Differential Leveling (HI Method) and Loop Misclosure
The vertical control the traverse tiles never carried: differential leveling reduces backsight/foresight rod readings by the height-of-instrument method (HI = elev + BS, elev = HI - FS) to carry an elevation from a benchmark across a site, and checks a loop for misclosure. A BM at 100.00 ft with backsights 4.32 / 5.60 and foresights 2.15 / 3.40 closes at 104.37 ft, the sum(BS) - sum(FS) rise the field book is balanced against; close on a known 104.40 and the -0.03 ft misclosure is the pass/fail. Arithmetic reduction, no adjustment distribution. A computational aid; the project control governs.
Formula and source
HI_i = elev_(i-1) + BS_i; elev_i = HI_i - FS_i; final_elev = bm + sum(BS) - sum(FS); misclosure = final_elev - known_close.
The height-of-instrument differential-leveling reduction and the loop-misclosure check, as compiled in the standard surveying references (Ghilani/Wolf, Elementary Surveying), by name.
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