cavity of the mirror, would unite by being reflected at an angle equal to that of their incidence: a very inconvenient situation for the summons, and it may be presumed, not what was meant by Strepsiades. In the second case, the summons would be held lower than the glass, at the focus in which the solar rays would unite, after having traversed the thickness of the spherical lens, which would occasion no difficulty, no embarrassment, in putting it into practice. The third mode is equally easy to be employed, for it requires only to dispose plane mirrors in such a manner, that the solar rays falling on them should be reflected in lines intersecting each other in a point, where they would form a burning focus.

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 xxxvi. 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.

The most memorable effect of burning glasses in all antiquity would be that of the mirrors of Archimedes, if the fact were sufficiently established. This is a disputable question, which I think it incumbent on me to examine with all the brevity possible, without omitting any of the arguments, that may be alleged on either side.

It is related by several ancient authors, that Archimedes set fire to the roman fleet, at the siege of Sy

racuse,

racuse, with burning glasses. This fact was con sidered by some of the moderns as fabulous and impossible by others it is admitted as certain, and even as easy to be carried into execution. I will begin with the arguments of the sceptics, at the head of whom we find the celebrated des Cartes. Diopt. Disc. VII.

In the first place they have observed, and this all the world concedes to them, that Archimedes could not employ a dioptric lens, or a burning glass by refraction, if local circumstances would have permitted it; because such a glass would not have collected into one focus a quantity of solar rays any thing like sufficient, to produce a fire of such magnitude; and because the radius of the sphere, of which it made a part, must be iminense This defect could not be remedied by employing several glasses of the same kind for all these glasses, exposed at the same time to the Sun, to produce a simultaneous conflagration, must have had the same curvature, the same focus, and the same position with respect to the Sun and the object to be burned; whence it is obvious, that they would mutually exclude each other.

For similar reasons des Cartes and his followers reject the catoptric mirror, saying, as is very true, that to unite the rays at the distance to which a dart might be thrown, that is about a hundred and fifty feet, the radius of sphericity must have been three hundred feet, which would render such a mirror impossible to be made with any degree of accuracy. Besides, it would not have furnished a sufficient

quantity

quantity of rays; and if, in order to augment this quantity, the extent of the mirror had been enlarged, the solar rays, ceasing to be physically parallel, would have been diffused over a wider space, whence their density and power would have been porportionably diminished. Lastly, in this case, as in the preceding, only one mirror could have been employed.

L

In this view of the question, it is certain, that des Cartes would completely gain his cause. But why should the mirrors be restricted to curves, that admit but one focus, and exclude the combination of several mirrors? Is it not possible, to collect a great number of little plane mirrors, and arrange them in such a manner, that they should reflect to one point, or to one small space, a quantity of solar rays sufficient to set fire to wood, cordage, or other parts of a ship's furniture? Certainly in this there is no theoretical impossibility. As to it's execution, can we suppose such a man as Archimedes, who possessed the genius of invention in mechanics in the highest degree, could be puzzled to find means of combining together several pieces of glass, and making them movable on joints or hinges, so as to assume at pleasure different inclinations, according to the exigencies of the case? It seems to me therefore, that the whole question is reducible to the point of fact, whether Archimedes really set fire to the roman fleet with burning glasses, or not.

On the one hand, not a word of this is mentioned by Polybius, Livy, or Plutarch: on the other hand, it has been positively affirmed by Hero, Diodorus Siculus,

Siculus, and Pappus. The works in which the former speak of the siege of Syracuse exist; those of the latter are lost: but these existed in the twelfth century, and the passages, in which the burning glass of Archimedes is particularly mentioned, are quoted by Zonaras and Tzetzes, writers of that period. The silence of Polybius, Livy, and Plutarch, is of the class of negative proofs, which should yield to a positive assertion, when the fact announced includes no impossibility. Besides, as Plutarch speaks generally with admiration of the effect of the engines of Archimedes, without specifying any particulars, the burning glasses might be included among these. Be this as it may, Zonaras and Tzetzes, being writers of very moderate abilities, are entitled from this very circumstance to our credit: as they were incapable of inventing such a story, their testimony must be considered as that of the authors they quote. Now Zonaras affirms, from the ancients, that Archimedes set fire to the roman fleet by means of the solar rays collected and reflected by a polished mirror: he then adds, that Proclus, taught by this example, burnt with mirrors of brass the fleet of Vitalian, who besieged Constantinople under the emperor Anastasius, in the year 514. Tzetzes, referring to the same authorities, gives a particular explanation of the mechanism of the burning glasses of Archimedes. When Marcellus,' says he, had removed his fleet out of reach of the

The authorities, taken together, are nearly equal in point of antiquity. Hero lived before Polybius; Diodorus and Livy were contemporaries; Pappus was subsequent to Plutarch.

darts,

darts, Archimedes brought into play a hexagon mirror, composed of several other smaller mirrors, each of which had twenty four angles, and which could be moved by means of their hinges and of certain plates of metal. He placed this mirror in such a position, that it was intersected through the centre by the meridian both in winter and summer; so that the rays of the Sun, being received on this mirror, and reflected by it, kindled a great fire, by which the roman vessels were reduced to ashes, though as far. off as a dart can be thrown.' Whether this passage contain an exact or defective description of the burning glasses of Archimedes, or whether it be supposed, if you please, to exaggerate their effects; at least it points out nearly the manner, in which the parts of the mirror turned, to assume the position suitable to their purpose, it's situation with respect to the Sun, and the distance at which it exerted it's burning properties; all of them circumstances neither impossible, nor improbable.

Some persons, struck with these arguments, but. still a little incredulous on the point in question, have made an objection, which has been deemed more forcible than it really is. Admitting, say they, that Archimedes might have set fire to the roman ships, if they had remained fixed in the same place; it will be very different, when we come to consider, as we ought to do, that a ship is coming nearer or moving farther off: for, they add, at every movement it makes, a considerable time will be required, to give the faces of the mirrors the positions, that will be rendered necessary by the change in the distance of.

the