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CONCENTRATING THE FIRE OF A GROUP OF GUNS, ETC. 
to the angles Oj A L O, and 0 3 A 3 0 must be made to the training of 
A 1 and A 3 respectively. 
Fig. 1. 
Since A x 0 1} A 2 0, A 3 0 3 are parallel the angle 0 A x 0 X = A 2 0 A 1 
and 0 A 3 0 3 = Ao 0 A 3 
sin A* 0 A. A, O 
sin A 1 Ao 0 A 2 A x 
. •. sin Ao 0 Aj_ = x l 1 - ? - sin A a A 3 0; 
A 2 A x 
similarly sin A 2 0 A 3 = ^ ^ sin A 3 A 2 0. 
Ag A 3 
Now Ao A 3 = A 3 Aj, let this distance in yards be represented by d; 
0 — A 3 0 — Ao 0 very approximately, since they will always be 
large in proportion to d, let them be represented in yards by R ; 
sin A x A 2 0 = sin A 3 Ao 0 since A 3 A 2 0 = 180°— A x A 2 0; 
and A 3 A 2 0 = A 2 A s B. 
Hence sin 0 A x O x = sin 0 A 3 0 3 = ^ sin A x A 2 B. 
Thus we find that the correction will be the same in amount for both 
