Fundamental geometry of a theodolite: Which statements about the three principal axes and their relationships are correct? Choose the most complete option.

Difficulty: Easy

Correct Answer: All of the above

Explanation:


Introduction / Context:
Theodolites measure horizontal and vertical angles precisely. Their accuracy depends on strict geometric relationships among three axes: the telescope (line of collimation) axis, the transit (trunnion) axis, and the vertical (rotation) axis. Understanding these relationships is vital for adjustments and reliable observations.


Given Data / Assumptions:

  • A properly adjusted theodolite is considered.
  • Definitions: telescope axis (line of collimation), trunnion axis (tilt axis), and vertical axis (instrument rotation).
  • Instrument is correctly leveled before testing the relationships.


Concept / Approach:
For perfect adjustment: (1) the telescope axis must be perpendicular to the trunnion axis so that elevation motion does not skew the line of sight; (2) the vertical axis must be perpendicular to the trunnion axis so that the vertical circle plane is truly vertical; and (3) all three axes intersect at the instrument’s center, ensuring consistent geometry during rotations and transits.


Step-by-Step Solution:

Level the instrument so the vertical axis is truly vertical.Check that the telescope axis is perpendicular to the trunnion axis using standard collimation tests.Verify that the three axes meet at a point by observing that readings are consistent upon transiting and rotating.Adjust as needed using manufacturer procedures for plate levels, crosshairs, and circles.


Verification / Alternative check:
Face-left and face-right readings of the same angle should agree within tolerance; discrepancies indicate axis misalignment.


Why Other Options Are Wrong:
Each of A–C is individually correct, but only D states the complete set required for proper theodolite geometry.


Common Pitfalls:
Assuming leveling alone guarantees perfect geometry; internal axial relationships still require testing and, sometimes, adjustment.


Final Answer:
All of the above

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