The artillerist's manual and British soldier's compendium

by F. A. Griffiths

7. By firing the charge in different parts (separately, or simultaneously), by compressing the charge, by the use of wads, by varying the weight of the gun to lessen the recoil, or even by stopping the recoil entirely, no sensible change is produced in the velocity of the ball.

8. The velocity increases with the charge, to a certain point, peculiar to each gun; but, by further increasing the charge, the velocity gradually diminishes; yet the recoil is always increased by an increase of charge. (Vide [3.])

9. The velocities of balls fired with equal charges increase to a certain point, when the gun is longer, in a proportion which is nearly the middle ratio between the square and cube roots of the length of the bore.

10. When shot of different weights are fired with the same charges of powder, the velocities communicated to them are nearly in the inverse ratio of the square roots of their weights. Therefore, shot which are of different weights, and impelled by the firing of different charges of powder, acquire velocities which are directly as the square roots of the charges of powder, and inversely as the square roots of the weights of the shot. By making use of shot of a heavier metal than iron (lead for instance) the momentum of the shot discharged with the same charge of powder would be increased in the ratio of the square root of the shot’s weight, which would both augment the force of the blow with which it would strike, and also the extent of the range.

Compound-shot, or shells filled with lead, fired with charges increased ⅛th, will increase the power of range considerably.

11. With common shells at 45° elevation, the time of flight is nearly equal to the square root of the range in feet, divided by 4; or, more nearly, equal to the square root of the quotient of the range in feet, divided by 16-1/12.

12. The range at 45° elevation is nearly equal to the square of the time of flight in seconds, multiplied by 16-1/12 feet. The range at 15° will be about half that at 45°.

13. Upon inclined planes, at any elevation, there are always two elevations with which any range may be obtained.

The elevation which gives the greatest range, on a given ascent, is equal to half the sum of 90° added to the ascent.

The elevations which give equal ranges on a given ascent, are the complements of each other added to the ascent.