Tacheometry – effect of an anallatic lens on stadia constants If a tacheometer is fitted with an anallatic lens (for internal focusing), what are the effective stadia constants used in the distance formula?

Introduction / Context:
Tacheometry determines horizontal distances and elevations quickly by reading staff intercepts through a telescope with stadia hairs. The distance formula uses two constants: a multiplying constant (k) and an additive constant (c). Instruments are often designed to simplify this relationship. This question checks your understanding of how an anallatic lens affects the stadia constants.

Given Data / Assumptions:

• Standard stadia distance formula: D = k * s + c, where s is the staff intercept.
• Internal focusing telescope with an anallatic lens to eliminate the additive term.
• Usual stadia interval factor adjusted to give k ≈ 100 for convenience.

Concept / Approach:

The anallatic lens is a special converging lens introduced into the telescope so that the additive constant c (which depends on instrument geometry and focusing) becomes zero. This makes the distance computation simply D = k * s, eliminating range-dependent offsets. Most instruments are built to yield k ≈ 100, allowing field staff to multiply the intercept by 100 mentally, greatly speeding calculations.

Step-by-Step Solution:

Verification / Alternative check:

Manufacturer specifications and surveying texts list anallatic lenses as eliminating c and commonly standardizing k to 100, confirming the selection.

Why Other Options Are Wrong:

Additive 100, k = 0: would make distances constant regardless of staff intercept, which is nonsensical.

Both 100 or both 50: do not reflect the effect of the anallatic lens and typical calibration practice.

Common Pitfalls:

Confusing external-focus systems (which may have a nonzero c) with anallatic setups; forgetting that k is set by stadia interval and optics, not by staff properties.

Final Answer:

Multiplying constant is 100, additive constant is zero