TRACT 37.

OF GUNNERY.

267

branches Avand vc,of thepath, on the right andleft of the vertex, beingquite unequal and dis-similar; anil, instead ofbeing parabolic curves,they are rather different legs of an hyperbolic kind, havingdissimilar asymptotes, di and ro, the former inclined to thehorizontal line ef, and the latter perpendicular to it.

113. In the parabolic theory, the horizontal velocity ofthe shot, or its motion estimated in the horizontal direc-tion, is always constant and uniform ; because the action ofgravity, being the only force that constantly acts on it, isexerted in a direction perpendicular to the horizon. But itis quite different in the other case ; where, besides the forceof gravity acting always perpendicular to the horizon, thereis the resistance of the air, acting in the line of the ball’spath, or directly opposite to its motion, which both diminishesits ascent, or descent, and its horizontal motion ; on whichaccount, its horizontal velocity mu-t be continually diminish-ing, in the whole course of the ball’s motion, both in the as-cending and descending branch of its path. Hence too itwill happen that, in ascending, the ball’s motion will decreasevery fast, from these double causes, and it will not ascendnear so high as in the former case, or the vertex of the curvewill not be either so high, or so far distant in the horizontaldirection ; that is, AB and vb will both of them he muchsmaller than they would have been in the former case.Again, in the descending branch vc, after having passed thevertex v, the gravity accelerates its motion downwards, thehorizontal motion continuing still to decrease ; by whichmeans it happens, that the direction of the descent ap-proaches always nearer and nearer to the perpendicular di-rection, or towards a parallel with vb; till at length, the ho-rizontal motion being quite destroyed, the ball descends byits gravity quite perpendicularly downwards, with a velocitywhich, though continually increasing, can never exceed, nor