540 MILITARY PROJECTILES. 



inconsistency between hypothesis and observation was 

 for a long time, a great perplexity to mathematicians and 

 gunners. No one could dispute the demonstration, and 

 it was still more difficult to deny the fact. It did indeed 

 occur to some that the resistance of the air might have 

 some influence upon the motion, while it was resolutely 

 denied by the most weighty authorities that so rare and 

 tenuous a substance could produce any sensible effect. 

 One writer endeavors to remove the difficulty by suppos- 

 ing that a ball projected with great velocity, describes in 

 the first part of its track, a straight line from the end of 

 which the parabolic track commenced. During the 

 straight part of its track the projectile force only could 

 operate of course. This imagined straight line, the dis- 

 coverer called the line of the impulse of the fire. 



Some of Sir Isaac Newton's calculations on the sub- 

 ject of the resistance of fluids led him to suppose that 

 the influence of the air was the true cause of the devia- 

 tions from the parabolic path. This has been since as- 

 certained to be the case. To determine, however, the 

 law by which this influence acts, and the degree of de- 

 viation which it will in each particular case produce, 

 is one of the most difficult problems in mathematics. 

 The resistance varies with the velocity, increasing very 

 rapidly as the velocity increases. Now this velocity is 

 very irregularly varied, changing at every instant, and 

 changing in a very different law, according to the angle 

 of elevation at which it is thrown. 



Many experiments have been instituted to determine 

 many points of practical importance in regard to the con- 

 struction and use of ordnance. The size and proportion 

 of the parts of the several species ; the quantity of pow- 

 der which produces a maximum effect ; the angle of 

 elevation at which the range is greatest, and the propor- 

 tion which the velocity of the ball bears to the quantity 

 of powder, the length of the piece, and the nature of 

 the ball. Various instruments have been contrived for 

 the purpose of facilitating these inquiries, which it is 

 unnecessary particularly to describe. 



Neither mathematical calculation however, nor experi- 

 ment have been able to ascertain with any great precision 



