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LECTURE IV.

segments of the first line, the curve in which all their extremities are found,is a parabola. Now supposing the first line to be placed in the direction ofthe initial motion of a projectile, anti parallel vertical lines to be drawnthrough any points of it, proportional to the squares of the segments whichthey cut off, these lines will represent the effect of gravitation, during thetimes in which the same segments would have been described, by the motionof 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. l ; ig. 17, Iff)

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 willafterwards describe, during its free descent; and by placing rings at differentparts of the curve, \v r e may observe that it will pass through them all withoutstriking them.(Plate II. Fig . Iff)

In practical cases, on a large scale, where the velocity of a projectile isconsiderable, 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 thepath, including all the circumstances which may influence it, is attendedwith difficulties almost insuperable. It appears from Robins’s experiments,that the resistance of the air to an iron ball of 4 ~ inches in diameter, movingat the rate of 800 feet in a second, is equal to four times its weight, and thatwhere the velocity is much greater, the resistance increases far more rapidly.Rut what must very much diminish the probability of our deriving any greatpractical advantage from the theory of gunnery, is an observation, made alsoby Mr. Robins, that a ball’sometimes deviates three or four hundred yardslaterally, without any apparent reason; so 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 tothe ball in its passage through the piece, causing therefore a greater frictionfrom 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 insuch a manner that its axis coincides at first with the path of the ball, so thatthe same face of the ball is turned in succession every way. For the ordinary