Step 1: The fundamental axes of a transit theodolite include the vertical axis, horizontal axis, line of collimation, and plate level axis.
Step 2: The correct relationship between these fundamental lines is:
The line of collimation (also called the sight axis) must be perpendicular to the horizontal axis at its intersection with the vertical axis. This ensures accurate angular measurements in both the horizontal and vertical planes.
Step 3: Evaluating other options:
(B) Incorrect – The axis of altitude level should be parallel, not perpendicular, to the line of collimation.
(C) Incorrect – The axis of the plate level must lie in a horizontal plane, not necessarily parallel to the vertical axis.
(D) Incorrect – The Vernier should read zero when the instrument is properly leveled and aligned.
Conclusion: The correct answer is option (A), which correctly states the fundamental relationship between the line of collimation and the horizontal axis.