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.

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 me tal, 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]

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]

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 1¹/₄, 2¹/₄, 3¹/₄, &c. or 1¹/₂, 2¹/₂, 3¹/₂, &c. and 1³/₄, 2³/₄, 3³/₄, 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 an cients, 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 3¹/₂ 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:

Thickness, 1, 2, 3, 4, 5, 6 lines

Diminution, ²/₇, ¹⁰/₄₉, ⁵⁰/₃₄₃, ²⁵⁰/₂₄₀₁, ¹²⁵⁰/₁₆₈₀₇, ⁶²⁵⁰/₁₁₇₆₄₉

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 17¹/₂ 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—24¹/₃. 2—22³/₄. 2—21. 2—17¹/₂. 2—15, or 592¹/₉. 517⁹/₁₅. 441. 306¹/₄. 225. Therefore the loss of the light, by the interposition of the glasses, is in the following progression: 84⁷⁹/₁₄₄. 151. 285⁷/₉. 367¹/₄.

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.

OBSERVATIONS AND EXPERIMENTS ON TREES AND OTHER VEGETABLES.