COMPOUND MOTION. 



75 



Fig. 45. Suppose from the point A, Fig. 45, about 240 feet 



above the earth, a ball to be projected in a perfectly 

 horizontal line, A B ; instead of traversing this line, 

 it would, at the end of the first second, be found 

 that the ball had fallen 15 feet, at the same time it 

 had moved onward in the direction of B. Its true 

 position would be, therefore, at a ; at the end of the 

 second second, it would have passed onward, but 

 have fallen to b, 60 feet below the horizontal hne; 

 and at the end of the third second, it would hav& 

 fallen 135 feet below the line, and be at c; and thus 

 it would move forward and reach the earth at d 240 feet, in precisely the same 

 time it would have occupied in falling from A to C. 



An oblique, or horizontal jet of water, is an YlQ. 46. 



instance of the curve described by a body act- 

 ed upon by gravity and the force of projection. 

 See Fig. 46. 



160. The Range of 

 a projectile, is the 

 horizontal distance to 



which it can be thrown. 



161. According to 

 theory, the range is 

 greatest when the angle 



of elevation is 45^ ; and is the same for elevations equally 

 above and below 45° ; as lor example 70"" and 20°. See 

 Fig. 47. 



These conclusions are, however, found to 

 be essentially modified in practice by the 

 resistance of the air, which not only changes 

 the path but the velocity of the projectile. 

 "With great velocities, as in the case of a 

 cannon-ball, the greatest range corres- 

 ponds with an elevation of about 30*, but 

 for slow motions it is near 45°. 



162. The laws of 

 projectiles are es- 

 pecially regarded in 

 the art of gunnery. 



By knowing the force of the powder which drives the ball, 

 the engineer is enabled to direct the cannon, or mortar, 

 in such a manner as to cause the ball, or bomb, to fall 



What is the 

 Kange of a 

 Projectile ? 



How can the 

 greatest Range 

 be obtained ? 



Fig. 47. 



Bow are the 

 Laws of Pro- 

 jectiles practi- 

 ciilly applied 

 in military en- 

 gineering ? 



