276

THEORY AND PRACTICE

TRACT 37.

the velocity is as Vd, the square-root of the diameter of theball. In this case then, the horizontal velocity at the vertexof the curve will be proportional to the terminal velocity;also the ranges, and heights, and all the other similar linesin the curve, will be proportional to d, the diameter of theball. And this principle may be of considerable use: for, bymeans of a proper series of experiments on one ball, pro-jected with different velocities and elevations, tables may beconstructed, by which may be ascertained the motions of allsimilar cases.

129. The following table also, deduced partly from theoryand partly from experiment, may be found of use, by analogy,in many other cases.

Table of the Motions of a ^14-pound Shot, projected at 45*Elevation.

Velocity

per

second.

Range

in

vacno.

Rangein theair.

Range

corrected

Heightthe ballrises to.

feet

yards

yards

yards

yards

200

415

320

330

100

400

1658

1000

1019

300

600

3731

1391

1419

400

800

6632

1687

1719

464

1000

10362

1840

1878

515

1200

14922

1934

1978

561

1400

20310

2078

2129

606

1600

26528

2206

2264

650

1800

33574

2326

2391

694

2000

41450

2438

2510

738

2200

50155

2542

2622

778

2400

59688

2640

2726

816

2600

70050

2734

2823

852

2800

81241

2827

2916

887

3000

93262

2915

3002

922

3200

106111

2995

3086

996 [

■

2

3

4

5 j

This table contains, in the first column, the velocities, infeet, of a 24-pound shot, projected at an angle of 45 da-