THE classical student will remember that Archimedes burned the fleet of Marcellus, by means of burning-glasses, from the heights of the fortifications of his native city of Syracuse. Unfortunately, any account of the system of catoptrics, or the science of reflections, employed by the ancient Syracusan in their construction is lost to us, and many modern writers have gone so far as to doubt the fact altogether. The knowledge of the properties, however, of concave mirrors which we have just been acquiring, will enable us to form a pretty good guess as to the means adopted by Archimedes for the destruction of the enemy’s fleet. The ancients, not having the means of either casting or grinding such enormous mirrors, must have constructed them of a large number of small ones, so arranged that the images of the sun reflected by them would all fall in the same place, or nearly so. In this case, the larger the number of mirrors, the greater would be the burning effect. In order to explain the reflection of rays incident upon the surface of concave mirrors, we supposed them to consist of an immense number of plane mirrors placed in a curve, so that the reflected rays might all meet in one point; but on examining into the history of burning mirrors, we find that the plan has been adopted in reality in a great number of instances. We have also said, that the reflection of the heating rays was governed by similar laws to those influencing the rays of light; consequently, by directing a pencil of sunlight upon the surface of a concave mirror, we obtain the maximum of light and heat at the focal point.