Levelling Methods – Limitation of the Line of Collimation (Height of Instrument) Method In differential levelling, the line of collimation method (also called the Height of Instrument method) is quick but offers fewer internal checks. Which of the following items does this method not inherently provide a check on during computations?

Introduction / Context:
The line of collimation (Height of Instrument) method is a popular approach for reducing level-book observations. It is efficient because it computes a height of instrument for each setup and then derives reduced levels directly. However, compared to the Rise and Fall method, it offers fewer built-in diagnostic checks on individual observations. This question asks which item is not automatically checked by the method.

Given Data / Assumptions:

• Standard levelling terminology: back sight (BS), intermediate sight (IS), fore sight (FS), reduced level (RL).
• Computation pathway: HI = RL_bench + BS; then RL_point = HI − staff_reading (IS or FS).
• An arithmetic check is usually: ΣBS − ΣFS = RL_last − RL_first.

Concept / Approach:

In the HI method, the principal arithmetic check is the equality ΣBS − ΣFS = net change in RL. This validates the overall run but does not test each IS individually. In contrast, the Rise and Fall method generates rise/fall between successive points, providing a line-by-line internal check that can reveal a single bad IS reading. Therefore, the HI method lacks an inherent check on intermediate sights.

Step-by-Step Solution:

Verification / Alternative check:

Compare with the Rise and Fall method, where each consecutive difference produces a rise or fall, creating a redundant check on every staff observation, including IS. This confirms the relative weakness of the HI method for detecting a single erroneous IS.

Why Other Options Are Wrong:

Fore sights and back sights are part of the ΣBS − ΣFS arithmetic check; reduced levels are computed consistently from HI. The arithmetic check itself is available in the HI method and is not the missing check.

Common Pitfalls:

Assuming that a successful ΣBS − ΣFS check validates all IS readings; it does not. A faulty IS can remain hidden if BS and FS accidentally balance the total.

Final Answer:

Intermediate sights