MILITARY PROJECTILES. 539 



which the course of the projectile was an arc of very 

 considerable curvature, they were not in sufficiently con- 

 stant and universal use to attract much attention to the 

 nature of the motions to whicli they gave rise. Indeed, 

 had this nature been well ascertained, the difficulty of 

 accurately aiming machines of such construction, would 

 have prevented the engineers of those days from deriving 

 much practical benefit from the knowledge. In later 

 days, however, when trains of artillery of great magni- 

 tude and variety, have become an essential part of the 

 retinue of every army, and when the management of 

 their operations have become one of the greatest objects 

 of attention, as a means of attack and defence, at every 

 battle, and at every siege, military men and military 

 governments have made great efforts to discover the true 

 theory of the motions in question, taking into considera- 

 tion the resistance of the air, which we neglected in the 

 view of this subject, presented at the commencement of 

 this tract. Courses of experiments, the most complete 

 and the most accurate, have been made at great expense, 

 especially under the direction of the governments of 

 France and England. And the attention of the greatest 

 mathematicians and mechanical philosophers, has been 

 devoted to the problem which this subject presents. The 

 result, however, has but partially rewarded these efforts. 

 There are so many circumstances varying by complicated 

 laws, affecting the phenomenon in question, that but lit- 

 tle progress has been made, and after all the experiments 

 and all the mathematics, a very large part of the iron 

 and the lead is projected in vain. Galileo was one of 

 the first who made any progress in examining the sub- 

 ject. He discovered from the nature of the two elements 

 of the nature of a projectile, viz. the projectile force, and 

 the force of gravity, that the course described by it must 

 be a parabola, as shown already in this tract. 



On instituting experiments, however, it was soon found 

 that the fact differed widely from theory. The place 

 upon which a ball fell after its discharge from a gun, es- 

 pecially where the velocity was great, was found to be 

 very different from what it would have been, if the laws 

 of the parabola had governed its movements. And this 



