Levelling operations — interpreting consecutive staff readings taken from the same instrument position: Which statements correctly indicate a rise or a fall?

Introduction / Context:In differential levelling, staff readings are taken on successive points using the same height of instrument (HI). Understanding how the numerical values of staff readings translate into “rise” or “fall” is essential for correctly reducing levels and avoiding sign mistakes in field books.

Given Data / Assumptions:

• Two consecutive staff readings are observed from one instrument setup.
• The height of instrument remains unchanged between the two readings.
• We interpret the trend (increase/decrease) to decide rise or fall.

Concept / Approach:Staff reading increases when the point is lower (farther down from the line of collimation). Staff reading decreases when the point is higher. Therefore, comparing two consecutive readings: a decrease indicates a rise; an increase indicates a fall.

Step-by-Step Solution:

Verification / Alternative check:Rise/fall method: Rise = R1 − R2 when positive; Fall = R2 − R1 when positive. The signs confirm the above logic.

Why Other Options Are Wrong:

• (a) and (d) reverse the meaning of increasing/decreasing readings.
• Any single option other than (e) is incomplete because both statements (b) and (c) are needed to fully describe the rule.

Common Pitfalls:Mixing backsight/foresight conventions with rise/fall logic; always compare readings from the same HI to avoid confusion.

Final Answer:Both (b) and (c)