of the Rays remain in it, and therefore that Light MO is
compounded of Rays differently refrangible. And because the Planes AB
and CD are parallel, and therefore by equal and contrary Refractions
destroy one anothers Effects, the incident Light FM must be of the same
Kind and Nature with the emergent Light MO, and therefore doth also
consist of Rays differently refrangible. These two Lights FM and MO,
before the most refrangible Rays are separated out of the emergent Light
MO, agree in Colour, and in all other Properties so far as my
Observation reaches, and therefore are deservedly reputed of the same
Nature and Constitution, and by Consequence the one is compounded as
well as the other. But after the most refrangible Rays begin to be
totally reflected, and thereby separated out of the emergent Light MO,
that Light changes its Colour from white to a dilute and faint yellow, a
pretty good orange, a very full red successively, and then totally
vanishes. For after the most refrangible Rays which paint the Paper at
P with a purple Colour, are by a total Reflexion taken out of the beam
of Light MO, the rest of the Colours which appear on the Paper at R and
T being mix'd in the Light MO compound there a faint yellow, and after
the blue and part of the green which appear on the Paper between P and R
are taken away, the rest which appear between R and T (that is the
yellow, orange, red and a little green) being mixed in the beam MO
compound there an orange; and when all the Rays are by Reflexion taken
out of the beam MO, except the least refrangible, which at T appear of a
full red, their Colour is the same in that beam MO as afterwards at T,
the Refraction of the Prism HJK serving only to separate the differently
refrangible Rays, without making any Alteration in their Colours, as
shall be more fully proved hereafter. All which confirms as well the
first Proposition as the second.
_Scholium._ If this Experiment and the former be conjoined and made one
by applying a fourth Prism VXY [in _Fig._ 22.] to refract the reflected
beam MN towards _tp_, the Conclusion will be clearer. For then the Light
N_p_ which in the fourth Prism is more refracted, will become fuller and
stronger when the Light OP, which in the third Prism HJK is more
refracted, vanishes at P; and afterwards when the less refracted Light
OT vanishes at T, the less refracted Light N_t_ will become increased
whilst the more refracted Light at _p_ receives no farther increase. And
as the trajected beam MO in vanishing is always of such a Colour as
ought to result from the mixture of the Colours which fall upon the
Paper PT, so is the reflected beam MN always of such a Colour as ought
to result from the mixture of the Colours which fall upon the Paper
_pt_. For when the most refrangible Rays are by a total Reflexion taken
out of the beam MO, and leave that beam of an orange Colour, the Excess
of those Rays in the reflected Light, does not only make the violet,
indigo and blue at _p_ more full, but also makes the beam MN change from
the yellowish Colour of the Sun's Light, to a pale white inclining to
blue, and afterward recover its yellowish Colour again, so soon as all
the rest of the transmitted Light MOT is reflected.
Now seeing that in all this variety of Experiments, whether the Trial be
made in Light reflected, and that either from natural Bodies, as in the
first and second Experiment, or specular, as in the ninth; or in Light
refracted, and that either before the unequally refracted Rays are by
diverging separated from one another, and losing their whiteness which
they have altogether, appear severally of several Colours, as in the
fifth Experiment; or after they are separated from one another, and
appear colour'd as in the sixth, seventh, and eighth Experiments; or in
Light trajected through parallel Superficies, destroying each others
Effects, as in the tenth Experiment; there are always found Rays, which
at equal Incidences on the same Medium suffer unequal Refractions, and
that without any splitting or dilating of single Rays, or contingence in
the inequality of the Refractions, as is proved in the fifth and sixth
Experiments. And seeing the Rays which differ in Refrangibility may be
parted and sorted from one another, and that either by Refraction as in
the third Experiment, or by Reflexion as in the tenth, and then the
several sorts apart at equal Incidences suffer unequal Refractions, and
those sorts are more refracted than others after Separation, which were
more refracted before it, as in the sixth and following Experiments, and
if the Sun's Light be trajected through three or more cross Prisms
successively, those Rays which in the first Prism are refracted more
than others, are in all the following Prisms refracted more than others
in the same Rate and Proportion, as appears by the fifth Experiment;
it's manifest that the Sun's Light is an heterogeneous Mixture of Rays,
some of which are constantly more refrangible than others, as was
proposed.
_PROP._ III. THEOR. III.
_The Sun's Light consists of Rays differing in Reflexibility, and those
Rays are more reflexible than others which are more refrangible._
This is manifest by the ninth and tenth Experiments: For in the ninth
Experiment, by turning the Prism about its Axis, until the Rays within
it which in going out into the Air were refracted by its Base, became so
oblique to that Base, as to begin to be totally reflected thereby; those
Rays became first of all totally reflected, which before at equal
Incidences with the rest had suffered the greatest Refraction. And the
same thing happens in the Reflexion made by the common Base of the two
Prisms in the tenth Experiment.
_PROP._ IV. PROB. I.
_To separate from one another the heterogeneous Rays of compound Light._
[Illustration: FIG. 23.]
The heterogeneous Rays are in some measure separated from one another by
the Refraction of the Prism in the third Experiment, and in the fifth
Experiment, by taking away the Penumbra from the rectilinear sides of
the coloured Image, that Separation in those very rectilinear sides or
straight edges of the Image becomes perfect. But in all places between
those rectilinear edges, those innumerable Circles there described,
which are severally illuminated by homogeneal Rays, by interfering with
one another, and being every where commix'd, do render the Light
sufficiently compound. But if these Circles, whilst their Centers keep
their Distances and Positions, could be made less in Diameter, their
interfering one with another, and by Consequence the Mixture of the
heterogeneous Rays would be proportionally diminish'd. In the twenty
third Figure let AG, BH, CJ, DK, EL, FM be the Circles which so many
sorts of Rays flowing from the same disque of the Sun, do in the third
Experiment illuminate; of all which and innumerable other intermediate
ones lying in a continual Series between the two rectilinear and
parallel edges of the Sun's oblong Image PT, that Image is compos'd, as
was explained in the fifth Experiment. And let _ag_, _bh_, _ci_, _dk_,
_el_, _fm_ be so many less Circles lying in a like continual Series
between two parallel right Lines _af_ and _gm_ with the same distances
between their Centers, and illuminated by the same sorts of Rays, that
is the Circle _ag_ with the same sort by which the corresponding Circle
AG was illuminated, and the Circle _bh_ with the same sort by which the
corresponding Circle BH was illuminated, and the rest of the Circles
_ci_, _dk_, _el_, _fm_ respectively, with the same sorts of Rays by
which the several corresponding Circles CJ, DK, EL, FM were illuminated.
In the Figure PT composed of the greater Circles, three of those Circles
AG, BH, CJ, are so expanded into one another, that the three sorts of
Rays by which those Circles are illuminated, together with other
innumerable sorts of intermediate Rays, are mixed at QR in the middle
of the Circle BH. And the like Mixture happens throughout almost the
whole length of the Figure PT. But in the Figure _pt_ composed of the
less Circles, the three less Circles _ag_, _bh_, _ci_, which answer to
those three greater, do not extend into one another; nor are there any
where mingled so much as any two of the three sorts of Rays by which
those Circles are illuminated, and which in the Figure PT are all of
them intermingled at BH.
Now he that shall thus consider it, will easily understand that the
Mixture is diminished in the same Proportion with the Diameters of the
Circles. If the Diameters of the Circles whilst their Centers remain the
same, be made three times less than before, the Mixture will be also
three times less; if ten times less, the Mixture will be ten times less,
and so of other Proportions. That is, the Mixture of the Rays in the
greater Figure PT will be to their Mixture in the less _pt_, as the
Latitude of the greater Figure is to the Latitude of the less. For the
Latitudes of these Figures are equal to the Diameters of their Circles.
And hence it easily follows, that the Mixture of the Rays in the
refracted Spectrum _pt_ is to the Mixture of the Rays in the direct and
immediate Light of the Sun, as the breadth of that Spectrum is to the
difference between the length and breadth of the same Spectrum.