THE EOYAL AETILLEEY INSTITUTION. 
57 
Similarly, taking the errors in a vertical direction, we shall find the 
probability of a shot falling in the horizontal band comprised between the 
lines a and b 
(19) 
And, since the probability of two events concurring is equal to the product 
of the probabilities of each separately, we find that 
The probability of hitting the test target , and consequently the accueacy 
OF THE GUN, is 
_ ^f* e „ pV dx J'z e . lVdy .(30) 
the value of which for any given case may be easily found by tables 
constructed for the purpose. 
31. It only remains to explain how the size of the test target should be 
determined for different ranges. This would require some little care at the 
outset, but being once correctly fixed, all difficulty ends. The conditions 
necessary are twofold : first, that it shall be sufficiently small; and secondly, 
that its dimensions shall vary, for different ranges, according to what we may 
call the march of precision of the best guns; so that a gun of the most 
perfect kind we know may have an equal probability of hitting it at all 
ranges. 
Our ballistic knowledge is not sufficient at present to enable us to deter¬ 
mine this condition a priori , but it might easily be deduced from good 
records of the practice of the best guns, and a table might thus be con¬ 
structed giving the size of test target suited to different ranges of fire. This 
might further, if necessary, be easily corrected from time to time as further 
knowledge was gained.* 
32. This method of determining the accuracy of a gun gives a certain 
degree of preference to compactness of fire. If two guns firing at the same 
range, delivered their shot on the target in the manner represented by Figures 
2 and 3 respectively, both covering an equal area, but differing in the dis¬ 
persive form ; most artillerists would give the preference to Figure 2, in which 
the fire was most compact. The test target system will shew this advantage, 
as the probability of hitting a square target of definite size will be greater in 
the first case than in the second.f • 
33. I will now state the practical rule by which the “test target” 
method of determining the accuracy may be applied; having given, the fall 
* According to the information I at present have, I believe that the side in yards, of a test 
target, which will take one-tenth of the shot of the best guns, will be about = 1 -, where r = 
110,000 
range in yards. 
f The difference will increase with the siz^of target Used at any given range. The disadvantage 
of want of compactness of fird is also shewn by the " figure of merit s ’ system* but in a much 
exaggerated degree. 
