1.  The fertile genius of Archimedes, illustriously appears, not only in those works of 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 o 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 demonstrate their impossibility. I intend in this chapter, 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, Naudeus and Descartes, have treated it as a mere fable, though the reality of it bath been attested by Diodorus Siculus, Lucian, Dion, Zonaras, Galen, Anthemius, Eustathias, 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, who ought to have prevented them from rejecting so lightly, a fact so well supported.

2.  Yet all 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 the solar heat, that at last by increasing the number of mirrors, he could produce the most intense degree of it.

3.  Tzetzes’ description of the glass Archimedes made use of, is indeed proper to raise such an idea as Kircher entertained. That author says, Archimedes set fire to Marcellus’ 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 one hundred and sixty-eight 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.

4.  Another testimony occurs, which leaves not the least doubt in this case. 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, entitled, “Mechanical Paradoxes.” That work, among other things, has a chapter respecting burning glasses, where we meet with the most complete description of the requisites that Archimides must have been possessed of, to enable him to set lire to the Roman fleet. He begins with this inquiry, "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. “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 considerable, it might appear at first impossible to effect this, by means of the reflection of the sun’s rays; but as the glory Archimides 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 principle he had laid down.” He afterward advances farther in this inquiry, establishing certain necessary 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 shown, 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 of glasses, reflecting the rays into the same focus, there must arise 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 lie, “it necessarily results, that by a proper number of plain mirrors duly 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.”

5.   “As to the manner of putting this in practice,” he says “it might be done by employing many bands to bold 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 a distance, lie fixes upon another method, that of a plain hexagon mirror, accommodated on every side by lesser ones, adhering 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 adapted 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 multiply compound mirrors of this kind, and giving them all the same direction, there must thence infallibly result, to whatever degree or intenses, the conflagration required at the place given.”

6.   “The better to succeed in this enterprise, there should be in. readiness,” he adds, “a considerable number of these 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 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 arrogance to refuse our suffrage to such invincible testimony. Vitellion, who lived about the 13th century, speaks of a work of Anthemius of Tralles, who had composed a burning glass, consisting 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.” Zonoras 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 Syracuse.” He intimates, that the manner in which Proclus effected was by launching upon the enemies’ vessels, from the surface of reflecting mirrors, such a quantity of flame, as reduced them to ashes.

7.  Eustathias, 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 experiment 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 showed 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!

8.  Again, it appears that the ancients were acquainted with refracting burning glasses; for we find in Aristophanes’ 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 forever of his debts. He replies, that” he thought of making use of a burning glass, which he bad 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 on fire.” Where we see he speaks of a glass which burned at a distance, and which could he 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 crystal, 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.

Chapter 13 - Of Universal Gravity, and Centripetal and Centrifugal Force

Chapter 13