Motion of Projectiles. 203 



ball is to be discharged.* Upon the explosion taking place, the 

 centre of gravity will remain unchanged, that is, the quantities 134< 

 of motion in opposite directions will be equal ; consequently, if 

 the motion of the gun, &c., be made so slow by means of the 

 attached weight, as to admit of its velocity being taken by actual 

 observation, the velocity of the ball will be as much greater as 

 its mass is less. Knowing the mass of each, we should use the 

 following proportion ; as the mass or weight of the ball to that of 

 the gun, carriage, &c., so is the velocity of the latter to that of 

 the former. 



322. (2.) The ball may be discharged into a large block of 

 wood suspended so as to move freely after the manner of a pen- 

 dulum,* and, the velocity being observed as before, we then say 

 as the mass of the ball to that of the pendulous body, so is the 

 velocity of the latter to that of the former. This latter method 

 is adapted to finding the velocity at different distances from the 

 cannon. 



It is thus found that the velocity of a cannon ball varies ac- 

 cording to the quantity and quality of the powder, the size of the 

 ball, the length of the piece, &c. At the commencement of the 

 motion, it is ordinarily between 800 and 1600 feet in a second. 



323. With a velocity equal to 800 feet in a second, the angle 



of projection being 45, for instance, the horizontal range, great- & c .' ' 

 est elevation, &c., are readily determined by our formulas. 



We first find the height h through which a body must fall to 

 acquire the velocity of projection 800 feet, and double this height 

 will be the horizontal range required. Now to acquire a veloc- 

 ity of 800 tf et in a second, a body must fall through a space equal 



(800) * 800 ft....log....2,90309 277. 



~ 



5,80618 

 64,4....1og....l,80889 



h = 9937,75 . . K * 3,99729 

 2 



Range = 19875,5 = 3,7 miles. 



* It will be seen hereafter at what point in the pendulum the im- 

 pulse must be applied, in order that no part of it may be expended 

 against the supports from which the pendulum is suspended. 



