Stadia staff handling — how does the observed staff intercept change with staff tilt relative to the line of sight in tacheometry?

Introduction / Context:
In tacheometric observations, the horizontal distance is computed from the staff intercept (difference between upper and lower stadia-hair readings). The value of this intercept depends not only on instrument constants but also on how the staff is oriented with respect to the line of sight. This question addresses the effect of staff tilt on the measured intercept.

Given Data / Assumptions:

• Fixed-hair stadia method is used.
• The line of sight makes an angle with the staff according to the staff's tilt.
• No staff-head prism or automatic normalizing device is assumed.

Concept / Approach:

The stadia intercept is proportional to the projection of the actual staff length between the stadia hairs onto a line perpendicular to the line of sight. When the staff is held truly normal (perpendicular) to the line of sight, this projection is maximum, yielding the largest intercept reading. If the staff is tilted away from the normal, the effective projected length reduces by the cosine of the deviation angle, thereby decreasing the intercept and leading to underestimated distances if uncorrected.

Step-by-Step Solution:

Verification / Alternative check:

Field practice requires the staffman to rock the staff through the normal position and freeze at the point of maximum reading; this ensures correct intercept capture.

Why Other Options Are Wrong:

Minimum at normal — opposite of the projection principle.
Decreases if tilted away — true but incomplete; the key maximum condition is at true normal.
Increases if tilted towards normal — only until normal is reached; beyond that it decreases again.

Common Pitfalls:

Accepting a reading without rocking the staff; ignoring that small tilt can introduce systematic underestimation of distance.

Final Answer:

is maximum if the staff is held truly normal to the line of sight.