Bullet under two forces, powder and gravity.
But no sooner does the bullet quit the muzzle, than it immediately comes under the influence of another force, called the force of gravity, which differs from the force caused by the explosion of the powder, which ceases to influence the bullet, after it has once communicated to it its velocity.
An accelerating force.
Effect of gravity.Gravity is an accelerating force, acting constantly upon, and causing the bullet to move towards the earth, with a velocity increasing with the length of time the bullet is exposed to its influence. It has been found from experiment that this increase of velocity will cause a body to move through spaces, in proportion to the squares of the time taken to pass over the distance. Thus, if a body falls a given space in one second, in two it will have fallen over a space equal to four times what it fell through in the first second, and in the three first seconds it will have fallen through a space equal to nine times that which it fell through in the first second.
Result of gravity.
The consequence of this principle is, that all bodies of similar figure, and equal density, at equal distances from the earth, fall with equal velocity; Course of the bullet.and if a body describes a space of 16ft. in the first second of time, it will, in the next second of time, fall three times 16, or 48 feet, and thus will have fallen, from the time it first dropped, four times 16 feet, or 64 feet, because 4 is the square of 2, the time the body was falling. In the third second, it will fall 5 times 16 feet, or 80 feet, and these sums collectively, viz., 16 + 48 + 80 = 144 feet, the whole distance described by the falling body in three seconds of time.
From this it is evident, that instead of moving in a straight line A. B., ([plate 21], fig. 5.), the bullet will be drawn from that course.
Parabolic theory.
From the point C., draw C. F., equal to the space that the bullet may be supposed to fall in one second of time, then at the end of the first second of time the bullet will be at F., instead of at C., and will have moved in the direction A. F., instead of A. C.; at the end of the next second it will have fallen a total distance D. G., equal to four times C. F., thus the bullet will have fallen at the end of the third second a distance E. H., equal to nine times C. F., and it will have moved in the line A. F. G. H. instead of the straight line A. B., in which it would have moved, had it not been affected by the force of gravity. The curve A. H., is of the form called a Parabola, and hence the theory is called the “Parabolic Theory.” It is founded on the principle that the velocity given to the bullet by the explosion of the gunpowder is continued throughout its course, but this would only be true in vacuo, and is therefore of little value in calculating the real course of the bullet in the air.