FIRED GUN-POWDER.

95

tical direction against the same block placed at an equal dis-tance, the (hot each time penetrated to the depth of 12inches.

190. Since the initial velocity of (hot of small diameter,is the same whatever be the elevation of the gun, it followsthat the increase of the elastic fluid produced when the pieceis at the highest elevation, is in the increase of resistance arisingfrom the elevation, in the same ratio as these two forces are,when the piece is fired horizontally.

191. Let AE be a horizontal line making with the linesAF, AG, AH, AK the same (Fig. 22) angles as theguns were fired under in the preceding experiments: set off thelengths AB, AC, AD, AE of the corresponding ranges,and erect the perpendiculars B F, C K, D G, E H ; the linesA F, A G, A H, A K, will express the spaces that the shotpassed through by the impulsion of the elastic fluid, and theperpendiculars B F, C K, D G, EH the spaces pasted throughby the power of gravity. Thus it will be easy to lay down thecurve that the (hot described in its flight, either geometricallyor by Dulac’s instrument.

192. A line drawn through the points A, F, G, H, K,will be a curved line of projections, and will (hew the pointwhere the (hot will strike the horizontal line A E when theelevation is less than 45 0 : on the contrary, if the point ofthe line A E which it ought to strike be given, the properdegree of elevation may be found without tracing the curvedescribed by the (hot in its flight. If the guns in June,1764 had been elevated above 45 0 , in order to know thecorresponding length A N of the ranges, the curve A F G HK M L of projections would have been complete.

193. This method of finding the curve described by pro-jectiles, may be used when the initial velocity remains thefame, though the elevation be altered; but when both thevelocities and elevations are different, the following me-thod may be adopted. (Fig. 23) Chuse a piece of groundon which the guns may be placed at the different heightsA, C, D ; fire some rounds from A, charging and layingthe piece always in the same manner; which in the presentcase will be supposed to be horizontally, and mark at eachdischarge the first graze of the (hot: then fire from C, D, Ewith exactly the same direction, elevation, and charge, andmark the first grazes L, B, Q. Erect the perpendicularsI H, L K, B M, Q_F which will be the abscissas of the curve

described