THE ROYAL ARTILLERY INSTITUTION. 
183 
BCR as an isosceles triangle of very small apex, we calculate b, knowing 
the length of our gun, from the formula 
sin 6 sin (y — </>)* 
“ 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 forgoing 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 assump¬ 
tions separately, and afterwards see how their combined result affects 
the range in practice.” 
Captain Leacock, whose paper will be found in the “Proceedings 
of the Eoyal Artillery Institution” for November, 1870, then proceeds 
to show that, in the first case, the resulting error will have a 
maximum in excess of L31 yds., or defect of *44 yds. The second 
may give an error of - 43 yards. The third an error of 1 yard 
per 1000 of the range. The fourth will give a maximum error 
of 2 per 1,000 in excess. 
Captain Leacock then continues as follows:— 
“Let us now assume a case, and see what will be the difference 
between the sides of the triangle, as obtained by the calculating 
roller, and as obtained by the ordinary method. 
BC is the known 
angle in the above 
pages 175 and 176 
has for known base 
angle C. 
A 
base, A the vertical 
reasoning, but at 
the supposed triangle 
AB, and for vertical 
Let BC = 40 yds. 
ABC = 35,82 = 89°33' 
ACB = 35,46 = 88°39' 
71,28 178°12' 
ABC = 72 = 1°48' 
