Tacheometry (stadia method): In a stadia theodolite, which extra hairs are provided on the diaphragm for distance measurement?

Introduction / Context:
Tacheometry allows rapid distance and elevation measurement using a theodolite or transit equipped with stadia hairs. Recognizing the diaphragm pattern is essential for reading intercepts on the staff and converting them into distances using the stadia constants.

Given Data / Assumptions:

• A standard stadia theodolite has a central horizontal cross hair for line of sight.
• Two extra hairs are placed symmetrically above and below the central horizontal hair.
• The vertical hair remains single for ranging/centering.

Concept / Approach:
Distance D is computed from the staff intercept s between the upper and lower stadia hairs using D = k * s + c, where k is the multiplying constant and c is the additive constant (both instrument-specific). Thus, the diaphragm must provide two additional horizontal hairs to read s directly on the staff.

Step-by-Step Solution:

Verification / Alternative check:
Manufacturers’ manuals and surveying texts depict the stadia diaphragm with two additional horizontal hairs; vertical hair remains single for sighting the staff centerline.

Why Other Options Are Wrong:

• Vertical extra hairs are not used for stadia measurement.
• Adding both horizontal and vertical extras is unnecessary and not standard for stadia work.
• “None of these” is false since the correct configuration is well known.

Common Pitfalls:
Reading the wrong pair of hairs; confusing stadia intercept with staff height difference; forgetting to apply the additive constant when required.

Final Answer:
Two additional horizontal hairs (stadia hairs) equidistant from the central horizontal hair