3rd Case. When a ball is fired at an angle of elevation it will reach the earth in the same length of time which it would occupy in falling the length of the tangent of the angle of projection; hence supposing F. G. (plate 22, fig. 3.) to be 16 feet, the ball would reach the point G. in one second, irrespective of the distance from D. to G. ATMOSPHERE. Let us now take into our consideration the course of a projectile while under the influence of _three_ forces, viz., powder, gravity, and air. ~Why named.~ The atmosphere, or sphere of gases, is the general name applied to the whole gaseous portion of this planet, as the term ocean is applied to its liquid, and land to its solid portions. Being much lighter than either land or water, it necessarily floats or rests upon them, and is in sufficient quantity to cover the highest mountains, and to rise nine or ten times their height, to about 45 miles above the sea level, so as to form a layer over the whole surface, averaging probably between forty and fifty miles in thickness, which is about as thick, in proportion to the globe, as the liquid layer adhering to the surface of an orange, after it had been dipped in water. ~Composition of air.~ It consists essentially of two gases, called oxygen and nitrogen, and also contains a variable quantity of aqueous vapour. ~Qualities of air.~ In common with matter in every state, the air possesses impenetrability. It can be compressed, but cannot be annihilated. It has weight, inertia, momentum, and elasticity. In consequence of its weight is its pressure, which acts uniformly on all bodies, and is equal to between 14lbs. and 15lbs. on every square inch of surface at the sea-level. ~Early idea of air’s resistance.~ ~How air acts.~ The first experiments that were made on projectiles, were carried out on the idea that the resistance of the air would not materially affect the track of a bullet which had great velocity. But the moment a body is launched into space, it meets with particles of the air at every instant of its movement, to which it yields part of its velocity, and the air being a constant force, the velocity of the body decreases at every instant from the commencement of its motion. RESULT OF THE AIR’S RESISTANCE. ~Robins, 1742, showed effect of air’s resistance.~ ~Course of ball was not a parabola.~ ~Why not a parabola.~