THE ROYAL ARTILLERY INSTITUTION. 
49 
Eig. 2 . 
9. The first thing to determine is the position of the central point. 
This is not directly shewn by the shooting; indeed, it is quite possible that 
it may not exactly coincide with any one of the shots. It must consequently 
be found by calculation, and the laws of probabilities teach us that it should 
be in that position where the sum of the squares of the distances from it to 
the various shots , will he a minimum ; and this is known to be the property 
of the centre of gravity of all the shots, which is easily found by well known 
rules. The point thus found is then, most probably* the true centre where 
the gun, if it had no error , would deliver all its shot, and is therefore the 
point at which it may be said to be aimed. It is a very important element 
in all calculations of accuracy, and I shall call it the centre of impact, or 
point of aim. 
10. Having determined this point, let us now endeavour to form some 
idea of the accuracy of the gun. 
Perhaps the most obvious mode of doing this, would be to adopt a plan 
often used in comparing the accuracy of small arms, i.e. to measure the 
linear distance of each shot from the central point (or what is called its 
absolute error) j to add the whole together, and to divide by their number. 
The quotient will give a quantity which is popularly called the “figure of 
merit,” or which may be more definitely termed the mean absolute error . 
This quantity will undoubtedly give some idea of the accuracy of the gun, 
for when we find the “ figure of merit 99 to be less, we may rightly infer the 
accuracy to be greater, and vice versa . 
11. But suppose we are engaged on a problem which requires us to go 
farther, and to define how much better one gun is than another. We have 
no ground whatever for assuming the degree of accuracy to be proportional 
(inversely) to the mean absolute error. It may vary, for aught we know, as 
the square, or the cube, or the square root, or in no definite proportion at all. 
We can only say that a gun that makes a small figure of merit is a better 
gun than one which makes a large one; how much better, we have no right 
to pronounce without further reasoning. 
1£. To guide us in this reasoning, we must enquire, what do we mean 
by the accuracy of a gun ? How do we define the term ? To be enabled to 
* This probability being greater, in proportion as the central point is deduced from a larger 
number of rounds. 
