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.~ ~Elongated projectiles easily 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; 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. DEVIATIONS OF PROJECTILES FROM SMOOTH-BORED GUNS. ~Causes of deviation of shot.~ Very great irregularities occur in the paths described by projectiles fired from smooth-bored guns. It is a fact well known to all practical artillerists, that if a number of solid shot or any other projectile be fired from the same gun, with equal charges and elevations, and with gunpowder of the same quality, the gun carriage resting on a platform, and the piece being laid with the greatest care before each round, very few of the shot will range to the same distance; and moreover, the greater part will be found to deflect considerably (unless the range be very short) to the right or left of the line in which the gun is pointed. ~Four causes of deviation.~ The causes of these deviations may be stated as follows:--1st, Windage; 2nd, Rotation; 3rd, Wind; 4th, from Rotation of the Earth. 1st CAUSE, WINDAGE. ~Action from windage.~ ~False direction.~ ~Gives rotation.~