Tacheometry – staff attitude for small vertical angles If vertical angles of inclined sights do not exceed 10° and the staff's non-verticality is within 1°, stadia observations in the ordinary tacheometric system are preferably taken on:

Introduction / Context:
Tacheometry uses stadia hairs to obtain distances and elevations from staff intercepts. There are two practical conventions for staff attitude during inclined sights: holding the staff vertical or holding it normal to the line of sight (“staff normal”). Each leads to slightly different reduction formulae. This question asks which attitude is preferred when vertical angles are small (≤ 10°) and the staff can be kept within about 1° of vertical.

Given Data / Assumptions:

• Vertical angles up to about 10° only.
• Staff can be kept within 1° of true vertical.
• Standard stadia constants and procedures apply.

Concept / Approach:

For small vertical angles and good staff discipline, the “staff vertical” method is standard because the reduction formulas (e.g., D = k * s * cos^2 θ + c * cos θ) are straightforward and errors from small non-verticality are negligible compared with reading precision. The “staff normal” method is adopted for steep sights where holding the staff vertical introduces larger errors and a modified relation (D = k * s + c) simplifies reductions.

Step-by-Step Solution:

Verification / Alternative check:

Worked examples in surveying texts present staff-vertical reductions as the default; staff-normal is recommended mainly for steep sights (large θ) or in mountainous terrain.

Why Other Options Are Wrong:

Staff normal is not necessary for small θ and can complicate practice.

“Either equally” ignores the preferred standard when conditions are mild.

“None” is clearly incorrect.

Common Pitfalls:

Using staff-normal formulas inadvertently with staff-vertical observations; ignoring the cosine-squared factor in distance computations; neglecting to note staff attitude in the field book.

Final Answer:

Staff held truly vertical