332 On the Path of the projectile Weapon 



as the square). And since both the plane and curved sur- 

 faces of the body act simuhaneously on the air, and are, there- 

 fore, simultaneously reacted on by it ; and since this reaction 

 is so much greater (5.) against the plane than the curved side, 

 it follows manifestly that there remains an excess of force act- 

 ing on the plane side, which will cause it to deviate from the 

 direction of its first motion. And in what direction will it be 

 turned ? Evidently in the direction imparted to it by the force 

 acting on it. To ascertain this direction, we must bear in 

 mind, that the body was projected with its plane surface ma- 

 king with the horizon an angle of 40° or 50° ; and if we esti- 

 mate, as we may, (see Wood's Mechanics, Comp. and Res. of 

 Forces,) the total efficient resistance in a direction perpendi- 

 cular to its plane surface, it is manifest that the direction of 

 the force in question will be a line making with the horizon 

 an angle of 40° or 50°, or in other words its direction in the 

 first instant after projection will be that angle with the plane 

 of the horizon which is the complement of the angle of in- 

 clination. Therefore, as this force acts at an angle of 40° or 

 50° with the horizon, it is an upward force. The same pro- 

 cess will be gone through in the second instant, and so on 

 until the velocity of projection is spent ; and then the up- 

 ward impulse, depending for its existence on the continuance 

 of the projectile force, will also cease. Hence this force is, as 

 I said, superior for a time to gravitation, 



9. I said that we may estimate the total efficient force 

 which acts on the plane side in a direction perpendicular to 

 that side (8.). Should this be objected to, we may ascertain 

 its real direction. It cannot be forgotten that the pressure on 

 the plane surface is much greater than on the curved ; and 

 the particles of air are acting on it in every direction, but cer- 

 tainly not with equal force in every direction. For the par- 

 ticles that impinge on the plane surface with the greatest effect, 

 are those that act on it at an angle of something about 54° 

 with the direction of its motion. My reason for this assertion 

 is, because it is proved (Vince's Fluxions, Max. and Min. 

 p. 24, edition 5.) that the greatest effect produced by the wind 

 on the sails of a windmill is when the wind acts on them at an 

 angle of 54° 44'. Since it is the same thing whether the body 

 moves against the fluid or the fluid against the body (see 

 Principles of Hydrostatics), it follows, that when the body is 

 in motion, those particles which impinge on it at the aforesaid 

 angle with the direction of its motion, resist it more powerfully 

 than any other particles acting on the same side, and conse- 

 quently have the same tendency to make it deviate from the 

 line of projection as the causes already explained. 



10. I have now, as briefly as I could consistently with per- 



