LXII. Thus much for the fact; but, with regard to the possibility of executing the deed, the mathematicians who have disputed on the subject are of various opinions, some denying the possibility, and others affirming it. All the difficulty in the execution seems to depend upon the distance of the ships from the walls, which some suppose to have been so great, that it was next to impossible to make a burning-glass of such a size that the focus of it would have been capable of reaching them. It is proper to observe here, that the distance to which the focus or burning point may be extended, bears a certain proportion to the diameter of the glass. Some have fancied that they had found out a contrivance, by which the burning-glass might be made to set fire to a thing at any given distance; but the best mathematicians consider as chimerical, the infinite extension of the line of the focus; which being excluded, and the supposed distance the moderns allow to have been between the ships and the walls established, which, according to Father Kircher, who extends it the furthest, was thirty geometrical paces; it will hardly be found possible to have made a glass that was large enough to set the ships on fire. To obviate this difficulty, some have imagined they had recourse to the invention of many concave or parabolical glasses, which reflected the rays from one to the other. But I can’t help remarking on the mathematicians, who have treated of this matter, a great mistake, which they have been led into with regard to the supposed distance: for Polybius, Livy, and Plutarch, place the ships so near the walls, that the people on board them were capable of annoying the besieged with darts and other missive weapons tipped with iron; and Polybius goes so far as to say, that with ladders resting on the ships, the Romans could pass from them to the walls; and if this was the fact, there was no necessity to have recourse to a burning-glass of so large a size, that it was next to impossible to have made, in order to set fire to the ships. Thus it appears to me, that we may safely deny the fact in opposition to the generality of the historians; and affirm the possibility, in opposition to the common opinion of the mathematicians. _Vid. Buffon._