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(v). v. D(v). 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

Range Table For 6-inch Gun.

 Charge { weight, 13 lb 4 oz. Projectile { Palliser shot, Shrapnel shell. Muzzle velocity, 2154 f/s. gravimetric density, 55.01/0.504. Weight, 100lb. Nature of mounting, pedestal. nature, cordite, size 30 Jump, nil.
 Remaining Velocity. To strikean object10 ft.highrangemust beknown to Slope of Descent. 5′ elevation ordepression alterspoint of impact. Elevation. Range. Fusescale forT. and P.middleNo. 54Marks I.,II., or III. 50% of roundsshould fall in: Time of Flight. PenetrationintoWroughtIron. Range. LaterallyorVertically Length. Breadth. Height. f/s. yds. 1 in yds. yds. ° ′ yds. yds yds yds secs. in. 2154 .. .. .. 0.00 0 0 0 .. .. .. .. 0.00 13.6 2122 1145 687 125 0.14 0 4 100 &FRAC14; .. 0.4 .. 0.16 13.4 2091 635 381 125 0.29 0 9 200 &FRAC34; .. 0.4 .. 0.31 13.2 2061 408 245 125 0.43 0 13 300 1 .. 0.4 .. 0.47 13.0 2032 316 190 125 0.58 0 17 400 1&FRAC14; .. 0.4 .. 0.62 12.8 2003 260 156 125 0.72 0 21 500 1&FRAC34; .. 0.5 0.2 0.78 12.6 1974 211 127 125 0.87 0 26 600 2 .. 0.5 0.2 0.95 12.4 1946 183 110 125 1.01 0 30 700 2&FRAC14; .. 0.5 0.2 1.11 12.2 1909 163 98 125 1.16 0 34 800 2&FRAC34; .. 0.5 0.2 1.28 12.0 1883 143 85 125 1.31 0 39 900 3 .. 0.6 0.3 1.44 11.8 1857 130 78 125 1.45 0 43 1000 3&FRAC14; .. 0.6 0.3 1.61 11.6 1830 118 71 125 1.60 0 47 1100 3&FRAC34; .. 0.6 0.3 1.78 11.4 1803 110 66 125 1.74 0 51 1200 4 .. 0.6 0.3 1.95 11.2 1776 101 61 125 1.89 0 55 1300 4&FRAC12; .. 0.7 0.4 2.12 11.0 1749 93 56 125 2.03 0 59 1400 4&FRAC34; .. 0.7 0.4 2.30 10.8 1722 86 52 125 2.18 1 3 1500 5 .. 0.7 0.4 2.47 10.6 1695 80 48 125 2.32 1 7 1600 5&FRAC12; 25 0.8 0.5 2.65 10.5 1669 71 43 125 2.47 1 11 1700 5&FRAC34; 25 0.9 0.5 2.84 10.3 1642 67 40 100 2.61 1 16 1800 6&FRAC14; 25 1.0 0.5 3.03 10.1 1616 61 37 100 2.76 1 22 1900 6&FRAC12; 25 1.1 0.6 3.23 9.9 1591 57 34 100 2.91 1 27 2000 7 25 1.2 0.6 3.41 9.7

The last column in the Range Table giving the inches of penetration into wrought iron is calculated from the remaining velocity by an empirical formula, as explained in the article ARMOUR PLATES.