Discussion
A surveyor started a longitudinal section leveling survey by taking starting bench mark of elevation 53.85 m. During the survey, he takes an observation of intermediate sight of 2.42 m with the staff held on another bench mark of 85.45 m. The sum of the back sights from the start to the point is 50.28 m and that of fore sight is 16.30 m. If the surveyor ends the survey operation on the second bench mark, the error of closure on the second bench mark, in m, is __________. (Rounded off to 2 decimal places)
Answer: B
The error of closure is 0.04 m.
The reduced level of a point is the starting level plus all back sights minus all fore sights, with the reading on the point itself counted as its final sight:
\[ \begin{aligned} RL &= 53.85 + 50.28 - 16.30 - 2.42 \\ &= 85.41\ \text{m} \end{aligned} \]
The bench mark's known elevation is 85.45 m, so the survey closes with an error of \(85.41 - 85.45 = -0.04\) m, a closing error of 0.04 m (the levels run 0.04 m low).
Leaving out the 2.42 m sight would give a nonsensical error of over 2 m, and 0.02, 0.06 and 0.08 m do not follow from the given sums.
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