130 OF DEfLECTlV£ lOKCLS. 



For gravitation, being considered as a uniformly ac- 

 celerating force, must act, by the definition of such a 

 force, equally on a body in motion and at rest, so that the 

 vertical motion will not be affected by the horizontal mo- 

 tion ; and the diagonal motion, resulting from the combina- 

 tion, will terminate in the same vertical line as the simple 

 horizontal motion would have done ; and consequently the 

 horizontal motion must remain unaltered. 



Scholium. Thus if we let fall, from the head of the 

 mast of a ship, sailing uniformly along in smooth water, a 

 weight, which partakes of its progressive motion, the 

 weight will descend by the side of the mast in the same 

 manner, and in the same time, as if neither the ship nor 

 the weight had any horizontal motion. 



275. Theorem. The greatest height, to 

 which a projectile will rise, may be determined 

 by finding the height from which a body must 

 fall, in order to gain a velocity equal to its 

 vertical velocity; and the horizontal range 

 may be found, by calculating the distance 

 described by its horizontal velocity, in twice 

 the time of rising to its greatest height. 



This is evident from the equaUty of the velocity of 

 ascending and descending bodies at equal heights, and 

 from the independence of the vertical and horizontal mo- 

 tions of the projectile. 



Scholium. For example, suppose a musket to be 

 so elevated, that the muzzle is higher than the but end by 

 half of the length, that is, at an angle of 30^ ; and let the 

 ball be discharged with a velocity of 1000 feet in a second ; 

 then its vertical velocity will be half as great, or 500 feet 



