or, for a small angle, expressed in minutes, taking the radian as 3438′,
(42) S = 1146h/R.
So also the angle β must be increased by S to obtain the angle at which the shot strikes a horizontal plane—the water, for instance.
A systematic exercise is given here of the compilation of a range table by calculation with the ballistic table; and it is to be compared with the published official range table which follows.
A discrepancy between a calculated and tabulated result will serve to show the influence of a slight change in the coefficient of reduction n, and the muzzle velocity V.
Example 3.—Determine by calculation with the abridged ballistic table the remaining velocity v, the time of flight t, angle of elevation φ, and descent β of this 6-in. gun at ranges 500, 1000, 1500, 2000 yds., taking the muzzle velocity V = 2150 f/s, and a coefficient of reduction n = 0.96. [For Table see p. 274.]
An important problem is to determine the alteration of elevation for firing up and down a slope. It is found that the alteration of the tangent elevation is almost insensible, but the quadrant elevation requires the addition or subtraction of the angle of sight.
Example.—Find the alteration of elevation required at a range of 3000 yds. in the exchange of fire between a ship and a fort 1200 ft. high, a 12-in. gun being employed on each side, firing a shot weighing 850 lb with velocity 2150 f/s. The complete ballistic table, and the method of high angle fire (see below) must be employed.
| Range. | s. | s/C. | S(v). | v. | T(v). | t/C. | t. | T(v0). | v0. | D(v0). | φ/C. | φ. | β/C. | β. |
| 0 | 0 | 0 | 20700.53 | 2150 | 28.6891 | 0.0000 | 0.000 | 28.6891 | 2150 | 50.9219 | 0.0000 | 0.000 | 0.0000 | 0.000 |
| 500 | 1500 | 518 | 20182.53 | 1999 | 28.4399 | 0.2492 | 0.720 | 28.5645 | 2071 | 50.8132 | 0.1087 | 0.315 | 0.1135 | 0.328 |
| 1000 | 3000 | 1036 | 19664.53 | 1862 | 28.1711 | 0.5180 | 1.497 | 28.4301 | 1994 | 50.6913 | 0.2306 | 0.666 | 0.2486 | 0.718 |
| 1500 | 4500 | 1554 | 19146.53 | 1732 | 27.8815 | 0.8076 | 2.330 | 28.2853 | 1918 | 50.5542 | 0.3677 | 1.062 | 0.4085 | 1.181 |
| 2000 | 6000 | 2072 | 18628.53 | 1610 | 27.5728 | 1.1163 | 3.225 | 28.1310 | 1843 | 50.4029 | 0.5190 | 1.500 | 0.5989 | 1.734 |