BY MERIT IN SHOOTING. 
257 
On the other hand, the determination of the probable circle in the case 
of common shell with percussion fuzes involves neither trouble, time, 
nor expense; and the length of its radius gives a clear and definite 
idea not only of the relative , but of the absolute value of the practice of 
a battery at the standard range. The number of shot which fall 
within the circle pegged out round the target (which may be called 
the “ standard circle ”) furnishes us no doubt with as reliable a 
standard of comparison of the relative efficacy of fire of different bat¬ 
teries as the probable circle; but it is far from being so convenient a 
standard. It is much easier to remember that 31 yds. is the radius of 
the probable circle at the standard range, than to remember that the 
battery put 7 shot out of 40 into the standard circle at the standard 
range. If the number of shot which fall within the standard circle be 
somewhat inferior to the probable circle as a means of estimating the 
relative practice of a battery, it is infinitely inferior as a means of esti¬ 
mating the absolute value of the practice of a battery. Nothing can be 
vaguer or more indefinite than to be told that a battery put 7 shots 
out of 40 into a circle of 34 yds/ radius at 2000 yds.: nothing can be 
more definite or precise than to be told that the radius of the probable 
circle is 31yds. at 2000 yds. In fact, if we know the radius of the 
probable circle at a given range, we know all that needs to be known 
about the practice at that range under ordinary circumstances. 
Further, knowing the radius of the probable circle at a given range, 
we can calculate the probability of throwing a shell into any other 
circle of given radius at that range—say the circle occupied by a gun- 
carriage in action. The probable circle, then, is in every way superior 
to the number of shell which fall within the standard circle as a means 
of classifying batteries by order of merit in shooting. 
Suppose, for the sake of example, 1800 yds. to be the standard range 
laid down for all 9-pr. batteries for competition common shell practice, 
and 20 yds. to be the radius of the standard circle pegged out on the 
ground round the target. Suppose, further, that 10 shell out of 50 
fired, or 20 per cent., fall within the circle. The radius of the 
probable circle is calculated from the formula 
JR = 
where r is the radius of the circle pegged out, and m is the per-centage 
of misses . 
In the present case, r— 20 yds., and m — T 8 o°o = “8. Then 
12 = 20 
„ = 20 
/-8010S /-; 
W 1-90309 / V r 
\/ r m 
30103 X 100,000 
90309 X 100,000 
30103 
90309 x 100,000 — 1 x 100,000 
-V 
30103 
9691 
„ = 20 x/3’12 = 35’2yds. 
Such is the plan I propose for a classification of batteries according 
to order of merit in shooting. It is simple; it is inexpensive ; it does 
not increase the time required for annual practice; it involves no 
trouble; and it does not demand one-thousandth part of the calcu- 
