Page:The New International Encyclopædia 1st ed. v. 16.djvu/506

PROJECTILES. grape shot, hot shot ( these were heated in special ovens), shrapnel, canister. Grape shot consisted of iron balls piled around a central spindle rising from a disk which was nearly equal in diameter to the calibre of the gun. A ring of the same size as the disk rested over the outer parts of the balls of each layer, and the next layer above rested partly in the ring. While the rings kept the balls in position, they were additionally held by a canvas cover lashed down tightly over the balls. When the gun was fired, the balls broke loose, but the rings and canvas kept them somewhat together for a considerable distance from the muzzle.

To reduce the expense of target practice (q.v.), sub-calibre ammunition is greatly used. A smaller barrel is fitted in the bore of the gun and its own projectiles used in it. In the United States Navy, one-pounder guns are fitted in the breech of guns of five-inch calibre and larger—musket barrels being used in the smaller guns. To further decrease the cost of the practice, the shells are cheaply made and are blind (i.e. they have neither bursting charges nor fuses). "See articles on Ammunition ; Armor Plate; Artillery; Explosives; Field Artillery; Guns, Naval; Ballistics; Gunnery; Ordnance; etc.

Bibliography. Consult: Cooke, Text Book of Ordnance and Gunnery (1878); Ingersoll, Text Book on Ordnance and Gunnery ( Annapolis, 1899) ; Bruff, Ordnance and Gunnery (New York, 1000) ; Proceedings of the United States Naval Institute (professional notes on projectiles in every issue and numerous articles in different numbers) ; Journal of United States Artillery (Fort Monroe) : Annual Report of the Office of Naval Intelligence (United States Navy).

PROJECTILES, Motion of. By this is understood the path followed by a particle of matter projected either obliquely upward, or horizontally from a height above the earth's surface. The problem of predicting this path was solved by Galileo, the solution depending upon the assumption that the horizontal velocity of projection of the particle is unaffected by the vertical force of gravity which produces a constant vertical acceleration g (approximately 980 on the C.G.S. system). If the particle is projected in an oblique direction upward, which makes the angle $$\theta$$ with the horizon, with a velocity V, it will have a horizontal component $$\mathrm{V}\cos{\theta}$$, and a vertical one $$\mathrm{V}\sin{\theta}$$. The former remains unaltered; the latter is subject to a negative acceleration $$g$$. The particle will continue to rise until the initial vertical velocity is decreased to zero. If $$t$$ is the time of ascent $$gt = \mathrm{V}\sin{\theta}$$ or$$t=\mathrm{V}\sin{\theta g}$$. In this time the particle will have gone horizontally a distance $$\mathrm{V}\cos{\theta} \times t$$ or $$\frac{V^2\cos{\theta}\sin{\theta}}{g} = \frac{1}{2} \frac{V^2\cos{\theta}\sin{2\theta}}{g}$$

After the particle reaches its highest point, it will fall and will take the same time to reach the horizontal plane through its point of projection as it did to rise to the summit of its path. In the entire time, therefore, of rising and falling, the particle will move horizontally a distance \frac{\mathrm{V}\sin{2\theta}}{g}. Since the time taken to rise to its highest point was $$\frac{\mathrm{V}\sin{\theta}}{g}$$ against an acceleration $$g$$, the height of this point is $$\frac{1}{2}gt^2$$, or T, — ■ For a given value of V, the great- 3 V-siii^!# est distance of horizontal motion, ■ is ' 9 when sin20 has its greatest value, viz. 1 ; for this 2e — 90°, and hence 6 = 45°. (This con- clusion is seriously moditied in practice by the resisting action of the air.) The path of the particle may be deduced: if horizontal distances are called x, and vertical ones y, then at a time t after projection J- = A'cosS y=t'n'me — igl

If t is climiualcd from these equations, 2i/V-'cos"e =: a;-siu'je — gx which is the equation of a parabola. In the simplest case, when the point of projec- tion is at a height above the surface of the earth, and the particle is projected horizontally ' with a velocity V, x^t, 1/=: — igt'^ w'here y is vertically down. g Eliminating t, these equations give 1/= Kyi *"• As a solid moves through the air, it meets opposition of various kinds due to the air. There is an opposing force which diminishes the linear speed. For speeds less than 100 feet per second the resistance of the air varies directly as the S(piarc of the velocity, as stated by New- ton. According to Duchemin ( 1842) . this resist- ance = 0!'- -}- 61'* for speeds below 1370 feet per second, and =: cv' for higher speeds. In these expressions i' is the speed of the projectile and a, b, c, are factors of proportionalitj'. The first formula has been verified by the recent work of Dr. A. F. Zahm. If the projectile is rotating on an axis, the angular speed is decreased, owing to friction ; and owing to the unequal friction on th« various sides, there is a sidewise force producing the 'curves' of a baseball and the 'drift' of a bullet. If the projectile is elongated or broad, the centre of pressure of the air against it and its centre of inertia are not in general in the line of motion ; so there is a moment tending to make the projectile turn around an axis at right angles to the plane including the line of motion, the centre of pressure, and the centre of inertia. If the projectile is not rotating, it will turn so as to move with its broadest face front ; e.g. a ])enny falling in water falls face down, not edge down ; a sheet of cardboard falling through the air tries to fall face down. If, however, the projectile is rotating around an axis,* e.g. an I elongated bullet, the effect is to change the direction of the axis. ' PROJECTION (Lat. pro/ec/i'o, from ?)»-o/iccrp, to throw forward). The act or result of con- structing a figure upon a given surface, usually by means of a pencil of rays, so that it corre- sponds point by point to another given figure. It thus includes perspective (q.v.), and is most j simply illustrated by the shadow of an object thrown by a light on a wall, the shadow being I the projection, and the light being the vertex ^ of the pencil or sheaf of rays. If the centre of projection is infinitely distant the projection is called parallel projection : if also the projection rays are perpendicular to the plans of projection, we have orthogonal projection. The theory of projections is of great importance, both in mathe- matics and in geography, being in the former