THE ROYAL ARTILLERY INSTITUTION. 
47 
This is greatest when ~ = 100. 
Making b = 40 yds. ~ = 100, we have 0 = *43678 yds. 
This error is too small to affect our elevation. 
With regard to the third error, we find by actual reference to the tables, 
that sin 200 = 9*99 sin 20; so that we should only have an error of 1 per 
1000 if our roller could be graduated with perfect accuracy. 
A 
Our fourth error is that of assuming that the angles read by the finders 
are the true base angles. This error is not at first sight very apparent, but 
may be seen by reference to the above exaggerated diagram. When the 
long telescopes are laid in the directions BA and CA , the red spots on the 
paper discs will be at X and Z, ABX and ACZ being right angles. Our 
short telescopes will consequently be laid in the directions BZ and CX, and 
we shall have read the angles ABZ and ACX, giving us respectively as 
errors CBZ and BCX, which we may call </> and 
Draw AM perpendicular to BC. Let BAM = ^ + 0, CAM = - — 0 t 
Then 
2?C£ = |-0S 
CBX = 5 + 0\ 
Kf 
