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

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:

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