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MINUTES OF PEOCEEDINGS OF 
Having therefore these positions given, Captain Noble calculates the 
length and breadth of a certain rectangle, which may be supposed to be 
drawn on the ground where the shot have fallen, and denoting the space 
within which it is an eq.ual chance that any shot will strike, or, which is 
the same thing, into which half the shot will certainly fall in a very large 
number of rounds. This is called the “probable rectangle ” and it may be 
inferred from the paper (though it is not directly stated) that the author 
proposes to use the area of this rectangle, to express, inversely, the measure 
of the accuracy of the gun; so that a gun, which, fired at the same range 
and elevation, makes a probable rectangle of half the area, will be said to be 
twice as accurate, and so on. 
The process by winch the mathematical theory of probabilities is applied 
by Captain Noble to obtain this result, is singularly elegant, and the 
calculations necessary for carrying it out in actual practice are remarkably 
simple. Its general correctness is sufficiently proved by its acceptance and 
adoption by the highest authorities in artillery practice. 
3. The objections which have been raised against the system of probable 
rectangles may be reduced to four in number. 
In the first place it has been objected, that the determination of the 
accuracy by the area of the rectangle takes no account of the form in which 
the shot may be distributed. A gun, for example, which has a probable error 
in range of 40 yards, and in lateral deviation of 5 yards, will be pronounced 
equally accurate with one that has an error in range of 20 yards and in 
deviation of 10 yards, or one with an error in range of 200 and in deviation 
of 1 yard. Tor here all the areas are equal, although the shooting of the gun 
is of very different character in the three cases. 
Now if there were any clear and logical reason why different values should 
be assigned to errors in the two directions, and if the differences in these 
values could be stated in any definite way, a test of accuracy that did not 
include these variations would undoubtedly be defective. But unfortunately 
this is not the case. Tiie question has over and over again been submitted 
to the most eminent and experienced artillerists, and the differences of 
opinion are so wide as to shew that'it is hopeless to arrive at any definite 
conclusion in this way. Some will consider error in lateral deviation of 
more importance than in range; others, the contrary; and this is natural 
when we consider the variety of objects for which, and ways in which, 
artillery may be used. In firing, for example, at lines of men in front, 
error in lateral deviation is of less importance than in range; but in firing 
at columns, or at the same lines in flank, the contrary is the case. In firing 
from a fort at a ship approaching or leaving, error in range is of less moment 
than in deviation. In firing at her broadside on, the reverse is true. Tor 
these reasons, Captain Noble has preferred to adopt a definition of accuracy 
founded on a basis of mathematical exactitude, and free from all arbitrary or 
empirical distinctions ; and I shall hereafter shew that it is a legitimate con¬ 
sequence of this principle that the accuracy must be measured by the area 
of the rectangle only, independent of the form . 
4. Then secondly, it is urged that it would be more natural and more 
correct to judge of a gun by the position of its shots on a vertical than on a 
