40 LECTURE IV. 



segments of the fiist line, the curve in wliich all their extremities arc found, 

 is a parabola. ' Now supposing the first line to be placed in the direction of 

 the initial motion of a projectile, and parallel vertical lines to be drawn 

 through any points of it, proportional to the squares of the segments which 

 they cut off, these lines will represent the eft'ect of gravitation, during the 

 times in which the same segments would have been described, by the motion 

 of projection alone; consequently the projectile will always be found at the ex- 

 tremity of the vertical line corresponding to the time elapsed, and will there- 

 fore describe a parabola. (Plate II. Fig. 17, ^9-) 



It is easy to show by experiment, that the path of a projectile is a parabola : 

 if we only let a ball descend from a certain point, along a groove, so as to ac- 

 quire a known velocity, we may trace on a board the parabola which it will 

 afterwards describe, during its free descent ; and by placing rings at different 

 parts of the curve, we 'may observe that it will pass through them all without 

 striking them. (Plate II. Fig. 19-) 



In practical cases, on a large scale, wliere the velocity of a projectile is 

 considerable, the resistance of the atmosphere, is so great as to render the Ga- 

 lilean propositions of little or no use ; and a complete determination of the 

 path, mcluding all the circumstances which may influence it, is attended 

 with difficulties almost insuperable. It appears from Robins's experiments, 

 that the resistance of the air to an iron ball of 4-4: inches in diameter, moving 

 at the rate of 800 feet in a secqnd, is equal to four times its weight, and that 

 where the velocity is much greater, the resistance increases far more rapidly. 

 I3ut what must very much diminish the probability of our deriving any great 

 practical advantage from the theory of gunnery, is an observation, made also 

 by J^Ir. Robins, that a ball sometimes deviates three or four hundred yards 

 laterally, without any apparent reason; bo that we cannot be absolutely cer- 

 tain to come within this distance of our mark in any direction. The circum- 

 stance is probably owing to an accidental rotatory motion communicated to 

 the ball in its passage through the piece, causing therefore a greater friction 

 from the air on one side than on the other; and it may in some measure be re- 

 medied by employing a rifle barrel, which determines the rotation of the ball in 

 such a manner that its axis coincides at first with the path of the ball, so that 

 the same face of tlie ball is turned in succession every way. For the ordinary 



