To find out the collimation error of the instrument
To find the elevation of the benchmark
To find the elevation of the point over which the staff is held during the backsight
Show Solution
The Correct Option isA
Solution and Explanation
Step 1: Set the levelling scene using the rise-and-fall / HI method.
Picture a level set up between a benchmark of known elevation and several points whose elevations are unknown. The staff is first held on the benchmark and a reading is taken through the telescope; this reading is called the backsight.
Step 2: Work out what that single reading gives you.
Since the benchmark's elevation is already known, say $RL_{BM}$, and the backsight reading is $BS$, adding them gives $HI = RL_{BM} + BS$. This $HI$ is nothing but the reduced level of the horizontal line of sight passing through the telescope at that instrument position, it is not the elevation of the ground, it is the elevation of the sightline itself.
Step 3: Show why this is essential.
Every other staff reading taken from this same instrument position, whether an intersight on an intermediate point or the final foresight before shifting the instrument, is subtracted from $HI$ to get that point's ground elevation: $RL_{point} = HI - \text{reading}$. Without first fixing $HI$ through the backsight, none of the other elevations in that instrument setup could be worked out.
Step 4: Dismiss the incorrect choices.
A backsight alone cannot reveal the instrument's collimation error, that needs a reciprocal or two peg test comparing readings at different distances. It does not "find" the benchmark elevation either, that value must already be known beforehand for the method to work at all. And while the staff is indeed held over a known point, the outcome of the reading is the sightline elevation, not simply the elevation of the point below the staff, which is already given data.
\[ \boxed{\text{To ascertain the elevation of line of sight}} \]
