How good is good enough
The FGCS 1984 standards set the allowable section misclosure in millimetres as a coefficient times the square root of the section length in kilometres:
- First order, class I: 3 √K
- First order, class II: 4 √K
- Second order, class I: 6 √K
- Second order, class II: 8 √K
- Third order: 12 √K
Square root, never the length itself. A 25 km second-order class II section may misclose by 8 × 5 = 40 mm.
The same idea governs traverse azimuth closure between checkpoints, in arc-seconds per √N stations: 1.7 (first), 3.0 (second I), 4.5 (second II), 10 (third I), 12 (third II).
Why the bubble matters
A level vial is rated in arc-seconds per 2 mm division. One division off centre tilts the line of sight by that many seconds, and the error on the rod is the sight distance times the angle in radians. One arc-second is 4.848 × 10⁻⁶ rad, so a 20″ vial off by one division at 100 m puts the reading out by about 10 mm. Sensitive vials and short sights are how precise leveling keeps this small.
Precise leveling with two rods
Rods leapfrog: the rod that was the foresight becomes the next backsight. Run each section with an even number of setups so the same rod is on both the opening and closing benchmarks. Any index error in that rod's zero then appears in the first backsight and the last foresight and cancels.