Effect of staff tilt on stadia intercepts In stadia tacheometry, tilting the staff tends to increase the observed stadia intercept under which condition?

Introduction / Context:
In stadia measurements, the apparent intercept on the staff depends on the relative orientation between the staff and the line of sight. Deviations from a vertical staff can either increase or decrease the intercept, affecting computed distances and elevations if not accounted for.

Given Data / Assumptions:

• Line of sight may be inclined up-hill or down-hill.
• Staff may be held vertical or tilted towards/away from the instrument.
• We consider the qualitative effect on the stadia intercept (the distance between upper and lower hair readings).

Concept / Approach:

For an up-hill sight, tilting the staff away from the instrument makes it more nearly normal to the line of sight, which increases the projected intercept compared with a vertical staff. Conversely, for a down-hill sight, tilting the staff towards the telescope produces a similar effect. Among the choices, the condition explicitly increasing the intercept is “away from the telescope while sighting up-hill.”

Step-by-Step Solution:

Verification / Alternative check:

Using projection geometry, the apparent intercept is proportional to 1 / cos ψ, where ψ is the angle between staff and the normal to line of sight; minimizing ψ (by appropriate tilt) increases the intercept.

Why Other Options Are Wrong:

Tilt away with down-hill (A) or tilt toward with up-hill (B) do not maximize normality for the given sight, giving smaller intercepts relative to the correct condition.

Keeping the staff vertical (E) is the baseline and does not increase intercept compared with the optimized tilt.

“None” (D) is false because a definite increasing condition exists.

Common Pitfalls:

Confusing “staff vertical” with “staff normal to line of sight”; neglecting to record staff attitude in field notes when reduction formulas differ.

Final Answer:

When the staff is tilted away from the telescope while sighting up-hill