4. With balls of different diameters, and equal velocities, to what is the resistance of the air proportional? Their surfaces, or the squares of their diameters. 5. Would the velocity of the shot be increased by lengthening the gun? Only up to a certain point; in a proportion which is nearly the mean ratio between the square and cube roots of the length of the bore. It is found that the velocity given by long guns is reduced to an equality with that of short guns within a short distance from the muzzle when fired with similar charges. 6. Would the velocity of a shot be increased by entirely preventing the recoil, or by adding greatly to the weight of the gun? In neither case would any sensible effect be produced on the velocity. 7. Would the velocity of the shot be increased by using a larger charge of powder? Only to a certain point, peculiar to each gun; by further increasing the charge the velocity would be gradually diminished; yet the recoil is always increased by an increase of charge. 8. What is the ratio of the velocities of shot, when of different weights, but fired with similar charges? The velocities are inversely as the square roots of their weights. 9. What is the ratio of the velocities of shot of equal weights when fired with different charges of powder? The velocities are directly as the square roots of the charges. [Sidenote: 149]] 10. How may the velocity be increased without augmenting the charge of powder? By decreasing the windage; the loss of velocity by a given windage being directly as the windage. From 1-8 to 1-12 is lost by a windage of 1-40 diameter. 11. What is meant by the time of flight of a shot or shell? The time during which it is passing through the air from the piece to the first graze. 12. When firing with common shells at 45° elevation, how is the time of flight found? Extract the square root of the range in feet and divide by 4, or divide the range in feet by 16 and extract the square root of this quotient. NOTE.—Range in feet = ½_gt_² × cotangent elevation. = 16_t_² × cotangent elevation. = 16_t_² where the elevation is 45°. _______________________________ Or _t_ = ¼√range in feet for elevation 45°. 13. Having the time of flight, how is the range ascertained? Multiply the square of the time of flight by 16 for the range in _feet_ (the elevation being 45°). 14. What is meant by the penetration of projectiles? The depth to which they are forced when fired into any resisting medium. 15. What depth do shot penetrate? The penetration of balls of the same size, with different velocities or charges, is nearly as the squares of the velocities; where the balls are of different sizes the penetration will be proportionate to their diameters multiplied by the density, and inversely as the tenacity of the medium. [Sidenote: 150]]