219. =Projectiles.=--I have already spoken of projectiles in § 211. You saw there that any body, as a cannon-ball, which is projected horizontally, falls to the earth in a curved line. Two forces act on the ball; viz., the projectile force given by the powder and the force of gravitation. The force of gravity being always the same, the shape of the curve which the projected body describes must depend on the force with which it is projected. This is very strikingly exemplified in the curves described by the different streams of water in Fig. 141. But whether the projectile force be great or small, the moving body thrown horizontally will in every case reach the ground in the same time. Thus if two cannons stand side by side on a height, one of which will send a ball a mile and the other half a mile, the two balls, if fired together, will reach the ground at the same instant, though at first thought it would seem that the ball which travels twice as far as the other would take a longer time to do it in. This is because the _horizontal_ force of the ball does not oppose in the least the _downward_ force of gravity. If it were thrown upward instead of horizontally, the projectile force would be opposed to gravity, and in proportion as the direction came near to being vertical. As horizontal force does not interfere with the action of the force of gravity, it follows that a ball dropped at the instant at which another is fired will reach the ground at the same instant that the fired ball does. This can be made clear by Fig. 155. Suppose it takes three seconds for a ball to fall from the top of a tower to its foot. In the first second it falls to _a_. The ball projected horizontally from the cannon, being operated upon by the same force of gravity, will fall just as far, and will be on a level with it at _b_. Both balls fall farther and farther each second, both being accelerated in the same degree because it is done by the same force. The projected ball will reach _d_ when the falling ball is at _c_, and the plain at _f_ when the falling ball is at _e_, the foot of the tower. The same holds true in all cases. A bullet dropped from a level with the barrel of a gun, paradoxical as it may seem, will fall to the ground no sooner than one which is shot from the gun. [Illustration: Fig. 156.]