or

BURNING MIRRORS.

The name of certain glasses or mirrors which have the property of inflaming combustible substances by the action of the sun's rays, being so formed as to collect all the rays which fall over their whole surface into a single point or spot, more or less distant, according to the form of the glass. In this point the natural heat of the sun is found to be so augmented, owing to such a multitude of rays being all concentrated in so narrow a space, that it produces an intense temperature, and such as is quite sufficient, even with very ordinary glasses, to inflame wood or other combustible substances. There is always one particular point at a certain distance from the glass where the heat is the greatest. If we place the burning body nearer the glass the heat diminishes, till it will no longer take fire; and if we place it farther from it, the same effect takes place. Hence this point, where the heat is the most intense, has received the name of the focus of the glass.

This property of burning glasses, however familiar it may now appear, is certainly very remarkable, and must, at the time of its invention, have excited no small degree of astonishment and of interest, from the striking nature of the effect, and from the uses to which it might be applied. The operation is now perfectly understood from the principles of optics, and is indeed extremely simple. See Optics. The rays of light are collected either by refraction in passing through a transparent glass, or by reflection from the polished surface of a mirror. Burning glasses are hence divided into two kinds,—refracting glasses, which can only be made of glass or other transparent substance; and reflecting glasses, which are either made of glass silvered behind, or of polished metal, or any other reflecting substance. Reflectors of polished metal are generally termed specula. In the former kind the glasses are of a convex form, and collect the rays of the sun into a focus behind the glass, as at fig. 1, Plate CLII.; each ray, as it strikes more or less obliquely on the surface of the glass, being more or less bent out of its natural course by the refractive medium, so that they are all made to converge to one point or focus of refraction. Reflecting glasses, again, are all concave, and the rays of the sun are collected into a focus in front of the mirror by reflection; each ray, as it strikes more or less obliquely on the surface of the mirror, being reflected back, but at the same time inclined to the centre so that they are all made to converge to a point or focus of reflection in a similar manner, as at fig. 2.

In both these cases it is by the peculiar shape or figure of the glass or mirror that the convergence of all rays to one point is produced; and to ascertain therefore the figure which would do this most perfectly becomes an important object in the construction of glasses, and is, besides, a curious mathematical problem. In the case of refracting glasses, where we have a double surface, one on each side of the glass, it was first shown by the celebrated Descartes, that a glass having its exterior surface convex, and a portion of an elliptic curve, while its interior surface was concave, and formed a portion of a circle, would cause parallel rays, or those of the sun, to converge to a perfect focus, as at fig. 3, where the exterior surface of the lens BAC forms a portion of an ellipse, whose greater axis AX is to the distance between the foci FF, as the index of refraction is to unity, and a circle whose centre is at F. Various other forms have been proposed, but, owing to the great difficulty of forming glasses of these compound curves, it was found more convenient in practice to rest content with the exterior surface BAC, a portion of the simple curve of the circle or sphere, particularly as in large glasses, or those of slight convexity, the sphere approaches very nearly to that of the ellipse. Each side of the glass, therefore, is carefully turned and ground into the portion of a sphere, forming together what is termed a lens; and the greater the radius of convexity is, the greater is the distance of the focus from the glass. It happens by a curious coincidence, that in glass the focal distance of parallel rays, usually termed the principal focus of the lens, in a double convex lens, is just equal to the radius of convexity. In every burning glass, therefore, of this description, it is easy to find the focus by measuring from the centre of the lens a distance equal to the radius of curvature. In the case of burning mirrors, the true figure for converging the rays to a perfect focus is that of the parabola; a form which is frequently constructed, the mirrors being either turned or hammered out of metal, and the figure therefore more readily attained than in glass. The focal distance is always equal to the radius of the concavity at the centre of the mirror. Hence in large mirrors of a shallow concavity, or with a large radius, the spherical form will approach very nearly to that of the parabola, and will therefore produce very nearly the full effect of it. The focus may also be found practically by holding the glass up to the sun, and observing where the concentration of the light is the greatest. In doing this a remarkable circumstance is observed. However perfect the figure of the glass, the rays in the focus are never converged to a mathematical point; they are always diffused over a certain space, forming a spot of determinate magnitude. The reason of this will appear very obvious, when we consider that the sun presents a very sensible magnitude, even at the enormous distance at which he is viewed. The rays from different parts of the body, from the opposite limbs, for instance, instead of being parallel, subtend sensible angles. Though all the rays therefore from any one point in the sun are sensibly parallel to each other, and those which fall on different parts of the glass from this single point are all converged to a mathematical point in the focus, this is not the case with rays coming from different points of the sun. These not being parallel, cannot by any means be thrown together in the focus, but each to a distinct point corresponding to that from which it issues in the sun, whether by refraction or reflection, so as to form on the whole an image or figure of the sun, subtending the same angle at the glass as the sun does. This is evident from an inspection of figures 4 and 5, where the rays from each limb by refraction cross one another in the centre of the glass, and again diverge, forming the boundary of the focal image at the same angle as the image itself, or by reflection meet and diverge in returning at the same angle. Hence it follows that the magnitude of the focal image will depend entirely on the focal distance, and in no respect on the magnitude of the glass or mirror. The greater the focal distance the larger will the image be. In every case it will be proportional to the sine of 32°, the angle at which the sun subtends at the glass; and hence the focal diameter will be very nearly 1/10th part of the focal distance. Hence the reason of a very curious fact, that in any large glass or mirror, though we were to cut off a zone from the exterior circumference, it would not alter in the least the magnitude of the focal image; it would only diminish the intensity of the light. Whether the figure of the glass also be square, or circular, or elliptical, or any other shape, the figure of the image will be invariably a circle. Such then is the limit of concentration even for the most perfect glasses; and hence we see that it is not absolutely necessary to have the glasses of the perfect figure required by theory, at least it is not of such essential consequence as in the case of telescopes or microscopes, where the distinctness of the image is of as much consequence as the concentration of rays. Here, though the image be ever so confused, seeing it is heat only which we want, it is of no consequence, so that they fall within the limits of the focus. If the spherical figure, then, has been adapted with success to the nice purposes of vision, by using spherical lenses and reflectors of gentle curvature, much more may it suffice for burning glasses, where any imperfections of this kind are of less importance; the only effect of these being to produce in the focus a somewhat less powerful concentration of the rays. In practice, however, the difference with small glasses, such as four, five, or six inches diameter, and focal distances of two or three feet, is really hardly measurable. Even with very large glasses it is far from being considerable. In the great burning glasses of Tschirnhausen, for example, three or four feet in diameter, the focal distance was twelve feet; and hence a perfect image of the sun should have been \( \frac{1}{12} \times 12 = 1 \) inch; and it was actually about an inch and a half. The famous lens of Parker had a focal distance of six feet eight inches; and hence the perfect image should have been 0.8 inches, and the actual burning focus was one inch diameter. In reflection, again, the mirror of Vilette had a focal length of about thirty-eight inches, and therefore an image by calculation of 6.38 inches; it was actually about the size of half a louis d'or.

In regard to the actual heating power of burning glasses, if this depended only on the concentration of the rays power, it would be easily calculated. The degree of concentration is in every case proportional as the square of the diameter of the glass to the square of the diameter of the focal image. In an ordinary reading glass, therefore, say of two inches diameter and six inches focal distance, the focal diameter being thus 0.06, the concentration would be as four to 0.036, or as one to 0.009, or nearly 1000 times. No wonder, then, that such a glass should so readily produce inflammation. Even in some of the large burning glasses the actual concentration did not so much exceed this as might be imagined. In the compound burning glasses of Tschirnhausen the diameter of the first glass being three and four feet, and the focal diameter of the second glass only eight lines or two thirds of an inch, the concentration would be as 2304 and 1296 to 0.44, or 5184 times in the one case, and 2916 in the other. In Vilette's burning mirror the diameter was thirty inches, and the focal diameter about half an inch. The concentration would thus be 3600 times. But the most powerful of all these glasses is the compound one of Parker. In this the diameter of the first glass was thirty-two and a half inches, and the focal diameter of the second three eighths of an inch; hence the concentration was equal to 7168 times.

In order, however, to calculate the actual increase of temperature, we must first know the effect of the sun's natural heat. The most accurate experiments on this subject are those made by Professor Leslie with his photometer, an instrument of great delicacy, peculiarly adapted for measuring the heat of the sun, as it is entirely free of any extraneous impression from the surrounding atmosphere. "In the latitude of Edinburgh," he says, "the direct impression of the sun at noon, during the summer solstice, amounts to 90° (= 102 Fahrenheit); but it regularly declines as his rays become more oblique. At the Burning altitude of 17° it is already reduced to one half; and at 3° above the horizon the whole effect exceeds not 1°. In the same parallel of latitude, the greatest force of the solar beams in the depth of winter measures only $25^\circ$ (42° Fahrenheit). Taking the average effect, then, at 10°, it would appear that the above reading glass would be capable of producing a heat of 10,000°, which is far above the melting point of brass, copper, silver, and lead. The glasses of Tschirnhausen would produce a heat of 29,160° and 51,840°, the mirror of Vilette 36,000°, and Parker's glass the enormous heat of 71,680°, which is nearly double the highest heat measurable by Wedgwood's pyrometer.

But the temperature due to the mere concentration of the rays will evidently be considerably modified, according as the accumulating heat is more or less rapidly dissipated from the focal point into the surrounding medium; and this will depend chiefly on the conducting power of the substance receiving heat, and of those with which it is in contact. This effect is observed, indeed, in the case of a body exposed to the natural heat of the sun. As the accumulating heat raises the temperature of the body, this causes a dispersion both by radiation and contact into the surrounding atmosphere, so that there will be a stream of heat continually escaping from the body, as well as one running in; and when the final temperature is attained, these two effects will exactly balance each other, the quantity dispersed being exactly equal to that which is received during the same time. Now, the quantity dispersed must evidently be proportional to the excess of temperature of the body above the surrounding atmosphere, and also to the surface exposed. Hence a slow-conducting body exposed to the sun,—a ball of wood, for instance,—will acquire a higher temperature than a similar ball of copper. In the latter the heat will be quickly diffused over the whole mass, and dispersed into the atmosphere from every part of its surface; in the former it will pass very slowly through the mass, and accumulating more at one side, and having a smaller surface to disperse itself by, will produce there a greater elevation of temperature; or if the copper be surrounded by any slow-conducting substance,—if it be bedded in a mass of charcoal or brick, the temperature acquired will be greater, as in the case of fruit-trees on a wall, the brick confining the heat, and causing a greater accumulation and a higher temperature, just as the damming up of any stream of water raises the level of the fluid. The same thing must take place with the rays of light concentrated by the burning glass. The temperature in the focus must continue rising until the dispersion of the heat from the focal point equals what is constantly received; and the more, therefore, this dispersion can be retarded by the interposition of slow conducting substances, the higher will the temperature rise. It has always been found, accordingly, that refractory metals, or stones, melt much more readily when laid in a mass of charcoal. This circumstance explains a fact first proved by Buffon, and invariably experienced in burning glasses, that, even with the same degree of concentration of rays, the effect will be much greater with a large focus than with a small one. The latter operating in a very narrow space, and dispersing the heat rapidly into the surrounding mass, there is little left for accumulation. In the former, the heat increasing as the square of the diameter, while the dispersion into the surrounding substance only increases merely as the diameter, much more remains to accumulate in the centre; and the central portion of the focus, indeed, being surrounded by a zone almost as hot as itself, much less dispersion burning can take place, and the temperature, therefore, will rise much higher. If we take, for example, a glass two inches diameter, with a concentrating power of 300, and another six inches diameter of the same power, the one will inflame paper in two or three seconds, while the other will hardly accomplish it at all. These circumstances, therefore, greatly modify the effects of concentration, and serve to account for the very feeble powers of small glasses, and the intense heat of larger ones not greatly differing in concentrative action. The most powerful glass, for instance, ever constructed, was that of Parker, and yet its concentrative power was only seven times greater than that of an ordinary reading glass; and this is the reason also, as we shall see, that the reflecting mirrors of Buffon for burning at a distance produced such powerful effects, the concentration being small compared with that of single glasses, but the focal image much larger.

Such being the general principles of burning glasses History and mirrors, we shall now describe some of the principal and descriptions of instruments of this kind which have been constructed, and their effects. The invention of mirrors or looking-glasses, glasses, constructed probably of polished brass, remounts to a very remote antiquity, as they are mentioned by Moses in the sacred writings. At what period they were employed in a concave form to concentrate the solar rays by reflection is not known, but it is very probable that mirrors of this kind were used to rekindle the vestal fires. Plutarch, in his life of Numa, 700 years before Christ, describes the expédiés, or dishes which were employed for this purpose, and which appear to have been concave segments of a sphere; and he states that the combustible matter was placed in the centre, meaning, no doubt, the focus or centre of concentrated rays. In the time of Socrates, 430 years before Christ, the manufacture of glass had made considerable progress; and it appears from a passage in one of the plays of Aristophanes, that the use of burning glasses was common. The author introduces Socrates as giving lessons in philosophy to Strepsianes, a citizen of Athens, and a man of low cunning. The subjects of these lessons are silly trifles, intended to make Socrates appear ridiculous. Strepsianes, after having asked him how he should avoid paying his debts, proposes the following expedient himself:—“Strepsianes, You have seen at the druggists that fine transparent stone with which they kindle fires? Socrates, You mean glass, do not you? Strepsianes, The very thing. Socrates, Well, what will you do with that? Strepsianes, When a summons is sent to me, I will take this stone, and, placing myself in the sun, I will melt all the writing of the summons at a distance.” The writing, as we know, was traced on wax spread upon a more solid substance.

This description must refer to a burning glass by refraction. Several other ancient observations on the same phenomenon exist. Pliny mentions globes of glass or of crystal, which, being exposed to the sun, would burn clothes, or the flesh of a patient when cauterization was requisite. Hist. Nat. lib. xxxvi. and xxxvii. Lactantius, who lived about the year 303, says, “a globe of glass filled with water, and exposed to the sun, will kindle a fire even in the coldest weather.” (De Ira Dei.)

But the most memorable account of burning glasses, Burning and of their effects in all antiquity, and what has excited glasses of no small degree of speculation in succeeding times, is the Archimedes' extraordinary achievement ascribed to Archimedes, of setting fire to the Roman fleet engaged in the siege of

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1 Experimental Enquiry into the Nature and Propagation of Heat, p. 440. Also, by the same author, An Account of Experiments and Instruments depending on the relations of Air to Heat and Moisture. Syracuse, "launching against it," as Buffon says, "the fire of the solar beams." This, if it can be proved, must, without doubt, be viewed as the most surprising effort of genius and practical skill which the history of human invention presents. By modern opticians, at the head of whom stood Descartes, the fact was long treated as fabulous, chiefly on account of its supposed impracticability; and no doubt this would be the case with single concave mirrors or reflectors, as they imagined Archimedes to have used, and which could not obviously be constructed of sufficient magnitude and focal distance to have any sensible effect. But if we suppose, as is far more probable, and as it is actually described by some authors, that the effect was produced by a number of plane mirrors arranged in a curve, and all uniting their rays in a focus, the impossibility of such a combination is by no means clear; and in fact its perfect practicability, first suggested by Anthemius, and rendered extremely probable by Kircher, was demonstrated by Buffon, and the apparatus actually constructed by him, so as to kindle wood and other inflammable substances at the distance of 200 yards. No doubt, therefore, can remain as to the possibility of producing the effects described. The only question now is in regard to the probability of the fact itself, and the evidence advanced for its support. In the first place, there is nothing improbable in the situation of the place; for Kircher, in his great zeal to throw light on this curious subject, actually made a voyage to Syracuse, in order to examine the situation of the hostile fleet, accompanied by his pupil Scholtus, and they were both satisfied that the ships of Marcellus could not have been more than thirty paces distant from the place where Archimedes might have stood; and in regard to an objection which has been stated, that the vessels might have moved out of the way of the glasses, this does not seem to have much weight, as a moment might have been chosen when they were off their guard, and the glass could have been turned so as to follow them to a certain extent; besides that, the vessels might have been at anchor, or even aground at the time, and not capable of moving away with sufficient expedition. Let us just consider, therefore, the evidence for the fact itself. On the one hand, we have Polybius, Livy, and Plutarch, all silent on the subject, affording certainly a strong proof against the fact, when we consider also that the two former describe so particularly the mechanical contrivances of Archimedes; on the other hand, it has been positively affirmed by Vero, Diodorus Siculus, and Pappus; and though the works of the latter, which speak of the siege of Syracuse, are now lost, they existed in the twelfth century, and the passages which speak particularly of the burning glass of Archimedes are quoted by Zonaras and Tzetzes, writers of that period, and who appear incapable of inventing such a story of themselves. Zonaras states that "Archimedes burnt the fleet of the Romans in an admirable manner, for he turned a certain mirror towards the sun, which received its rays. The air having been heated on account of the density and smoothness of the mirror, he kindled an immense flame, which he precipitated on the vessels which were in the harbour, and reduced them to ashes." He then adds that Proclus, taught by this example, burnt with mirrors of brass the fleet of Vitellius, who besieged Constantinople under the emperor Anastasius in the year 514. Tzetzes, referring to the same authorities, states, that "when the fleet of Marcellus was within bow shot, the old man (Archimedes) brought out a hexagonal mirror which he had made. He placed at proper distances from the mirror other smaller mirrors, which were of the same kind, and which were moved by means of their hinges and certain square plates of metal. He afterwards placed his mirrors in the midst of the solar rays precisely at noon-day. The rays of the sun being reflected by this mirror, he kindled a dreadful fire on the ships, which were reduced to ashes at a distance equal to that of a bow-shot." Dion and Diodorus, who wrote the life of Archimedes, and several other authors, speak of this fact, but chiefly Anthemius, who wrote on the prodigies of mechanics. It is in these works that we read the history of the conflagration occasioned by the mirror of Archimedes.

This passage contains evidently a description of a combination of plane mirrors, so adapted and set to the position of the sun as to unite all the rays reflected from them into one focus. Besides these, we have the direct testimony, as above noticed, of Anthemius of Tralles, an eminent architect, and one besides deeply learned in the mathematical sciences, particularly mechanics. He flourished about the end of the fifth century, in the time of Justinian, with whom he was a favourite, and who employed him in the erection of various edifices, particularly the church of St Sophia at Constantinople, which he carried on for some time in conjunction with Isidore, and, after his death, finished himself. He was also a disciple of Proclus, from whom he may have received information regarding burning mirrors. In a fragment entitled Ἀπομνημονεύματα Παραδείγματα, Of Wonderful Machines, and translated and illustrated by Dupuy, a member of the Academy of Belles Lettres in 1777, Anthemius treats particularly of the burning mirrors of Archimedes, on the effects of which he never seems to entertain any doubt. After acknowledging that it was universally admitted in his time that Archimedes had destroyed the Roman fleet by means of burning mirrors, Anthemius observes, "Let us, therefore, bring and collect at one point other different rays, by means of plain and similar mirrors, in such a manner that all these rays, united after reflection, may produce inflammation. This may be effected by means of several persons holding mirrors, which, according to the positions indicated, send the rays to one point.

"But, in order to avoid the embarrassment resulting from intrusting this operation to several persons (for we shall find that the matter intended to be burnt does not require less than twenty-four reflectors), the following construction may be followed: Let there be a hexagonal plain mirror, and other adjoining similar mirrors, attached to the sides of the hexagonal mirror by the smallest diameter, so that they may be moved on these lines by means of plates or bands applied, which unite them to each other, or by means of what are called hinges. If, therefore, we bring the surrounding mirrors into the same plane with the mirror in the centre, it is clear that all the rays will undergo a reflection similar and conformable to the common position of all the parts of the instrument. But if, the centre mirror remaining as it were immovable, we dexterously incline upon it all the other mirrors which surround, it is evident that the rays reflected by them will tend towards the middle of the place where the first mirror is directed. Repeat the same operation, and around the mirrors already described placing other similar mirrors, all of which may be inclined towards the central mirror, collect towards the same point the rays which they send, so that all these united rays may excite inflammation in the given spot.

"But this inflammation will take place better if you can employ for this purpose four or five of these burning mirrors, and even seven, and if they are all at the same distance from the substance to be burnt, so that the rays which issue from them, mutually intersecting, may render the inflammation more considerable. For, if the mirrors are all in one place, the rays reflected will intersect at very acute angles, so that all the place around the axis..." Burning glasses being heated, the inflammation will not take place at the single point given.

"It is therefore possible, by means of the burning mirrors just mentioned, to carry inflammation to a given distance. Those who have made mention of the mirrors constructed by the divine Archimedes, have not said that he made use of a single burning mirror, but of several; and I am of opinion that there is no other way of carrying inflammation to any distance."

These testimonies are certainly very favourable, and the subject has been still further explained and illustrated by the labours of succeeding inquirers. About the end of the sixteenth century we find mention of a burning glass on the plan of that of Archimedes, in a work by our countryman Leonhard Digges, entitled *Pantometria*, published in London in 1571, and republished by his son Thomas Digges in 1591. In the preface to the second edition the latter observes, "Archimedes also (as some supposed), with a glass framed by revolution of a section parabolical, fired the Roman nausie in the sea, comming to the seige of Syracusa. But, to leave these celestial causes, and things done of antiquitie, long agoe, my father hath at sundrie times, by the summe beams, fired powder and discharged ordnance half a mile and more distant; which things I am the boulder to report, for that there are yet living diverse of these his doings (oculati testes, eye-witnesses), and many other matters far more strange and rare, which I omit as impertinent to this place."

In the twenty-first chapter of the first book, the subject of burning glasses is resumed. "Some have fondly surmised that Archimedes burned the Roman nausie with a portion of a section parabolical, artificially made to reflect and unite the sunne beames a great distance off; and for the construction of this glass, toke great pains with high curiositie, to unite large and many intricate demonstrations; but it is a mere fantastic, and utterly impossible with any one glass, whatsoever it be, to fire any thing only one thousand paces off, no, though it were an hundred foote over; marry true it is, the parabola, for his small distance, most perfectly doth unite beames, and most vehemently burneth, of all other reflecting glasses. But how by application of mo glasses to extend this unitle or conourse of beames in his full force, yea to augment and multiply the same, that the farther it is carried the more violently it shall pearse and burne. Hoc opus hic labor est, wherein God sparing life and the time which opportunitie serving, and minde to impart to my countrymen some such secrets, as hath, I suppose, in this our age been reueld to very few, no lesse seruing for the securitie and defence of our naturall countrey, than surely to be marualled at of strangers."

A few years after the publication of the *Pantometria* of Leonhard Digges, our illustrious countryman Baron Napier of Merchiston drew up a list of "Secret inventions, profitable and necessary in these days for the defense of this island, and notwithstanding of strangers, enemies of God's truth and religion." The first and second of these inventions are burning mirrors, which are very briefly described in the following words:

First, "The invention, proof, and perfect demonstration, geometrical and algebraical, of a burning mirror, which receiving of dispersed beams of the sun, both reflect the same beams altogether united and concurring precisely in one mathematical point, in the which point most necessarily it engendreth fire; what an evident demonstration of their error who affirm this to be made a parabolic section. The use of this invention serveth for the burning of the enemy's ships, at whatsoever appointed distance."

Secondly, "The invention and sure demonstration of another mirror, which receiving the dispersed beams of any material fire or flame, yieldeth also the former effect, Burning Glasses, and serveth for the like use."

It does not appear that Napier ever condescended to give any further account of these burning mirrors; for when he was solicited a short time before his death, by one of his most particular friends, "not to bury such excellent inventions in the grave with him," he replied, "that for the ruin and overthrow of man there were too many devices already framed, which, if he could make to be fewer, he would with all his might endeavour to do; and that therefore seeing the malice and rancour rooted in the heart of mankind will not suffer them to diminish the number of them, by any new conceit of his they should never be increased."

The next author whom we find treating on the subject of the burning glasses of Archimedes, is the learned and indefatigable Kircher, whose zeal we have already mentioned as having led him to Syracuse to examine the practicability of the project on the spot, and who beside investigated the subject by a great variety of experiments. "He began with combining a number of parabolic specula; but this method was quickly abandoned, and he resorted to the use of plane mirrors. Having procured a number of plane and circular glasses, he placed them upon a wall, at such degrees of inclination that they all reflected the light of the sun to one point, and produced a considerable heat. His principal experiments, however, were made with five plain specula fixed in a frame, so that they collected the solar rays at the distance of more than one hundred feet. At this distance he produced a degree of heat which sufficiently convinced him, that by increasing the number of his mirrors, he could have consumed inflammable substances at a much greater distance. He informs us in his *Magica Catoptrica*, that the heat of the first reflection was different from that of direct light; that the light, when doubled, gave a very perceptible increase of heat; that it had the heat of a fire when tripled; that when quadrupled, the heat could still be endured; but that a five-fold reflection made the heat almost intolerable. From these results he concludes that a combination of plane mirrors was capable of producing more powerful effects than mirrors of a parabolic, hyperbolic, or elliptic form; and he entreats future mathematicians to prosecute the subject with a more numerous combination of plane specula."

But of all the authors who have laboured in this curious speculation, Buffon is the one who has thrown the clearest light on the subject; and, by the ingenuity, extent, and multiplicity of his experiments, has left little further to be accomplished by succeeding philosophers. Being soon convinced, like his predecessors, of the utter inefficiency of single mirrors, he then tried by experiment the powers of different plane surfaces in reflecting the sun's light, and found that glass, somewhat carefully polished and silvered behind, reflected more powerfully than the best polished metals, better even than what is employed for the specula of telescopes. He next found, by Loss of letting the direct light of the sun into a darkened room, light by comparing it there with the reflected light from glass, reflection, that it only lost one half by reflection, which he judged of by causing one reflected light to cover another, when the two seemed together equal to the direct light. Thirdly, having received, at distances of one hundred, two hundred, and three hundred feet, the same reflected light from large glasses, he found it had lost almost nothing of its intensity by the thickness of the mass of air which it had traversed. Having established these preliminary facts, he then tried what the effect would be of receiving the image of the sun from different glasses at still greater distances; and a curious fact was observed, namely, that whatever shape the glass might be, whether square or triangular, or any other; the same was the figure of the reflection at short distances; but as the distance increased, the figure became rounded at the angles; as the distance increased, the rounding of the angles increased along with it, until at last the square or triangular figure was changed into one nearly circular, whatever was the original figure of the glass. This effect Buffon justly ascribed to the circumstance of the apparent magnitude of the sun, every portion of the glass reflecting in reality an image of the sun, and the whole reflection being composed of an infinite number of such images, each of which subtended an angle of half a degree. At small distances, therefore, the images are too small in proportion to the magnitude of the figure to affect the shape. As the distance increases, the magnitude of each of the images increasing along with it, while the figure and magnitude of the whole reflection remains in other respects the same, the former becomes at last equal to the latter, and the square or triangular figure is absorbed in that of the circular image of the sun, and every glass comes at last to give nearly the same figure. Hence it followed that the light could be no otherwise enfeebled by distance than as it was diffused by the increasing magnitude of the image. Putting all these circumstances together, Buffon had hopes of being able to burn in this manner at a great distance, by combining a sufficient number of glasses. Still he had doubts; for supposing we wish to burn at two hundred and forty feet distant, the focus or image of the sun at this distance could not be less than two feet. What a diffusion of light, compared with the degree of concentration in very ordinary glasses,—in the mirror of the Academy of Sciences, for instance, of which the diameter is three feet! This was a hundred times larger than the diameter of its focus, which was only one third of an inch; and hence he concluded, that to burn as powerfully at two hundred and forty feet, the diameter of the mirror would have required to be two hundred and sixteen feet, which was impossible. Still, however, he had a suspicion that the effect of a large focus might be greater than the mere effect of concentration, although this was contrary to the received opinion of Descartes and other opticians; and on appealing to actual experiment, he found his suspicions satisfactorily confirmed. On trying, for example, a small burning glass three inches diameter, and the focal distance six inches, and diameter one eighteenth of an inch, with a glass thirty-two inches diameter, and a focus of two thirds of an inch,—in the focus of the latter copper melted in less than a minute, while in that of the former the copper would scarcely be gently heated, according to the principle we have already explained. Encouraged by this experiment, Buffon proceeded to put his plan in execution, and constructed, with the aid of M. Passemant, a compound mirror, represented at fig. 6. This consisted at first of sixty-eight silvered glasses, each eight inches long and six broad, arranged in a square frame parallel to each other, and separated by spaces, about one fourth or one third of an inch. These allowed the glasses to move easily independent of one another, and also allowed the operator to see through and to direct the reflections to one point. In this manner the whole sixty-eight mirrors could be made to unite their force at twenty, thirty, or even a hundred and fifty feet; and by augmenting the size of the compound mirror by adding to the number of small mirrors, the effect might be increased to any extent. The only difficulty consists in moving such a number of glasses, and directing them all to the same object. Great attention must also be paid to the choice of the glasses, which are often very defective, though they may appear well enough at first sight. The sixty-eight above described had to be picked out of more than five hundred. They were tried by observing the reflection on a wall a hundred and fifty feet distant, and those only which gave distinct and well-defined images were taken.

The first experiment was made with the mirror on the Effects of 23rd of March 1747, at mid-day. With forty glasses only, mirror, it set fire to a plank of tarred beech. Not being yet mounted, however, on its stand, it acted under a great disadvantage.

The same day, a plank done over with tar and brimstone was set fire to at a hundred and twenty-six feet with ninety-eight glasses, the mirror being still more disadvantageously placed.

On the 3d of April, at four o'clock in the afternoon, the mirror being mounted and placed on its stand, a slight inflammation was produced on a plank covered with shreds of wool at a hundred and thirty-eight feet distance, with a hundred and twelve glasses, although the sun was weak, and the light very pale. One requires to take care of himself in approaching the place where the combustible materials are placed, and avoid looking at the mirror; for unfortunately the eyes are found in the focus, they would be struck blind by the brightness of the light.

On the 4th of April, at eleven in the morning, the sun being very pale, and covered with vapours and light clouds, the mirror was still capable of producing, with a hundred and fifty-four glasses, at a hundred and fifty feet distance, a heat so considerable, that in less than two minutes it made a tarred plank smoke, which would certainly have been inflamed if the sun had not disappeared all of a sudden. The next day at three p.m., with the sun still more feeble than the preceding, chips of fir coated with sulphur and mixed with charcoal were kindled in less than a minute and a half, with a hundred and fifty-four glasses, at the distance of a hundred and fifty feet. When the sun was brisk it only required a few seconds to produce inflammation.

On the 10th of April, after mid-day, with the sun pretty clear, a plank of tarred fir was kindled at a hundred and fifty feet with only a hundred and twenty-eight glasses; the inflammation was very sudden, and extended over the whole breadth of the focus of sixteen inches diameter. The same day at half-past two the light was directed on a plank of beech tarred in part and covered in some places with shreds of wool. The inflammation was very quickly produced; it commenced with those parts of the wood that were uncovered, and the fire was so violent that it was necessary to immerse the plank in water to extinguish it: there were a hundred and forty-eight glasses, and the distance was a hundred and fifty feet.

On the 11th of April, the focus being only twenty feet distant from the mirror, twelve glasses only were required to inflame little combustible matters. With twenty-one glasses a plank of beech which had been already partly inflamed was set fire to; with forty-five glasses a large flagon of tin, weighing about six pounds, was melted; and with a hundred and seventeen glasses thin pieces of silver were melted, and an iron plate made red hot; and "I am persuaded," says he, "that at fifty feet distant the metals might have been melted as well as at twenty, by employing all the glasses of the mirror; and as the focus at this distance is six or seven inches diameter, it affords a very convenient method of making experiments on the metals, which could not be done with ordinary mirrors, the foci of which are either of feeble power, or a hundred times smaller than that of mine. I remarked that the metals, and particularly silver, smoked much before melting; the smoke was so sensible as to cast a shade on the ground. This I particularly observed, for it was not possible to look at the metal in the focus, the light being much brighter than that of the sun." Such are the results of Buffon's original experiments, and they are certainly very remarkable, and such as could not have been well anticipated from any previous knowledge of the subject. We have already seen that, according to Professor Leslie's experiments, the greatest heat of the sun in our latitude is $16^\circ$; suppose that in France it may amount to $15^\circ$ in the month of April. The heat required to inflame beech or fir coated with tar cannot be estimated at less than $600^\circ$ or $800^\circ$, which would require a concentration of forty or fifty times; and seeing one half is lost by reflection, it would require eighty or one hundred mirrors; and yet we see at the distance of twenty feet beech was inflamed with only twenty-one mirrors, which we should not have calculated to produce a higher temperature than $155^\circ$. Silver, again, cannot be melted with less heat than $4500^\circ$, or a concentration of 300 times, requiring, therefore, 600 mirrors; and yet the pieces of it were melted with 117 mirrors.\footnote{This is Wedgwood's estimate of the melting point of silver, but the more recent investigations of Daniel reduce it to $1873^\circ$ Fahr.} The same effects were observed at greater distances, making allowance for the distance. At 66 feet tarred beech was inflamed with 40 glasses, at 126 feet with 98, and at 150 feet tarred fir was inflamed very suddenly with 128 glasses. It is not easy to determine the exact diminution of effect by distance, so much will depend on the glasses themselves. Were the reflected image to enlarge itself regularly in receding from the glass, and the light to be equally diffused over the image, the calculation would be simple; but this is not the case, seeing there are rays proceeding from every point of the glass parallel to one another, and the effect of which therefore does not decrease with distance. The rays are also more accumulated in the centre than at the extremities of the image. Still, however, a decided diminution must arise from the distance of the object from the mirror; and the above results, therefore, are still far beyond what could have been looked for from so small a number of glasses employed. The cause of these extraordinary effects of the mirrors it is not easy to explain; and the discrepancy does not seem to have occurred to Buffon, nor to any of the succeeding philosophers who have considered the subject. It is certainly, however, very palpable; and either the original estimate of $15^\circ$ for the natural heat of the sun is too low, which, however, we have no reason to think from other considerations, as well as the acknowledged accuracy of the observer, and his perfect means of observation; or else, what is more probable, the heat accumulates in the heated body in a higher ratio than that of the amount continually flowing in and discharged. The level of a reservoir, as is well known, rises higher than in proportion to the quantity running in, and discharged by a given opening. It rises to a level increasing as the square of the flow; and something of this kind may perhaps occur with the stream of heat. The subject, however, would require a careful examination, and various new experiments made in a more accurate manner than has yet been done. It is much to be regretted that Buffon did not make use of a thermometer to measure the actual heat in the focus of the mirror. We have no doubt that a few observations with this instrument, or still better with Leslie's thermometric photometer, would lead to curious results.

Besides the above experiments, which were made on the first trials of the mirror, a great number of other experiments were afterwards made, which all confirmed the first. Wood was kindled at 200 feet, and even at 210 feet, with the summer's sun, every time the sky was clear; and with four such mirrors it might be done at 400 feet, and perhaps farther. All the metals also, and metallic minerals, were melted at twenty-five, thirty, and forty feet. It took about half an hour to mount the mirror, and to make all the images coincide in one point; but when it is once adjusted it will serve at all times for any particular burning distance; but if the focus is to be changed, it will take half an hour to do this,—to change, for example, from 100 feet to 150 feet. The above experiments were made publicly in the Jardin du Roi.

The mirror represented in fig. 6 has 360 glasses. The frame is supported on the axis AB, round which it can be turned by means of the rack FG, and the pinion and handle HK. The axis rests on the two uprights AL BM, which are firmly fixed by mortises into the bottom piece OQ, and cross piece ab, and steadied by diagonals; the uprights and frame are movable round an upright pillar or axis, the feet being provided with rollers to cause the whole mirror to turn easily round. The upright pillar or axis is fixed in the centre of a broad square base, or sole of wood, which is capable of turning on rollers or castors, and the whole is moved in any direction. Each of the glasses is fixed on a square plate of metal ABCD, fig. 12, movable on an axis CD, which turns on a small frame, seen from behind in fig. 10, and in front in fig. 11: the screw E pressing against the back of the plate, and the spring L resisting and pressing in the opposite direction, the plate is held firm in its position, and by turning the screw in or out the angle of the glass is altered. The whole frame and plate are besides movable round another axis CD, perpendicular to the former; this motion being regulated and directed by screws and springs in the same manner; and thus the glass having a universal motion, can easily be set so as to throw the reflection in any direction, and all the glasses by the same means directed towards one point or focus.

Such are the effects and construction of the celebrated Effects of mirror of Buffon, which actually set fire to wood at so considerable a distance; and proves, therefore, clearly the desirability of practicability, with such an apparatus, of setting fire to a vessel at the same distance. That it proves, however, the actual fact related of Archimedes, seems to admit of considerable doubts. A distinguished philosopher in the end of the eighteenth century, with all the advantages of the amazing progress of science and the arts up to that period, has, after a laborious research and numerous experiments with all the leisure of philosophical inquiry, at last succeeded in constructing a combination of mirrors, which inflames combustible materials at a distance, and in a convenient situation. But when we consider the low state of the arts in the time of the Syracusan philosopher, the inferior reflecting power of any mirror then in use, the difficulty and expense of procuring such a number as would be necessary, and of combining them together so as to act with facility and effect on an enemy's fleet,—seeing that even in Buffon's apparatus it took half an hour to bring the mirrors to a focus; and, therefore, in the case of a vessel in motion, it would be next to impossible to follow it, and keep all the glasses steadily directed to one point,—if we consider all these circumstances, the difficulties of the undertaking must appear so enormously increased, that it seems to be no disparagement to the genius even of Archimedes to require stronger proof than has yet been adduced to convince us of the fact; and particularly, as Polybius, Livy, and Plutarch, who have described the prodigies of his mechanical skill, are silent in regard to this, which would have been as wonderful as any, and was calculated to excite fully greater astonishment. That Archimedes had conceived such an idea, and perhaps in part reduced it to practice, appears certain from so many concurring testimonies; but that he actually reduced the Roman fleet to ashes, is probably only one of those exaggerations to which every action, in any degree marvellous, naturally gives rise.

Since the time of Buffon scarcely any thing further has Burning Glasses.

Peyrard's mirrors.

been done on the subject of these compound burning mirrors; and as the subject is one more of curiosity than of real utility, for, as to its application as an engine of war, it is now out of the question, enough has perhaps been done. In Peyrard's edition of the works of Archimedes, however, there is a memoir on the subject by the translator, who seems to have bestowed a good deal of attention on the subject, and suggested various ingenious improvements on the mode of combining the mirrors, and directing them with facility to any object even though in motion; but he does not seem actually to have constructed any on this plan. To direct and change so many mirrors quickly would require evidently several operators at the same time, as each mirror must be set separately. But it is extremely difficult in the ordinary way for different hands to act in concert, because if any one of the glasses, for instance, were out of the focus, it would be impossible to tell which it was, and each operator would be moving his own, and thus deranging the whole. Peyrard, therefore, proposes to furnish each mirror with a telescope, adjustable in such a manner that, being turned to any object, the reflected rays from the mirror should fall in the same direction. The adjusting apparatus consists of a telescope attached parallel to the sides of the mirror, and also capable of turning on its axis and carrying the mirror round with it. The mirror is besides capable of turning on an axis of its own, perpendicular to that of the telescope, and by this double motion the adjustment is effected. The mirror is first turned on the axis of the telescope until its own particular axis becomes perpendicular to the plane of the incident and reflected rays; and this is done by observing when the shadow of the edge of the frame of the mirror falls on a particular point, marked on an index projecting from the telescope. The mirror is then turned on its own axis until the angle of incidence becomes equal to the angle formed by the mirror and telescope; and this is known by a shadow made through an opening in the silver of the mirror falling on a particular spot in the index. In this manner one operator can adjust all the mirrors intrusted to him with accuracy and facility, and without knowing at all what the others are doing. The apparatus is represented at fig. 7, and the following is Peyrard's description.

Where AB is a common telescope with only one tube, containing the object-glass at B, and the eye-glass at A. The tube is movable on its axis between the two collars CC, C'C', which are fixed to a piece of metal, DD. This piece of metal is supported on a stand like a common telescope, having a vertical and horizontal motion, by which the axis of the telescope may be directed with facility to any given point. The axis of the instrument is marked out by the intersection of a pair of cross wires placed in the anterior focus of the eye-glass; and when this point of intersection is directed to any object, the whole instrument is kept steady in its place by the screws F and G, the former of which prevents any motion in a vertical direction, and the latter in a horizontal direction. From the middle of the tube AB rises a cylindrical piece of metal MM, and upon the eye-glass extremity a branch of iron HHH, wrought square, is fixed firmly in a direction parallel to the axis of the cylindrical piece MM.

A plane silvered glass mirror II, inserted into a proper frame, is made to turn on two pivots, one of which, m m, rests on the cylinder MM, while the other, o o, is inserted in the horizontal part of the branch HH. The straight line which passes through the centre of these pivots must be exactly parallel to the silvered back of the mirror, and at right angles to the axis of the telescope, and the black mark N, produced by a scratch upon the silvered surface, must be bisected by the axis of the mirror.

Above the object end B of the tube is fixed a plate of burning metal, seen in the figure; and behind this plate is seen another square plate, zz, on which are shown the lines zz, yy, crossing each other at right angles. By means of a piece of brass fixed to the last of these plates, and traversing a square hole made in the other plate, the square plate may be moved up and down, and from right to left; and it is kept in any position which is thus given to it, by a screw on the back of the fixed plate. The movable square plate must be adjusted in such a manner that the line zz may intersect the axis of the telescope, and be parallel to the axis oo of the mirror. The position of the line yy must also be such that its distance from the axis of the telescope is equal to the distance of the line IK from the same axis. When the plate zz is thus adjusted, the straight line yy will always be in the same plane with the line IK, whatever may be the position of the mirror; and a line drawn from a point at N, where the axis of the mirror cuts IK, to the point where yy intersects zz, will be parallel to the axis of the telescope.

The spring QQ' is fixed at Q to the arm HH, and by a screw R working into its other extremity Q' the end H of the horizontal arm may be made to press the pivot oo upon the frame of the mirror. The horizontal branch HH, which is represented separately in fig. 10, is surrounded with several pieces. The piece db and pivot oo are fixed in an invariable manner. The pivot oo is inserted in a square hole through the piece VV, and through the extremity of the arm HH. The piece db may be moved either before or behind by turning the screw; and the piece VV may be moved from right to left with the piece db by means of the screw S.

The apparatus being thus constructed, the next thing to be considered is the method of adjusting it. In order to effect this, the axis of the mirror must be perpendicular to the axis of the telescope; the line drawn from a point near N, where the axis of the mirror cuts the line IK, to the point of intersection of zz and yy, must be parallel to IK, and the straight line yy must always be in the same plane with IK.

The mirror is first placed in such a manner that the line IK is at right angles to the axis of the telescope. By turning the screw I, the lower edge of the frame is made a tangent to the circular surface MM, which is parallel to the axis of the telescope. The screw I is then turned in order to fix the piece db in an invariable manner.

The axis of the telescope is next directed to a point on a plane surface placed at a certain distance. This point must be situated in a vertical plane, perpendicular to the plane surface, and passing through the eye of the observer and the centre of the sun. A horizontal line being drawn through this point, a second point is taken, as far from the first as the centre of the mirror is distant from the axis of the object-glass. By unscrewing S, turning the telescope on its axis, and the mirror also about its own axis, the piece VV is moved backwards or forwards until the centre of the reflected image falls upon the second point. The square plate zz is then adjusted in such a manner that the shadow of the line IK falls on the line yy, and that the shadow of NN is bisected by the line zz. When this happens, the plate zz is firmly fixed. Hence it follows that whenever this adjustment is made, and when the intersection of the cross wires of the telescope is directed to any point, the rays reflected by the mirror will be parallel to the axis of the telescope, and will always continue so while the shadow of IK falls on yy, and while the shadow of NN is bisected by zz.

In making use of the mirror, the intersection of the cross wires must be first directed to any point of the ob- Burning Glasses.

The telescope must next be turned round in the collars CC', C'C', till the shadow of the line IK falls upon y y; and finally, the mirror must be turned about its own axis till the shadow of NN is bisected by the line xx. The centre of the reflected image will consequently fall upon a point of the object as far distant from the point to which the intersection of the wires was directed, as the centre of the mirror is from the axis of the telescope. The image may obviously be preserved in this position as long as we choose, by keeping the shadow of IK and N in the same position.

The above apparatus is certainly well contrived for effecting its object, but seems at the same time rather complex and expensive for any purpose to which such a mirror might be required. In regard to the power of such a combination of mirrors, M. Peyrard has only made some calculations founded on the observations of Buffon. In the first place, in regard to the effect of the distance of the mirrors from the object, he calculates that, with one about eighteen inches diameter, the rays are so diffused as to reduce the heating effect to one half at 66 feet; to one third at 118 feet; to one fourth at 161 feet; to one fifth at 200 feet; and to one tenth at 348 feet. The next question is to determine, at the shortest distance from the glass, how many times the sun's heat must be multiplied by the glasses to produce inflammation, or boiling or fusing of metals, or any other similar effects, in order to calculate how many glasses would be sufficient for the purpose, such reflection being, as Buffon found, one half of the sun's heat. This question is solved by Peyrard, from the observations of Buffon already stated, allowing for the distances by the above rule, and reducing them all to the shortest, or when the object is placed as close as possible to the glasses. Hence he finds, that on the 23rd March, calculating for the number of glasses and the distance, four times the heat of the sun would set fire to a plank of tarred beech, and $4\frac{1}{2}$ times to a plank coated with tar and sulphur; 2dly, that on the 10th of April a plank of tarred fir was set fire to by $4\frac{1}{2}$ times the sun's heat; 3dly, on the 11th of April a plank of beech which had been already on fire was inflamed by $5\frac{1}{2}$ times the sun's heat. The same day small combustible materials were inflamed with three times the sun's heat, and also a block of tin weighing six pounds was melted by $11\frac{1}{2}$ times the sun's heat; also thin pieces of silver were melted, and a plate of iron made red hot, by $2\frac{1}{2}$ times the sun's heat; and Peyrard on the whole draws the conclusion, in the view of setting fire to a fleet of ships, that five times the heat of the sun would be sufficient to inflame tarred planks, and eight times this heat would be sufficient to inflame all sorts of wood, and less in general would do it. Hence he deduced, in regard to distance, that sixteen of these glasses would be sufficient to inflame wood at the distance of 66 feet; twenty-four at 118 feet; thirty-two at 161 feet; forty at 200; eighty at 348; and at 3750, or nearly three quarters of a mile, it would require 590.

In regard to these calculations, and particularly that of the effect of the sun's heat, it appears so much beyond what might naturally be looked for, that its accuracy may well be questioned; and it is surprising this should have escaped the notice of the author, and of succeeding writers, who have copied without comment all these results. If four times the sun's heat be sufficient to inflame wood, then eight glasses would do it at a small distance, which is hardly credible. At any rate, if it be so, it implies an accumulation of heat which is quite unaccountable on any of the usual principles on which this fluid acts. In fact, we have already seen, from the observations of the photometer, that the greatest effect of the sun's heat in our latitude does not exceed sixteen degrees. Supposing this the amount of it in France in the month of April, four times this would only be sixty-four degrees, while the heat of inflammation cannot be less than 800°, twelve times what Peyrard supposes. Again, thirty times the sun's heat would only amount to 480°; and yet he says that silver was melted with this heat, which requires a temperature of 4500°, nearly ten times as much. We have already stated and explained how much the effects of Buffon's mirrors exceed what might reasonably be expected from their concentrative power. But these calculations carry them still farther. The difference seems to arise from the principle on which Peyrard has calculated the effect of distance. He supposes it to diminish as the square of the distance from a point situated so far behind the mirror, that the latter subtends at that point the same angle with the sun as at fig. 9, where AB is the diameter of the glass, AG and BG two lines, one from each extremity of the glass, and forming together an angle, AGB, of 32°. These lines being prolonged, indicate the boundary of the extreme rays reflected from the glass; and the sections ML ON RS of the cone diminish as the square of GD GP and G. In this view it would be the same as if all the light proceeded from the point G, so that all the rays would diverge from it. This, however, is far from being the case, as all the rays which fall on the glass from any given point of the sun are reflected in lines sensibly parallel, which do not diverge from that or any other point, and cannot therefore suffer diminution from distance. This calculation, therefore, would require considerable modification; and the whole subject would require, as already stated, to be re-examined experimentally.

Such are the compound mirrors which have been made single on the principle of that of Archimedes. In regard to single flectors concave mirrors, a great many of these have been constructed at different periods, remarkable for their powerful effects. We shall just describe some of the principal ones. M. Vilette's Vilette, a French artist at Lyons, constructed no fewer burning than five mirrors of this kind, of considerable magnitude, mirrors. One of them was bought by M. d'Alibert for 1500 livres; another was purchased by Tavernier, and presented to the king of Persia; a third was sent by the French king to the Royal Academy; a fourth was bought by the king of Denmark; and the fifth was brought to England for public exhibition. The first of these mirrors was thirty inches in diameter, and weighed above a hundredweight. Its focal length was about three feet, and the size of the sun's image was about half a louis d'or. It was mounted on a circular frame of steel, and could easily be put into any required position. This mirror was made in 1670, and having been brought to St Germain's by order of the king, his majesty was so well pleased with it, that he rewarded Vilette with a hundred pistoles for the sight of it, and afterwards purchased it and placed it in the Royal Observatory of Paris. The effects were the following:

| Effect | Seconds | |-----------------------------------------------------------------------|---------| | A small piece of pot iron was melted in | 40 | | A silver piece of fifteen pence was pierced in | 24 | | A thick nail (le clou de paysan) melted in | 30 | | The end of a sword blade of Olinde burnt in | 43 | | A brass counter was pierced in | 6 | | A piece of red copper was melted in | 42 | | A piece of chamber quarrystone was vitrified in | 45 | | Watch-spring steel melted in | 9 | | A mineral stone, such as is used in harquebusses à rouet, was calcined and vitrified in | 1 | | A piece of mortar was vitrified in | 52 | | Green wood and other bodies took fire instantly | |

The mirror of M. Vilette which was brought to England was put into the hands of Dr Harris and Dr Desaguliers, who made several trials with it. It was a composi- Burning Glasses.

tion of copper, tin, and tin glass; and its reflection had something of a yellow cast. There were only a few small flaws in the concave surface, but there were some holes in the convex side, which was polished. The diameter of the mirror was 47 inches, its radius of curvature 76 inches, and its focal length 38 inches. The following results were obtained in June 1718, between nine and twelve o'clock in the morning, and the time was measured by a half-second pendulum.

| Seconds | |---------| | A red piece of Roman patera began to melt in... | 3 | | and was ready to drop in... | 100 | | A black piece of the same melted in... | 4 | | and was ready to drop in... | 64 | | Chalk taken out of an echinus spatangus filled with chalk only fell away in... | 23 | | A fossil shell calcined in... | 7 | | and did no more in... | 64 | | The black part of a piece of Pompey's pillar melted in... | 50 | | and the white part in... | 54 | | Copper ore, with no metal visible, vitrified in... | 8 | | Slag or cinder of the iron work said to have been wrought by the Saxons was ready to run in... | 29½ |

The mirror now became hot, and burned with much less force.

| Seconds | |---------| | Iron ore fled at first, but melted in... | 24 | | Talc began to calcine at... | 40 | | and held in the focus... | 64 | | Calculus humanus was calcined in... | 2 | | and only dropped off in... | 60 | | The tooth of an anonymous fish melted in... | 32½ | | The asbestos seemed condensed a little in... | 28 | | But it now became cloudy. M. Vilette says that the mirror usually calcines asbestos. | | A golden marcasite broke, and began to melt in... | 30 | | A silver sixpence melted in... | 7½ | | A King William's copper halfpenny melted in... | 20 | | and ran with a hole in it... | 31 | | A King George's halfpenny melted in... | 16 | | and ran in... | 34 | | Tin melted in... | 3 | | Cast iron melted in... | 16 | | Slate melted in... | 3 | | and had a hole in... | 6 | | Thin tile melted in... | 4 | | and had a hole and was vitrified through in... | 90 | | Bone calcined in... | 4 | | and vitrified in... | 33 | | An emerald was melted into a substance like Turquoise stone, and a diamond that weighed 4 grains lost ½ths of its weight. |

This mirror was made by M. Vilette some years after the first, and with the assistance of his two sons. It came into the possession of M. Vilette the son, engineer and optician to his electoral highness of Cologne, bishop and prince of Liege, where he commonly resides. At the desire of several learned men, M. Vilette brought it to London, where its effects were exhibited in Priory Garden, Whitehall.

Large burning mirrors were made by Maginus, and by Manfredi, canon of Milan, one twenty inches diameter, and the other three and a half feet; but, from the accounts of them in the Philosophical Transactions, they appear to have had but a feeble power compared with those of Vilette.

In the year 1685 M. de la Garouste presented to the Academy of Sciences a large metallic mirror, five feet two inches in diameter, and five feet in focal length. It was not equally polished, and a piece was inserted in the middle of it where the metal had failed. This circumstance, however, did not seem to diminish its force. Several trials were made with this mirror in the academy, by order of M. de Louvois, but the precise effects which it produced have not been detailed. It is merely stated that those who tried it were satisfied with the results, and that its effects would have been much greater had it been better polished, and mounted upon a proper stand.

On the 27th of February 1667–8, Francis Smethwick, Esq. produced before the Royal Society two burning con-wick's cave glasses, ground of a newly invented figure, which was probably that of a parabola. One of them was six inches diameter, with three inches of focal length; and the other was of the same diameter, with its focus ten inches distant. When these were brought towards a large lighted candle, they somewhat warmed the faces of those that were four or five feet distant; and when held to the fire, they burnt gloves and garments at the distance of about three feet from the fire. At another experiment made in the presence of Dr Seth Ward, the deeper of the two burned a piece of wood into flame in the space of ten seconds, and the shallower one in five seconds. This experiment was made in autumn, at nine o'clock in the morning, when the weather was gloomy. By exposing the deeper concave to a northern window on which the sun did not shine, it was found to warm the hand by "collecting the warmed air in the day time, which it would not do after sunset."

This last effect is extremely remarkable; it must have arisen from the mirror collecting the radiations of heat from the distant atmosphere warmed by the heat of the day. The existence of these radiations was then perfectly unknown, and not suspected, indeed, until they were discovered only a few years ago by Professor Leslie, and actually measured by the ethroscope.

The burning mirror to which we have already alluded, made by the celebrated Tschirnhausen, was formed of thin copperplate, about one sixteenth of an inch thick. According to one account it was about three Leipsic ells, equal to five feet diameter, and burnt at the distance of three feet and a half. According to another its diameter was four feet and a half, and its focal distance twelve feet.

The following are its effects:

1. A piece of wood held in the focus flames in a moment, so that a fresh wind can hardly put it out. 2. Water applied in an earthen vessel immediately boils; and the vessel being kept there some time, the water evaporates all away. 3. A piece of tin or lead three inches thick melts away in drops as soon as it is put in the focus; and when held there a little time is in a perfect flour, so that in two or three minutes it is quite pierced through. 4. A plate of iron or steel becomes immediately red hot, and soon after a hole is burnt through it. 5. Copper, silver, &c. melt in five or six minutes. 6. Stones, brick, &c. soon become red hot. 7. Slate becomes red hot, but in a few minutes turns into a fine sort of black glass. 8. Tiles which had been exposed to the most intense heat of fire melt down into a yellow glass. 9. Pot-shreds that had been much used in the fire melt into a blackish yellow glass. 10. Pumice stone melts into a white transparent glass. 11. A piece of a very strong crucible melted into a glass in eight minutes. 12. Bones were converted into a kind of opaque glass, and a clod of earth into a yellow or greenish glass. 13. The beams of the full moon when at her greatest altitude were concentrated by this speculum; but no perceptible degree of heat was experienced.

A plan for constructing burning mirrors of wood gilded Burning Glasses.

It was proposed by Zacharias Quackenbus, in his work *In Nero Optico*. They were joined in twenty, or even a hundred concave pieces, on a turned wooden dish or scuttle, and the surface coated with pitch and gilded.

It is possible to construct mirrors of still more slender materials; and Zahnius, in his work *In Oculo Artificio*, fundam. 3, states, that an engineer of Vienna of the name of Neuman formed burning mirrors of pasteboard, covered in the inside with straw glued to it; and that they were capable of melting metals almost instantly. It is evident from what we have stated, that mirrors of this kind, from the great surface exposed, and the concentration in a perfect form not being absolutely necessary, may produce very powerful effects.

Parabolic mirrors of a large size and very considerable power were constructed by M. Hoesen of Dresden, and afterwards by M. Ehrard. These mirrors were composed of several pieces of solid wood, and on the convex part were pieces of wood, both diverging from the vertex and transversely, nicely fitted and strengthened. The concave part of this framing was covered with copperplate one eighth of an inch in thickness, four and a half feet long, and two and a half feet broad, so as to resemble one piece finely polished. The speculum was so supported as to be easily managed, and the anterior part of it was subtended by an iron arch half an inch thick. The middle of this arch, which coincided with the place of the burning focus, was perforated into a ring, which supported from both sides an iron fork for receiving the body to be examined. Four of M. Ehrard's mirrors constructed in this way had the following dimensions:

| No. | Perimeter | Diameter or Ordinate | Depth or Absciss | Focal Length | |-----|-----------|----------------------|------------------|-------------| | | Feet Inches | Feet Inches | Feet Inches | Feet Inches | | 1 | 29 4 | 9 | 7 | 1 | | 2 | 21 0 | 6 | 8 | 0 | | 3 | 16 4 | 5 | 1 | 0 | | 4 | 13 2½ | 4 | 2 | 0 |

The celebrated Wolfius, who had witnessed the effects of these mirrors, states that in burning, calcining, melting, and vitrifying, they far exceeded any thing of the kind ever known. The hardest stones scarcely resisted a few seconds. Metals were rapidly perforated, and vegetables and bones were immediately burnt to a cinder and vitrified.

Our celebrated countryman Dr James Gregory turned his attention to the construction of burning machines about the year 1670; and in a letter to Mr Collins, dated St Andrews, 7th March 1673, he states his views on this subject, and requests Mr Collins to communicate them to Sir Isaac Newton, who returns a favourable opinion of the invention in a letter to Mr Collins. The passages in these letters are too interesting to be given in any other form than in the original words of these distinguished authors.

"Mr Newton's discourse of reflection," says Dr Gregory, "puts me in mind of a notion I had of burning glasses several years ago, which appears to me more useful than sublime. If there be a concave speculum of glasses, the leaded convex surface having the same center with the concave, or to speak precisele, albeit perchance to little more purpose, let the radius of the convexite be \( r \), the thickness of the glasses in axis transitu \( f \), the radius of the convexite equal to \( \frac{9e^2 + 18ef + 5f^2}{9e + f} \), this speculum sal have the foci of both the surfaces in the same point; and not onlie that, but all the rays which are reflected betwixt the two surfaces, sal, in their egressse, come, quam proxime, to the common focus. The making of such an speculum requireth not much more art than an ordinary plane glasse, seing great subtiltie is not necessar here; so that I believe they who mak the plane miroir glasses, wold mak one of these, three foot in diameter, for four or five pounds sterling, or little more: for I have seen plane glasses, almost of that bignes, sold even here for less money. Now seing (as Mr Newton observeth) that al reflecting metalls lose more than one third of the rayes; this concave glasse, even eexter paribus, wold have an great advantage of a metall one; for certainlie an exactlie polished thin miroir glasse, of good transparent mater, after a few reflections, doeth not lose one fourth of the rayes: and, upon other accounts, this hath incomparable advantages, seing it is more portable, free from tarnishing, and, above al, hardlie 20th of the value. The great usefulness of burning concaves, this being so obvious, and as yet (for quhat I kno) untouched by anle, makes me jealous that there may be in the practice some fallacie. Ye may communicate this to intelligent persons, and especiallie to Mr Newton; assuring him that none hath a greater veneration for him, admiring more his great and subtile inventions, than his and yours."

"P. S. If ye please, let me hear, with the first convenience, what may be judged the result of this burning concave; for I am as much concerned to be undeceived, if ther be any insuperable difficulie, as to be informed of an most surprising success. I have spoke of it to severals here, but al were as ignorant of it as my self," &c.

Sir Isaac Newton's reply to Mr Collins is dated Cambridge, April 9th, 1673, and contains the following passage:

"The design of the burning speculum appears to me very plausible, and worthy of being put in practice. What artists may think of it I know not; but the greatest difficulty in the practice that occurs to me, is to proportion the two surfaces so that the force of both may be in the same point according to the theory. But perhaps it is not necessary to be so curious; for it seems to me that the effect would scarce be sensibly less, if both sides should be ground to the concave and gage of the same tool," &c. &c.

The attention of Sir Isaac Newton being thus accidently directed to the subject of burning instruments, he Newton's procured seven concave glass mirrors, each of which was mirror, eleven and a half inches in diameter, and six of these were placed round the seventh, and contiguous, but so as to have one common focus. The general focal length was twenty-two inches and a half, and about an inch in diameter. It melted gold in about half a minute, and vitrified brick or tile in one second. The effect of these specula was obviously much less than seven times the effect of any one of them. The rays of the sun could fall perpendicularly only on the one in the middle; and, in consequence of this obliquity of incidence, none of the specula intercepted a column of rays of the same diameter, and the image formed in the focus of each could not be exactly circular.

Burning mirrors composed of glass were constructed by Zelher's mirrors.

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1 No account of this burning glass of Sir Isaac Newton's is given in the *Philosophical Transactions*; and we are informed, upon very good authority, that no such instrument is in the possession of the Royal Society. Mr Derham, however, a fellow of the Royal Society, gives the same account which we have followed in the text. (See Derham's *Astrotheologia*, lib. vii. cap. i. note.) M. Zeilier of St Petersburg. His object was to convert plates of plain glass into concave mirrors, which he effected by placing the glass upon a convex tool, and exposing it to a strong heat, till it assumed the exact curvature of the tool. Zeilier made numerous trials with plates of various sizes, and, after several failures, he succeeded in finding the proper method of conducting the operation. No particular difficulties occurred in giving the proper shape to plates five or six inches in diameter; but, in forming one of sixteen inches, the circumference was moulded to the tool before the central parts, where a number of vesicles of air had collected; and, in some other cases, the glasses cracked after they had received the proper shape. The following method is that which Zeilier always found to succeed:

A small bit of the glass to be used must first be exposed to the fire till it becomes red hot, and if, after cooling, it has preserved its polish and transparency, the glass is fit for the required purpose; for it sometimes happens that the glass becomes quite black after the operation. The plate of glass is next placed on a concave iron dish of the required curvature, and put into a furnace. Coals are placed below and above the dish, and on all sides of it. The greatest care must then be taken that the glass shall become equally hot both at the circumference and at the centre; for if the red colour should get deeper in the middle, the glass will be in great danger. As soon as the whole is red hot, the instant of its bending to the shape of the mould must be carefully watched; and when this happens, which may be observed from the reflected images of the surrounding coals, all the fire must be removed from above the glass, and also a great part of the fire at its sides. The glass must then be covered with warm ashes, that have been passed through a sieve, and it must be allowed to cool gradually. It is of the utmost importance to mark the precise moment when the glass applies itself to the surface of the mould; for, if it remain too long, a part of the scoriae which separates from the mould will adhere to the glass. When the glass is covered with the hot ashes the fire must still be allowed to remain below the mould, lest the glass should crack by being cooled too suddenly. When the glass is taken from the furnace, its convex sides may then be silvered for a burning speculum; or, if a lens is required, two of the pieces of glass may be joined, so as to contain a fluid.

M. Zeilier also constructed burning glasses by making a concave frame of wood, and covering the concave surface with a paste made of flour, chalk, &c. till it had the requisite degree of curvature. A number of pieces of silvered glass mirrors, about half an inch square, were then fixed upon the concave side, so as to constitute a polygonal reflecting surface.

Buffon also, besides the experiments already related, made a good many on the bending of flat plates into a curve. He took circular plates of glass about eighteen inches, two feet, and three feet, in diameter, and having perforated them at the centre with an aperture two or three lines in diameter, he placed them in a circle of iron that was truly turned. A very fine screw, connected with a box stretching across the back of the glass, passed through the hole in the centre into a nut on the other side, so that by turning the screw the circular piece of flat glass was gradually incurvated till it formed a concave mirror. The glass of three feet diameter, when it was bent about five eighths of a line, had its focus fifty feet distant, and set fire to light substances; when it was bent two lines, it burned at the distance of forty feet; when it was bent two and three-fourth lines, its focal length was thirty feet; but in attempting to reduce its focal length to twenty feet, it was broken in pieces. The glass of two feet diameter shared the same fate; but the one of eighteen inches, which had a focal length of twenty-five feet, was preserved as a model of this species of mirror. The accident which happened to the two largest of these mirrors appears to have been owing to the perforation in the centre. In order to remedy this evil, Buffon proposed to place a circular piece of glass at the extremity of a cylindrical drum, made of iron or copper, and completely air tight. The cavity being exhausted by means of an air-pump, the glass at one extremity would be pressed in by the weight of the atmosphere, and would have its focal length inversely proportional to the degree of refraction. This contrivance is represented in fig. I, Plate CLIII., and also a section of it.

A still more simple and ingenious method of exhausting the air in the drum was contrived by Buffon. He proposed to grind the central part of the plain glass into the form of a small convex glass, and in the focus of this convex portion to place a sulphur match, so that when the mirror was directed to the sun, the rays concentrated by the convex portion would inflame the match, which, being set on fire, would absorb the air, and thus produce a partial vacuum, and consequently an incurvation of the plain glass.1 See fig. 2.

Mirrors of this kind, with a movable focus, were regarded by Buffon as of great use for measuring the effects of the solar rays, when concentrated into foci of different sizes. As the quantity of incident light and heat is nearly the same to whatever curvature the glass is successively bent, we might thus determine the size of focus by which a maximum effect was produced.

Buffon likewise made a number of concave mirrors by bending plates of glass on moulds of a spherical form. Some of these were as large as three, four, four feet six, and four feet eight inches, in diameter; but the utmost care is requisite in the formation of those of such a large diameter. After these glasses were moulded to the proper shape in appropriate furnaces, their concave and convex sides were carefully ground so as to be perfectly concentric, and the convex side was afterwards silvered by M. de Bernieres. Out of twenty-four mirrors of this kind which Buffon had moulded, he was able to preserve only three, the rest having broken, either by exposure to the air, or in the operation of grinding. One of these three, which was forty-six inches in diameter, was presented to the king of France, and was regarded as the most powerful burning mirror in Europe. The other two were thirty-seven inches in diameter, and one of them was deposited in the Cabinet of Natural History in the Jardin du

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1 Instead of grinding the central part of the glass plate into a convex form, Zeilier proposes that a small burning glass should be applied to inflame the sulphur; or, what is still better than either of these plans, a convex lens might be fastened, by the balsam of Tolu, or any transparent cement, to the centre of the glass plate.

M. Zeilier employed a more effectual method of bending circular plates of glass than that which was used by Buffon. The circular piece of glass was placed in an iron ring, across which was fixed a thin piece of iron, with a hole containing a female screw, so placed as to be above the centre of the glass. A strong bar of brass was also placed across the centre of the speculum; and a screw working in the centre of this, and in the female screw already mentioned, pressed the thin iron bar against the glass, and bent it into the proper curvature. A plate of Venetian glass, two lines thick and twenty Rhineland inches in diameter, was bent in this way till it protruded two lines in the middle, so as to have a focal length of fifteen feet, which was a greater curvature in proportion than any of Buffon's. The glass was kept in this state for several days without suffering any injury. (See Nov. Comment. Petrop. 1758, 1769, p. 230, note.) Buffon concentrated the rays of the moon by means of the mirror of forty-six inches diameter; but, though his thermometer was very sensible, no heat was perceived.

In regard to burning lenses, the first of any magnitude were constructed by M. Tschirnhausen. These were compound glasses; the light, after passing through one large glass, being still farther concentrated by a second smaller one. The large glasses were three and four feet in diameter, their focal length was about twelve feet, and the focal image about one and a half inch diameter. The focal image of the smaller glass did not exceed eight lines. The large lens, which weighed 160 pounds, was purchased by the Duke of Orleans, and presented by him to the French Academy. The following are the remarkable effects produced by it:

1. All sorts of wood, whether hard or green, and even when wet, were burnt in an instant. 2. Water in a small vessel boiled immediately. 3. All the metals, when the pieces were of a proper size, were easily melted. 4. Tiles, slates, delft ware, pumice stone, talc, whatever was their size, grew red and vitrified. 5. Sulphur, pitch, and resins, melted under water. 6. When the metals were placed in charcoal, they melted more readily, and were completely dissipated. 7. The ashes of wood, vegetables, paper, and cloth, were converted into a transparent glass. 8. All the metals were vitrified upon a plate of porcelain. Gold received a fine purple colour. 9. Substances that would not melt in pieces were easily melted in powder; and those that resisted the heat in this form melted by adding a little salt. 10. A substance easily fused assists in melting more refractory substances when placed along with them in the focus; and it is very singular, that two substances which are very difficult to melt separately, are very easily melted when exposed together, such as flint and English chalk. 11. A piece of melted copper being thrown suddenly into cold water, produced such a violent concussion that the strongest earthen vessels were broken to pieces, and the copper was thrown off in such small particles that not a grain of it could be found. This did not happen with any other metal. 12. All bodies except the metals lose their colour. The precious stones are instantly deprived of it. 13. Certain bodies vitrify easily, and become as transparent as crystal; but by cooling they grow as white as milk, and lose all their transparency. 14. Other bodies that are opaque when melted become beautifully transparent when they are cooled. 15. Substances that are transparent both when melted and cold become opaque some days after. 16. Substances which the heat renders at first transparent, but which afterwards become opaque by being melted with other substances that are always opaque, produce a beautiful glass, always transparent. 17. The rays of the moon concentrated by this lens, though extremely brilliant, have no heat.

M. de Buffon, whose ingenuity and research extended fluid burn-themselves into every branch of this subject, constructed various burning lenses of different kinds. His first object was to form burning glasses, by combining two circular segments of a glass sphere so as to form a lenticular cavity to be filled with water. These glass segments were first moulded into their proper shape, and then regularly ground on both sides, so that the concave and convex surfaces were exactly parallel. The one which he constructed was thirty-seven inches in diameter, with a focal length of about five feet and a half; and the segments were of considerable thickness, to prevent them from breaking or altering their form by the weight of the included water. This lens is represented at fig. 3. As the refractive power of water is very small, Buffon proposed to increase it by saturating it with salt; but notwithstanding every precaution, he found that the focus of lenses of this kind was never well terminated, nor reduced to its smallest size, and that the different refractions which the rays sustained produced a very great degree of aberration. Buffon also proposed to make each segment consist of a number of smaller segments put together into a frame; but as the water could not easily be prevented from sinuating itself between the joints of the segments, and as there would be a great difficulty in arranging them in the same spherical circumference, this kind of burning glass does not seem to have ever been executed.

Having made some experiments on the loss of light in Buffon's passing through thick glasses, Buffon found it very considerable, so that it detracted greatly from the power of large concentric burning glasses, which must of necessity be proportionally thick in the centre. Bouguer had formerly estimated the loss of light in passing through glass one twelfth of an inch, at two sevenths of the whole. But the glass used by him must have been extremely imperfect; for Buffon found, with glass from St Gobin, the loss of light in passing through one twelfth of an inch, one seventh of the whole, or only half the amount of Bouguer's estimate. Through glass one third of an inch thick, the loss was about two thirds. Hence in very large lenses the central portions must become nearly quite inefficient, from the quantity of light obstructed by them. On considering this subject, Buffon conceived a very ingenious plan for obviating the effect, and which has since become of great importance, from the extensive application of it in France in the construction of the large lenses now used there with such advantage in the light-houses, in place of reflectors. It consisted in forming the lens, not of one mass, but of several detached pieces united together into one. The central portion was a lens of much smaller diameter than the one intended to be formed, not one third perhaps, but having the same focal distance, and being therefore much thinner than the central portion of a whole lens would be; round this a second portion is set, forming a complete zone, and filling up another third of the diameter of the glass; lastly, another similar zone round the second, forming the exterior portion of the lens. Each of these zones forms a portion of a lens of the same focal distance as the central one, only much thinner; and then we obtain a very large lens, and yet extremely thin in proportion, so as to pass a much larger quantity of light than the others. Fig. 4 is a view of one of this sort of lenses, and fig. 5 sections of several lenses, which will render it quite intelligible. This species of glass Buffon considers as the most perfect of the kind; and when it is made three feet diameter, and an inch and a fourth thick at the centre, and six feet focus, he thinks it will give a degree of heat four times greater than that of the most powerful lenses yet known. "I venture to predict," he says, "that this glass in pieces, which I have thought of for twenty years, will be one of the most useful instruments of physics." Instead of having each zone in one entire piece, it is obvious that, without altering the effect, the zones, as proposed by Sir David Brewster, may be composed of two or more pieces, which facilitates the perfect execution; and this is the mode in which they are now constructed in France, constituting one of the most important improvements hitherto made in light-houses. Besides their thinness, these glasses possess other advantages. The pieces which compose the compound ones can be easily obtained, and selected of the purest kind and freest from flaws and veins; whereas in large lenses it was extremely difficult to obtain one entire mass of glass free from impurities and imperfections. The spherical aber- ration, which is very considerable in large glasses, can here be avoided by making the exterior segments of such focal lengths as to throw the rays to the same point with the central part. Fig. 6 shows a section of one of these lenses, and a view of one of the pieces.

The next burning lens of any magnitude was constructed by M. Bernieres, for M. Trudaine de Montigny, an honorary member of the Royal Academy of Sciences. This gentleman, whose liberality and zeal deserve to be recorded, engaged to be at the expense of a large burning glass, formed under the direction of several commissioners named by the academy. This lens consisted of two spherical segments eight feet radius and eight lines thick. The lenticular cavity was four feet in diameter, and six inches and five lines thick at the centre, and was filled with spirits of wine, of which it held no less than 140 pints. The focal length of a zone at the circumference, about six or seven lines broad, was ten feet and six lines, the focal length of a portion at the centre, about six inches in diameter, was ten feet seven inches and five lines, the diameter of the focus was fourteen lines and three fourths. When the whole surface was covered, except a zone at the circumference of six or seven lines, the following were the foci of the different rays:

| Feet | Inches | Lines | |------|--------|-------| | Violet | 9 | 6 | 4½ from the centre of the lens. | | Blue | 9 | 7 | 10½ | | Yellow | 10 | 2 | 3 | | Orange | 10 | 2 | 10 | | Red | 10 | 3 | 11½ |

The following experiments were made in October 1774, in the Jardin de l'Infante, by MM. Trudaine, Macquer, Cadet, Lavoisier, and Brisson, the commissioners appointed by the academy.

1. The burning power of the anterior half of the lens was much greater than that of the exterior half.

2. On the 5th of October, after mid-day, the sky not being very clear, two farthings placed upon charcoal were completely melted in half a minute.

3. In order to melt forged iron, it was found necessary to concentrate the rays by a second lens eight inches and a half diameter, twenty-two inches eight lines in focal length, and placed at eight feet seven inches from the centre of the great lens. At this place the cone of rays was eight inches in diameter, and the burning focus, now reduced to eight lines in diameter, was one foot from the small lens.

4. In the focus of the small lens, upon a piece of hollow charcoal small pieces of forged iron were placed, which were instantly melted. After fusion, the metal bubbled up, and fumed like nitre in fusion, and then sent off a great number of sparks. This effect (which was observed during the experiments with Tschirnhausen's lens) always took place after the fusion of iron, forged iron, or steel.

5. In order to try the effect upon greater masses, pieces of forged iron, and the end of a nail, were exposed to the focus, and were melted in fifteen seconds. A piece of nail five lines long and one fourth of a line square, which was added to the rest, was instantly fused; and the same was

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1 Messrs Macquer and Beaume are said to have melted small grains of platina by a concave glass twenty-two inches in diameter and twenty-eight inches focus.

2 Cadet and Brisson, in the course of their experiments, were led to the discovery of achromatic fluid object-glasses, a discovery which has hitherto been referred to a much later date. This discovery is most distinctly contained in the following passage.

"Comme la térebenthine cause une dispersion de rayons assez différente de celle que cause le verre, comme nous nous en sommes assurés par l'expérience, ne pourrait-on pas faire des objectifs dans lesquels pour les rendre achromatiques, on ferait usage de cette résine à la place du flint-glass, matière si difficile à se procurer d'une densité uniforme, et sans défauts, surtout en grands morceaux ; mais le développement de cette idée nous menaçait trop loin, et ne fait pas partie de notre sujet actuel !" (Mem. Acad. Par., 1777, p. 551.) Burning glasses are placed at the extremities of a truncated conical frame, consisting of twelve ribs of wood. Near the smaller end B is fixed a rack D, which passes through the pillar L, and is movable by means of a pinion within the pillar, driven by the handle E. A bar of wood F, fixed at G, between the two lower ribs of the cone, carries an apparatus H, which turns on a universal joint at K, and also moves to or from F in a chased mortise. This apparatus, which carries the iron plate I for holding the substances to be examined, may thus be placed exactly in the focus of the lens B. The conical framing is supported by pivots upon a strong iron bow AC, which rests upon a mahogany frame LL, with three feet MMM furnished with castors. Friction wheels are placed under the table N, to facilitate the horizontal motion.

The following experiments with this lens were made in the presence of Major Gardner, and of several members of the Royal Society.

| Substances fused, with their weight and time of fusion | Weight in grains | Time in seconds | |--------------------------------------------------------|-----------------|----------------| | Common slate | 10 | 2 | | Scoria of wrought iron | 12 | 2 | | Gold, pure | 90 | 3 | | Platina, do. | 10 | 3 | | Nickel | 16 | 3 | | Cast iron, a cube | 10 | 3 | | Silver, pure | 20 | 4 | | Crystal pebble | 7 | 6 | | Terra ponderosa, or barytes | 10 | 7 | | Lava | 10 | 7 | | Asbestos | 10 | 10 | | Steel, a cube | 10 | 12 | | Bar iron, do. | 10 | 12 | | Garnet | 10 | 17 | | Copper, pure | 33 | 20 | | Onyx | 10 | 20 | | Zeolites | 10 | 23 | | Pumice stone | 10 | 24 | | An oriental emerald | 2 | 25 | | Jasper | 10 | 25 | | White agate | 10 | 30 | | Flint, oriental | 10 | 30 | | A topaz or chrysolite | 3 | 45 | | Common limestone | 10 | 55 | | Volcanic clay | 10 | 60 | | Corriss moor-stone | 10 | 60 | | White rhomboidal spar | 10 | 60 | | Rough carnelian | 10 | 75 | | Rotten stone | 10 | 80 |

A diamond of ten grains, when exposed to the lens for thirty minutes, was reduced to six grains. It opened, foliated, and emitted whitish fumes, and when again closed it bore a polish and kept its form.

Gold retained its metallic state though exposed for many hours.

The specimens of platina were in different states of approach to a metallic form.

Copper did not lose any of its weight after an exposure of three minutes.

Iron steel shear melted first at the part in contact with the charcoal, while the other part exposed to the focus was unfused.

Iron scoria melted in much less time than the turnings of iron.

Calx of iron from vitriolic acid, precipitated by mild fixed alkali, weighed five grains before exposure, and five and a quarter after it.

The remains of regulus of zinc, after it had melted and was nearly evaporated, were magnetic. It was not pure.

Regulus of cobalt was completely evaporated in 57°.

Regulus of bismuth exposed in charcoal was nearly evaporated. In black lead it began to melt in 2°, and was soon after completely fused. Iron, on exposure of 180°, lost only half a grain; when placed on bone ash it fused in 3°.

Regulus of antimony, thirty-three grains, on charcoal, were fused in 3°, and eleven grains only remained after 195°.

Fine kersh from the cannon foundery evaporated very fast during 120°; and 30° afterwards the remainder flowed in globules, which were attracted by the magnet when cold.

Crystal pebble of North America, five grains, contracted in 15°, were perfectly glazed in 135°, ebullienced in 150°, and became of a slate colour and semitransparent.

Agate, oriental flint, cornelian, and jasper, were rendered externally of a glossy form.

Garnet, placed upon black lead, fused in 120°. It became of a darker hue, lost one fourth of a grain, and was attracted by the magnet. Ten cut garnets from a bracelet ran into one another in a few seconds.

Mr Wedgwood's pyrometric clay ran into a white enamel in a few seconds. Other seven kinds of clay sent by that gentleman were vitrified.

Limestone was sometimes vitrified and sometimes agglutinated. A globule from one of the specimens flew into a thousand pieces when put into the mouth.

Stalactites zeolitius spatiosus, nine grains, took a globular form in 60°. The globule began to become clear in 148°. It became perfectly transparent in 155°. When cold, its transparency diminished, and it assumed a beautiful red colour.

Lavas and other volcanic products likewise yielded to the power of this lens.

In the year 1802 Sir Joseph Banks, Dr Crawford, and some other members of the Royal Society, were present at an experiment for concentrating the lunar rays; but though the most sensible thermometers were applied, it was rather thought that there was a diminution than an increase of heat.

It was not to be expected that this powerful lens, which cost so large a sum of money, could have been retained in the hands of Mr Parker. That ingenious artist was naturally desirous to indemnify himself for the expense of its construction. A subscription was therefore opened for purchasing the lens as a national instrument; but this subscription failing, Mr Parker was induced to sell it to Captain Mackintosh, who accompanied Lord Macartney to China. This valuable instrument was left at Pekin, where it still remains.

This glass of Parker's is perhaps the largest solid lens that can be made in practice, without very great difficulties and expense in procuring so large a quantity of material of sufficient purity, and casting it in the lenticular form free of faults; and supposing these overcome, we have still the great thickness in the centre, and the enormous absorption of light in consequence of it, while the exterior portion of the glass by the spherical aberration disperses the rays from the focal point. With the compound lenses of Buffon, again, there is no limit to the magnitude further than what arises from the reflection of light near the circumference of the glass when the rays fall there very obliquely. If the diameter of the lens were to be equal to the chord of 48° of the sphere to which the lens has been formed, the whole of the incident light near the circumference would be reflected.

To augment still further the power of burning instruments, Sir David Brewster proposes a compound instrument, sphere of which he terms a burning sphere, consisting of lenses Sir David and reflectors combined together,—a series of lenses be- Burnisher ing arranged in a circle having their foci all in the centre, and having each a plane reflector so situated as to throw the sun's rays in the direction of the axis of the lens. The following is his description of it as represented in fig. 8, which is merely a section of the sphere, and represents only five of the lenses and four of the mirrors. The lenses A, B, C, D, E, which may be of any diameter and focal length, are so placed in the spherical surface AMN, that their principal foci exactly coincide in the point F. If any of the lenses have a different focal length from the rest, the coincidence of its focus with that of the other may be easily effected by varying its distance from F. The whole spherical surface, whose section is AMN, except a small opening for admitting the object to be fused, may be covered with lenses, having all their foci coincident at F; though it will, perhaps, be more convenient to have the posterior part MN without lenses, and occupied by a mirror of nearly the same radius FA as the sphere. The object of this mirror is to throw back upon the object at F the light that passes by it, without producing any effect. Each of the lenses, except the lens A, is furnished with a plane glass mirror, which may be either fixed to the general frame of the sphere, or placed upon a separate stand. When this combination is completed the sphere is exposed to the sun, so that its rays may fall at right angles upon the lens A, which will of course concentrate them at F, and produce a pretty intense heat. The plane mirror PQ, when properly adjusted, will reflect the sun's light perpendicularly upon the lens B, by which it will be refracted accurately to the focus F, and produce a degree of heat fully one half of what was produced by the direct refracted rays of the sun through the lens A. A similar effect will be produced by the mirror RS and lens D, the mirror TU and lens C, the mirror VW and lens E, and by all the other mirrors and lenses which are not seen in the section. The effect may be still further increased by the addition of a large lens at XX. As the angle which the surface of each mirror forms with the axis of its corresponding lens is a constant quantity, the mirrors may be all fixed to the general frame of the sphere, and therefore the only adjustment which the instrument will require is to keep the axis of the lens A parallel to the direction of the solar rays.

In order to estimate the advantages of this construction, let us compare its effects with those of a solid lens, which exposes the same area of glass to the incident rays.

1. In the burning sphere, almost the only diminution of light is that which arises from reflection by the plane mirrors, and which may be estimated pretty accurately at one half of the incident light; but this loss can be amply compensated by adding a few more lenses.

2. In the solid lens a great diminution of light arises from the thickness of the central portions, and from the obliquity of the parts at the circumference, which, we conceive, will be fully equal to the light lost by reflection in the burning sphere.

3. In the burning sphere the lenses may be obtained of much purer glass than can be got for a solid lens; and therefore, ceteris paribus, they will transmit more light.

4. Owing to the small size of each lens in the burning sphere, the diminution of effect arising both from spherical aberration and from the aberration of colour will be very much less than in the solid lens.

5. In the burning sphere the effect is greatly increased, in consequence of the shortness of the focal length of each lens, and the greater concentration of the incident light.

6. In the burning sphere all kinds of lenses may be combined. They may be made of any kind of glass, of any diameter, and of any focal length; and the lenses belonging to different individuals may be combined for any occasional experiment in which a great intensity of heat is requisite.

For further information on the subject of burning instruments, see Buffon, Supplément à Histoire Naturelle, tome première, 4to; Sixième Mémoire, p. 399; Kircher, Ars Magna Lucis et Umbrae, p. 772; Wolfii, Opera Mathematica, tom. ii. p. 165; Traberus, In Nero Optic lib. ii.; Phil. Trans. No. 6, p. 95; Ibid. No. 33, p. 631; Ibid. No. 40, p. 795; Ibid. 1719, vol. xxxx.; No. 360, p. 976; Ibid. 1687, tom. xvi.; Tschirnhausen, vol. xix. 1768; Vilette, Journal des Savans, 1666; La Garouste, Mém. Acad. Par. 1679, tom. i.; Nollet, Mém. Acad. Par. 1757; Courtivron, Mém. Acad. Par. 1747; Trudaine, Mém. Acad. Par. 1774; Cadet et Brisson, Mém. Acad. Par. 1777; Act. Erudit. 1687; Richman, Nov. Com. Petrop. tom. iii.; Zeiller, Nov. Com. Petrop. tom. vii. 1758, 1759; Journal Encyclopédique, 1777; Dupuy, Mém. Acad. Inscrip. 1777; Œuvres d'Archimède, par T. Peyrard, tom. ii.; Bossuet, Histoire des Mathématiques; Dutten, Du Miroir Ardent d'Archimède, Paris, 1755; A description of the great Burning Glass made by M. Vilette and his two Sons, with some Remarks on the surprising and wonderful effects thereof, London, 1719, &c. (G.B.)

BURNISHER, one who burnishes. The instrument called a burnisher is of different kinds; as a piece of round polished steel, a dog's or wolf's tooth, a piece of agate, &c. The burnishers of engravers on copper usually serve with one end to burnish, and with the other to scrape.