202 Dynamics. 



sight ; so that the precaution is the same as if we had taken aim 

 in the direction of the axis, but at a point above the object. 



3 1 9. We remark further, that there are cases in which, al- 

 though we have given no impulse to a body, and seem to aban- 

 don it to gravity alone, yet this body describes a curved line 

 common to all projectiles. A body, for example, which is suf- 

 fered to fall from the mast-head of a vessel under sail, really des- 

 cribes a curved line. If we attend to the point of the deck where 

 it strikes, we shall find it just as far from the mast, other things 

 being the same, as the point from which it started, so that the 

 body describes a line parallel to the mast ; but with respect* to a 

 spectator at rest, it has actually described a parabola (the resist- 

 ance of the air not being considered), for, at the instant it was 

 dropped, it must have had the same velocity with the vessel ; the 

 case is therefore precisely the same, as if, the vessel being sta- 

 tionary, we had thrown it with a velocity equal to that of the 

 vessel, and in the same direction. It will be seen, also, at the 

 same time, why it describes with respect to the mast a straight 

 line parallel to this mast ; it is because they both move with the 

 same velocity, and in the same direction; considered horizontal- 

 ly, therefore, they must preserve the same distance from each 

 other. 



320. In the foregoing theory, we have taken it for granted; 

 (1.) That the force of gravity is the same throughout the whole 

 range of the projectile. (2.) That it acts in lines parallel to 

 each other. (3.) That there is no resisting medium. The two 

 first suppositions, although not strictly conformable to fact, are 

 attended with no material error in practical gunnery, and those 

 arts to which this theory is subservient. But the third is of es- 

 sential importance to the truth of the results we have obtained. 

 We can readily put the theory to the test of actual experiment. 



The initial velocity of a cannon ball, for instance, may be 

 obtained with considerable accuracy, by either of the following 

 methods. 



321. (1.) Let the cannon together with the carriage and 

 other weight if necessary, be suspended like a pendulum so 

 as to move freely in the direction opposite to that in which the 



