Tangential Tacheometry – How Should the Staff Be Held for Inclined Sights? In the tangential method of tacheometry, when observing to a levelling staff on an uphill or downhill line of sight, how should the ordinary staff be held to ensure correct angle–intercept geometry?

Introduction / Context:
Tangential tacheometry determines distance and elevation from two angular readings to distinct staff marks (or to the same mark with different tangent angles), without relying on stadia hairs. The geometry assumes a particular orientation of the staff. This question checks the correct field practice for holding the staff on slopes.

Given Data / Assumptions:

• Ordinary levelling staff graduations are vertical when the staff is vertical.
• Tangential method uses angular measurements relative to horizontal and vertical planes.
• Instrument is properly levelled and centered.

Concept / Approach:

Whether the line of sight is upward or downward, the staff must remain vertical so that readings correspond to true vertical distances along a straight scale aligned with gravity. Tilting the staff introduces trigonometric distortions, invalidating the tangential relationships from which distances and elevations are computed. Therefore, the correct procedure is to keep the staff vertical for all observations in the tangential method, just as in stadia work with a vertical staff assumption.

Step-by-Step Solution:

Verification / Alternative check:

Standards for tacheometry (both stadia and tangential) consistently assume a vertical staff; any deviation requires special corrections not used in routine practice.

Why Other Options Are Wrong:

Tilted staff options (a), (b), and (e) corrupt the geometric basis and cause systematic errors. 'None of these' is wrong because there is a clearly correct practice.

Common Pitfalls:

Allowing the staff to lean on steep ground; not checking the staff bubble; attempting to 'compensate' tilt with ad-hoc adjustments instead of keeping the staff vertical.

Final Answer:

Kept vertical in all cases