Levelling computations – rise and fall method: The rise-and-fall method provides an internal arithmetic check on which set(s) of staff readings?

Introduction / Context:
The rise-and-fall method determines reduced levels by comparing successive staff readings to compute rises and falls between points. One of its strengths is the built-in arithmetic check that improves reliability of field data before office reductions are finalized.

Given Data / Assumptions:

• A properly levelled instrument with clear staff readings.
• Sequential observations categorized as BS, IS, and FS.
• Reduction by rise-and-fall with a final arithmetic check.

Concept / Approach:
The method requires the equality: ΣBS − ΣFS = RL_last − RL_first. Additionally, ΣRises − ΣFalls = RL_last − RL_first. Because rises and falls are derived from differences of consecutive staff readings (including IS), errors in any class of sight (BS, IS, or FS) disturb both equalities, so the method effectively checks all readings taken during the run.

Step-by-Step Solution:

Verification / Alternative check:
Cross-check both equalities; if both hold, the entries for BS, IS, and FS are self-consistent.

Why Other Options Are Wrong:

• Choosing only BS, FS, or IS ignores that all contribute to the computed rises/falls and thus to the check.

Common Pitfalls:
Recording rises/falls with the wrong sign; skipping IS differences; failing to reconcile misclosures before leaving site.

Final Answer:
All of these