CHAP. IV.

BURNING MIRRORS.

THE fertile genius of Archimedes illustriously appears, not only in those works his which have been handed down to us, but also in the admirable descriptions which the authors of his time have given us of his discoveries in mathematics and mechanics. Some

of the inventions of this great man have appeared so far to surpass human ability and imagination, that some celebrated philosophers have called them in question *, and even gone so far as to pretend to prove their impossibility, The following pages will produce many proofs of what is here advanced meanwhile, our present object is to examine into the subject of the burning glasses, employed by Archimedes to set fire to the Roman fleet at the siege of Syracuse. Kepler, Naudéus, and Descartes, have treated it as a mere fable, though the reality of it hath been attested by Diodorus Sicu. lus, Lucian, Dion, Zonaras, Galen, Anthemius, Eustathius, Tzetzes, and others. Nay, some have even pretended to demonstrate by the rules of catoptrics the impossibility of it, notwithstanding the asseveration of such respectable authors, whose testimony ought to have prevented them from rejecting so lightly a fact so well supported.

Yet all modern enquiries have not been involved in this mistake. Father Kircher, attentively observing the description which Tzetzes gives of the burning glasses of Archimedes, resolved to prove the possibility of this; and having, by means of a number of plain. mirrors, collected the sun's rays into one focus, he so augmented †

Descartes in his Dioptrics, Discourse 8th, p. 128. Fontenelle, and many

other.

+ Kircher, de Arte Magna Lucis, et Umbræ, lib. 10, p. 3. p. 874 ad finem, et Problem. 4, 3a part. de Magia Catoptricâ-And p. 884, 887, he delivers the catoptric rules for making burning glasses by a proper disposition of many plain mirrors. And in p. 88, relates an experiment of his own, whereby he produced a heat intense enough to burn, by means of five mirrors directing the rays of the sun into one focus; he supposes that Proclus by such means might set fire to Vitellius's fleet, and invites the skilful to bring this assay to perfection.

the solar heat, that at last by encreasing the number of mirrors, he could produce the most intense degree of it.

Tzetzes's description of the glass Archimedes made use of, is indeed very proper to raise such an idea as Kircher entertained. That author says, that Archimedes set fire to Marcellus's navy, by means of a burning glass composed of small square mirrors, moving every way upon hinges; which, when placed in the sun's rays, directed them upon the Roman fleet, so as to reduce it to ashes at the distance of a bow-shot. It is probable Mr. De Buffon availed himself of this description, in constructing his burning glass, composed of 168 little plain mirrors, which produced so considerable a heat, as to set wood in flames at the distance of two hundred and nine feet; melt lead, at that of one hundred and twenty ; and silver, at that of fifty.

Another testimony occurs, which leaves not the least doubt in this case, but resolves all in favour of Archimedes. Anthemius of Tralles, in Lydia, a celebrated architect, able sculptor, and learned mathematician, who in the emperor Justinian's time built the church of St. Sophia, at Constantinople, wrote a small treatise in Greek, which is extant only in manuscript, intitled Mechanical Paradoxes. That work, among other things, has a chapter respecting burning glasses, where we meet with the most complete descrpition of the requisites that Archimedes, according to this author, must needs have been possessed of, to enable him to set fire to the Roman fleet. He begins with this enquiry, "How in any given place, at a bow-shot's distance, a conflagration may be raised by means of the sun's rays?" And immediately lays it down as a first principle "That the situation of the place must be such, that the rays of the sun may be reflected upon it in an oblique, or even opposite direction to that in which they came from the sun itself." And he adds, "that the assigned distance being so very considerable, it might appear at first impossible to effect this by means of the reflection of the sun's rays; but as the glory Archi medes had gained by thus setting fire to the Roman vessels, was a fact universally agreed in, he thought it reasonable to admit the possibility of it, upon the principles he had laid down." He afterwards advances farther, in this enquiry, establishing certain neces sary propositions in order to come at a solution of it. To find out therefore in what position a plain mirror should be placed to carry the sun's rays by reflection to a given point, he demonstrates

that the angle of incidence is equal to the angle of reflection; and having shewn that, in so just a position of the glass, the sun's rays might be reflected to the given place, he observes that by means of a number or glasses reflecting the rays into the same focus, there must arise at the given place the conflagration required, for inflaming heat is the result of thus concentrating the sun's rays: and that when a body is thus set on fire, it kindles the air around it, so that it comes to be acted upon by the two forces at once, that of the sun, and that of the circumambient air, reciprocally augmenting and increasing the heat; whence", continues he, "it necessarily results, that by a proper number of plain mirrors culy disposed, the sun's rays might be reflected in such quantity into a common focus, at a bow. shot distance, as to set all in flames around it. As to the manner of putting his in practice," he says, "it might be done by employing many hands to hold the mirrors in the described position: but to avoid the confusion that might thence arise, twenty-four mirrors at least being requisite to communicate flame at such distance, he fixes upon another method, that of a plain hexagon mirror, accommodated on every side by lesser ones, ad. hering to it by means of plates, bands, or hinges connecting them mutually together, so as to be moved or fixed at pleasure in any direction. Thus having a apted the large or middle mirror to the rays of the sun, so as to point them to the given place, it will be easy in the same manner to dispose the rest, so that all the rays together may meet in the same focus; and by multiplying com pound mirrors of this kind, and giving them all the same direction there must thence infallibly result, to whatever degree of intense. ness, the conflagration required at the place given. The better to succeed in this enterprize, there should be in readiness," he adds, "a considerable number of those compound mirrors to act all at once, from four at least, to seven." He concludes his dissertation with observing, "that all the authors who mention the burning machine of the divine Archimedes, never, speak of it as of one compound mirror, but as a combination of many." So large and accurate a description is more than sufficient to demonstrate the possibility of a fact, so well attested in history, and by such a number of authors, that it would be the highest degree of arrogance and conceit, to refuse our suffrage to such invincible testimony. Vitellion, who lived about the thirteenth century, speaks of a work of Anthemius of Tralles, who had composed a burning glass consist.

ing of twenty-four mirrors, which conveying the rays of the sun into a common focus, produced an extraordinary degree of heat. And Lucian speaking of Archimedes, says, that at the siege of Syracuse he reduced, by a singular contrivance, the Roman ships to ashes. And Galen; that with burning glasses he fired the ships of the enemies of Syracuse. Zonaras also speaks of Archimedes' glasses, in mentioning those of Proclus, who, he says, burnt the fleet of Vitellius at the siege of Constantinople, in imitation of Archimedes, who set fire to the Roman fleet at the siege of Syra. cuse. He intimates, that the manner wherein Proclus effected this, was by launching upon the enemies vessels, from the surface of reflecting mirrors, such a quantity of flame as reduced them to ashes.

Eustathius, in his Commentary upon the Iliad, says that Archimedes, by a catoptric machine, burnt the Roman fleet at a bow-shot's distance. Insomuch that there is scarcely any fact in history, warranted by more authentic testimony; so that it would be difficult not to surrender to such evidence, even although we could not comprehend how it were possible for Archimedes to have constructed such glasses: but now that the experiments of father Kircher and Mr. de Buffon have made it apparent, that nothing is more easy in the execution, than what some gentlemen have denied the possibility of; what ought they to think of the genius of that man, whose inventions, even by their own accounts, surpass the conception of the most celebrated mathematicians of our days, who think they have done something very extraordinary, when they have shewed themselves capable of imitating in some degree, the sketches of those great masters, of whom, however, they are very unwilling to be thought the disciples?

Again, it appears that the ancients were acquainted with re fracting burning glasses; for we find in Aristophanes's Comedy of the Clouds, a passage which clearly treats of the effects of those glasses. The author introduces Socrates as examining Strepsiades about the method he had discovered for getting clear for ever of his debts. He replies, that he thought of making use of a burn. ing-glass, which he had hitherto used in kindling his fire; for, says he, should they bring a writ against me, I'll immediately place my glass in the sun, at some little distance from the writ, and set it a fire. Where we see he speaks of a glass which burned at a distance, and which could be no other than a convex glass. Pliny

and Lactantius have also spoken of glasses that burnt by refraction. The former calls them balls or globes of glass, or chrystal, which exposed to the sun, transmit a heat sufficient to set fire to cloth, or corrode away the dead flesh of those patients who stand in need of caustics; and the latter, after Clemens Alexandrinus, takes notice that fire may be kindled, by interposing glasses filled with water, between the sun and the object, so as to transmit the rays to it. [Dutens.

Among the moderns one of the earliest who devised a burning mirror, was the celebrated Lord Napier, the inventor of logarithms, who, in a paper containing hints of secret inventions, dated June 2, 1596, (the original of which is now among the MSS. in the Lambeth library, marked 658, anno 1596), says,

"First, The invention, proof, and perfect demonstration, geometrical and algebraical, of a burning mirror, which receiving of dispersed beams of the sun, doth reflex the same beams altogether united, and concurring precisely in one mathematical point, in the which point, most necessarily it engendereth fire; with 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, and serveth for the like

use."

Of the moderns, the most remarkable burning-glasses, are those of Magine of 20 inches diameter; of Sepatala of Milan, near 42 inches diameter, and which burnt at the distance of 15 feet; of Settala, of Vilette, of Tchirnhausen, of Buffon, of Trudaine, and of Parker.

That of M. de Villette was three feet eleven inches in diameter, and its focal distance was three feet two inches. Its substance is a composition of tin, copper, and tin-glass. Some of its effects, as found by Dr. Harris and Dr. Desaguliers, are, that a silver sixpence melted in 7"; a King George's halfpenny melted in 16", and ran in 34"; tin melted in 3", and a diamond weighing 4 grains, lost ths of its weight.

That of M. de Buffon is a polyhedron, six feet broad, and as many high, consisting of 168 small mirrours, or flat pieces of look