THE ROYAL ARTILLERY INSTITUTION. 
53 
quadratically. They correspond with what the French call the "moyen ecart” 
and may be represented by h and h 3 respectively,^ thus 
h 
h 
7 5 x 2 
vertical error (determined quadratically) = 
mean 
( 5 ) 
( 6 ) 
20. Now having these mean errors, taken from a sufficient number of shots 
upon a normal target, we have all that is necessary for determining the 
accuracy of the gun; and moreover they possess the great advantage over the 
single absolute distance plan, that they shew, of themselves, the tendency of 
the gun to error in the two directions respectively. It remains to point out 
how the probability of hitting the centre of impact (which we have stated to 
be the correct definition of the accuracy of the gun) may be deduced from 
them. 
21. In order to simplify the expressions used in the following somewhat 
complicated formulae, we will make 
P . 
1 
1 ks/% 
p and q being called the “ measures of precision ” in each direction. 
Assuming that there are no abnormal causes of error tending to produce 
special variations, the laws of probabilities give us the following theorem 
applicable to this case. 
Taking first the horizontal errors; let us call an error to the right+, and 
an error to the left —. 
Then the probability of a shot striking at a horizontal distance = + x 
(see Fig. 4), to the right of the centre line (or to speak more correctly 
between the distances x and x + dx) 3 will be 
== -^= e-v^dx ......( 10 ) 
V 7T 
And, similarly, for the vertical errors; let the errors above the centre be 
called +, and those below —. 
* If the number of shots is not very large, it has been shewn by Captain Noble that it will bo 
more correct to divide each of the mean errors by n — 1. 
If a very large number of rounds are taken, it is found that 
= 1-25 
millMUMIIMIIMUtllil 
(?) 
[VOL. V.] 
