In differential leveling, which equation correctly expresses Height of Instrument (HI)?

• A. HI = Elevation + BS
• B. Elevation = HI - FS
• C. HI = Elevation - BS
• D. Elevation = FS - HI

Answer: (A)

In differential leveling the height of instrument (HI) is found by combining the known elevation of a reference point with the back sight reading taken on that point. The back sight (BS) tells you how high the instrument is above the benchmark, so adding BS to the benchmark elevation gives the instrument’s height above the datum: HI = Elevation + BS. This is the correct form because HI is the sum of the reference point’s elevation and how much higher the instrument is when aimed at that point.

Once HI is known, you can find the elevation of any new point by subtracting the fore sight (FS) reading from HI: Elevation = HI - FS. The other expressions would mix signs or refer to a different quantity, which doesn’t align with how HI is defined.