Curvature and refraction
Over a long sight the earth curves away from the line of sight and the atmosphere bends the line back down. The net effect makes rod readings too high by
c&r = 0.0206 F² feet, with F in thousands of feet, or 0.0675 K² metres with K in kilometres.
At 1,000 ft that is 0.021 ft. Curvature alone is 0.0239 F²; refraction takes back about a seventh of it. Subtract c&r from the reading, or, better, balance your sights and never compute it.
Three-wire leveling
Read all three crosshairs. Two checks come free: upper − middle should equal middle − lower, and the stadia intercept (upper − lower) × 100 is the sight distance, which is how you know the sights are balanced. The reading you use is the mean of the three.
Testing the level: the peg test
Set up midway between two points and take the difference. With equal sights that difference is true, whatever the instrument's collimation. Then set up near one of the points and take the difference again. Any disagreement is the collimation error over that distance, and the instrument can be adjusted to remove it.
When you cannot balance: reciprocal leveling
At a river too wide to balance, level from one bank to the other, then move the instrument across and level back. The long-sight errors, curvature, refraction, and collimation, enter the two determinations with opposite effect, so averaging the two elevation differences cancels them.