The calculation of the height of the instrument (HI) in surveying is an important part of leveling. The HI is determined by the formula:
HI = RL of benchmark + back sight
Where:
- RL of benchmark: This is the reduced level of a known reference point, called the benchmark. It serves as the starting elevation data for the survey.
- Back sight (BS): This is the reading taken on a leveling rod held on the benchmark. It helps establish the height of the instrument above the benchmark.
Given the options:
- back sight + fore sight: This combination is incorrect as it involves observations to calculate the reduced level at a new point, not the HI.
- RL of benchmark + fore sight: This is incorrect because the fore sight is used to determine the reduced level of a new survey point, not to calculate HI.
- RL of benchmark + intermediate sight: This is not correct as the intermediate sight is for calculating reduced levels at points between backsight and fore sight on the leveling route.
- RL of benchmark + back sight: This is the correct relationship used to compute the height of the instrument above the benchmark.
Hence, the correct answer is RL of benchmark + back sight.