_z_ The opposite hole enlarged, to admit the pinion _c_ to pass
through.
XCVIII. _An Account of some Experiments concerning the different
Refrangibility of Light. By Mr._ John Dollond. _With a Letter from_
James Short, _M. A. F.R.S. Acad. Reg. Suec. Soc._
[Read June 8, 1758.]
_To the Rev. Dr._ Birch, _Secret. R. S._
Dear Sir,
I Have received the inclosed paper from Mr. Dollond, which he desires
may be laid before the Royal Society. It contains the theory of
correcting the errors arising from the different refrangibility of
the rays of light in the object-glasses of refracting telescopes; and
I have found, upon examination, that telescopes made according to
this theory are intirely free from colours, and are as distinct as
reflecting telescopes. I am,
Dear Sir,
Your most obedient humble Servant,
Ja. Short.
Surrey-street, 8th June, 1758.
IT is well known, that a ray of light, refracted by passing thro’
mediums of different densities, is at the same time proportionally
divided or spread into a number of parts, commonly called homogeneal
rays, each of a different colour; and that these, after refraction,
proceed diverging; a proof, that they are differently refracted, and
that light consists of parts that differ in degrees of refrangibility.
Every ray of light passing from a rarer into a denser medium, is
refracted towards the perpendicular; but from a denser into a rarer
one, from the perpendicular; and the sines of the angles of incidence
and refraction are in a given ratio. But light consisting of parts,
which are differently refrangible, each part of an original or compound
ray has a ratio peculiar to itself; and therefore the more a heterogene
ray is refracted, the more will the colours diverge, since the ratios
of the sines of the homogene rays are constant; and equal refractions
produce equal divergencies.
That this is the case when light is refracted by one given medium only,
as suppose any particular sort of glass, is out of all dispute, being
indeed self-evident; but that the divergency of the colours will be
the same under equal refractions, whatsoever mediums the light may be
refracted by, tho’ generally supposed, does not appear quite so clearly.
However, as no medium is known, which will refract light without
diverging the colours, and as difference of refrangibility seems thence
to be a property inherent in light itself, Opticians have, upon that
consideration, concluded, that equal refractions must produce equal
divergencies in every sort of medium: whence it should also follow,
that equal and contrary refractions must not only destroy each other,
but that the divergency of the colour from one refraction would
likewise be corrected by the other; and there could be no possibility
of producing any such thing as refraction, which would not be affected
by the different refrangibility of light; or, in other words, that
however a ray of light might be refracted backwards and forwards by
different mediums, as water, glass, _&c._ provided it was so done, that
the emergent ray should be parallel to the incident one, it would ever
after be white; and, conversely, if it should come out inclined to the
incident, it would diverge, and ever after be coloured. From which it
was natural to infer, that all spherical object-glasses of telescopes
must be equally affected by the different refrangibility of light, in
proportion to their apertures, whatever material they may be formed of.
But it seems worthy of consideration, that notwithstanding this notion
has been generally adopted as an incontestable truth, yet it does not
seem to have been hitherto so confirmed by evident experiment, as the
nature of so important a matter justly demands; and this it was that
determined me to attempt putting the thing to issue by the following
experiment.
I cemented together two plates of parallel glass at their edges, so as
to form a prismatic or wedge-like vessel, when stopped at the ends or
bases; and its edge being turned downwards, I placed therein a glass
prism with one of its edges upwards, and filled up the vacancy with
clear water: thus the refraction of the prism was contrived to be
contrary to that of the water, so that a ray of light transmitted thro’
both these refracting mediums would be refracted by the difference only
between the two refractions. Wherefore, as I found the water to refract
more or less than the glass prism, I diminished or increased the angle
between the glass plates, till I found the two contrary refractions to
be equal; which I discovered by viewing an object thro’ this double
prism; which, when it appeared neither raised nor depressed, I was
satisfied, that the refractions were equal, and that the emergent rays
were parallel to the incident.
Now, according to the prevailing opinion, the object should have
appeared thro’ this double prism quite of its natural colour; for
if the difference of refrangibility had been equal in the two equal
refractions, they would have rectified each other: but the experiment
fully proved the fallacy of this received opinion, by shewing the
divergency of the light by the prism to be almost double of that by
the water; for the object, tho’ not at all refracted, was yet as much
infected with prismatic colours, as if it had been seen thro’ a glass
wedge only, whose refracting angle was near 30 degrees.
_N. B._ This experiment will be readily perceived to be the same as
that which Sir Isaac Newton mentions[154]; but how it comes to differ
so very remarkably in the result, I shall not take upon me to account
for; but will only add, that I used all possible precaution and care
in the process, and that I keep the apparatus by me to evince the
truth of what I write, whenever I may be properly required so to do.
I plainly saw then, that if the refracting angle of the water-vessel
could have admitted of a sufficient increase, the divergency of
the coloured rays would have been greatly diminished, or intirely
rectified; and there would have been a very great refraction without
colour, as now I had a great discolouring without refraction: but the
inconveniency of so large an angle, as that of the vessel must have
been, to bring the light to an equal divergency with that of the glass
prism, whose angle was about 60 degrees, made it necessary to try some
experiments of the same kind, by smaller angles.
I ground a wedge of common plate glass to an angle of somewhat less
than 9 degrees, which refracted the mean rays about 5 degrees. I then
made a wedge-like vessel, as in the former experiment, and filling it
with water, managed it so, that it refracted equally with the glass
wedge; or, in other words, the difference of their refractions was
nothing, and objects viewed thro’ them appeared neither raised nor
depressed. This was done with an intent to observe the same thing over
again in these small angles, which I had seen in the prism: and it
appeared indeed the same in proportion, or as near as I could judge;
for notwithstanding the refractions were here also equal, yet the
divergency of the colours by the glass was vastly greater than that
by the water; for objects seen by these two refractions were very
much discoloured. Now this was a demonstration, that the divergency
of the light, by the different refrangibility, was far from being
equal in these two refractions. I also saw, from the position of the
colours, that the excess of divergency was in the glass; so that I
increased the angle of the water-wedge, by different trials, till the
divergency of the light by the water was equal to that by the glass;
that is, till the object, tho’ considerably refracted, by the excess
of the refraction of the water, appeared nevertheless quite free from
any colours proceeding from the different refrangibility of light;
and, as near as I could then measure, the refraction by the water was
about ⁵⁄₄ of that by the glass. Indeed I was not very exact in taking
the measures, because my business was not at that time about the
proportions, so much as to shew, that the divergency of the colours, by
different substances, was by no means in proportion to the refractions;
and that there was a possibility of refraction without any divergency
of the light at all.
Having, about the beginning of the year 1757, tried these experiments,
I soon after set about grinding telescopic object-glasses upon the
new principles of refractions, which I had gathered from them;
which object-glasses were compounded of two spherical glasses with
water between them. These glasses I had the satisfaction to find,
as I had expected, free from the errors arising from the different
refrangibility of light: for the refractions, by which the rays were
brought to a focus, were every-where the differences between two
contrary refractions, in the same manner, and in the same proportions,
as in the experiment with the wedges.
However, the images formed at the foci of these object-glasses were
still very far from being so distinct as might have been expected
from the removal of so great a disturbance; and yet it was not very
difficult to guess at the reason, when I considered, that the radii of
the spherical surfaces of those glasses were required to be so short,
in order to make the refractions in the required proportions, that
they must produce aberrations, or errors, in the image, as great, or
greater, than those from the different refrangibility of light. And
therefore, seeing no method of getting over that difficulty, I gave up
all hopes of succeeding in that way.
And yet, as these experiments clearly proved, that different substances
diverged the light very differently, in proportion to the refraction;
I began to suspect, that such variety might possibly be found in
different sorts of glass, especially as experience had already shewn,
that some made much better object-glasses, in the usual way, than
others: and as no satisfactory cause had as yet been assigned for such
difference, there was great reason to presume, that it might be owing
to the different divergency of the light by their refractions.
Wherefore, the next business to be undertaken, was to grind wedges
of different kinds of glass, and apply them together, so that the
refractions might be made in contrary directions, in order to discover,
as in the foregoing experiments, whether the refraction and divergency
of the colours would vanish together. But a considerable time elapsed
before I could set about that work; for tho’ I was determined to try
it at my leisure, for satisfying my own curiosity, yet I did not
expect to meet with a difference sufficient to give room for any great
improvement of telescopes; so that it was not till the latter end of
the year that I undertook it, when my first trials convinced me, that
this business really deserved my utmost attention and application.
I discovered a difference, far beyond my hopes, in the refractive
qualities of different kinds of glass, with respect to their divergency
of colours. the yellow or straw-coloured foreign sort, commonly called
Venice glass, and the English crown glass, are very near alike in that
respect, tho’ in general the crown glass seems to diverge the light
rather the least of the two. The common plate glass made in England
diverges more; and the white crystal or flint English glass, as it is
called, most of all.
It was not now my business to examine into the particular qualities of
every kind of glass that I could come at, much less to amuse myself
with conjectures about the cause, but to fix upon such two sorts
as their difference was the greatest; which I soon found to be the
crown, and the white flint or crystal. I therefore ground a wedge of
white flint of about 25 degrees, and another of crown of about 29
degrees, which refracted nearly alike; but their divergency of the
colours was very different. I then ground several others of crown to
different angles, till I got one, which was equal, with respect to the
divergency of the light, to that in the white flint: for when they were
put together, so as to refract in contrary directions, the refracted
light was intirely free from colour. Then measuring the refractions
of each wedge, I found that of the white glass to be to that of the
crown nearly as 2 to 3; and this proportion would hold very nearly in
all small angles. Wherefore any two wedges made in this proportion,
and applied together, so as to refract in a contrary direction, would
refract the light without any difference of refrangibility.
To make therefore two spherical glasses, that shall refract the light
in contrary directions, it is easy to understand, that one must be
concave, and the other convex; and as the rays are to converge to a
real focus, the excess of refraction must evidently be in the convex;
and as the convex is to refract most, it appears from the experiment,
that it must be made with crown glass, and the concave with white flint
glass.
And further, as the refractions of spherical glasses are in an inverse
ratio of their focal distances; it follows, that the focal distances
of the two glasses should be inversely as the ratio’s of the fractions
of the wedges: for being thus proportioned, every ray of light, that
passes thro’ this combined glass, at whatever distance it may pass from
its axe, will constantly be refracted, by the difference between two
contrary refractions, in the proportion required; and therefore the
different refrangibility of the light will be intirely removed.
Having thus got rid of the principal cause of the imperfection of
refracting telescopes, there seemed to be nothing more to do, but to go
to work upon this principle: but I had not made many attempts, before
I found, that the removal of one impediment had introduced another
equally detrimental (the same as I had before found in two glasses with
water between them): for the two glasses, that were to be combined
together, were the segments of very deep spheres; and therefore the
aberrations from the spherical surfaces became very considerable, and
greatly disturbed the distinctness of the image. Tho’ this appeared
at first a very great difficulty, yet I was not long without hopes
of a remedy: for considering, the surfaces of spherical glasses admit
of great variations, tho’ the focal distance be limited, and that by
these variations their aberrations may be made more or less, almost at
pleasure; I plainly saw the possibility of making the aberrations of
any two glasses equal; and as in this case the refractions of the two
glasses were contrary to each other, their aberrations, being equal,
would intirely vanish.
And thus, at last, I obtained a perfect theory for making
object-glasses, to the apertures of which I could scarce conceive any
limits: for if the practice could come up to the theory, they must
certainly admit of very extensive ones, and of course bear very great
magnifying powers.
But the difficulties attending the practice are very considerable.
In the first place, the focal distances, as well as the particular
surfaces, must be very nicely proportioned to the densities or
refracting powers of the glasses; which are very apt to vary in the
same sort of glass made at different times. Secondly, the centres
of the two glasses must be placed truly on the common axis of the
telescope, otherwise the desired effect will be in a great measure
destroyed. Add to these, that there are four surfaces to be wrought
perfectly spherical; and any person, but moderately practised in
optical operations, will allow, that there must be the greatest
accuracy throughout the whole work.
Notwithstanding so many difficulties, as I have enumerated, I have,
after numerous trials, and a resolute perseverance, brought the matter
at last to such an issue, that I can construct refracting telescopes,
with such apertures and magnifying powers, under limited lengths, as,
in the opinion of the best and undeniable judges, who have experienced
them, far exceed any thing that has been hitherto produced, as
representing objects with great distinctness, and in their true colours.
John Dollond.
XCIX. _An Account of some extraordinary Effects arising from
Convulsions; being Part of a Letter to_ John Huxham, _M.D. and F.R.S.
from_ William Watson, _M.D. F.R.S._