“Several remarks may be made upon this table, which are of great importance in the construction of cannon. First, when the charge is but a quarter of the shot’s weight, the difference between the velocities, when the length is 12 and 15 diameters, is but 9 feet in a second; and the differences between the other velocities decrease as the length increases.
“Hence, as the difference between the velocities when the piece is 15 and 36 diameters long, is but 22 feet in a second, it is easily perceived, that when the pieces are charged with one quarter of the shot’s weight, the length from 12 to 15 diameters is the best.
“Secondly, When the charge is one third of the shot’s weight, the difference of the velocities, when the piece is 12, 15, and 18 diameters long, are 14, 10 seconds; and from thence decrease more and more, as the length of the piece increases: so the length, from 15 to 18 diameters seems to be the best, every thing being considered.
“Thirdly, and lastly, it appears, from the same manner of reasoning, that when the charge is one-half of the shot’s weight, the length ought to be from 18 to 21 diameters; and when the charge is two thirds of the shot’s weight, the length ought to be from 21 to 24 diameters.” Muller’s Artillery.
As one of the effects of the bomb results from its weight, the range of mortars is extremely different from that of cannon, because the former is not pointed at a certain object, like the latter, but inclined to the horizon at a certain angle; so that the bomb, being thrown up obliquely, much in the same direction as a tennis-ball struck by the racket, may fall upon the place intended. Hence it appears that the mortar has no point-blank range, or at least that no use is made of it.
The mortar, being fixed in a situation obliquely with the horizon, so as that the line a c, which passes through the middle of it longitudinally, being continued, would make an angle b a d with the horizon a b; a bomb, discharged in the direction of this continued line, would deviate from it every instant of its motion by its weight, which inclines it downwards, and by this means it would describe a curve-line, as a e b, called a parabola[[49]].
The line a b, fig. 19. plate [VI]. is called the extent of the range, or the amplitude of the parabola; and the line a d, the elevation of the mortar.
To make a bomb fall on a given place, two things are to be considered; viz. the elevation of the mortar; and the quantity of powder used to charge it; both of which may be ascertained as follows: A bomb discharged from a mortar, pointed vertically, will describe a line nearly perpendicular to the horizon: I say nearly, because the mortar will always have some little motion, which will destroy the exact perpendicularity of the bomb’s flight; but abstracted from this, a bomb, discharged vertically, would fall again into the mortar[[50]].
If the mortar be afterwards inclined more and more towards the horizon, the bomb will fall still farther and farther distant from the mortar, till the elevation rests at 45°; and the more the mortar is pointed under this angle, the more will the range of the bomb be diminished: all of which is strictly demonstrated by geometry. But the following is a very simple manner of conceiving it, without having recourse to that science.
A bomb, discharged in the direction of a line, nearly perpendicular to the horizon, will fall at a little distance from the bomb-vessel. This requires no proof. A bomb, thrown according to a line that makes a very acute angle with the horizon, will presently come to the ground by its weight, and by consequence will not, any more than the other, fall at a considerable distance from the mortar.