Subtract each range from this mean range thus obtained, and the results obtained will be the _errors in range_ for each shot. Add these errors together and divide their sum by the number of shots, and this will give the _mean error_ in range. Multiply this mean error by 1.69, and the product will be the depth in the direction of the range of a belt or zone which will probably contain one half the whole number of shots fired. In the same way the width of the probable zone, laterally, may be obtained, and also the height of the probable zone vertically. The origin of reference for the points of impact of the shots in the last two cases is generally taken at the lower left-hand corner of the target. The intersection of the first two zones will give a rectangle which will contain 25 per cent of all the shots. Similarly we may consider only the vertical and lateral errors, thus obtaining a vertical in lieu of a horizontal rectangle containing 25 per cent of all the shots. The 50 per cent "breadth column" should, in practice, generally be neglected, as most of the errors in shooting are always over and under, and not lateral, ones. The =Point of Mean Impact= is the intersection of the lines of _mean range_ and _mean lateral deviation_. The =Probable Rectangle= is one which contains 50 per cent of all the shots. To find the probable rectangle for any gun, multiply the _mean error in range_ by 2.637 for the side of the rectangle parallel to the range, and the _mean error in lateral deviation_ by 2.637 for the side perpendicular to the range. In all range tables for guns the 50-per-cent zones for length, breadth, and height should be given; and by means of them and the following table of probability factors the dimensions of zones of other percentage, and also the percentage due to certain dimensions at different ranges, can be obtained. PROBABILITY FACTORS. -----------+-------+-----------+-------+-----------+---------- Percentage.|Factor.|Percentage.|Factor.|Percentage.|Factor. -----------+-------+-----------+-------+-----------+---------- 1 | .02 | 25 | .47 | 60 | 1.25 3 | .06 | 30 | .57 | 70 | 1.54 5 | .09 | 35 | .67 | 80 | 1.9 10 | .18 | 40 | .78 | 90 | 2.44 15 | .28 | 45 | .89 | 95 | 2.91 20 | .38 | 50 | 1.00 | 100 |[infinity](say 4) -----------+-------+-----------+-------+-----------+---------- _First._--Opposite any given percentage, say 20, we find in the contiguous column a factor, .38. If we multiply the dimensions of the 50-per-cent zone, given in the range table, by this factor .38, we will obtain the corresponding dimension of the 20-per-cent zone.