MINUTES OF PROCEEDINGS OF 
44 
We now proceed to the method by which the range is ascertained with 
one finder only. 
The guns are dressed so as to be in line with some object to the right or 
left, and laid on the object aimed at. The angle-finder is then placed first 
on one gun and then on the other, and the short telescope is each time laid 
on the object to the flank, the long one on the object aimed at. We thus 
read the angles fi and 8 (Diagram I.) 
Let ft = 100 m + 
8 = 100 n + q. 
Then 
P + y = 72,00 — a, 
= 72,00 — (8 — /3), 
= 72,00 - {(100 n + q) - (100 m + p)}, 
— (72 + m — n) . 100 — (q —p). 
Hence we have the rule— 
“ Prom the gun-number of the gun nearest the square object, take the 
gun-number of the gun furthest from the square object, and subtract the 
difference from 100.” 
In working without a tape, we have to lay one angle-finder first on the 
breech and then on the muzzle of the other gun; then taking the triangle 
BCH as an isosceles triangle of very small apex, we calculate h , knowing 
the length of our gun, from the formula 
l = l 
sin 0 sin (y — <j>) * 
There is a special scale for solving this formula on the top of the roller. 
Its general principle is similar to that of the scale on the body of the roller. 
We have, in the course of the foregoing demonstration, made use of four 
assumptions, none of which are strictly true, and from each of which an 
error will consequently result. 
These are:— 
(1) That when in a triangle BAC, the apex A is directly opposite some 
point in base, and the angle a is small, the length of the side 
AB will be much the same, whether the triangle be isosceles or not. 
(2) That when a is small 
(3) That sin 2,00 = 10 sin 20. 
(4) That the angles read by finders are the true base angles of the triangle 
BAC. 
We will first examine the errors produced by each of these assumptions 
separately, and afterwards see how their combined result affects the range in 
practice. 
