Horizontal angle errors from imperfect plate levelling Considering horizontal angle observations with a theodolite, the error caused by imperfect levelling of the plate bubble becomes:

Introduction / Context:
If the instrument’s vertical (rotation) axis is not truly vertical due to imperfect plate bubble levelling, directions read on the horizontal circle can be biased. This bias depends on the vertical angle of the line of sight. Understanding how the error varies helps observers choose appropriate targets and procedures to minimize angular error.

Given Data / Assumptions:

• Vertical axis has a small tilt due to imperfect levelling.
• Horizontal angles are formed by two sight lines with possibly different vertical angles.
• Other instrument errors are negligible or removed by face-left/face-right averaging.

Concept / Approach:

The induced azimuth error from a tilted vertical axis increases with the tangent of the vertical angle of the sight. Nearly horizontal sights produce small errors; steep sights produce larger azimuth errors for the same small axis tilt. Hence, the effect is “large for steeply inclined sights.”

Step-by-Step Solution:

Verification / Alternative check:

Instrument adjustment theory derives this dependence; practical field advice always prefers balanced, near-level sights when very precise azimuths are required.

Why Other Options Are Wrong:

“Large when sights are nearly level” contradicts the tan v dependence.

“Large for long sights” relates to pointing precision but not specifically to vertical-axis tilt.

“Less for steeply inclined sights” is the opposite of the actual behavior.

Common Pitfalls:

Ignoring steep-sight sensitivity; not balancing vertical angles when possible; forgetting to average face-left/right to reduce related errors.

Final Answer:

Large for steeply inclined sights