THE FORCE OF
96
described by the shot, and the horizontal lines A H, C IC,DM, EF will be corresponding ordinates ; then from thevalue of these lines the nature of the curve may tie deduced,or traced mechanically ; and will be most applicable to thoseelevations where the initial velocity remains nearly the fame.If the ground at the points I, L, B, Q_ be such that the shotcan penetrate in the same direction with which it impinges,the holes being the tangents of the curves, the sub-tangentsand sub-normals Brat correspond with these points may belikewise known. Thus an equation to the curve may befound by the inverse method of tangents.
194. The curve thus found may be resolved into the simplemovements of which it is compounded, by knowing thetime that the (hot is pasting from the mouth of the pieceplaced succeffively in A, C, D, E, to the points I, B, L, Q_,where it touches the ground ; for this purpose, a commonpendulum or watch that marks very small divisions of timeas ~ or y of a second will answer. Place it near the menwho are stationed to observe the first grazes, and let them be-gin to reckon the instant they perceive the flash of the gun.Suppose that the (Fig. 24.) time of the shots flight fromA to I — a from C to L ar b, from D to B —d, and from Eto Q_~ f ; mark on the line A E, the times A B ~ a, ACr^,AD - d, AE — and make the ordinates BH, CI, D K,E L, equal to the spaces that the shot acted on by the im-pelling power has passed through in the corresponding times(193); AHIKL will then be the scale of spaces passedthrough in these times, from which may be deduced thescale of initial velocities; and again from this last, the scale ofmomentaneous resistances of the air to the motion of theshot.
Fig. XXV. Mark in the same manner on thedirectrix M V, the times MR=u, MT — si, MS ~d,MVr/ and erect the ordinates Rr, T t, S r, V a,each equal to the spaces that the shot has passed through*' by the power of gravity ( 193.); M rtsu will then be
the scale of velocities, and give the scale of momen-taneous resistances opposed by the air to the movement’ of gravitation.
195. If the law of the air’s resistance only be required,one of the following methods maybe used, and will giveresults more accurate than any of the former ones (186, 193*194.): the first consists in finding the scale of spaces that the
shot