The superficial contents of circles are as the squares of their diameters. Hence if the ball A. ([plate 23], fig. 3) be 2in. in diameter, and the ball B. 4in., the amount of resistance experienced would be as four to sixteen.
Contents of spheres.
The cubical contents, or weights of spheres, are in proportion to the cubes of their diameters. Hence the power to overcome resistance in the balls A and B would be as eight to sixty-four. Thus the power to overcome resistance increases in much greater proportion than the resistance elicited by increasing the surface.
Advantages of elongated bullets.
Suppose an elongated body to have the diameter of its cylindrical portion equal to that of the ball A., i.e., E.F. = C.D., ([plate 23], fig. 4), and elongated so that its weight should be equal to that of the spherical shot B., it is evident that it would meet equal resistance from the air, to the ball A., having, at the same time, as much power to overcome resistance as the body B.
Elongated balls, by offering a larger surface to the sides of the barrel, are less liable to be affected by any imperfections in the bore; whereas the spherical ball, pressing only on its tangential point, will give to any little hollows, or undulations, wherever they occur.
Balls cannot be expanded.
A spherical ball cannot be expanded into the grooves, unless there be very little windage, except by blows from the ramrod, the gas escaping round the circumference of the ball, and giving it an irregular motion while passing down the barrel; Elongated projectiles easily expanded.but an elongated projectile can be readily expanded, and the facility of doing so is in proportion to the difference of length between its major and minor axis.