The vertical fires are supposed to commence only when the enemy opens his third parallel, as the distance previous to this would render their effects less certain. From this period till the opening of the breaches, the usual calcula tions allow 10 clays; and the effects of the vertical fires during these 10 days may be found thus.
Supposing the third parallel to be 100 yards from the flanked angles of the bastion and of the ravelin, and the length of the exterior side of the polygon 360 yards, the field occupied by the besieging army will be nearly 36,000 square yards ; but, in order to calculate on the minimum effect of the fire, call it 60,000 yards.
It is now necessary to ascertain how much of this space is actually covered by the bodies of the men who act as la bourers and guards of the besiegers works. The number of these men is generally estimated at three-fourths of the garrison, a smaller proportion being found too weak for resisting the sallies of the besieged. Supposing then that the garrison consists only of 4000, the guard of the trench es will be at least 3000, that is, 3000 men will be spread over the surface of the ground forming the avenues of the place ; but these avenues, it has been shewn, are contain ed within a space of 60,000 square yards, therefore the number of the besiegers occupying the avenues or pas sages. will be one-twentieth of the square yards, that is in the proportion of one man to 20 square yards.
Let it now be supposed that a man's body projected ho rizontally covers one square foot, and nine men will thus be required to cover completely a square yard. But it has already been caicu,ated that there is one man in every 20 yards of the space occupied by the besiegers, therefore the space actually covered by the bodies of the enemy's troops and workmen, will be the 180th of the whole ; and, consequently, out of every 180 shots falling in an inclined or parabolic line within that space, one, in the course of a long continued fire, will strike the enemy. It is to be ob served, however, that this is the minimum, or least possi ble effect to be expected from such a fire, because all the data on which the preceding estimate is founded, have been assumed on the most unfavourable suppositions. The enemy has been supposed equally distributed over all the space, instead of being very much concentrated, as they really are on the glacis, towards the capitals of the saliant angles, to which the vertical fire may also be readily con fined. A man's body, too, has been supposed to cover only one square foot when horizontally projected ; but if he is working or marching, which must be the case with the greater part of the besiegers, it will occupy a much larger space ; besides, as the line described by the shot is not perpendicular, but inclined, the surface presented to it by a man's body, must be double his horizontal projection.
All these circumstances considered, it would not, perhaps, be too much to suppose that one ball in 50 takes effect ; but to prevent every possible objection on this score, let it be supposed, as above, that one ball in 180 proves fatal to one of the besiegers.
Let it be supposed, in the next place, that there arc mounted on the attacked front, six twelve-inch mortars, two on each of the bastions, and two on the ravelin, so si tuated as to fire along the capital of each. The mortars, as formerly observed, are protected from the direct fire of the enemy by the parapet, and from the ricochetts by a shell-proof covering, having only one opening sufficient to allow the escape of the shot at an angle of 45°. The side towards the place may be open to prevent the collection of smoke, and surrounded with a small fosse to secure it from the shells that may fall near it.
To estimate the effect of each piece then, it is to be observed, that as the shell of a twelve-inch mortar weighs 150 pounds, the same weight of balls, each a quarter of a pound, may be fired with the same charge ; that is, each mortar, at a single shot, will discharge 600 such balls, be ing 3600 from the whole. But it has been shewn, that out of 180 balls, one may be supposed to strike the enemy ; therefore at each discharge of the six mortars, twenty of the besiegers will be put hors de combat.
It remains now to inquire how many rounds may be fired in the space of 24 hours, the fire being continued during the night as well as the day. These, at a moderate cal culation, may be rated at 100, which allows nearly a quar ter of an hour to each round. But at every discharge 20 of the besiegers are disabled ; therefore in 24 hours, 2000 men will be destroyed or rendered unfit for duty. In the course of the ten days then, between the opening of the third parallel and effecting a breach in the rampart, the besiegers will sustain a loss of 20,000 men. But if the garrison consist only of 4000, the whole of the besieging army will probably not exceed 20,000, being in the pro portion of five to one ; that is to say, the besieging army will be completely destroyed before it is able to effect a breach. If the garrison were stronger, and of course the besiegers more numerous, it may be shown, by a similar calculation, that their loss would be proportionally great ; or in general, that a garrison of any strength may, by means of a vertical fire alone, destroy five times its own numbers, in the space of ten clays after the opening of the third parallel.