ACCURACY OF The firing for accuracy, whether with artillery or small-arms, involves two entirely separate and distinct con ditions: (1) The determination of the personal skill of the individual using the weapon; (2) the determination of the qualities as regards accuracy of the weapon itself. The most com mon way of determining the relative accuracy of guns is to ascertain their mean errors in range and deflection for a given mean range, and compare them. It is not always possible tq test the practice of guns under precisely similar circumstances.
It is easier to determine, from the practice of the gun itself, a rectangle with which there would be an equal chance of any shot from the gun striking or not striking; or, if a given number of shpts were fired, the number which fall within the area. The accuracies of two guns would be in the inverse order of rectangles for the same range. The relative precision of small-arms is decided by various methods. To determine the centre of impact the piece should be fixed in a frame and be pointed at the centre of a target stationed at the required.dis tance, and fired a certain number of times, and the positions of the shot-holes, measured in vertical and horizontal directions from the lower left-hand corner of the target, are ar ranged in tabular form. The sum of all the vertical distances divided by the number of shots gives the height of the centre of impact above the origin. Similarly the sum of all the horizontal distances divided by the number of shots gives the horizontal distance from the origin to the centre of impact. The co-ordi nates of the centre of impact being known, the point itself is Icnown, and its distance from the centre of the target is called the absolute mean deviation. This is equal to the square-root of the sum of the squares of its vertical and horizontal distances from the centre of the tar get. To obtain the mean deviation it is neces sary to refer each shot-hole to the centre of impact as a new origin of co-ordinates, and this is done by taking the differences between each tabular distance and the distance of the centre of impact and adding them. The sum of all the distances thus obtained in one direc tion divided by the number of shots gives the mean deviation or figure of merit.
The mean horizontal error is found by add ing the horizontal distances by which the balls have missed the centre of the target and di viding this sum by the number of balls; this quotient indicates how much the average of the halls have missed horizontally the point aimed at. To get the absolute mean error there
arc two methods. The first is short and sim ple, and consists in calculating the hypothenuse of a right angle triangle, in which the other two sides are the mean horizontal and mean vertical errors. The second, which should be called the calculation of the mean of the abso lute errors, consists in measuring for each ball its absolute error, a distance from the point aimed at, and to take the mean of these ab solute errors by dividing their sum by the number of balls fired. This method is very long, since to have the absolute error of each ball it is necessary to square two numbers and then extract the square-root of these sums as the distance of the points struck have been measured upon the vertical and horizontal lines passing through the point aimed at. The re sults are not exactly the same; the mean of the absolute errors will be greater than the ab solute mean error.
The trajectory from the gun to the mean point of impact is called the mean trajectory, and the divergencies of the trajectories of par ticular shots from the mean trajectory have a multitude of independent causes, such as initial angular deviations; variations of the muzzle velocity; variations of the form and weight of the projectiles; variations in the angular posi tion of the gun when it is fired, and in its jump; variations in the force and direction of the wind; and variations in the drift due to rotation.
If the actual mean initial velocity is that for which the sights of the gun are graduated; if the range is exactly known and the sights are set accordingly; if the density of the air is standard; and if there is no wind and no mo tion of gun or target, then the mean point of impact will coincide with the point at which the line of sight is directed. These conditions, however, are never fulfilled, nor is it possible to compensate exactly for their non-fulfillment, and consequently the mean point of impact is never exactly at the centre of the target. To bring it as near as possible to that point is the object of the regulation of gun-fire. See GUN NERY.