THE ROYAL ARTILLERY INSTITUTION. 
177 
To return to theory, let us suppose A ™ 81° and B— 98°, 
or, otherwise, as 81° = 32 (2J°) + 1° 
and 98° = 39 (21°) + i° 
A = 32 (2J°) + 1° 
B= 39 (21°) + J°, 
the range-finders or angle measurers only record the fact that— 
A = xm°) + 1 ° 
£ = y (H°) + i°; 
or, as they express it, 
A = 40 
B = 20 
.% A + B = 60. 
This 60 may mean 179°, or it may .mean 176J° (the other values need 
not be considered), neither angle-measurers nor roller tell the gunner 
which is the true value ; hut supposing his guns to be 19 yards apart, the 
rollers say, if the range is 1,083 yards, 60 means 179°; if the range is 310 
yards, 60 means 1761°. 
The artilleryman’s eye must enable him to judge which of the above 
two is the right range, unless, indeed, he has time to take a second obser¬ 
vation with a different base, in which case the true range is repeated, the 
false ones rejected. 
Theory of the Muzzle System- of Measuring Angles. 
The range can be obtained without using a tape ; the object of con¬ 
structing the instrument so as to allow of this being effected is three¬ 
fold :— 
(1st.) To obviate the damage caused by the loss of a tape. 
(2nd.) To be prepared for certain exceptional circumstances in which 
a tape could not be employed. 
(3rd and chiefly.) To allow of the length of the tape being corrected 
at any moment. 
If two guns are placed parallel to each other it is clear that one will 
always, at the same distance, subtend the same angle when viewed from 
the breech of the other, also that, when the distance between the guns 
exceeds ten times the length of a gun, the distance between the guns will 
vary inversely as the angle subtended. 
In finding a range without directly measuring a base, we first 
lay upon the breech and then upon the muzzle of the opposite 
gun, which is always practically parallel to that at which the angles 
are attained, and the roller subtracts the second angle from the first, 
or M from B. Then the mark at the top of the roller is set to the 
quantity B — M, and it will be found on trial that the tape mark 
shews the actual distance between the guns. 
The explanation of this is, that on the top of the roller is engraved a 
scale of sines, on line Gr, to determine the position of the gun-mark 
on H, of the mark, the distance between two 12-pr. A.B.L. guns 
was carefully measured, the angles at breech and muzzle found, and 
their difference, or B — M , found. Then the tape on the roller was 
brought under the distance, and opposite the quantity B — M the 
gun-mark was made. 
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