RANGE (continued)

"We made use of the diameter of a 9 pound shot, which being inches, is more convenient in the calculation; and this diameter expresses the heighth of the charge when it is a quarter of the weight of the shot, and the rest in proportion.

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 shell 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 shell, 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 shell, 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.

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