diminish the Diameters of the Circles. Now these would be diminished if
the Sun's Diameter to which they answer could be made less than it is,
or (which comes to the same Purpose) if without Doors, at a great
distance from the Prism towards the Sun, some opake Body were placed,
with a round hole in the middle of it, to intercept all the Sun's Light,
excepting so much as coming from the middle of his Body could pass
through that Hole to the Prism. For so the Circles AG, BH, and the rest,
would not any longer answer to the whole Disque of the Sun, but only to
that Part of it which could be seen from the Prism through that Hole,
that it is to the apparent Magnitude of that Hole view'd from the Prism.
But that these Circles may answer more distinctly to that Hole, a Lens
is to be placed by the Prism to cast the Image of the Hole, (that is,
every one of the Circles AG, BH, &c.) distinctly upon the Paper at PT,
after such a manner, as by a Lens placed at a Window, the Species of
Objects abroad are cast distinctly upon a Paper within the Room, and the
rectilinear Sides of the oblong Solar Image in the fifth Experiment
became distinct without any Penumbra. If this be done, it will not be
necessary to place that Hole very far off, no not beyond the Window. And
therefore instead of that Hole, I used the Hole in the Window-shut, as
follows.
_Exper._ 11. In the Sun's Light let into my darken'd Chamber through a
small round Hole in my Window-shut, at about ten or twelve Feet from the
Window, I placed a Lens, by which the Image of the Hole might be
distinctly cast upon a Sheet of white Paper, placed at the distance of
six, eight, ten, or twelve Feet from the Lens. For, according to the
difference of the Lenses I used various distances, which I think not
worth the while to describe. Then immediately after the Lens I placed a
Prism, by which the trajected Light might be refracted either upwards or
sideways, and thereby the round Image, which the Lens alone did cast
upon the Paper might be drawn out into a long one with Parallel Sides,
as in the third Experiment. This oblong Image I let fall upon another
Paper at about the same distance from the Prism as before, moving the
Paper either towards the Prism or from it, until I found the just
distance where the Rectilinear Sides of the Image became most distinct.
For in this Case, the Circular Images of the Hole, which compose that
Image after the same manner that the Circles _ag_, _bh_, _ci_, &c. do
the Figure _pt_ [in _Fig._ 23.] were terminated most distinctly without
any Penumbra, and therefore extended into one another the least that
they could, and by consequence the Mixture of the heterogeneous Rays was
now the least of all. By this means I used to form an oblong Image (such
as is _pt_) [in _Fig._ 23, and 24.] of Circular Images of the Hole,
(such as are _ag_, _bh_, _ci_, &c.) and by using a greater or less Hole
in the Window-shut, I made the Circular Images _ag_, _bh_, _ci_, &c. of
which it was formed, to become greater or less at pleasure, and thereby
the Mixture of the Rays in the Image _pt_ to be as much, or as little as
I desired.
[Illustration: FIG. 24.]
_Illustration._ In the twenty-fourth Figure, F represents the Circular
Hole in the Window-shut, MN the Lens, whereby the Image or Species of
that Hole is cast distinctly upon a Paper at J, ABC the Prism, whereby
the Rays are at their emerging out of the Lens refracted from J towards
another Paper at _pt_, and the round Image at J is turned into an oblong
Image _pt_ falling on that other Paper. This Image _pt_ consists of
Circles placed one after another in a Rectilinear Order, as was
sufficiently explained in the fifth Experiment; and these Circles are
equal to the Circle J, and consequently answer in magnitude to the Hole
F; and therefore by diminishing that Hole they may be at pleasure
diminished, whilst their Centers remain in their Places. By this means I
made the Breadth of the Image _pt_ to be forty times, and sometimes
sixty or seventy times less than its Length. As for instance, if the
Breadth of the Hole F be one tenth of an Inch, and MF the distance of
the Lens from the Hole be 12 Feet; and if _p_B or _p_M the distance of
the Image _pt_ from the Prism or Lens be 10 Feet, and the refracting
Angle of the Prism be 62 Degrees, the Breadth of the Image _pt_ will be
one twelfth of an Inch, and the Length about six Inches, and therefore
the Length to the Breadth as 72 to 1, and by consequence the Light of
this Image 71 times less compound than the Sun's direct Light. And Light
thus far simple and homogeneal, is sufficient for trying all the
Experiments in this Book about simple Light. For the Composition of
heterogeneal Rays is in this Light so little, that it is scarce to be
discovered and perceiv'd by Sense, except perhaps in the indigo and
violet. For these being dark Colours do easily suffer a sensible Allay
by that little scattering Light which uses to be refracted irregularly
by the Inequalities of the Prism.
Yet instead of the Circular Hole F, 'tis better to substitute an oblong
Hole shaped like a long Parallelogram with its Length parallel to the
Prism ABC. For if this Hole be an Inch or two long, and but a tenth or
twentieth Part of an Inch broad, or narrower; the Light of the Image
_pt_ will be as simple as before, or simpler, and the Image will become
much broader, and therefore more fit to have Experiments try'd in its
Light than before.
Instead of this Parallelogram Hole may be substituted a triangular one
of equal Sides, whose Base, for instance, is about the tenth Part of an
Inch, and its Height an Inch or more. For by this means, if the Axis of
the Prism be parallel to the Perpendicular of the Triangle, the Image
_pt_ [in _Fig._ 25.] will now be form'd of equicrural Triangles _ag_,
_bh_, _ci_, _dk_, _el_, _fm_, &c. and innumerable other intermediate
ones answering to the triangular Hole in Shape and Bigness, and lying
one after another in a continual Series between two Parallel Lines _af_
and _gm_. These Triangles are a little intermingled at their Bases, but
not at their Vertices; and therefore the Light on the brighter Side _af_
of the Image, where the Bases of the Triangles are, is a little
compounded, but on the darker Side _gm_ is altogether uncompounded, and
in all Places between the Sides the Composition is proportional to the
distances of the Places from that obscurer Side _gm_. And having a
Spectrum _pt_ of such a Composition, we may try Experiments either in
its stronger and less simple Light near the Side _af_, or in its weaker
and simpler Light near the other Side _gm_, as it shall seem most
convenient.
[Illustration: FIG. 25.]
But in making Experiments of this kind, the Chamber ought to be made as
dark as can be, lest any Foreign Light mingle it self with the Light of
the Spectrum _pt_, and render it compound; especially if we would try
Experiments in the more simple Light next the Side _gm_ of the Spectrum;
which being fainter, will have a less proportion to the Foreign Light;
and so by the mixture of that Light be more troubled, and made more
compound. The Lens also ought to be good, such as may serve for optical
Uses, and the Prism ought to have a large Angle, suppose of 65 or 70
Degrees, and to be well wrought, being made of Glass free from Bubbles
and Veins, with its Sides not a little convex or concave, as usually
happens, but truly plane, and its Polish elaborate, as in working
Optick-glasses, and not such as is usually wrought with Putty, whereby
the edges of the Sand-holes being worn away, there are left all over the
Glass a numberless Company of very little convex polite Risings like
Waves. The edges also of the Prism and Lens, so far as they may make any
irregular Refraction, must be covered with a black Paper glewed on. And
all the Light of the Sun's Beam let into the Chamber, which is useless
and unprofitable to the Experiment, ought to be intercepted with black
Paper, or other black Obstacles. For otherwise the useless Light being
reflected every way in the Chamber, will mix with the oblong Spectrum,
and help to disturb it. In trying these Things, so much diligence is not
altogether necessary, but it will promote the Success of the
Experiments, and by a very scrupulous Examiner of Things deserves to be
apply'd. It's difficult to get Glass Prisms fit for this Purpose, and
therefore I used sometimes prismatick Vessels made with pieces of broken
Looking-glasses, and filled with Rain Water. And to increase the
Refraction, I sometimes impregnated the Water strongly with _Saccharum
Saturni_.
_PROP._ V. THEOR. IV.
_Homogeneal Light is refracted regularly without any Dilatation
splitting or shattering of the Rays, and the confused Vision of Objects
seen through refracting Bodies by heterogeneal Light arises from the
different Refrangibility of several sorts of Rays._
The first Part of this Proposition has been already sufficiently proved
in the fifth Experiment, and will farther appear by the Experiments
which follow.
_Exper._ 12. In the middle of a black Paper I made a round Hole about a
fifth or sixth Part of an Inch in diameter. Upon this Paper I caused the
Spectrum of homogeneal Light described in the former Proposition, so to
fall, that some part of the Light might pass through the Hole of the
Paper. This transmitted part of the Light I refracted with a Prism
placed behind the Paper, and letting this refracted Light fall
perpendicularly upon a white Paper two or three Feet distant from the
Prism, I found that the Spectrum formed on the Paper by this Light was
not oblong, as when 'tis made (in the third Experiment) by refracting
the Sun's compound Light, but was (so far as I could judge by my Eye)
perfectly circular, the Length being no greater than the Breadth. Which
shews, that this Light is refracted regularly without any Dilatation of
the Rays.
_Exper._ 13. In the homogeneal Light I placed a Paper Circle of a
quarter of an Inch in diameter, and in the Sun's unrefracted
heterogeneal white Light I placed another Paper Circle of the same
Bigness. And going from the Papers to the distance of some Feet, I
viewed both Circles through a Prism. The Circle illuminated by the Sun's
heterogeneal Light appeared very oblong, as in the fourth Experiment,
the Length being many times greater than the Breadth; but the other
Circle, illuminated with homogeneal Light, appeared circular and
distinctly defined, as when 'tis view'd with the naked Eye. Which proves
the whole Proposition.
_Exper._ 14. In the homogeneal Light I placed Flies, and such-like
minute Objects, and viewing them through a Prism, I saw their Parts as
distinctly defined, as if I had viewed them with the naked Eye. The same
Objects placed in the Sun's unrefracted heterogeneal Light, which was
white, I viewed also through a Prism, and saw them most confusedly
defined, so that I could not distinguish their smaller Parts from one
another. I placed also the Letters of a small print, one while in the
homogeneal Light, and then in the heterogeneal, and viewing them through
a Prism, they appeared in the latter Case so confused and indistinct,
that I could not read them; but in the former they appeared so distinct,
that I could read readily, and thought I saw them as distinct, as when I
view'd them with my naked Eye. In both Cases I view'd the same Objects,
through the same Prism at the same distance from me, and in the same
Situation. There was no difference, but in the Light by which the
Objects were illuminated, and which in one Case was simple, and in the
other compound; and therefore, the distinct Vision in the former Case,
and confused in the latter, could arise from nothing else than from that
difference of the Lights. Which proves the whole Proposition.
And in these three Experiments it is farther very remarkable, that the
Colour of homogeneal Light was never changed by the Refraction.
_PROP._ VI. THEOR. V.
_The Sine of Incidence of every Ray considered apart, is to its Sine of
Refraction in a given Ratio._
That every Ray consider'd apart, is constant to it self in some degree
of Refrangibility, is sufficiently manifest out of what has been said.
Those Rays, which in the first Refraction, are at equal Incidences most
refracted, are also in the following Refractions at equal Incidences
most refracted; and so of the least refrangible, and the rest which have
any mean Degree of Refrangibility, as is manifest by the fifth, sixth,
seventh, eighth, and ninth Experiments. And those which the first Time
at like Incidences are equally refracted, are again at like Incidences
equally and uniformly refracted, and that whether they be refracted
before they be separated from one another, as in the fifth Experiment,
or whether they be refracted apart, as in the twelfth, thirteenth and
fourteenth Experiments. The Refraction therefore of every Ray apart is
regular, and what Rule that Refraction observes we are now to shew.[E]
The late Writers in Opticks teach, that the Sines of Incidence are in a
given Proportion to the Sines of Refraction, as was explained in the
fifth Axiom, and some by Instruments fitted for measuring of
Refractions, or otherwise experimentally examining this Proportion, do
acquaint us that they have found it accurate. But whilst they, not
understanding the different Refrangibility of several Rays, conceived
them all to be refracted according to one and the same Proportion, 'tis
to be presumed that they adapted their Measures only to the middle of
the refracted Light; so that from their Measures we may conclude only
that the Rays which have a mean Degree of Refrangibility, that is, those
which when separated from the rest appear green, are refracted according
to a given Proportion of their Sines. And therefore we are now to shew,
that the like given Proportions obtain in all the rest. That it should
be so is very reasonable, Nature being ever conformable to her self; but
an experimental Proof is desired. And such a Proof will be had, if we
can shew that the Sines of Refraction of Rays differently refrangible
are one to another in a given Proportion when their Sines of Incidence
are equal. For, if the Sines of Refraction of all the Rays are in given
Proportions to the Sine of Refractions of a Ray which has a mean Degree
of Refrangibility, and this Sine is in a given Proportion to the equal
Sines of Incidence, those other Sines of Refraction will also be in
given Proportions to the equal Sines of Incidence. Now, when the Sines
of Incidence are equal, it will appear by the following Experiment, that
the Sines of Refraction are in a given Proportion to one another.
[Illustration: FIG. 26.]
_Exper._ 15. The Sun shining into a dark Chamber through a little round
Hole in the Window-shut, let S [in _Fig._ 26.] represent his round white
Image painted on the opposite Wall by his direct Light, PT his oblong
coloured Image made by refracting that Light with a Prism placed at the
Window; and _pt_, or _2p 2t_, _3p 3t_, his oblong colour'd Image made by
refracting again the same Light sideways with a second Prism placed
immediately after the first in a cross Position to it, as was explained
in the fifth Experiment; that is to say, _pt_ when the Refraction of the
second Prism is small, _2p 2t_ when its Refraction is greater, and _3p
3t_ when it is greatest. For such will be the diversity of the
Refractions, if the refracting Angle of the second Prism be of various
Magnitudes; suppose of fifteen or twenty Degrees to make the Image _pt_,
of thirty or forty to make the Image _2p 2t_, and of sixty to make the
Image _3p 3t_. But for want of solid Glass Prisms with Angles of
convenient Bignesses, there may be Vessels made of polished Plates of
Glass cemented together in the form of Prisms and filled with Water.
These things being thus ordered, I observed that all the solar Images or
coloured Spectrums PT, _pt_, _2p 2t_, _3p 3t_ did very nearly converge
to the place S on which the direct Light of the Sun fell and painted his
white round Image when the Prisms were taken away. The Axis of the
Spectrum PT, that is the Line drawn through the middle of it parallel to
its rectilinear Sides, did when produced pass exactly through the middle
of that white round Image S. And when the Refraction of the second Prism
was equal to the Refraction of the first, the refracting Angles of them
both being about 60 Degrees, the Axis of the Spectrum _3p 3t_ made by
that Refraction, did when produced pass also through the middle of the
same white round Image S. But when the Refraction of the second Prism
was less than that of the first, the produced Axes of the Spectrums _tp_
or _2t 2p_ made by that Refraction did cut the produced Axis of the
Spectrum TP in the points _m_ and _n_, a little beyond the Center of
that white round Image S. Whence the proportion of the Line 3_t_T to the
Line 3_p_P was a little greater than the Proportion of 2_t_T or 2_p_P,
and this Proportion a little greater than that of _t_T to _p_P. Now when
the Light of the Spectrum PT falls perpendicularly upon the Wall, those
Lines 3_t_T, 3_p_P, and 2_t_T, and 2_p_P, and _t_T, _p_P, are the
Tangents of the Refractions, and therefore by this Experiment the
Proportions of the Tangents of the Refractions are obtained, from whence
the Proportions of the Sines being derived, they come out equal, so far
as by viewing the Spectrums, and using some mathematical Reasoning I
could estimate. For I did not make an accurate Computation. So then the
Proposition holds true in every Ray apart, so far as appears by
Experiment. And that it is accurately true, may be demonstrated upon
this Supposition. _That Bodies refract Light by acting upon its Rays in
Lines perpendicular to their Surfaces._ But in order to this
Demonstration, I must distinguish the Motion of every Ray into two
Motions, the one perpendicular to the refracting Surface, the other
parallel to it, and concerning the perpendicular Motion lay down the
following Proposition.
If any Motion or moving thing whatsoever be incident with any Velocity
on any broad and thin space terminated on both sides by two parallel
Planes, and in its Passage through that space be urged perpendicularly
towards the farther Plane by any force which at given distances from the
Plane is of given Quantities; the perpendicular velocity of that Motion
or Thing, at its emerging out of that space, shall be always equal to
the square Root of the sum of the square of the perpendicular velocity
of that Motion or Thing at its Incidence on that space; and of the
square of the perpendicular velocity which that Motion or Thing would
have at its Emergence, if at its Incidence its perpendicular velocity
was infinitely little.
And the same Proposition holds true of any Motion or Thing
perpendicularly retarded in its passage through that space, if instead
of the sum of the two Squares you take their difference. The
Demonstration Mathematicians will easily find out, and therefore I shall
not trouble the Reader with it.
Suppose now that a Ray coming most obliquely in the Line MC [in _Fig._
1.] be refracted at C by the Plane RS into the Line CN, and if it be
required to find the Line CE, into which any other Ray AC shall be
refracted; let MC, AD, be the Sines of Incidence of the two Rays, and
NG, EF, their Sines of Refraction, and let the equal Motions of the
incident Rays be represented by the equal Lines MC and AC, and the
Motion MC being considered as parallel to the refracting Plane, let the
other Motion AC be distinguished into two Motions AD and DC, one of
which AD is parallel, and the other DC perpendicular to the refracting
Surface. In like manner, let the Motions of the emerging Rays be
distinguish'd into two, whereof the perpendicular ones are MC/NG x CG
and AD/EF x CF. And if the force of the refracting Plane begins to act
upon the Rays either in that Plane or at a certain distance from it on
the one side, and ends at a certain distance from it on the other side,
and in all places between those two limits acts upon the Rays in Lines
perpendicular to that refracting Plane, and the Actions upon the Rays at
equal distances from the refracting Plane be equal, and at unequal ones
either equal or unequal according to any rate whatever; that Motion of
the Ray which is parallel to the refracting Plane, will suffer no
Alteration by that Force; and that Motion which is perpendicular to it
will be altered according to the rule of the foregoing Proposition. If
therefore for the perpendicular velocity of the emerging Ray CN you
write MC/NG x CG as above, then the perpendicular velocity of any other
emerging Ray CE which was AD/EF x CF, will be equal to the square Root
of CD_q_ + (_MCq/NGq_ x CG_q_). And by squaring these Equals, and adding
to them the Equals AD_q_ and MC_q_ - CD_q_, and dividing the Sums by the
Equals CF_q_ + EF_q_ and CG_q_ + NG_q_, you will have _MCq/NGq_ equal to
_ADq/EFq_. Whence AD, the Sine of Incidence, is to EF the Sine of
Refraction, as MC to NG, that is, in a given _ratio_. And this
Demonstration being general, without determining what Light is, or by
what kind of Force it is refracted, or assuming any thing farther than
that the refracting Body acts upon the Rays in Lines perpendicular to
its Surface; I take it to be a very convincing Argument of the full
truth of this Proposition.
So then, if the _ratio_ of the Sines of Incidence and Refraction of any
sort of Rays be found in any one case, 'tis given in all cases; and this
may be readily found by the Method in the following Proposition.
_PROP._ VII. THEOR. VI.
_The Perfection of Telescopes is impeded by the different Refrangibility
of the Rays of Light._
The Imperfection of Telescopes is vulgarly attributed to the spherical
Figures of the Glasses, and therefore Mathematicians have propounded to
figure them by the conical Sections. To shew that they are mistaken, I
have inserted this Proposition; the truth of which will appear by the
measure of the Refractions of the several sorts of Rays; and these
measures I thus determine.
In the third Experiment of this first Part, where the refracting Angle
of the Prism was 62-1/2 Degrees, the half of that Angle 31 deg. 15 min.
is the Angle of Incidence of the Rays at their going out of the Glass
into the Air[F]; and the Sine of this Angle is 5188, the Radius being
10000. When the Axis of this Prism was parallel to the Horizon, and the
Refraction of the Rays at their Incidence on this Prism equal to that at
their Emergence out of it, I observed with a Quadrant the Angle which
the mean refrangible Rays, (that is those which went to the middle of
the Sun's coloured Image) made with the Horizon, and by this Angle and
the Sun's altitude observed at the same time, I found the Angle which
the emergent Rays contained with the incident to be 44 deg. and 40 min.
and the half of this Angle added to the Angle of Incidence 31 deg. 15
min. makes the Angle of Refraction, which is therefore 53 deg. 35 min.
and its Sine 8047. These are the Sines of Incidence and Refraction of
the mean refrangible Rays, and their Proportion in round Numbers is 20
to 31. This Glass was of a Colour inclining to green. The last of the
Prisms mentioned in the third Experiment was of clear white Glass. Its
refracting Angle 63-1/2 Degrees. The Angle which the emergent Rays
contained, with the incident 45 deg. 50 min. The Sine of half the first
Angle 5262. The Sine of half the Sum of the Angles 8157. And their
Proportion in round Numbers 20 to 31, as before.
From the Length of the Image, which was about 9-3/4 or 10 Inches,
subduct its Breadth, which was 2-1/8 Inches, and the Remainder 7-3/4
Inches would be the Length of the Image were the Sun but a Point, and
therefore subtends the Angle which the most and least refrangible Rays,
when incident on the Prism in the same Lines, do contain with one
another after their Emergence. Whence this Angle is 2 deg. 0'. 7''. For
the distance between the Image and the Prism where this Angle is made,
was 18-1/2 Feet, and at that distance the Chord 7-3/4 Inches subtends an
Angle of 2 deg. 0'. 7''. Now half this Angle is the Angle which these
emergent Rays contain with the emergent mean refrangible Rays, and a
quarter thereof, that is 30'. 2''. may be accounted the Angle which they
would contain with the same emergent mean refrangible Rays, were they
co-incident to them within the Glass, and suffered no other Refraction
than that at their Emergence. For, if two equal Refractions, the one at
the Incidence of the Rays on the Prism, the other at their Emergence,
make half the Angle 2 deg. 0'. 7''. then one of those Refractions will
make about a quarter of that Angle, and this quarter added to, and
subducted from the Angle of Refraction of the mean refrangible Rays,
which was 53 deg. 35', gives the Angles of Refraction of the most and
least refrangible Rays 54 deg. 5' 2'', and 53 deg. 4' 58'', whose Sines
are 8099 and 7995, the common Angle of Incidence being 31 deg. 15', and
its Sine 5188; and these Sines in the least round Numbers are in
proportion to one another, as 78 and 77 to 50.
Now, if you subduct the common Sine of Incidence 50 from the Sines of
Refraction 77 and 78, the Remainders 27 and 28 shew, that in small
Refractions the Refraction of the least refrangible Rays is to the
Refraction of the most refrangible ones, as 27 to 28 very nearly, and
that the difference of the Refractions of the least refrangible and most
refrangible Rays is about the 27-1/2th Part of the whole Refraction of
the mean refrangible Rays.
Whence they that are skilled in Opticks will easily understand,[G] that
the Breadth of the least circular Space, into which Object-glasses of
Telescopes can collect all sorts of Parallel Rays, is about the 27-1/2th
Part of half the Aperture of the Glass, or 55th Part of the whole
Aperture; and that the Focus of the most refrangible Rays is nearer to
the Object-glass than the Focus of the least refrangible ones, by about
the 27-1/2th Part of the distance between the Object-glass and the Focus
of the mean refrangible ones.
And if Rays of all sorts, flowing from any one lucid Point in the Axis
of any convex Lens, be made by the Refraction of the Lens to converge to
Points not too remote from the Lens, the Focus of the most refrangible
Rays shall be nearer to the Lens than the Focus of the least refrangible
ones, by a distance which is to the 27-1/2th Part of the distance of the
Focus of the mean refrangible Rays from the Lens, as the distance
between that Focus and the lucid Point, from whence the Rays flow, is to
the distance between that lucid Point and the Lens very nearly.
Now to examine whether the Difference between the Refractions, which the
most refrangible and the least refrangible Rays flowing from the same
Point suffer in the Object-glasses of Telescopes and such-like Glasses,
be so great as is here described, I contrived the following Experiment.
_Exper._ 16. The Lens which I used in the second and eighth Experiments,
being placed six Feet and an Inch distant from any Object, collected the
Species of that Object by the mean refrangible Rays at the distance of
six Feet and an Inch from the Lens on the other side. And therefore by
the foregoing Rule, it ought to collect the Species of that Object by
the least refrangible Rays at the distance of six Feet and 3-2/3 Inches
from the Lens, and by the most refrangible ones at the distance of five
Feet and 10-1/3 Inches from it: So that between the two Places, where
these least and most refrangible Rays collect the Species, there may be
the distance of about 5-1/3 Inches. For by that Rule, as six Feet and an
Inch (the distance of the Lens from the lucid Object) is to twelve Feet
and two Inches (the distance of the lucid Object from the Focus of the
mean refrangible Rays) that is, as One is to Two; so is the 27-1/2th
Part of six Feet and an Inch (the distance between the Lens and the same
Focus) to the distance between the Focus of the most refrangible Rays
and the Focus of the least refrangible ones, which is therefore 5-17/55
Inches, that is very nearly 5-1/3 Inches. Now to know whether this
Measure was true, I repeated the second and eighth Experiment with
coloured Light, which was less compounded than that I there made use of:
For I now separated the heterogeneous Rays from one another by the
Method I described in the eleventh Experiment, so as to make a coloured
Spectrum about twelve or fifteen Times longer than broad. This Spectrum
I cast on a printed Book, and placing the above-mentioned Lens at the
distance of six Feet and an Inch from this Spectrum to collect the
Species of the illuminated Letters at the same distance on the other
side, I found that the Species of the Letters illuminated with blue were
nearer to the Lens than those illuminated with deep red by about three
Inches, or three and a quarter; but the Species of the Letters
illuminated with indigo and violet appeared so confused and indistinct,
that I could not read them: Whereupon viewing the Prism, I found it was
full of Veins running from one end of the Glass to the other; so that
the Refraction could not be regular. I took another Prism therefore
which was free from Veins, and instead of the Letters I used two or
three Parallel black Lines a little broader than the Strokes of the
Letters, and casting the Colours upon these Lines in such manner, that
the Lines ran along the Colours from one end of the Spectrum to the
other, I found that the Focus where the indigo, or confine of this
Colour and violet cast the Species of the black Lines most distinctly,
to be about four Inches, or 4-1/4 nearer to the Lens than the Focus,
where the deepest red cast the Species of the same black Lines most
distinctly. The violet was so faint and dark, that I could not discern
the Species of the Lines distinctly by that Colour; and therefore
considering that the Prism was made of a dark coloured Glass inclining
to green, I took another Prism of clear white Glass; but the Spectrum of
Colours which this Prism made had long white Streams of faint Light
shooting out from both ends of the Colours, which made me conclude that
something was amiss; and viewing the Prism, I found two or three little
Bubbles in the Glass, which refracted the Light irregularly. Wherefore I
covered that Part of the Glass with black Paper, and letting the Light
pass through another Part of it which was free from such Bubbles, the
Spectrum of Colours became free from those irregular Streams of Light,
and was now such as I desired. But still I found the violet so dark and
faint, that I could scarce see the Species of the Lines by the violet,
and not at all by the deepest Part of it, which was next the end of the
Spectrum. I suspected therefore, that this faint and dark Colour might
be allayed by that scattering Light which was refracted, and reflected
irregularly, partly by some very small Bubbles in the Glasses, and
partly by the Inequalities of their Polish; which Light, tho' it was but
little, yet it being of a white Colour, might suffice to affect the
Sense so strongly as to disturb the Phaenomena of that weak and dark
Colour the violet, and therefore I tried, as in the 12th, 13th, and 14th
Experiments, whether the Light of this Colour did not consist of a
sensible Mixture of heterogeneous Rays, but found it did not. Nor did
the Refractions cause any other sensible Colour than violet to emerge
out of this Light, as they would have done out of white Light, and by
consequence out of this violet Light had it been sensibly compounded
with white Light. And therefore I concluded, that the reason why I could
not see the Species of the Lines distinctly by this Colour, was only
the Darkness of this Colour, and Thinness of its Light, and its distance
from the Axis of the Lens; I divided therefore those Parallel black
Lines into equal Parts, by which I might readily know the distances of
the Colours in the Spectrum from one another, and noted the distances of
the Lens from the Foci of such Colours, as cast the Species of the Lines
distinctly, and then considered whether the difference of those
distances bear such proportion to 5-1/3 Inches, the greatest Difference
of the distances, which the Foci of the deepest red and violet ought to
have from the Lens, as the distance of the observed Colours from one
another in the Spectrum bear to the greatest distance of the deepest red
and violet measured in the Rectilinear Sides of the Spectrum, that is,
to the Length of those Sides, or Excess of the Length of the Spectrum
above its Breadth. And my Observations were as follows.
When I observed and compared the deepest sensible red, and the Colour in
the Confine of green and blue, which at the Rectilinear Sides of the
Spectrum was distant from it half the Length of those Sides, the Focus
where the Confine of green and blue cast the Species of the Lines
distinctly on the Paper, was nearer to the Lens than the Focus, where
the red cast those Lines distinctly on it by about 2-1/2 or 2-3/4
Inches. For sometimes the Measures were a little greater, sometimes a
little less, but seldom varied from one another above 1/3 of an Inch.
For it was very difficult to define the Places of the Foci, without some
little Errors. Now, if the Colours distant half the Length of the
Image, (measured at its Rectilinear Sides) give 2-1/2 or 2-3/4
Difference of the distances of their Foci from the Lens, then the
Colours distant the whole Length ought to give 5 or 5-1/2 Inches
difference of those distances.
But here it's to be noted, that I could not see the red to the full end
of the Spectrum, but only to the Center of the Semicircle which bounded
that end, or a little farther; and therefore I compared this red not
with that Colour which was exactly in the middle of the Spectrum, or
Confine of green and blue, but with that which verged a little more to
the blue than to the green: And as I reckoned the whole Length of the
Colours not to be the whole Length of the Spectrum, but the Length of
its Rectilinear Sides, so compleating the semicircular Ends into
Circles, when either of the observed Colours fell within those Circles,
I measured the distance of that Colour from the semicircular End of the
Spectrum, and subducting half this distance from the measured distance
of the two Colours, I took the Remainder for their corrected distance;
and in these Observations set down this corrected distance for the
difference of the distances of their Foci from the Lens. For, as the
Length of the Rectilinear Sides of the Spectrum would be the whole
Length of all the Colours, were the Circles of which (as we shewed) that
Spectrum consists contracted and reduced to Physical Points, so in that
Case this corrected distance would be the real distance of the two
observed Colours.
When therefore I farther observed the deepest sensible red, and that
blue whose corrected distance from it was 7/12 Parts of the Length of
the Rectilinear Sides of the Spectrum, the difference of the distances
of their Foci from the Lens was about 3-1/4 Inches, and as 7 to 12, so
is 3-1/4 to 5-4/7.
When I observed the deepest sensible red, and that indigo whose
corrected distance was 8/12 or 2/3 of the Length of the Rectilinear
Sides of the Spectrum, the difference of the distances of their Foci
from the Lens, was about 3-2/3 Inches, and as 2 to 3, so is 3-2/3 to
5-1/2.
When I observed the deepest sensible red, and that deep indigo whose
corrected distance from one another was 9/12 or 3/4 of the Length of the
Rectilinear Sides of the Spectrum, the difference of the distances of
their Foci from the Lens was about 4 Inches; and as 3 to 4, so is 4 to
5-1/3.
When I observed the deepest sensible red, and that Part of the violet
next the indigo, whose corrected distance from the red was 10/12 or 5/6
of the Length of the Rectilinear Sides of the Spectrum, the difference
of the distances of their Foci from the Lens was about 4-1/2 Inches, and
as 5 to 6, so is 4-1/2 to 5-2/5. For sometimes, when the Lens was
advantageously placed, so that its Axis respected the blue, and all
Things else were well ordered, and the Sun shone clear, and I held my
Eye very near to the Paper on which the Lens cast the Species of the
Lines, I could see pretty distinctly the Species of those Lines by that
Part of the violet which was next the indigo; and sometimes I could see
them by above half the violet, For in making these Experiments I had
observed, that the Species of those Colours only appear distinct, which
were in or near the Axis of the Lens: So that if the blue or indigo were
in the Axis, I could see their Species distinctly; and then the red
appeared much less distinct than before. Wherefore I contrived to make
the Spectrum of Colours shorter than before, so that both its Ends might
be nearer to the Axis of the Lens. And now its Length was about 2-1/2
Inches, and Breadth about 1/5 or 1/6 of an Inch. Also instead of the
black Lines on which the Spectrum was cast, I made one black Line
broader than those, that I might see its Species more easily; and this
Line I divided by short cross Lines into equal Parts, for measuring the
distances of the observed Colours. And now I could sometimes see the
Species of this Line with its Divisions almost as far as the Center of
the semicircular violet End of the Spectrum, and made these farther
Observations.
When I observed the deepest sensible red, and that Part of the violet,
whose corrected distance from it was about 8/9 Parts of the Rectilinear
Sides of the Spectrum, the Difference of the distances of the Foci of
those Colours from the Lens, was one time 4-2/3, another time 4-3/4,
another time 4-7/8 Inches; and as 8 to 9, so are 4-2/3, 4-3/4, 4-7/8, to
5-1/4, 5-11/32, 5-31/64 respectively.
When I observed the deepest sensible red, and deepest sensible violet,
(the corrected distance of which Colours, when all Things were ordered
to the best Advantage, and the Sun shone very clear, was about 11/12 or
15/16 Parts of the Length of the Rectilinear Sides of the coloured
Spectrum) I found the Difference of the distances of their Foci from the
Lens sometimes 4-3/4 sometimes 5-1/4, and for the most part 5 Inches or
thereabouts; and as 11 to 12, or 15 to 16, so is five Inches to 5-2/2 or
5-1/3 Inches.
And by this Progression of Experiments I satisfied my self, that had the
Light at the very Ends of the Spectrum been strong enough to make the
Species of the black Lines appear plainly on the Paper, the Focus of the
deepest violet would have been found nearer to the Lens, than the Focus
of the deepest red, by about 5-1/3 Inches at least. And this is a
farther Evidence, that the Sines of Incidence and Refraction of the
several sorts of Rays, hold the same Proportion to one another in the
smallest Refractions which they do in the greatest.
My Progress in making this nice and troublesome Experiment I have set
down more at large, that they that shall try it after me may be aware of
the Circumspection requisite to make it succeed well. And if they cannot
make it succeed so well as I did, they may notwithstanding collect by
the Proportion of the distance of the Colours of the Spectrum, to the
Difference of the distances of their Foci from the Lens, what would be
the Success in the more distant Colours by a better trial. And yet, if
they use a broader Lens than I did, and fix it to a long strait Staff,
by means of which it may be readily and truly directed to the Colour
whose Focus is desired, I question not but the Experiment will succeed
better with them than it did with me. For I directed the Axis as nearly
as I could to the middle of the Colours, and then the faint Ends of the
Spectrum being remote from the Axis, cast their Species less distinctly
on the Paper than they would have done, had the Axis been successively
directed to them.
Now by what has been said, it's certain that the Rays which differ in
Refrangibility do not converge to the same Focus; but if they flow from
a lucid Point, as far from the Lens on one side as their Foci are on the
other, the Focus of the most refrangible Rays shall be nearer to the
Lens than that of the least refrangible, by above the fourteenth Part of
the whole distance; and if they flow from a lucid Point, so very remote
from the Lens, that before their Incidence they may be accounted
parallel, the Focus of the most refrangible Rays shall be nearer to the
Lens than the Focus of the least refrangible, by about the 27th or 28th
Part of their whole distance from it. And the Diameter of the Circle in
the middle Space between those two Foci which they illuminate, when they
fall there on any Plane, perpendicular to the Axis (which Circle is the
least into which they can all be gathered) is about the 55th Part of the
Diameter of the Aperture of the Glass. So that 'tis a wonder, that
Telescopes represent Objects so distinct as they do. But were all the
Rays of Light equally refrangible, the Error arising only from the
Sphericalness of the Figures of Glasses would be many hundred times
less. For, if the Object-glass of a Telescope be Plano-convex, and the
Plane side be turned towards the Object, and the Diameter of the
Sphere, whereof this Glass is a Segment, be called D, and the
Semi-diameter of the Aperture of the Glass be called S, and the Sine of
Incidence out of Glass into Air, be to the Sine of Refraction as I to R;
the Rays which come parallel to the Axis of the Glass, shall in the
Place where the Image of the Object is most distinctly made, be
scattered all over a little Circle, whose Diameter is _(Rq/Iq) x (S
cub./D quad.)_ very nearly,[H] as I gather by computing the Errors of
the Rays by the Method of infinite Series, and rejecting the Terms,
whose Quantities are inconsiderable. As for instance, if the Sine of
Incidence I, be to the Sine of Refraction R, as 20 to 31, and if D the
Diameter of the Sphere, to which the Convex-side of the Glass is ground,
be 100 Feet or 1200 Inches, and S the Semi-diameter of the Aperture be
two Inches, the Diameter of the little Circle, (that is (_Rq x S
cub.)/(Iq x D quad._)) will be (31 x 31 x 8)/(20 x 20 x 1200 x 1200) (or
961/72000000) Parts of an Inch. But the Diameter of the little Circle,
through which these Rays are scattered by unequal Refrangibility, will
be about the 55th Part of the Aperture of the Object-glass, which here
is four Inches. And therefore, the Error arising from the Spherical
Figure of the Glass, is to the Error arising from the different
Refrangibility of the Rays, as 961/72000000 to 4/55, that is as 1 to
5449; and therefore being in comparison so very little, deserves not to
be considered.
[Illustration: FIG. 27.]
But you will say, if the Errors caused by the different Refrangibility
be so very great, how comes it to pass, that Objects appear through
Telescopes so distinct as they do? I answer, 'tis because the erring
Rays are not scattered uniformly over all that Circular Space, but
collected infinitely more densely in the Center than in any other Part
of the Circle, and in the Way from the Center to the Circumference, grow
continually rarer and rarer, so as at the Circumference to become
infinitely rare; and by reason of their Rarity are not strong enough to
be visible, unless in the Center and very near it. Let ADE [in _Fig._
27.] represent one of those Circles described with the Center C, and
Semi-diameter AC, and let BFG be a smaller Circle concentrick to the
former, cutting with its Circumference the Diameter AC in B, and bisect
AC in N; and by my reckoning, the Density of the Light in any Place B,
will be to its Density in N, as AB to BC; and the whole Light within the
lesser Circle BFG, will be to the whole Light within the greater AED, as
the Excess of the Square of AC above the Square of AB, is to the Square
of AC. As if BC be the fifth Part of AC, the Light will be four times
denser in B than in N, and the whole Light within the less Circle, will
be to the whole Light within the greater, as nine to twenty-five. Whence
it's evident, that the Light within the less Circle, must strike the
Sense much more strongly, than that faint and dilated Light round about
between it and the Circumference of the greater.
But it's farther to be noted, that the most luminous of the Prismatick
Colours are the yellow and orange. These affect the Senses more strongly
than all the rest together, and next to these in strength are the red
and green. The blue compared with these is a faint and dark Colour, and
the indigo and violet are much darker and fainter, so that these
compared with the stronger Colours are little to be regarded. The Images
of Objects are therefore to be placed, not in the Focus of the mean
refrangible Rays, which are in the Confine of green and blue, but in the
Focus of those Rays which are in the middle of the orange and yellow;
there where the Colour is most luminous and fulgent, that is in the
brightest yellow, that yellow which inclines more to orange than to
green. And by the Refraction of these Rays (whose Sines of Incidence and
Refraction in Glass are as 17 and 11) the Refraction of Glass and
Crystal for Optical Uses is to be measured. Let us therefore place the
Image of the Object in the Focus of these Rays, and all the yellow and
orange will fall within a Circle, whose Diameter is about the 250th
Part of the Diameter of the Aperture of the Glass. And if you add the
brighter half of the red, (that half which is next the orange) and the
brighter half of the green, (that half which is next the yellow) about
three fifth Parts of the Light of these two Colours will fall within the
same Circle, and two fifth Parts will fall without it round about; and
that which falls without will be spread through almost as much more
space as that which falls within, and so in the gross be almost three
times rarer. Of the other half of the red and green, (that is of the
deep dark red and willow green) about one quarter will fall within this
Circle, and three quarters without, and that which falls without will be
spread through about four or five times more space than that which falls
within; and so in the gross be rarer, and if compared with the whole
Light within it, will be about 25 times rarer than all that taken in the
gross; or rather more than 30 or 40 times rarer, because the deep red in
the end of the Spectrum of Colours made by a Prism is very thin and
rare, and the willow green is something rarer than the orange and
yellow. The Light of these Colours therefore being so very much rarer
than that within the Circle, will scarce affect the Sense, especially
since the deep red and willow green of this Light, are much darker
Colours than the rest. And for the same reason the blue and violet being
much darker Colours than these, and much more rarified, may be
neglected. For the dense and bright Light of the Circle, will obscure
the rare and weak Light of these dark Colours round about it, and
render them almost insensible. The sensible Image of a lucid Point is
therefore scarce broader than a Circle, whose Diameter is the 250th Part
of the Diameter of the Aperture of the Object-glass of a good Telescope,
or not much broader, if you except a faint and dark misty Light round
about it, which a Spectator will scarce regard. And therefore in a
Telescope, whose Aperture is four Inches, and Length an hundred Feet, it
exceeds not 2'' 45''', or 3''. And in a Telescope whose Aperture is two
Inches, and Length 20 or 30 Feet, it may be 5'' or 6'', and scarce
above. And this answers well to Experience: For some Astronomers have
found the Diameters of the fix'd Stars, in Telescopes of between 20 and
60 Feet in length, to be about 5'' or 6'', or at most 8'' or 10'' in
diameter. But if the Eye-Glass be tincted faintly with the Smoak of a
Lamp or Torch, to obscure the Light of the Star, the fainter Light in
the Circumference of the Star ceases to be visible, and the Star (if the
Glass be sufficiently soiled with Smoak) appears something more like a
mathematical Point. And for the same Reason, the enormous Part of the
Light in the Circumference of every lucid Point ought to be less
discernible in shorter Telescopes than in longer, because the shorter
transmit less Light to the Eye.
Now, that the fix'd Stars, by reason of their immense Distance, appear
like Points, unless so far as their Light is dilated by Refraction, may
appear from hence; that when the Moon passes over them and eclipses
them, their Light vanishes, not gradually like that of the Planets, but
all at once; and in the end of the Eclipse it returns into Sight all at
once, or certainly in less time than the second of a Minute; the
Refraction of the Moon's Atmosphere a little protracting the time in
which the Light of the Star first vanishes, and afterwards returns into
Sight.
Now, if we suppose the sensible Image of a lucid Point, to be even 250
times narrower than the Aperture of the Glass; yet this Image would be
still much greater than if it were only from the spherical Figure of the
Glass. For were it not for the different Refrangibility of the Rays, its
breadth in an 100 Foot Telescope whose aperture is 4 Inches, would be
but 961/72000000 parts of an Inch, as is manifest by the foregoing
Computation. And therefore in this case the greatest Errors arising from
the spherical Figure of the Glass, would be to the greatest sensible
Errors arising from the different Refrangibility of the Rays as
961/72000000 to 4/250 at most, that is only as 1 to 1200. And this
sufficiently shews that it is not the spherical Figures of Glasses, but
the different Refrangibility of the Rays which hinders the perfection of
Telescopes.
There is another Argument by which it may appear that the different
Refrangibility of Rays, is the true cause of the imperfection of
Telescopes. For the Errors of the Rays arising from the spherical
Figures of Object-glasses, are as the Cubes of the Apertures of the
Object Glasses; and thence to make Telescopes of various Lengths magnify
with equal distinctness, the Apertures of the Object-glasses, and the
Charges or magnifying Powers ought to be as the Cubes of the square
Roots of their lengths; which doth not answer to Experience. But the
Errors of the Rays arising from the different Refrangibility, are as the
Apertures of the Object-glasses; and thence to make Telescopes of
various lengths, magnify with equal distinctness, their Apertures and
Charges ought to be as the square Roots of their lengths; and this
answers to Experience, as is well known. For Instance, a Telescope of 64
Feet in length, with an Aperture of 2-2/3 Inches, magnifies about 120
times, with as much distinctness as one of a Foot in length, with 1/3 of
an Inch aperture, magnifies 15 times.
[Illustration: FIG. 28.]
Now were it not for this different Refrangibility of Rays, Telescopes
might be brought to a greater perfection than we have yet describ'd, by
composing the Object-glass of two Glasses with Water between them. Let
ADFC [in _Fig._ 28.] represent the Object-glass composed of two Glasses
ABED and BEFC, alike convex on the outsides AGD and CHF, and alike
concave on the insides BME, BNE, with Water in the concavity BMEN. Let
the Sine of Incidence out of Glass into Air be as I to R, and out of
Water into Air, as K to R, and by consequence out of Glass into Water,
as I to K: and let the Diameter of the Sphere to which the convex sides
AGD and CHF are ground be D, and the Diameter of the Sphere to which the
concave sides BME and BNE, are ground be to D, as the Cube Root of
KK--KI to the Cube Root of RK--RI: and the Refractions on the concave
sides of the Glasses, will very much correct the Errors of the
Refractions on the convex sides, so far as they arise from the
sphericalness of the Figure. And by this means might Telescopes be
brought to sufficient perfection, were it not for the different
Refrangibility of several sorts of Rays. But by reason of this different
Refrangibility, I do not yet see any other means of improving Telescopes
by Refractions alone, than that of increasing their lengths, for which
end the late Contrivance of _Hugenius_ seems well accommodated. For very
long Tubes are cumbersome, and scarce to be readily managed, and by
reason of their length are very apt to bend, and shake by bending, so as
to cause a continual trembling in the Objects, whereby it becomes
difficult to see them distinctly: whereas by his Contrivance the Glasses
are readily manageable, and the Object-glass being fix'd upon a strong
upright Pole becomes more steady.
Seeing therefore the Improvement of Telescopes of given lengths by
Refractions is desperate; I contrived heretofore a Perspective by
Reflexion, using instead of an Object-glass a concave Metal. The
diameter of the Sphere to which the Metal was ground concave was about
25 _English_ Inches, and by consequence the length of the Instrument
about six Inches and a quarter. The Eye-glass was Plano-convex, and the
diameter of the Sphere to which the convex side was ground was about 1/5
of an Inch, or a little less, and by consequence it magnified between 30
and 40 times. By another way of measuring I found that it magnified
about 35 times. The concave Metal bore an Aperture of an Inch and a
third part; but the Aperture was limited not by an opake Circle,
covering the Limb of the Metal round about, but by an opake Circle
placed between the Eyeglass and the Eye, and perforated in the middle
with a little round hole for the Rays to pass through to the Eye. For
this Circle by being placed here, stopp'd much of the erroneous Light,
which otherwise would have disturbed the Vision. By comparing it with a
pretty good Perspective of four Feet in length, made with a concave
Eye-glass, I could read at a greater distance with my own Instrument
than with the Glass. Yet Objects appeared much darker in it than in the
Glass, and that partly because more Light was lost by Reflexion in the
Metal, than by Refraction in the Glass, and partly because my Instrument
was overcharged. Had it magnified but 30 or 25 times, it would have made
the Object appear more brisk and pleasant. Two of these I made about 16
Years ago, and have one of them still by me, by which I can prove the
truth of what I write. Yet it is not so good as at the first. For the
concave has been divers times tarnished and cleared again, by rubbing
it with very soft Leather. When I made these an Artist in _London_
undertook to imitate it; but using another way of polishing them than I
did, he fell much short of what I had attained to, as I afterwards
understood by discoursing the Under-workman he had employed. The Polish
I used was in this manner. I had two round Copper Plates, each six
Inches in Diameter, the one convex, the other concave, ground very true
to one another. On the convex I ground the Object-Metal or Concave which
was to be polish'd, 'till it had taken the Figure of the Convex and was
ready for a Polish. Then I pitched over the convex very thinly, by
dropping melted Pitch upon it, and warming it to keep the Pitch soft,
whilst I ground it with the concave Copper wetted to make it spread
eavenly all over the convex. Thus by working it well I made it as thin
as a Groat, and after the convex was cold I ground it again to give it
as true a Figure as I could. Then I took Putty which I had made very
fine by washing it from all its grosser Particles, and laying a little
of this upon the Pitch, I ground it upon the Pitch with the concave
Copper, till it had done making a Noise; and then upon the Pitch I
ground the Object-Metal with a brisk motion, for about two or three
Minutes of time, leaning hard upon it. Then I put fresh Putty upon the
Pitch, and ground it again till it had done making a noise, and
afterwards ground the Object-Metal upon it as before. And this Work I
repeated till the Metal was polished, grinding it the last time with all
my strength for a good while together, and frequently breathing upon
the Pitch, to keep it moist without laying on any more fresh Putty. The
Object-Metal was two Inches broad, and about one third part of an Inch
thick, to keep it from bending. I had two of these Metals, and when I
had polished them both, I tried which was best, and ground the other
again, to see if I could make it better than that which I kept. And thus
by many Trials I learn'd the way of polishing, till I made those two
reflecting Perspectives I spake of above. For this Art of polishing will
be better learn'd by repeated Practice than by my Description. Before I
ground the Object-Metal on the Pitch, I always ground the Putty on it
with the concave Copper, till it had done making a noise, because if the
Particles of the Putty were not by this means made to stick fast in the
Pitch, they would by rolling up and down grate and fret the Object-Metal
and fill it full of little holes.
But because Metal is more difficult to polish than Glass, and is
afterwards very apt to be spoiled by tarnishing, and reflects not so
much Light as Glass quick-silver'd over does: I would propound to use
instead of the Metal, a Glass ground concave on the foreside, and as
much convex on the backside, and quick-silver'd over on the convex side.
The Glass must be every where of the same thickness exactly. Otherwise
it will make Objects look colour'd and indistinct. By such a Glass I
tried about five or six Years ago to make a reflecting Telescope of four
Feet in length to magnify about 150 times, and I satisfied my self that
there wants nothing but a good Artist to bring the Design to
perfection. For the Glass being wrought by one of our _London_ Artists
after such a manner as they grind Glasses for Telescopes, though it
seemed as well wrought as the Object-glasses use to be, yet when it was
quick-silver'd, the Reflexion discovered innumerable Inequalities all
over the Glass. And by reason of these Inequalities, Objects appeared
indistinct in this Instrument. For the Errors of reflected Rays caused
by any Inequality of the Glass, are about six times greater than the
Errors of refracted Rays caused by the like Inequalities. Yet by this
Experiment I satisfied my self that the Reflexion on the concave side of
the Glass, which I feared would disturb the Vision, did no sensible
prejudice to it, and by consequence that nothing is wanting to perfect
these Telescopes, but good Workmen who can grind and polish Glasses
truly spherical. An Object-glass of a fourteen Foot Telescope, made by
an Artificer at _London_, I once mended considerably, by grinding it on
Pitch with Putty, and leaning very easily on it in the grinding, lest
the Putty should scratch it. Whether this way may not do well enough for
polishing these reflecting Glasses, I have not yet tried. But he that
shall try either this or any other way of polishing which he may think
better, may do well to make his Glasses ready for polishing, by grinding
them without that Violence, wherewith our _London_ Workmen press their
Glasses in grinding. For by such violent pressure, Glasses are apt to
bend a little in the grinding, and such bending will certainly spoil
their Figure. To recommend therefore the consideration of these
reflecting Glasses to such Artists as are curious in figuring Glasses, I
shall describe this optical Instrument in the following Proposition.
_PROP._ VIII. PROB. II.
_To shorten Telescopes._
Let ABCD [in _Fig._ 29.] represent a Glass spherically concave on the
foreside AB, and as much convex on the backside CD, so that it be every
where of an equal thickness. Let it not be thicker on one side than on
the other, lest it make Objects appear colour'd and indistinct, and let
it be very truly wrought and quick-silver'd over on the backside; and
set in the Tube VXYZ which must be very black within. Let EFG represent
a Prism of Glass or Crystal placed near the other end of the Tube, in
the middle of it, by means of a handle of Brass or Iron FGK, to the end
of which made flat it is cemented. Let this Prism be rectangular at E,
and let the other two Angles at F and G be accurately equal to each
other, and by consequence equal to half right ones, and let the plane
sides FE and GE be square, and by consequence the third side FG a
rectangular Parallelogram, whose length is to its breadth in a
subduplicate proportion of two to one. Let it be so placed in the Tube,
that the Axis of the Speculum may pass through the middle of the square
side EF perpendicularly and by consequence through the middle of the
side FG at an Angle of 45 Degrees, and let the side EF be turned towards
the Speculum, and the distance of this Prism from the Speculum be such
that the Rays of the Light PQ, RS, &c. which are incident upon the
Speculum in Lines parallel to the Axis thereof, may enter the Prism at
the side EF, and be reflected by the side FG, and thence go out of it
through the side GE, to the Point T, which must be the common Focus of
the Speculum ABDC, and of a Plano-convex Eye-glass H, through which
those Rays must pass to the Eye. And let the Rays at their coming out of
the Glass pass through a small round hole, or aperture made in a little
plate of Lead, Brass, or Silver, wherewith the Glass is to be covered,
which hole must be no bigger than is necessary for Light enough to pass
through. For so it will render the Object distinct, the Plate in which
'tis made intercepting all the erroneous part of the Light which comes
from the verges of the Speculum AB. Such an Instrument well made, if it
be six Foot long, (reckoning the length from the Speculum to the Prism,
and thence to the Focus T) will bear an aperture of six Inches at the
Speculum, and magnify between two and three hundred times. But the hole
H here limits the aperture with more advantage, than if the aperture was
placed at the Speculum. If the Instrument be made longer or shorter, the
aperture must be in proportion as the Cube of the square-square Root of
the length, and the magnifying as the aperture. But it's convenient that
the Speculum be an Inch or two broader than the aperture at the least,
and that the Glass of the Speculum be thick, that it bend not in the
working. The Prism EFG must be no bigger than is necessary, and its back
side FG must not be quick-silver'd over. For without quicksilver it will
reflect all the Light incident on it from the Speculum.
[Illustration: FIG. 29.]
In this Instrument the Object will be inverted, but may be erected by
making the square sides FF and EG of the Prism EFG not plane but
spherically convex, that the Rays may cross as well before they come at
it as afterwards between it and the Eye-glass. If it be desired that the
Instrument bear a larger aperture, that may be also done by composing
the Speculum of two Glasses with Water between them.
If the Theory of making Telescopes could at length be fully brought into
Practice, yet there would be certain Bounds beyond which Telescopes
could not perform. For the Air through which we look upon the Stars, is
in a perpetual Tremor; as may be seen by the tremulous Motion of Shadows
cast from high Towers, and by the twinkling of the fix'd Stars. But
these Stars do not twinkle when viewed through Telescopes which have
large apertures. For the Rays of Light which pass through divers parts
of the aperture, tremble each of them apart, and by means of their
various and sometimes contrary Tremors, fall at one and the same time
upon different points in the bottom of the Eye, and their trembling
Motions are too quick and confused to be perceived severally. And all
these illuminated Points constitute one broad lucid Point, composed of
those many trembling Points confusedly and insensibly mixed with one
another by very short and swift Tremors, and thereby cause the Star to
appear broader than it is, and without any trembling of the whole. Long
Telescopes may cause Objects to appear brighter and larger than short
ones can do, but they cannot be so formed as to take away that confusion
of the Rays which arises from the Tremors of the Atmosphere. The only
Remedy is a most serene and quiet Air, such as may perhaps be found on
the tops of the highest Mountains above the grosser Clouds.