G U N N E II Y 301 press against A and to sustain the weight by gripping the piece B (fig. 13) of the weight. In this position the keeper H is at a short distance from the poles of the electromagnet. Directly the current is allowed to circulate, the keeper is attracted down to the magnet, the spring G, G is pulled away, a small spring L presses on the arm CD, the jaw AC flies open and the weight is released. The two cylinders A, A (fig. 12) form part of the circuit of a secondary induc tion coil. The screens are similar to those employed for the Bash- forth chronograph ; they are traversed successively by the shot, which momentarily interrupts the primary current, and thus causes an induced current to pass through the cylinders A, A. As these,
> FIG. 13. Weight. FIG. 14. Holder. however, are not in electrical connexion, the current has to pass across through the brass wire of the weight, which is in the act of falling. The cylinders are covered with smoked paper, and the passages of the spark in and out leave minute spots showing the exact position of the weight at the moment : any number of screens may be used, and a duplicate record is obtained in one experiment of the space fallen through by the weight, while the shot is travers ing each interval between the screens. As before, a simple calcu lation connects time and space, and an ingenious scale enables the experimenter to read off the velocities whatever be the distance be tween the screens. In all these instruments slight errors exist, arising from mechanical imperfection, or from irregularity in the electric currents ; still, the accuracy arrived at is sufficient for practical purposes, as is well shown by the following table : TABLE II. Velocities of Martini- Henry Bullets fired with two different Charges, observed with several Instruments, Le Boulengd. Watkin. Instrument Instrument forili. Right Left A. B. Cylinder. Cylinder. 1167 1163 1163 1155 1157 1141 1140 1143 1137 1136 1140 1138 1138 1129 1132 1136 1133 1141 1138 1139 1147 1145 1142 1140 1140 Means of ) .. , . ,, 5 rounds! 1146 1144 1146 1140 1141 1272 1275 1269 1259 1259 1268 1264 1269 1267 1267 1270 1271 1277 1270 1268 1277 1279 1287 1272 1272 1285 1287 1290 1287 1285 1290 1294 1280 1284 1284 1264 1267 1263 1264 1264 1287 1289 1291 1285 1284 Means of) 1077 8 rounds L " 1278 1275 1274 1273 These instruments enable the experimenter to ascertain the velocity of a projectile up to considerable distances from the gun. With rifled ordnance no difficulty is found iu hitting screens of moderate size at a range of 2000 yards; and, practically, the loss of velocity due to the resistance of the air can be determined for all ranges and all velocities. It might be supposed that, having the means of acquiring this knowledge, the artillerist would find little difficulty in solving the grand problem of his art, which may be thus briefly ^stated : Given a projectile of known weight and dimensions, starting with a known velocity at a known angle of elevation iu a calm atmosphere of approximately known density ; to find its range and time of flight, its velocity, direction, and position at any moment, or, in other words, to construct its trajectory. This state of perfection has, however, not yet been reached ; mathematics has hitherto proved unable to furnish complete formulae satisfy ing the conditions. The resistance of the air to slow move ments of, say, 10 feet per second seems to vary with the first power of the velocity. Above this the ratio increases, and, as in the case of the wind, is usually reckoned to vary with the square of the velocity ; beyond this it increases still farther, till at 1200 feet per second the resistance is found to vary as the cube of the velocity. The ratio of increase after this point is passed is supposed to diminish again; but thoroughly satisfactory data for its determination do not exist. From this it would appear that, as the motion of the shot increases in rapidity, the air finds continually greater difficulty in filling up the space left by the advanc ing projectile, but that, when once a point is reached where the vacuum in rear is complete, further increase of speed only encounters additional difficulty in displacing the air in front. The difficulty of meeting the conditions by mathematical formulae is very great, since the velocity of the projectile changes continually, and moreover is resisted by air continually varying in density as the shot rises and falls again. It is evident that the greater the weight of a shot in proportion to the column cf air displaced by it, i.e., to the square of its diameter, the less effect will the resist ance of the atmosphere have upon its motion ; thus very heavy projectiles moving with very low velocities will be but little retarded by this cause. It is desirable, therefore, before proceeding to explain what has been done towards Trajcc the complete solution of the problem above stated, to estab- tor y lish the limit, and investigate the trajectory when the resist- vacuo - ance of the air is neglected. Fig. 15. Let v = muzzle velocity of projectile ; e = angle of elevation ; = time of flight. Let the projectile start with velocity v from the point (fig. 15) in the direction OM, so that MOX is the angle of elevation. Let OM be the distance which would be traversed in a period of time t, if gravity did not act. Draw ON" vertically downwards, equal to the distance through which the shot would fall in time t under the action of gravity only. Complete the parallelogram OMPN". Then P will be the position of the projectile at the end of the time t. We have then OM = rt, and ON = MP = 2 . Therefor OM 8 - MP. g Since OM 2 bears a constant ratio to MP, the trajectory is a para bola, having its axis vertical, and OM for a tangent. Again, the horizontal velocity = v cos e, and remains uniform; the initial vertical velocity = v sin e, and is acted against by gravity. Then x = OQ = vt cos e
y=TQ = vt sin e-P.
