The story of the burning glasses of Archimedes is famous; he is said
to have invented them for the defence of his country; and he threw,
say the ancients, the fire of the sun with such force on the enemy's
fleet, as to reduce it into ashes as it approached the ramparts of
Syracuse. But this story, which, for fifteen or sixteen centuries,
was never doubted, has been contradicted, and treated as fabulous in
these latter ages. Descartes, with the authority of a master, has
attacked this talent attributed to Archimedes; he has denied the
possibility of the invention, and his opinion has prevailed over the
testimonies and credit of the ancients. Modern naturalists, either
through a respect for their philosopher, or through complaisance for
their contemporaries, have adopted the same opinion. Nothing is allowed
to the ancients but what cannot be avoided. Determined, perhaps, by
these motives, of which self-love too often is the abettor, have
we not naturally too much inclination to refuse what is due to our
predecessors? and if, in our time, more is refused than was in any
other, is it not that, by being more enlightened, we think we have more
right to fame, and more pretensions to superiority?
Be that as it may, this invention was the cause of many other
discoveries of antiquity which are at present unknown, because the
facility of denying them has been preferred to the trouble of finding
them out; and the burning glasses of Archimedes have been so decried,
that it does not appear possible to re-establish their reputation;
for, to call the judgment of Descartes in question, something more is
required than assertions, and there only remained one sure decisive
mode, but at the same time difficult and bold, which was to undertake
to discover glasses that might produce the like effects.
Though I had conceived the idea, I was for a long time deterred from
making the experiment, from the dread of the difficulty which might
attend it; at length, however, I determined to search after the mode of
making mirrors to burn at a great distance, as from 100 to 300 feet. I
knew, in general, that the power of reflecting mirrors, never extended
farther than 15 or 20 feet, and with refringent, the distance was
still shorter: and I perceived it was impossible in practice to form a
metal, or glass mirror, with such exactness as to burn at these great
distances. To have sufficient power for that, the sphere, for example,
must be 800 feet diameter; therefore, we could hope for nothing of that
kind in the common mode of working glasses; and I perceived also that
if we could even find a new method to give to large pieces of glass, or
metal, a curve sufficiently slight, there would still result but a very
inconsiderable advantage.
But to proceed regularly, it was necessary first to see how much light
the sun loses by reflection at different distances, and what are the
matters which reflect it the strongest; I first found, that glasses
when they are polished with care, reflect the light more powerfully
than the best polished metals, and even better than the compounded
metal with which telescope mirrors are made; and that although there
are two reflectors in the glasses, they yet give a brighter and more
clear light than metal. Secondly, by receiving the light of the sun in
a dark place, and by comparing it with this light of the sun reflected
by a glass, I found, that at small distances, as four or five feet, it
only lost about half by reflection, which I judged by letting a second
reflected light fall on the first; for the briskness of these two
reflected lights appeared to be equal to that of direct light. Thirdly,
having received at the distances of 100, 200, and 300 feet, this light
reflected by great glasses, I perceived that it did not lose any of its
strength by the thickness of the air it had to pass through.
I afterwards tried the same experiments on the light of candles; and to
assure myself more exactly of the quantity of weakness that reflection
causes to this light, I made the following experiments:
I seated myself opposite a glass mirror with a book in my hand, in a
room where the darkness of the night would not permit me to distinguish
a single object. In an adjoining room I had a lighted candle placed at
about 40 feet distance; this I approached nearer and nearer, till I
could read the book, when the distance was about 24 feet. Afterwards
turning the book, I endeavoured to read by the reflected light, having
by a parchment intercepted the part of the light which did not fall
on the mirror, in order to have only the reflected light on my book.
To do so I was obliged to approach the candle nearer, which I did by
degrees, till I could read the same characters clearly by the same
light, and then the distance from the candle, comprehending that of the
book to the mirror, which was only half a foot, I found to be in all
15 feet. I repeated this several times, and had always nearly the same
results; from whence I concluded, that the strength, or quantity, of
direct light is to that of reflected light, as 576 to 225; therefore,
the light of five candles reflected by a flat glass, is nearly equal to
that of the direct light of two.
The light of a candle, therefore, loses more by reflection than by the
light of the sun; and this difference proceeds from the rays of the
former falling more obliquely on the mirror than the rays of the sun,
which come almost parallel. This experiment confirmed what I had at
first found, and I hold it certain, that the light of the sun loses
only half by its reflection on a glass mirror.
This first information being acquired, I afterwards sought what
became of the images of the sun when received at great distances. To
be perfectly understood we must not, as is generally done, consider
the rays of the sun as parallel; and it must also be remembered, that
the body of the sun occupies an extent of about 32 minutes; that
consequently the rays which issue from the upper edge of the disk,
falling on a point of a reflecting surface, the rays which issue
from the lower edge falling also on the same point of this surface,
they form between them an angle of 32 minutes in the incidence, and
afterwards in the reflection, and that, consequently, the image must
increase in size in proportion as it is farther distant. Attention
must likewise be paid to the figure of those images; for example, a
plain square glass of half a foot, exposed to the rays of the sun, will
form a square image of six inches, when this image is received at the
distance of a few feet; by removing farther and farther off, the image
is seen to increase, afterwards to become deformed, then round, in
which state it remains still increasing in size, in proportion as we
are more distant from the mirror. This image is composed of as many of
the sun's disks as there are physical points in the reflecting surface;
the middle point forms an image of the disk, the adjoining points form
the like, and of the same size, which exceed a little the middle disk:
it is the same with the other points, and the image is composed of
an infinity of disks, which surmounting regularly, and anticipating
circularly one over the other, form the reflected image, of which the
middle point of the glass is the centre.
If the image composed of all these disks is received at a small
distance, then their extent being somewhat larger than that of the
glass, this image is of the same figure and nearly of the same extent
as the glass; but when the image is received at a great distance from
the glass, where the extent of the disks is much greater than that
of the glass, the image no longer retains the same figure as the
glass, but becomes necessarily circular. To find the point of distance
where the image loses its square figure, we have only to seek for the
distance where the glass appears under an angle equal to that the sun
forms to our sight, i. e. an angle of 32 minutes, and this distance
will be that where the image will lose its square figure, and become
round, for the disks having always an equal line to the semi-circle,
which measures an angle of 32 minutes for a diameter, we shall find by
this rule that a square glass of six inches loses its square figure at
the distance of about 60 feet, and that a glass of a foot square loses
it at 120 feet, and so on of the rest.
By reflecting a little on this theory we shall no longer be astonished
to find, that at very great distances a large and small glass afford an
image of nearly the same size, and which only differs by the intensity
of the light; we shall no longer be surprised that a round, square,
long, or triangular glass, or any other figure, always yields round
images[E]; and we shall evidently see that images do not increase and
lessen by the dispersion of light, or by any loss in passing through
the air, as some naturalists have imagined; but that, on the contrary,
it is occasioned by the augmentation of the disks, which always occupy
a space of 32 minutes to whatever distance they are removed.
[E] This is the reason that the small images which pass betwixt the
leaves of high and full trees, and which falling on the walks are all
oval or round.
So, likewise, we shall be convinced, by the simple exposition of this
theory, that curves, of any kind, cannot be used with advantage to
burn at a great distance, because the diameter of the focus can never
be smaller than the chord, which measures an angle of 32 minutes, and
that, consequently, the most perfect concave mirror, whose diameter is
equal to this chord, will never produce double the effect of a plane
mirror of the same surface; and if the diameter of a curved mirror were
less than the chord, it would scarcely have more effect than a plane
mirror of the same surface.
When I had well considered the above I had no longer a doubt that
Archimedes could not burn at a distance but with plane mirrors, for,
independently of the impossibility they then felt, and which we feel at
pleasure, of making concave mirrors with so large a focus, I was well
aware that the reflection I have just made could not have escaped this
great mathematician. Besides, there is every reason to suppose that the
ancients did not know how to make large masses of glass; that they were
ignorant of the art of burning it to make large glasses, possessing
only the method of blowing it, and making bottles and vases; from which
consideration I was led to conclude, that it was with plane mirrors of
polished metals, and by the reflections of the sun, that Archimedes
had been enabled to burn at a distance. But as I perceived that glass
mirrors reflected the light more powerfully than the most polished
mirrors, I thought to construct a machine to coincide in the same point
the reflected images by a great number of these plane glasses, being
well convinced that this was the sole mode of succeeding.
Nevertheless, I had still some doubts remaining, which appeared to me
well founded, for thus I reasoned. Supposing the burning distance to
be 240 feet, I perceived clearly that the focus of my mirror could not
have a less than two feet diameter; in which case what would be the
extent I should be obliged to give to my assemblage of plane mirrors to
produce a fire in so great a focus? It might be so great that the thing
would be impracticable in the execution, for, by comparing the diameter
of the focus to the diameter of the mirror, in the best reflecting
mirrors, I observed that the diameter of the Academy's mirror, which
is three feet, was 108 times bigger than its focus, which was no more
than four lines; and I concluded, that to burn as strong at 240 feet it
was necessary that my assemblage of mirrors should be 216 feet diameter
to have a focus of two feet; now a mirror of 216 feet diameter was
certainly an impossible thing.
This mirror of three feet diameter burnt strong enough to melt gold,
and I was desirous to see how much I should gain by reducing its action
to the burning of wood. For this purpose I used circular zones of paper
on the mirrors to diminish the diameter, and I found that there was no
longer power enough to inflame dry wood when its diameter was reduced
to little more than four inches; therefore, taking five inches, or
sixty lines, for the diameter necessary to burn with a focus of four
lines, it appeared, that to burn equally at 210 feet, where the focus
should necessarily have two feet diameter, I should require a mirror
of 30 feet diameter, which appeared still as impossible, or at least
impracticable.
To such positive conclusions, and which others would have regarded
as demonstrations of the impossibility of the mirror, I had only a
supposition to oppose; but an old supposition, on which the more I
reflected the more I was persuaded that it was not without foundation;
namely, that the effects of heat might possibly not be in proportion to
the quantity of light, or, what amounts to the same, that at an equal
intensity of light large focuses must burn brisker than the small.
By estimating heat mathematically, it is not to be doubted but that
the power of a focus of the same length is in proportion to the surface
of the mirror. A mirror whose surface is double that of another, must
have the same sized focus, and this focus must contain double the
quantity of light which the first contained; and in the supposition,
that effects are always in proportion to their causes, it might be
presumed that the heat of this second focus should be double that of
the first.
So likewise, and by the same mathematical estimation, it has always
been thought, that at an equal intensity of light, a small focus ought
to burn as much as a large one, and that the effect of the heat ought
to be in proportion to this intensity of light: _insomuch_ (says
Descartes) _that glasses, or extremely small mirrors, may be made,
which will burn with as much violence as the large_. I at first thought
that this conclusion, drawn from mathematical theory, might be found
false in practice, because heat being a physical quality, of the action
and propagation of which we know not the laws, it seemed to me, that
there was some kind of temerity in thus estimating its effects by a
simple speculation.
I had, therefore, once more, recourse to experiments. I took metal
mirrors of different focuses and different degrees of polish, and by
comparing the different actions on the same fusible or combustible
matters, I found, that at an equal intensity of light, large focuses
constantly have more effect than small, and I discovered the same to be
the case with refracting mirrors.
It is easy to assign the reason of this difference, if we consider that
heat communicates nearer and nearer, and disperses, if I may so speak,
when it is even applied on the same point: for example, if we let the
focus of a burning glass fall on the centre of a crown piece, and that
this focus was only a line in diameter, the heat produced on the centre
disperses and extends over and throughout the whole piece: thus all the
heat, although used at first to the centre of the crown, does not stop
there, and consequently cannot produce so great an effect as if it did.
But if, instead of a focus of a line which falls upon the centre of the
crown, we let fall a focus of equal intensity on the whole crown, every
part being alike heated, then instead of experiencing the less heat, it
acquires an augmentation; for the middle profiting of the heat with the
other points which surround it, the crown piece will be melted in this
latter case, while in the first, it will only be slightly heated.
After these experiments and reflections, I began to entertain sanguine
hopes of making mirrors to burn at a great distance; for I no longer
dreaded as before, the great extent of the focus; I was persuaded, on
the contrary, that a focus of a considerable breadth, as two feet, and
which in the intensity of the light would not be near so great as in a
small focus of four lines, might, nevertheless, produce inflammation,
and with more power; and that, consequently, this mirror, which, by
mathematical theory, ought to have at least thirty feet diameter, would
be reduced to one of eight or ten feet at most, which was not only a
possible, but even a very practicable thing.
I then thought seriously of executing my project: I had at first a
design of trying to burn at 200 or 300 feet distance with circular or
hexagonal glasses of a square foot in surface, and I was desirous of
having four iron carriages for them, with screws to each to move them,
and a spring to adjust them; but the considerable expense that this
required made me quit that idea, and I took two common glasses of six
inches by eight, and a wooden adjustment, which, in fact, was less
solid and precise, but the expence was more consistent with a mere
experiment: the mechanism of which was executed by M. Passement.
It is sufficient to say, that it was at first composed of 168 glasses
of six inches by eight each, about four lines distant from each other;
these glasses moved in all directions, and the four lines of space
between them not only served for the freedom of this motion, but also
to let the operator see the place where he was to conduct his images.
By means of this construction, 168 images could be thrown on one point,
and, consequently, burn at several distances, as at 20, 30, and to 150
feet. By increasing the size of the mirror, or by making other mirrors
like the first, we are certain of throwing fire to still greater
distances, or to increase as much as we please the force or activity of
those first distances.
It is only to be observed, that the motion here spoken of is not very
easy to be executed, and that also there is a very great choice to
be made in the glasses; for they are not all equally good, though
they appear so at the first inspection. I was obliged to pick out of
more than 500 the 168 I made use of. The method of trying them is to
receive at 150 feet distance the reflected image of the sun, as a
vertical plane; we must select those which give a round and terminated
image, and reject those, whose thicknesses being unequal in different
parts, or the surface a little concave or convex, have images badly
terminated, double, treble, oblong, &c. according to the different
defects found in the glasses.
By the first experiment which I made the 23d of March, 1747, at noon, I
set fire to a plank of fir at 66 feet distance, with 40 glasses only,
about a quarter of the mirror. It must be observed that not being yet
mounted, it was very disadvantageously placed, forming an angle with
the sun of twenty degrees declination, and another of more than ten
degrees inclination.
The same day I set fire to a pitchy and sulphureous plank at 126 feet
distance, with eighty-eight glasses, the mirror being still placed
disadvantageously. It is well known, that to burn with the greatest
advantage the mirror should be directly opposed to the sun, as well as
the matters to be inflamed; so that, by supposing a perpendicular plane
on the plane of the mirror, it must pass by the sun, and, at the same
time, through the midst of combustible matters.
The 3d of April, at four o'clock in the afternoon, the mirror being
mounted, produced a slight inflammation on a plank covered with
pitch at 138 feet distance, although the sun was weak and the light
pale. Great care must be taken, when we approach the spot where
the combustible matters are, not to look on the mirror; for if,
unfortunately, the eyes should meet the focus, inevitable blindness
will ensue.
The 4th of April, at eleven in the morning, although the sun appeared
watery, and the sky cloudy, yet it produced, with 154 glasses, so
considerable a heat at 158 feet, that in less than two minutes it made
a deal plank smoke, and which would certainly have flamed, if the sun
had not suddenly disappeared.
The ensuing day, the 5th of April, at three o'clock in the afternoon,
we set fire, in a minute and a half, at 150 feet distance, to a plank
sulphured and mixed with coals, with 154 glasses. When the sun is
powerful, only a few seconds is required to produce inflammation.
The 10th of April in the afternoon, the sun being bright, we set
fire to a fir plank at 150 feet distance, with only 128 glasses: the
inflammation was very sudden, and made in all the extent of the focus,
which was about sixteen inches diameter at this distance.
The same day, at half past two o'clock, we threw the fire on another
plank, partly pitched and covered with sulphur in some places: the
inflammation was made very suddenly; it began by the parts of the wood
which were uncovered, and the fire was so violent, that the plank was
obliged to be dipt in water to extinguish it: there were 148 glasses at
150 feet distance.
The eleventh of April, the focus being only 20 feet distant from the
mirror, it only required 12 glasses to inflame small combustible
matters; with 21 glasses we set fire to another plank which had already
been partly burnt; with 45 glasses we melted a block of tin of 6lb.
weight; and with 117 glasses we melted thin pieces of silver, and
reddened an iron plate; and I am also persuaded, that by using all the
glasses of the mirror we should have been enabled to have melted metals
at 50 feet distance; and as the focus at this distance was six or seven
inches broad, we should be able to make trials on all metals, which
it was not possible to do with common mirrors, whose focus is either
very weak or 100 times smaller than that of mine. I have remarked, that
metals, and especially silver, smoke much before they melt; the smoke
was so striking that it shaded the ground, and it was there I looked on
it attentively, for it is not possible to look a moment on the focus
when it falls on the metal, the lustre being much more dazzling than
that of the sun.
The experiments which I have here related, and which were made
immediately after the invention of the mirrors, have been followed by
a great number of others, which confirm them. I have set fire to wood
at 210 feet distance with this mirror, by the sun in summer; and I am
certain, that with four similar mirrors I could burn at 400 feet, and,
perhaps, at a greater distance. I have likewise, melted all metals,
and metallic minerals, at 25, 30, and 40 feet. We shall find, in the
course of this article, the uses to which these mirrors can be applied,
and the limits that must be assigned to their power for calcination,
combustion, fusion, &c.[F]
[F] It requires about half an hour to mount the mirror and to make all
the images fall on the same point; but when this is once adjusted, it
may be used at all times by simply drawing a curtain.
This mirror burns according to the different inclination given it, and
what gave it this advantage over the common reflecting mirrors was that
its focus was very distant, and had so little curvature, that it was
almost imperceptible: it was seven feet broad by eight feet high, which
makes about the 150th part of the circumference of the sphere, when we
burn at 150 feet distance.
The reason that determined me to prefer glasses of six inches broad
by eight inches high to square glasses of six or eight inches, was,
that it is much more commodious to make experiments upon a horizontal
and level ground than otherwise, and that with this figure, the height
of which exceeded the breadth, the images were rounder; whereas with
square glasses they would be shortened, especially at small distances,
in a horizontal situation.
This discovery furnishes us with many useful hints for physic, and
perhaps for the arts. We know that what renders common reflecting
mirrors most useless for experiments is, that they burn almost always
upwards, and that we are greatly embarrassed to find means to suspend
or support to their focus matters to be melted or calcined. By means
of my mirror we burn concave mirrors downwards, and with so great an
advantage that we have what degree of heat we please; for example, by
opposing to my mirror a concave one of a foot square in the surface,
the heat produced to this last mirror, by using 154 glasses only, will
be upwards of 12 times greater than that generally produced, and the
effect will be the same as if 12 suns existed instead of one, or rather
as if the sun had 12 times more heat.
Secondly, By means of my mirror we shall have the true scale of the
augmentation of heat, and make a real thermometer, whose divisions will
be no longer arbitrary, from the temperature of the air to what degree
of heat we chuse, by letting fall, successively, the images of the sun
one on the other, and by graduating the intervals, whether by means of
an expansive liquor, or a machine of dilatation, and from that we shall
know, in fact, what a double, treble, quadruple, &c. augmentation of
heat is, and shall find out matters whose expansion, or other effects,
will be the most suitable to measure the augmentations of heat.
Thirdly, We shall exactly know how many times is required for the
heat of the sun to burn, melt, or calcine different matters, which
was hitherto only known in a vague and very indefinite manner; and
shall be in a state to make precise comparisons of the activity of
our fires with that of the sun, and have exact relations and fixed
and invariable measures. In short, those who examine my theory, and
shall have seen the effect of my mirror, I think will be convinced the
mode I have used was the only one possible to succeed to burn far off,
for, independant of the physical difficulty of making large concave,
spherical, parybolical mirrors, or of any other curvature whatsoever,
regular enough to burn at 150 feet distance, we shall easily be
convinced that they would not produce but nearly as much effect as
mine, because the focus would be almost as broad; that besides, these
curved mirrors, if even it should be possible to make them, would have
the very great disadvantage to burn only at a nigh distance, whereas
mine burns at all distances; and, consequently, we shall abandon the
scheme of making mirrors to burn at a great distance by means of
curves, which has uselessly employed a great number of mathematicians
and artists, who were always deceived, because they considered the rays
of the sun as parallel, whereas they should be considered as they are,
namely, as forming angles of all sizes, from 0 to 32 minutes, which
makes it impossible, whatsoever curve is given to a mirror, to render
the diameter of the focus smaller than the chord, which measures 32
minutes. Thus, even if we could make a concave mirror to burn at a
great distance; for example, at 150 feet, by employing all its points
on a sphere of 600 feet diameter, and by employing an uncommon mass
of glass or metal, it is evident that we shall have a little more
advantage than by using, as I have done, only small plane mirrors.
On the whole, although this mirror is susceptible of a very great
perfection, both for the adjustment, and many other particulars, and
though I think I shall be able to make another, whose effects will be
superior, yet, as every thing has its limits, it must not be expected
that every one can be formed to burn at extreme distances; to burn,
for example, at the distance of half a mile, a mirror 200 times larger
would be required; and I am of opinion that more will never be effected
than to burn at the distance of 8 or 900 feet. The focus, whose motion
is always correspondent to that of the sun, moves so much the quicker
as it is farther distant from the mirror; and at 90 feet it would move
about six feet a minute.
However, as I have given an account of my discovery, and the success of
my experiments, I should render to Archimedes, and the ancients, the
glory that is their due. It is certain that Archimedes could perform
with metal mirrors what I have done with glass, and that, consequently,
I cannot refuse him the title of the first inventor of these mirrors,
and the opportunity he had of using them rendered him, without doubt,
more celebrated than the merit of the thing itself.
Many advantages may be derived from the use of these mirrors; by an
assemblage of small mirrors, with hexagonal planes, and polished steel,
which will have more solidity than glasses, and which would not be
subject to the alterations which the light of the sun may cause, we may
produce very useful effects, and which would amply repay the expences
of the construction of the mirror.
"For all evaporations of salt waters, where great quantities of
wood and coal are consumed, or structures raised for the purpose of
carrying the waters off, which cost more than the construction of many
mirrors, such as I mention; for the evaporation of salt waters, only an
assemblage of twelve plane mirrors of a square foot each is necessary.
The heat reflected by their focuses, although directed below their
level, and at fifteen or sixteen feet distance, will be still great
enough to boil water, and consequently produce a quick evaporation:
for the heat of boiling water is only treble the heat of the sun in
summer; and as the reflection of a well polished plane surface only
diminishes the heat one half, only six mirrors are required to produce
at the focus a heat equal to boiling water; but I shall double the
number to make the heat communicate quicker; and likewise by reason of
the loss occasioned by the obliquity, under which the light falls on
the surface of the water to be evaporated, and because salt water heats
slower than fresh. This mirror, whose assemblage would form only a
square four feet broad by three high, would be easy to be managed; and
if it were required to double or treble the effects in the same time,
it would be better to make so many similar mirrors, than to augment the
scale of them; for water can only receive a certain quantity of heat,
and we should not gain any thing by increasing this degree; whereas, by
making two focuses with two equal mirrors, we should double the effect
of the evaporation, and treble it by three mirrors, whose focuses would
fall separately one from the other on the surface of the water to be
evaporated. We cannot avoid the loss caused by the obliquity; nor can
it be remedied but by suffering a still greater, that is, by receiving
the rays of the sun on a large glass, which would reflect them broken
on the mirror; for then it would burn at bottom instead of the top,
but it would lose half the heat by the first reflection, and half of
the remainder by the second; so that instead of six small mirrors, it
would require a dozen to obtain a heat equal to boiling water. For the
evaporation to be made with more success, we ought to diminish the
thickness of the water as much as possible; a mass of water a foot deep
will not evaporate nearly so quick as the same mass reduced to six
inches, and increased to double the superfices. Besides, the bottom
being nearer the surface, it heats quicker, and this heat, which the
bottom of the vessel receives, contributes still more to the celerity
of the evaporation.
2. These mirrors may be used with advantage to calcine plaisters, and
even calcareous stones, but they would require to be larger, and the
matters placed in an elevated situation, that nothing might be lost by
the obliquity of the light. It has already been observed that gypsum
heats as soon again as soft calcareous stone, and nearly twice as quick
as marble, or hard calcareous stone; their calcination, therefore,
must be in a respective ratio. I have found by an experiment repeated
three times, that very little more heat is required to calcine white
gypsum, called alabaster, than to melt lead. Now the heat necessary
to melt lead is, according to the experiments of Newton, eight times
stronger than the heat of the summer sun; it therefore would require
at least sixteen small mirrors to calcine gypsum; and because of the
losses thereby occasioned, as well by the obliquity of the light as by
the inequality of the focus, which is not removed above fifteen feet,
I presume it would require twenty, and perhaps twenty-four mirrors of
a foot square each, to calcine gypsum in a short time, consequently it
would require an assemblage of forty-eight small mirrors to calcine the
softest calcareous stone, and seventy-two of a foot square to calcine
hard calcareous stones. Now a mirror twelve feet broad by six feet
high, would be a large and cumbersome machine; yet we might conquer
these difficulties if the product of the calcination were considerable
enough to surpass the expense of the consumption of wood. To ascertain
this, we ought to begin by calcining plaister with a mirror of
twenty-four pieces, and if that succeeded, to make two other similar
mirrors, instead of making a large one of seventy-two pieces; for by
coinciding the focuses of these three mirrors of twenty-four pieces, we
should produce an equal heat, strong enough to calcine marble or hard
stone.
But a very essential matter remains doubtful, that is, to know how much
time would be requisite, for example, to calcine a cubical foot of
matter, especially if that foot were struck with the heat only in one
part. Some time would pass before the heat penetrated its thickness;
during this time, a great part of the heat would be lost, and which
would issue from this piece of matter after it had entered it. I fear,
therefore, much that the stone not being touched by the heat on every
side at once, the calcination would be slower, and the produce less.
Experience alone can decide this, but it would be at least necessary to
attempt it on gypsous matters, whose calcination is as quick again as
calcareous stone.
By concentrating this heat of the sun in a kiln, which has no other
opening than what admits the light, a great part of the heat would
be prevented from flying off, and by mixing with calcareous stone a
small quantity of coal dust, which is the cheapest of all combustible
matters, this slight supply of food would suffice to feed and augment
the quantity of heat, which would produce a more ample and quick
calcination, and at very little expense.
3. These mirrors of Archimedes might be, in fact, used to set fire to
the sails of vessels, and even to pitched wood at more than 150 feet
distance; they might also be used against the enemy, by burning the
grain and other productions of the earth; this effect would be no less
sudden than destructive; but we will not dwell on the means of doing
mischief, conceiving it to be more our duty to think on those which may
do some real service to mankind.
4. These mirrors furnish the sole means of exactly measuring heat.
It is evident that two mirrors, whose luminous images unite, produce
double heat in all the points of their surfaces, that three, four,
five, or more mirrors, will also give a treble, quadruple, quintuple,
&c. heat, and that, consequently, by this mode we can make a
thermometer whose divisions will not be too arbitrary, and the scales
different, like those of the present thermometers. The only arbitrary
thing which would enter into the composition of the thermometer, would
be the supposition of the total number of the parts of the quicksilver
by quitting the degree of absolute cold; but by taking it to 10000
below the congelation of water, instead of 1000, as in our common
thermometers, we should approach greatly towards reality, especially
by choosing the coldest day in winter to mark the thermometers, for
then every image of the sun would give it a degree of heat above the
temperature of ice. The point to which the mercury rises by the first
image of the sun, would be marked 1, and so on to the highest, which
might be extended to 36 degrees. At this degree we should have an
augmentation of heat, thirty-six times greater than that of the first,
eighteen times greater than that of the second, twelve times greater
than that of the third, nine times greater than that of the fourth,
and so on; this augmentation of thirty-six of heat above that of ice
would be sufficient to melt lead; and there is every appearance to
think that mercury, which volatilizes by a much less heat, would by
its vapour break the thermometer. We cannot therefore, at most, extend
the division farther than twelve, and perhaps not farther than nine
degrees, if mercury be used for these thermometers, and by these means
we shall have only nine degrees of the augmentation of heat. This is
one of the reasons which induced Newton to make use of linseed oil
instead of quicksilver; and, in fact, by making use of this liquor,
we can extend the division not only to twelve degrees, but as far
as to make this oil boil. I do not propose spirits of wine, because
that liquor decomposes in a very short time, and cannot be used for
experiments of a strong heat.[G]
[G] Many travellers have told and written to me, that Reaumur's
thermometers of spirit of wine, became quite useless to them, because
this liquid lost its colour, and became charged with a sort of mud in a
very short time.
When on the scale of these thermometers filled with oil or mercury,
the first divisions 1, 2, 3, 4, &c. are marked to indicate the double,
treble, quadruple, &c. augmentations of heat, we must search after the
aliquot parts of each division; for example, of the point 1-1/4, 2-1/4,
3-1/4, &c. or 1-1/2, 2-1/2, 3-1/2, &c. and 1-3/4, 2-3/4, 3-3/4, and
which will be obtained in an easy manner, by covering the 1/4, 1/2,
or 3/4, of the superfices of one of those small mirrors; for then the
image which it reflects, will contain only the 1/4, 1/2, or 3/4, of
the heat which the whole image will contain, and, consequently, the
division of the aliquot parts will be as exact as those of the whole
numbers.
If once we succeed in this real thermometer, which I call real,
because it actually marks the proportion of the heat, every other
thermometer whose scale is arbitrary and different, will become not
only superfluous, but even inimical, in many cases, to the precision of
natural truths sought after by these means.
5. By means of three mirrors we may easily collect in their entire
purity, the volatile parts of gold, silver, and other metals and
minerals; for, by exposing to the large focus of those mirrors a large
piece of metal, as a dish, or silver plate, we shall see smoke issue
from it in great abundance, and for a considerable time, till the
metal is in fusion; and by giving only a smaller heat than what fusion
requires, we shall evaporate the metal so as to diminish the weight
considerably.
I am certain of this circumstance, which also elucidates the intimate
composition of metals. I was desirous of collecting this plentiful
vapour, which the pure fire of the sun causes to issue from metal,
but I had not the necessary instruments, and I can only recommend to
chemists and naturalists to follow this important experiment, the
results of which would be as much less equivocal as the metallic vapour
is pure; whereas, in all like operations made with common fire, the
metallic vapour is necessarily mixed with other vapours proceeding from
combustible matters, which serve for food to this fire.
Besides, this means is the only one we have to volatilize fixed metals,
such as gold and silver; for I presume that this vapour, which I have
seen rise in such great quantities from these fixed metals, heated in
the large focus of my mirror, is neither of water, nor of any other
liquor, but of the parts even of the metal which the heat detaches by
volatilizing them. By receiving these vapours of different metals, and
thus mixing them together, more intimate and pure alloys would be made
than can be by fusion, and the mixture of these metals when melted,
which never perfectly unites on account of the inequality of their
specific weight, and many other circumstances which are opposed to the
intimate and perfect equality of the mixture. As the constituent parts
of the metallic vapours are in a much greater state of division than
fusion, they would join and unite closer and more readily. In short,
we should attain the knowledge of a general fact by this mode, and
which, for many reasons, I have a long time suspected, that there is
penetration in all alloys made in this manner, and that their specific
weight would be always greater than the sum of the specific weights
of the matters of which they are composed: for penetration is only a
greater degree of intimacy; every thing equal in other respects will
be so much the greater as matters will be in a more perfect state of
division.
By reflecting on the vessels used to receive and collect these metallic
vapours, I was struck with an idea, which appeared to me to be of too
great utility not to publish; it is also easy enough to be realized by
good able chemists; I have even communicated it to some of them, who
appeared to be quite satisfied with it. This idea is to freeze mercury
in this climate, and with a much less degree of cold than that of the
experiments of Petersburgh or Siberia. For this purpose the vapour
of mercury is only required to be received, and which is the mercury
itself volatilized by a very moderate heat in a crucible, or vessel,
to which we give a certain degree of artificial cold. This vapour, or
this mercury, minutely divided, will offer, to the action of the cold,
surfaces so large, and masses so small, that instead of 187 degrees of
cold requisite to freeze mercury, possibly 18 or 20 will be sufficient,
and perhaps even less to freeze it when in vapour. I recommend this
important experiment to all those who endeavour earnestly for the
advancement of the sciences.
To these principal uses of the mirror of Archimedes, I could add
many other particular ones; but I have confined myself to those only
which appeared the most useful, and the least difficult to be put in
practice; nevertheless I have subjoined some experiments that I made
on the transmission of light through transparent bodies, to give some
new ideas on the means of seeing objects at a distance with the naked
eye, or with a mirror, like that spoken of by the ancients, and by the
effect of which vessels could be perceived from the port of Alexander,
as far as the curvature of the earth would permit.
Naturalists at present know, that there are three causes which prevent
the light from uniting in a point, when its rays have passed the
objective glass of a common mirror. The first is the spherical curve of
this glass, which disperses a part of the rays in a space terminated
by a curve. The second is the angle under which the object appears to
the naked eye: for the breadth of the focus of the objective glass has
a diameter nearly equal to the chord of which this angle measures.
The third is the different refrangibility of the light; for the most
refrangible rays do not collect in the same place with the lesser.
The first cause may be remedied by substituting, as Descartes has
proposed, elliptical, or hyperbolical, glasses to the spherical. The
second is to be remedied by a second glass, placed to the focus of the
objective, whose diameter is nearly equal the breadth of this focus,
and whose surface is worked on a sphere of a very short ray. The third
has been found to be remedied, by making telescopes, called Acromatics,
which are composed of two sorts of glasses, which disperse the coloured
rays differently; so that the dispersion of the one is corrected
by the other, without the general refraction, which constitutes the
mirror, being destroyed. A telescope 3-1/2 feet long, made on this
principle, is in effect equivalent to the old telescopes of 25 feet.
But the remedy of the first cause is perfectly useless at this time,
because the effect of the last being much more considerable, has such
great influence on the whole effect, that nothing can be gained by
substituting hyperbolical, or elliptical glasses to spherical, and
this substitution could not become advantageous, but in the case where
the means of correcting the effect of the different refrangibility of
the rays of light might be found; it seems, therefore, that we should
do well to combine the two means, and to substitute, in acromatic
telescopes, elliptical glasses.
To render this more obvious, let us suppose the object observed to be a
luminous point without extent, as a fixed star is to us. It is certain,
that with an objective glass, for example, of 30 feet focus, all the
images of this luminous point will extend in the form of a curve to
this focus, if it be worked on a sphere; and, on the contrary, they
will unite in one point if this glass be hyperbolical; but if the
object observed have a certain extent, as the moon, which occupies
half a degree of space to our eyes, then the image of this object will
occupy a space of three inches diameter in the focus of the objective
glass of thirty feet; and the aberration caused by the sphericity
producing a confusion in any luminous point, it produces the same on
every luminous point of the moon's disk, and, consequently, wholly
disfigures it. There would be, then, much disadvantage in making use of
elliptical glasses or long telescopes, since the means have been found,
in a great measure, to correct the effect produced by the different
refrangibility of the rays of light.
From this it follows, that if we would make a telescope of 30 feet,
to observe the moon, and see it completely, the ocular glass must be
at least three inches diameter, to collect the whole image which the
objective glass produces to its focus; and if we would observe this
planet with a telescope of 60 feet, the ocular glass must be at least
six inches diameter, because the chord which the angle measures under
which the moon appears to us, is, in this case, nearly six inches;
therefore astronomers never make use of telescopes that include the
whole disk of the moon, because they would magnify but very little. But
if we would observe the planet Venus with a telescope of 60 feet, as
the angle under which it appears to us is only 60 seconds, the ocular
glass can only have four lines diameter; and if we make use of an
objective of 120 feet, an ocular glass of eight lines diameter would
suffice to unite the whole image which the objective forms to its focus.
Hence we see, that even if the rays of light were equally refrangible
we could not make such strong telescopes to see the moon with as to see
the other planets, and that the smaller a planet appears to our sight
the more we can augment the length of the telescope, with which we can
see it wholly. Hence it may be well conceived, that in this supposition
of the rays, equally refrangible, there must be a certain length more
advantageously determined than any other for each different planet, and
that this length of the telescope depends not only on the angle under
which the planet appears to our sight, but also on the quantity of
light with which it is brightened.
In common telescopes the rays of light being differently refrangible,
all that could be done in this mode to give them perfection would be of
very little advantage, because, that under whatever angle the object,
or planet, appears to our sight, and whatever intensity of light it
may have, the rays will never collect in the same part; the longer the
telescope the more interval it will have between the focus of the red
and violet rays, and consequently the more confused the image of the
object observed.
Refracting telescopes, therefore, can be rendered perfect only by
seeking for the means of correcting this effect of the different
refrangibility, either by composing telescopes of different densities,
or by other particular means, which would be different according to
different objects and circumstances. Suppose, for example, a short
telescope, composed of two glasses, one convex and the other concave;
it is certain that this telescope might be reduced to another whose
two glasses would be plain on one side, and on the other bordering on
spheres, whose rays would be shorter than that on the spheres on which
the glasses of the first telescopes have been constructed. However,
to avoid a great part of the effect of the different refrangibility
of the rays, the second telescope may be made with one single piece
of massive glass, as I had it done with two pieces of white glass,
one of two inches and a half in length, and the other one inch and a
half; but then the loss of transparency is a greater inconvenience
than the different refrangibility which it corrects, for these two
small massive telescopes of glass are more obscure than a small common
telescope of the same glass and dimensions; they indeed give less
iris, but are not better; for in massive glass the light, after having
crossed this thickness of glass, would no longer have a sufficient
force to take in the image of the object to our eye. So to make
telescopes 10 or 20 feet long, I find nothing but water that has
sufficient transparency to suffer the light to pass through this great
thickness. By using, therefore, water to fill up the intervals between
the objective and the ocular glass, we should in part diminish the
effect of the different refrangibility, because water approaches nearer
to glass than air, and if we could, by loading the water with different
salts, give it the same refringent degree of power as glass, it is not
to be doubted, that we should correct still more, by this means, the
different refrangibility of the rays. A transparent liquor should,
therefore, be used, which would have nearly the same refrangible power
as glass, for then it would be certain that the two glasses, with their
liquor between them, would in part correct the effect of the different
refrangibility of the rays, in the same mode as it is corrected in the
small massive telescope which I speak of.
According to the experiments of M. Bouguer, the thickness of a line of
glass destroys 2/7 of light, and consequently the diminution would be
made in the following proportion: