Tacheometry – Horizontal distance by stadia formula (line of collimation horizontal) f = 200 mm, distance from instrument vertical axis to object-glass centre = 100 mm, stadia hair spacing i = 4 mm. Staff readings: top = 1.000 m, middle = 2.000 m, bottom = 3.000 m. Compute the horizontal distance (m) from instrument to staff.

Introduction / Context:
Tacheometry employs a stadia diaphragm to quickly measure horizontal distance without chaining. When the line of sight is horizontal, the classic formula D = k * s + C applies, where k = f / i and C = f + d (additive constant from instrument geometry).

Given Data / Assumptions:

• Focal length f = 200 mm = 0.2 m.
• Distance from instrument vertical axis to objective centre d = 100 mm = 0.1 m.
• Stadia hair interval i = 4 mm = 0.004 m.
• Staff readings: top = 1.000 m, middle = 2.000 m, bottom = 3.000 m (collimation horizontal).

Concept / Approach:

For a horizontal line of collimation, the horizontal distance equals the stadia constant times the intercept plus the additive constant. The intercept s is the difference between top and bottom readings in metres.

Step-by-Step Solution:

Verification / Alternative check:

A quick ratio check shows that with k = 50, every 0.02 m intercept corresponds to 1 m distance; an intercept of 2 m gives ~100 m, and the additive constant adds 0.3 m → 100.3 m.

Why Other Options Are Wrong:

103.0, 150.0, and 153.0 m ignore the computed constants or misuse the intercept sign/units.

Common Pitfalls:

Confusing mm and m for f and i, using the middle reading incorrectly, or forgetting to add C.

Final Answer:

100.3