THE ROYAL ARTILLERY INSTITUTION. 
399 
PROBABLE RECTANGLES. 
BY 
CAPTAIN” W. H. NOBLE, R.A. 
This method of comparing the shooting of different guns was pro¬ 
posed by Captain A. Noble, F.R.S., late R.A. It is fully described 
in the “ Occasional Papers of the Royal Artillery Institution” 
Vol. I.p;173. 
The “ probable rectangle ” represents an area on the horizontal 
plane, within which there is an even chance of any one shot falling; 
that is to say, the area would probably contain half the number of 
shots fired. The smaller the rectangle, therefore, the greater the 
accuracy of the shooting. The length of the probable rectangle 
depends upon the value of the “ mean difference of range ;” the 
breadth upon that of the “ mean reduced deflection,” or— 
r ,, sum of differences of range from mean range , , 
Length =--------— x constant. 
one Less than the number ot shots 
Breadth = 
sum of differences of deflection from mean deflection 
one less than the number of shots 
X constant. 
The mean difference of range* and mean difference of deflection*— 
or mean reduced deflection, as it is usually called—are given in all 
abstracts of practice; and a table has been computed to facilitate the 
calculation of the corresponding dimensions of-the rectangle. It com¬ 
prises values from 0 to 100, and is calculated to two places of decimals. 
For example, the following, taken from p. 22 of the Report of the 
Special Committee on Field Artillery Equipment for India, gives an 
abstract of the shooting of the 9-pr. rifled M.L. gun with shell of 
9 lbs. and charge of 1J lb.:—- 
N umber 
of 
shots. 
Elevation. j^ge.' 
Mean 
difference 
of 
range. 
Mean 
reduced 
deflection. 
Length and breadth of 
coi-responding probable 
rectangle direct from 
table. 
Length. 
Breadth. 
yds. 
yds. 
yds. 
yds. 
yds. 
10 
1 i 703 
15-0 
0-4 
46-68 
1-05 
10 
2 1176 
14-2 
0-5 
41-67 
1-58 
10 
3 | 1552 
| 
17*1 
0-8 
50-11 
2-37 
* Sometimes called mean error of range and mean error of deflection. 
