THE ROYAL ARTILLERY INSTITUTION. 47 
horizontal target,, and that the figures obtained in the two cases would not 
be similar. But a little consideration will shew that the area in one case 
will be only a simple multiple of that in the other, (for the width is the 
same in both, and the length on the horizontal is only a simple multiple of 
that on the vertical); so that for two guns tried under similar circumstances, 
the ratios of the probable areas, in each case, will be the same; and therefore 
the relative accuracy of the two guns will come out precisely similar, whether 
the vertical or the horizontal target be used. 
5. A third objection is, that the probable rectangle does not give the 
same result as would be deduced from what is called the “ figure of merit 5> 
system, usually adopted in testing small arms. This is true, as the two systems 
are founded on different principles, and I shall hereafter endeavour to shew 
that Captain Noble's is the more correct and the preferable of the two. 
6. The fourth and last objection has more foundation than either of the 
others; it is, want of completeness. The system of probable rectangles was 
only intended by its author to apply to guns fired at about the same range, 
and with about the same angle of elevation; and hence it is not applicable 
(without further provisions than those hitherto given), to the comparison, 
with each other, of guns fired at different ranges, and different angles. 
Bor suppose two guns to be fired at very different ranges; it is evident 
that the spread of the fire, increasing largely with the range, will cause the 
more distant shot to fall more widely than the other, and consequently to 
form a much larger probable rectangle, though the gun may, when properly 
compared, prove to be equal or even superior in accuracy. 
Again, if two guns are fired at the same range, but with different elevations 
(as might be the case under different charges of powder), the one with the 
flatter trajectory would, although the accuracy might be equal, make a longer 
rectangle, and therefore one of larger area, than the other. An example will 
illustrate how this difficulty may arise. Suppose it were desired to test 
the comparative accuracy of three guns, by firing them at several different 
elevations (giving of course widely different ranges), and with projectiles of 
several different kinds ; and suppose it were found that while one of the guns 
would turn out the most accurate at one range, or with one projectile, 
another would be superior at another range, or with another projectile. 
Now, although the probable rectangles would give a fair test of the accuracy 
of the three guns at the same elevation, and the same (or about the same) 
range, the comparison could not, without new provisions, be carried further, 
and consequently no summary of the aggregate results of the whole series of 
trials could be made. 
I conceive it would not be difficult so to extend and amplify Captain 
Noble's method as to fit it for this case, but I propose now to offer some 
observations on the subject generally. 
7. Premising that the accuracy of a gun must always be tested by a large 
number of shots fired, with the axis in a fixed direction, the first question is> 
as to the position of the target on which these shots shall be received and 
recorded. 
