Levelling logic check: if the back sight (BS) reading exceeds the fore sight (FS), what does it imply about relative elevations? In a single set of readings taken with the same instrument setup, if BS > FS, select the correct interpretation of the forward point's elevation relative to the back point.

Introduction / Context:
In differential levelling, each instrument setup produces a back sight (BS) and a fore sight (FS). Interpreting BS and FS correctly is essential for deciding whether the ground is rising or falling from the back point to the forward point. This question reinforces the core relationship used in both the Rise & Fall and Height of Instrument methods.

Given Data / Assumptions:

• Both BS and FS are observed from the same instrument setup.
• Standard sign convention: Rise = BS − FS; Fall = FS − BS.
• Readings are taken on a vertical staff; instrument is properly levelled.

Concept / Approach:

The Height of Instrument (HI) equals RL(back point) + BS. The reduced level (RL) of the forward point equals HI − FS. If BS is greater than FS, the computed RL at the forward point becomes larger than the back point's RL, indicating a rise. The same conclusion follows from the Rise & Fall method where Rise = BS − FS; if positive, the forward point is higher.

Step-by-Step Solution:

Verification / Alternative check:

Using the Rise & Fall method directly: Rise = BS − FS. If the numerical result is positive, there is a rise from back to fore—identical conclusion.

Why Other Options Are Wrong:

Lower elevation (fall) corresponds to FS > BS, not BS > FS.

Indeterminate is incorrect; a single BS–FS pair from one setup is sufficient to infer rise or fall.

Equal elevation would require BS = FS.

Common Pitfalls:

Reversing the sign convention; mixing readings from different setups; forgetting that larger staff reading implies lower point only for a fixed HI, whereas the BS–FS comparison already embeds HI consistently.

Final Answer:

The forward staff point is at a higher elevation (there is a rise from back to fore).