Note 154 — SIEGE OF CIUDAD RODRIGO.
Reading edition
The probability of hitting the same object at different ranges, with the same gun, may be considered to be in the inverse ratio of the distances respectively; the advantage, however, being always in favour of guns at or under the line of metal.
The probabilities of hitting objects of various size, the gun and range being the same, are somewhat in the ratio of the square roots of the surfaces fired at.
Of any given number of rounds, with 24-pounders of nine feet six inches, under favourable circumstances, the range being accurately ascertained, the object on, or nearly on, a level with the gun—the traverse or trunnion—axis of the gun—being horizontal, the following proportion of shot may be expected to hit without grazing:
Range in yards 600 900 1200 1500 1800
A six feet target, 36 square ft. 5/8 4/9 1/3 2/9 1/7
A nine feet target, 81 square ft. 7/8 2/3 1/2 1/3 3/14
Ranges of a 32-pounder long gun, 9½ feet, charge 10 lbs. 11 oz. powder, single shot, initial velocity 1600 feet.
Elevation in Degrees. RL | ½ | 1 | 1½ | 2 | 2½ | 3 | 3½ | 4 | 4½ | 5 | 5½ | 6
Range in Yards. 100 | 390 | 670 | 900 | 1000 | 1250 | 1390 | 1515 | 1630 | 1740 | 1850 1955 | 2055
First Differences. 280 | 230 | 190 | 160 | 140 | 125 | 115 | 110 | 110 | 105 | 100
Second Differences. 50 | 40 | 30 | 20 | 15 | 10 | 5 | 0 | 5 | 5