So that by the sum of these six terms we should find, that the light
which passes through six lines of glass would lose 102024/117649, that
is about 10/11 of its quantity. But it must be considered, that M.
Bouguer makes use of glasses which are but little transparent, since he
has observed, that the thickness of a line of these glasses destroys
2/7 of the light. By the experiments which I have made on different
kinds of white glass, it has appeared to me that the light diminishes
much less. These experiments are easy to be made, and are what all the
world may repeat.
In a dark chamber, whose walls were blackened, and which I made use of
for optical experiments, I had a candle lighted of five to the pound;
the room was very large and the candle the only light in it; I then
tried at what distance I could read by this light, and found that I
read very easily at 24 feet four inches from the candle. Afterwards,
having placed a piece of glass, about a line thick, before it, at two
inches distance, I found that I still read very plainly at 22 feet nine
inches; and substituting to this glass another piece of two lines in
thickness and of the same glass, I read at 21 feet distance from the
candle. Two of the same glasses joined one to the other, and placed
before the candle diminished the light so much that I could only read
at 17-1/2 feet distance; and at length, with three glasses, I could
only read at 15 feet. Now the light of a candle diminishing as the
square of the distance augments, its diminution should have been in the
following progression, if glasses had not been interposed: 2--24-1/3.
2--22-3/4. 2--21. 2--17-1/2. 2--15, or 592-1/9. 517-9/15. 441. 306-1/4.
225. Therefore the loss of the light, by the interposition of the
glasses, is in the following progression: 84-79/144. 151. 285-7/9.
367-1/4.
From hence it may be concluded, that the thickness of a line of this
glass diminishes only 84/592 of light, or about 1/7; that two lines
diminishes 157/592, not quite 1/4 and three glasses of two lines
397/592, i. e. less than 2/3.
As this result is very different from that of M. Bouguer, and as I was
cautious of suspecting the truth of his experiments, I repeated mine
with common glass. For long telescopes water alone can be used; and
it is still to be feared that an inconveniency will subsist, from the
opacity resulting from the quantity of liquor which fills the interval
between the two glasses.
The longer the telescope the greater loss of light will ensue; so that
it appears at first sight that this mode cannot be used, especially
for long telescopes; for following what M. Bouguer says in his Optical
Essay, on the gradation of light, nine feet seven inches sea-water
diminishes the light in a relation of 14 to 5; therefore these long
telescopes, filled with water, cannot be used for observing the sun,
and the stars would not have light enough to be perceived across a
thickness of 20 or 30 feet of intermediate liquor.
Nevertheless, if we consider, that by allowing only an inch, or an
inch and a half, for the bore of an objective of 30 feet, we shall
very distinctly perceive the planets in the common telescopes of this
length; we may suppose that by allowing a greater diameter to the
objective we should augment the quantity of light in the ratio of the
square of this diameter, and, consequently, if an inch before suffices
to see a star distinctly, in a common telescope, three inches bore
would be sufficient to see it distinctly through a thickness of 10 feet
water, and that with a glass of three inches diameter we should easily
see it through a thickness of 20 feet water, and so on. It appears,
therefore, that we might hope to meet with success in constructing
a telescope on these principles; for, by increasing the diameter of
the objective, we partly regain the light lost by the defect of the
transparency of the liquor.
But it appears to me certain that a telescope constructed on this mode
would be very useful for observing the sun; for supposing it even
the length of 100 feet, the light of that luminary would not be too
strong after having traversed this thickness of water, and we should
be enabled to observe its surface easily, and at leisure, without
the need of making use of smoked glasses, or of receiving the image
on pasteboard; an advantage we cannot possibly derive from any other
telescope.
There would require only some trifling difference in the construction
of this solar telescope, if we wanted the whole face of the sun
presented; for supposing it the length of 100 feet, in this case, the
ocular glass must be ten inches diameter; because the sun, taking up
more than half a celestial degree, the image formed by the objective
to its focus at 100 feet, will at least have this length of ten
inches; and to unite it wholly, it will require an ocular glass of this
breadth, to which only twenty inches of focus should be given to render
it as strong as possible. It is necessary that the objective, as well
as the ocular glass, should be ten inches in diameter, in order that
the image of the sun, and the image of the bore of the telescope, be of
an equal size with the focus.
If this telescope, which I propose, should only serve to observe the
sun exactly, it would be of great service; for example, it would be
very curious to be able to discover whether there be any luminous parts
larger than others in the sun; if there be inequalities on its surface;
and of what kind; if the spots float on its surface; or whether they be
fixed there, &c. The brightness of its light prevents us from observing
this luminary with the naked eye, and the different refrangibility of
its rays, renders its image confused when received in the focus of
an objective glass, or on pasteboard, so that the surface of the sun
is less known to us than that of any of the planets. The different
refrangibility of its rays would be but little corrected in this long
telescope filled with water; but if the liquor could, by the addition
of salts, be rendered as dense as glass, it would then be the same
as if there were only one glass to pass through; and it appears to me
that infinitely more advantage would result from making use of these
telescopes filled with water, than from the common telescopes with
smoked glasses.
Whether that would or would not be the fact, this however is certain,
that to observe the sun, a telescope quite different is required from
those that we make use of for the different planets; and it is also
certain, that a particular telescope is necessary for each planet,
proportionate to their intensity of light, that is, to the real
quantity of light with which they appear to be enlightened. In all
telescopes the objectives are required as large, and the ocular glass
as strong, as possible, and, at the same time, the distance of the
focus proportioned to the intensify of the light of each planet. To
do this with the greatest advantage, it is requisite to use only an
objective glass so much the larger, and a focus so much the shorter,
according to the light of the planet. Why has there not hitherto been
made objective glasses of 243 feet diameter? The aberration of the
rays, occasioned by the sphericity of the glasses, is the sole cause
of the confusion, which is as the square of the diameter of the
tube; and it is for this reason that spherical glasses, with a small
bore, are of no value when enlarged; we have more light, but less
distinction and clearness. Nevertheless, broad, spherical glasses are
very good for night telescopes. The English have constructed telescopes
of this nature, and they make use of them very advantageously to see
vessels at a great distance in dark nights But at present, that we
know, in a great measure, how to correct the effects of the different
refrangibility of the rays, it seems, that we should make elliptical
or hyperbolical glasses, which would not produce the alteration caused
by sphericity, and which, consequently, would be three or four times
broader than spherical glasses. There is only this mode of augmenting
to our sight the quantity of light sent to us from the planets, for
we cannot put an additional light on them, as we do on objects which
we observe with the microscope, but must at least employ to the
greatest possible advantage, the quantity of light with which they are
illumined, by receiving it on as great a surface as possible. This
hyperbolical telescope, which would be composed only of one single
large objective glass, and of an ocular one proportionate, would
require matter of the greatest transparency; and we should unite by
this means all the advantages possible, that is, those of the acromatic
to that of the elliptical or hyperbolical telescopes, and we should
profit by all the quantity of light each planet reflects to our sight.
I may be deceived; but what I propose appears to be sufficiently
founded to recommend its execution to persons zealously attached to the
advancement of the sciences.
Employing myself thus on these reveries, some of which may one day
be realized, and in which hope I publish them, I thought of the
Alexandrian mirror, spoken of by some ancient authors, and by means
of which vessels were seen at a great distance on the sea. The most
positive passage which I have met with is the following.
"Alexandria ... in Pharo vero erat speculum e ferro sinico. Per quod
a longe videbantur naves Græcorum advenientes; sed paulo postquam
Islamismus invaluit, scilicet tempore califatus Walidfil: Abdi-I-melec,
Christiani, fraude adhibita illud deleverunt. Abu-l-feda, &c.
Descriptio Ægypti."
Having dwelt for some time on this, I have thought, 1. That such a
mirror was possible to be made. 2. That even without a mirror or
telescope, we might by certain dispositions obtain the same effect,
and see vessels from land, as far, perhaps, as the curvature of the
earth would permit. We have already observed that persons whose sight
was very good, have perceived objects illumined by the sun at more
than 3400 times their diameter, and at the same time we have remarked,
that the intermediate light was of such great hurt to that of distant
objects, that by night a luminous object is perceived at ten, twenty,
and perhaps a hundred times greater distance than during the day. We
know that at the bottom of very deep pits, stars may be seen in the
daytime[H]; why therefore should we not see vessels illumined by the
rays of the sun, by placing one's self at the end of a very long dark
gallery, situated on the seashore, in such a manner as to receive no
other than that of the distant sea, and the vessels which might be on
it? This gallery would be only a horizontal pit, which would have the
same effect with respect to ships as the vertical pit has with respect
to the stars; and it appears to me so simple, that I am astonished it
has never before been thought of and tried. It seems to me, that by
taking the time of the day for our observations when the sun should
be behind the gallery, we might see them from the dark end of it ten
times at least better than in the open light. Now a man on horseback is
easily distinguished at a mile distance, when the rays of the sun shine
on him, and by suppressing the intermediate light which surrounds us,
and darkening our sight, we should see him at least ten times farther;
that is to say, ten miles. Ships, therefore, being much larger, would
be seen as far as the curvature of the earth would permit, without any
other instrument than the naked eye.
[H] Aristotle is, I believe, the first that ever mentioned this
observation.
But a concave mirror, of a great diameter, and of any focus, placed at
the end of a long black tube, would have nearly the same effect as our
great objective glasses of the same diameter and form would have during
the night, and it was probably one of these concave mirrors of polished
steel that was established at the port of Alexandria[I]. If this steel
mirror did really exist, we cannot refuse to the ancients the glory
of the first invention, for this mirror can only be effective by as
much as the light reflected by its surface was collected by another
concave mirror placed at its focus, and in this consists the essence
of the telescope and the merit of its construction. Nevertheless this
does not deprive the great Newton of any glory, who first renewed the
almost-forgotten invention. As the rays of light are by their nature
differently refrangible, he was inclined to think there were no means
of correcting this effect, or, if he had perceived those means, he
judged them so difficult that he chose rather to turn his views another
way, and produce, by means of the reflection of the rays, the great
effects which he could not obtain by their refraction; he, therefore,
constructed his telescope, the reflection of which is infinitely
superior to those that were in common use. The best telescopes are
always dark in comparison of the acromatic, and this obscurity does not
proceed only from the defect of the polish, or the colour of the metal
of mirrors, but from the nature even of light, the rays of which being
differently refrangible are also differently reflexible, although in
much less unequal degrees.
[I] From time immemorial the Chinese, and particularly the Japanese,
have possessed the art of working in steel both in large and small
bodies; and hence I have thought that the words _e ferro sinico_ in the
preceding quotation should be understood as applying to polished steel.
It still remains, therefore, to bring the telescope to perfection, and
to find the manner of compensating this different reflexibility, as we
have discovered that of compensating the different refrangibility.
After all, I imagine that it will be well perceived that a very good
day-glass may be made, without using either glasses or mirrors, and
simply by suppressing the surrounding light, by means of a tube 150
or 250 feet long, and by placing ourselves in an obscure place. The
brighter the day is, the greater will be the effect. I am persuaded
that we should be able to see at 15, and perhaps 20 miles distance. The
only difference between this long tube, and the dark gallery, which
I have spoken of, is, that the field, or the space seen, would be
smaller, and precisely in the ratio of the square of the bore of the
tube to that of the gallery.