GRAVITY.
Bullet as influenced by powder and gravity only.
We will now proceed to consider the course of a bullet, as affected by two forces only, viz., 1st. The velocity communicated to it by the explosion of the powder; and 2nd. By the force of Gravity.
The attraction of the earth acts on all bodies in proportion to their quantities of matter.
If no air, all bodies would fall in same time.
The difference of time observable in the fall of bodies through the air, is due to the resistance of that medium, whence we may fairly conclude, that if the air was altogether absent, and no other resisting medium occupied its place, all bodies of whatever size, and of whatever weight, must descend with the same speed. Under such circumstances, a balloon and the smoke of the fire would descend, instead of ascending as they do, by the pressure of the air, which, bulk for bulk, is heavier than themselves. Gold and dry leaf in same time.A dry leaf falls very slowly, and a piece of gold very rapidly, but if the gold be beaten into a thin leaf, the time of its descent is greatly prolonged. If a piece of metal and a feather are let fall at the same instant from the top of a tall exhausted receiver, it will be found that these two bodies, so dissimilar in weight, will strike the table of the air-pump, on which the receiver stands, at the same instant. Supposing the air did not offer any resistance to the onward course of a projectile, and that the instantaneous force communicated to a bullet, from the explosion of the gunpowder, were to project it in the line A.B. ([plate 21], fig. 4.) from the point A., with a velocity that will send it in the first second of time as far as C., then if there were no other force to affect it, it would continue to move in the same direction B., and with the same velocity, and at the next second it would have passed over another space, C.D., equal to A.C., so that in the third second it would have reached E., keeping constantly in the same straight line.
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.