Only when this inclination is very considerable. For the ordinary inclination, from 0° to 15°, above or below the horizon, the difference may be wholly neglected. 12. What is the effect on the point-blank range of firing upwards under a large angle? The action of the weight being nearly directly opposed to the impulsive force, the trajectory becomes compressed and the point-blank distance diminishes. The contrary effect obtains in firing downwards under a similar angle, as the weight and the force then act in nearly the same direction. [Sidenote: 66]] 13. Why may the point-blank be considered constant for the same calibre? The dimensions, charges, and weights of projectiles, being constant, and the inclination of the natural line of sight, except in a very few cases, being comprised between 0° and 15°, it follows that for the same calibre, the point-blank may be considered constant, and may serve as a point of reference in firing at different distances. 14. What is the extreme range of a piece of artillery? The distance from the piece to where the projectile finally rests. 15. For a given velocity what effect has an increase of the angle of lire on the range? It increases with the angle of fire up to a certain limit, beyond which it diminishes. 16. What angle gives the greatest range in _vacuo_? Forty-five degrees. 17. When will this angle give the maximum range in practice? Only for feeble charges, and very heavy projectiles. 18. How is the angle of greatest range in practice affected by a change in the velocity and size of the projectile? It seems to diminish as the velocity is increased, and as the ball is reduced. For the musket the angle of maximum range varies from 28° to 30°; and is nearly 42° for mortars. 19. Under what angle is a mortar usually fired? Under the constant angle of 45°, and the charge is varied according to the range required. 20. What are the advantages of this practice? Economy of ammunition; the recoil being inconsiderable, the mortar and its bed receive but little strain; the ranges are more uniform, and the effect of a slight error in the angle of fire is less than with any other. [Sidenote: 67]] 21. Is the mortar ever fired at any other angle than 45°? Yes; sometimes at 60°. 22. When is the mortar fired under an angle of 60°? When the battery is situated very near the object assailed, and it is desired that the shells may fall upon the magazines of the besieged. It is evident that projectiles the higher they are thrown up acquire more velocity in falling, besides striking the object more directly and with increased violence. 23. Under what angle are stone-mortars usually fired? Under an angle of 60°, and sometimes of 75°, that in falling from a great height, the stones may have the maximum force of percussion. 24. Under what angle should grenades be thrown from stone-mortars? About 33°; otherwise they will be buried in the earth, and their fragments will not be sufficiently destructive.