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

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)

The relationship being tested is how instrument height relates to a known point and the backsight in differential leveling. When you set up the instrument, you read a backsight on a point with a known elevation. That backsight reading represents how far the instrument is above that point. To get the Height of Instrument, you add that backsight to the known elevation of the reference point: HI = Elevation + BS. This makes sense because if the reference point is at elevation E and the backsight reads BS, the instrument is at height E + BS. Once HI is known, the elevation of any point you measure with fore sights is found by Elevation = HI - FS, which is why the other sign patterns aren’t used for HI. Using HI = Elevation - BS would imply subtracting the backsight would increase HI improperly, and Elevation = FS - HI reverses the relationship entirely. So the correct expression for Height of Instrument is HI = Elevation + BS.

The relationship being tested is how instrument height relates to a known point and the backsight in differential leveling. When you set up the instrument, you read a backsight on a point with a known elevation. That backsight reading represents how far the instrument is above that point. To get the Height of Instrument, you add that backsight to the known elevation of the reference point: HI = Elevation + BS. This makes sense because if the reference point is at elevation E and the backsight reads BS, the instrument is at height E + BS.

Once HI is known, the elevation of any point you measure with fore sights is found by Elevation = HI - FS, which is why the other sign patterns aren’t used for HI. Using HI = Elevation - BS would imply subtracting the backsight would increase HI improperly, and Elevation = FS - HI reverses the relationship entirely. So the correct expression for Height of Instrument is HI = Elevation + BS.