THE ROYAL ARTILLERY INSTITUTION. 
175 
The surveyor calculates the required distance AC from the formula 
AC = AB 
sin B 
sin (180 °-A-B)' 
If B be a right angle, sin. B = 1, and then AC = sin. 
If B = 85° or 95° 
Sin B = -997 ; 
If B = 80° or 100° 
Sin B = -986. 
AB 
(180°-A-B) 
Therefore, should we treat sin B in every case as equal to unity, the 
actual distance A C would, when B = 85° or 95°, be less than the calculated 
AC by 3 yards per 1,000, and when B — 80° or 100° by 14 yards 
per 1,000. 
On the range-finder system sin B is always supposed equal to unity, 
consequently it is theoretically possible to have a mistake of 14 yards per 
1,000 ; but in practice such an error can only take place when the angles 
differ more than 5° from a right angle. 
The formula employed is then: 
A C or Range = —— ^ n - n - 0 --7- jk , 
sin (180 — A — B) 
consequently AB,A, and B have to be found. 
The process of using the range-finder consists in laying the main 
telescopes of the angle-finders upon a distant object, and the short 
telescopes upon each other, or, for convenience, on their cases, and also in 
measuring the distance between the axes of the main telescopes (or for 
convenience the distance between the trail handles, which are 17 inches 
nearer to each other than the axes, this being allowed for in the tape). 
"We thus get AB, A, and B, and the roller works out the formula: 
R = AB - AB 
an ° e sin (180° — A — B) ~~ sin ( A + B )' 
How does it work out this formula ? 
The first step is evidently to add A to B. 
This is done by bringing a mark on the addition-scale of the roller 
under a quantity = to A, and taking beyond this mark a number = B, 
over this number will be found the quantity (A + R). 
Having got (A -f B) we use the upper circumference of the roller to find 
AB 
—— 7 -t--. . The line F on the roller is marked with common numbers 
sm (A + B) 
10, 20, 30, 40, &c., but these numbers are at distances apart, represented 
by the differences of the logs of 20 and of 10, of the differences of logs 30 
and 20, of logs 40 and 30, &c. The line E has inscribed upon it, in a 
similar fashion, a scale corresponding to the logs of the sines. E and E 
then give us a contrivance for finding 
log AB — log sin (A 4 B) = log AC 
= log Range. 
