58 A CALCULATION OF PROBABILITY OF FIRE. 
and of a 40 per cent., the percentage of hits would be 30 per cent. 
But when firing under ordinary conditions and at a moving target other 
errors besides those inherent in the gun itself come into play. M and 
N would become larger in value than the length and breadth of the 
50 per cent. zones. 
We have now to calculate the dimensions of the 50 per cent. zones 
or the probable longitudinal and lateral dispersion of shots fired under 
ordinary service conditions and at a moving objective. 
If two or three causes affect the accuracy of the shooting of a gun 
each one of which taken by itself would produce a certain probable 
error, the total error when all are acting together is found by the 
expression 
IHN G EI GPG ERIS, so5o000060000000000006005000000005% (3). 
Example: if the probable error of a gun fired as for range and 
accuracy test at a certain range is 10 yds., and if a particular gun layer 
lays with a certain normal error, which at that range would produce a 
variation of 20 yds., the resultant error from these two causes would be 
E=NV 10? +20?=22°4, 
and as this error # may have a positive or negative value, 
M or the length of the longitudinal dispersion will equal 
2 N10? + 20°, 
To apply this to the case under consideration the causes leading to 
error in range will be 
(1) the inherent error in the gun AT; 
(2) the personal error of the number giving, or reading, the 
elevation given AP; 
(8) The error in taking the range AY. 
Then 
I 3) NSB le NPE AOE son poveanoppbboodooseeSonskeenbe (4). 
AT is simply the length of the 50 per cent. length zone. 
AP can be tested for each individual, or an average can be struck. 
AX is rather more difficult to evaluate, it is compounded of two 
errors. 
One, the error in measuring the range which we will call dz, and 
the other the prediction error, or the error in estimating the distance 
the objective will have advanced or retired during the “time of 
firmg”; dy. 
dx will be a percentage of the range and may be written dX where 
X is the range. This is only true within certain limits; for instance, 
with the Mark 7D D.R.F. if the error for short ranges is 1 per cent. or 
10 yds. per 1000 at 10000 yds. the error will be much greater than 
100 yds. 
