330 On the Path of the projectile Weapon 



produced by each of these forces separately, and we shall be 

 better able to estimate with precision their conjoint effects. 



2. Before the body is projected, it must be observed, that 

 there are a variety of angles with the horizon, at each of which 

 it might be thrown ; but, for the present, we shall confine our- 

 selves to two, I mean the angles of projection and inclination. 

 By the former, I understand the angle which the plane of the 

 horizon makes with the direction in which the body is pro- 

 jected ; and by the latter, I mean the angle which the plane 

 side of the body makes with the horizon. These two angles 

 should be accurately attended to, as they are quite distinct. 



3. When the body is projected in any direction, and at any 

 angle of inclination, say 40° or 50°, the effect of the first force, 

 viz. projection, will be to impel it forward; that of the se- 

 cond, viz. gravitation, to cause it to descend : but the effect of 

 the third force, I mean that which acts on the plane side, will 

 be, first, to counteract and nullify the fourth force, which acts 

 on its curved side, and by this means, becoming itself 5wpmor 



for a time to gravitation, its ultimate effect will be to bear the 

 body upwards in a curvilinear direction. Finally, it will co- 

 operate with the fifth force, (the effect of which, inasmuch 

 as it acts on the edge of the body, is scarcely estimable,) in 

 causing the body to gyrate around its axis. This axis is ob- 

 viously an imaginary line at right angles to the plane surface 

 of the body, and passing through the point on which the body 

 would balance itself, in the position in which its plane surface 

 would be parallel to the horizon ; i. e. if the body be supposed 

 for a moment to rest on the paper on its level side, and if 

 the paper be parallel to the plane of the horizon, the position 

 of the axis is a perpendicular to the horizon passing through 

 the centre'of gravity of the body while in this position. 



4. It is easy to perceive that the body will ascend in a 

 curvilinear direction, if the five forces above mentioned are ca- 

 pable of producing the different effects which I have attri- 

 buted to them. That the projectile force will impel the body 

 forward, and that of gravity downward, cannot be questioned. 

 Not so the effects ascribed to the other three. I shall there- 

 fore proceed to explain whatever may appear not sufficiently 

 satisfactory in my assertions regarding them. The third force 

 above mentioned is the resistance of the air to the plane or 

 level side of the body. This force, if not twice as great, is at 

 least much greater than the force acting against the curved 

 side. This truth will appear evident, if we consider atten- 

 tively the following facts. 



5. If a globe and cylinder of the same diameter move in an 

 uncompressed fluid in the same direction, viz. that of the axis 

 of the cylinder, the base of the cylinder suffers twice as much 



