Tacheometry fundamentals — one of the two tacheometric instrument constants is the additive constant; identify the other fundamental constant used in staff intercept reduction.

Introduction / Context:
Tacheometry determines horizontal distance and elevation differences from the staff intercept observed through a telescope fitted with stadia hairs. The distance formula involves two instrument constants that depend on the optics. Recognizing these constants is essential for reducing field observations accurately and checking instrument calibration.

Given Data / Assumptions:

• Stadia method with fixed-hair telescope is used.
• The distance formula is typically D = k·s + c, where s is the staff intercept.
• Instrument has been factory-calibrated so that the constants are stable during normal use.

Concept / Approach:

In the stadia equation D = k·s + c, k is called the multiplying constant (often ≈ 100 for many instruments) and c is called the additive constant (≈ the distance from objective to instrument axis plus focusing offset). The multiplying constant scales the staff intercept to distance; the additive constant corrects for the fixed spacing between the instrument centre and the focal point. Field checks (e.g., observing a staff at two known distances) can be used to verify or re-determine these constants if needed.

Step-by-Step Solution:

Verification / Alternative check:

Instrument manuals for tacheometers specify k and c explicitly; many are designed for k = 100 to simplify mental arithmetic.

Why Other Options Are Wrong:

Subtractive/dividing/indicative constants are not standard terms in stadia reduction.

Common Pitfalls:

Forgetting to apply the additive constant in short sights; using wrong units for s, leading to scaled errors in D.

Final Answer:

multiplying constant