50 
MINUTES OE PROCEEDINGS OE 
answer this question, we must propose another. What is the object of 
accuracy ? What use or duty of a gun is accuracy intended to promote ? 
To this there can be but one answer. Clearly the duty of a gun is to hit 
the object aimed at; and that gun will be most accurate that best performs 
this duty. And hence the degree of accuracy of a gun is evidently measured 
by the degree in which it promotes the efficiency of the gun in this respect. 
Por example, if two guns are each fired 100 rounds, at a small object, under 
precisely similar circumstances, and one gun hits it 10 times, and the other 
20 times, it is matter of common sense that the second gun will be twice as 
useful;—twice as well adapted to its duty;—in short, twice as accurate as 
the first one. 
Now the number of times a gun will hit its object, cateris paribus , in a 
large number of rounds, is equivalent to what mathematicians call the pro¬ 
bability of hitting it, and hence we arrive at the conclusion that by the 
accuracy of a gun is meant simply the probability of its hitting the object at 
which it is aimed. 
IB. It is however necessary to the correctness of the definition that the 
object should be of small size ; for of course if it were very large, a bad gun 
would be almost as likely to hit it as a good one. Any dimensions not 
exceeding the mean error of the best guns will answer the purpose in a 
practical point of view; but the principle becomes more correct when the 
object is reduced to an indefinitely small area , covering what we have called 
the centre of impact, or point of aim. 
And hence the probabilitij of hitting this small area , is the true scientific 
definition of the accuracy of the gun. 
14. If now we turn back to our attempt to determine the accuracy of a 
gun by its “ figure of merit,” or mean absolute error, we shall at once see 
that this quantity of itself tells us nothing to the purpose; for it only gives 
the degree of average proximity to the centre, which by no means corresponds 
with the probability of hitting it. It is indeed possible, in some cases, to 
deduce the probability from the mean absolute error ;* but as we shall here¬ 
after shew that there is a better method of finding this probability, of much 
more general application, we need not consider this “ figure of merit ” system 
further. It is merely a rough popular mode of estimation, devoid of any 
scientific basis, and its use is unjustifiable where any scientific accuracy is 
required. 
It is however worth while to add that this system fails, like that of the 
probable rectangles, to give any means of comparing the accuracy of guns 
tried at different ranges. Tor it is evident that a gun fired at a long range 
will give a much greater figure of merit, and therefore appear much more 
* If the error of the gun is equal in all directions, and l = mean absolute error, deduced quadratically, 
then the probability of hitting an indefinitely small circle of radius = dx, covering the centre of 
impact, will be ~-j 2 dx^, that is, the accuracy varies inversely as the square of thc^figure of merit. 
When the error is much greater in one direction than another, as is generally the case with 
ordnance, the method failsi 
