Levelling practice (dumpy/auto level): Which statements correctly describe a back sight (BS) reading and how it is used to obtain the height of instrument (HI)?

Introduction / Context:
In differential levelling, the first staff reading after setting up the level is usually a back sight (BS). Correctly identifying and calculating with BS ensures accurate transfer of elevations from a known benchmark to new points. The question verifies understanding of what a BS is, how it produces height of instrument (HI), and sign conventions for special cases like inverted staff readings.

Given Data / Assumptions:

• Reduced level (RL) of a starting point or benchmark is known or can be computed.
• Line of sight is assumed horizontal after proper instrument leveling.
• Inverted staff readings occur under structures or when sighting to soffits; sign convention must be respected.

Concept / Approach:
A back sight establishes the height of the collimation (HI). If RL_known is the reduced level of the point and BS is the staff reading, then HI = RL_known + BS for a normal upright staff. For an inverted staff (held upside down), the reading represents a vertical offset below the line of sight and is algebraically negative in the levelling computation.

Step-by-Step Solution:

Verification / Alternative check:
Levelling field books consistently show BS in the BS column, added to the RL of the known point to get HI; any inverted-reading entries are specially marked and signed to avoid mistakes.

Why Other Options Are Wrong:

• The only complete choice that captures definition, calculation, and sign convention is the inclusive option. Any single statement alone is incomplete.

Common Pitfalls:
Confusing BS and FS; forgetting to reverse the sign for inverted staff; mixing instrument change (IC) entries leading to incorrect HI carry-over; omitting arithmetic checks (sum of BS − sum of FS = last RL − first RL).

Final Answer:
All of the above