History of tacheometry: Stadia tacheometry (use of stadia lines and fixed constants for distance measurement) was introduced by James Watt in which year?

Introduction / Context:
Tacheometry is a rapid surveying technique for determining horizontal distance and elevation differences using angular measurements and a graduated staff. The stadia method, which employs fixed stadia hair constants, is historically associated with James Watt, who popularized fast optical distance estimation well before electronic distance measurement became available.

Given Data / Assumptions:

• Question targets a historical milestone (not a formula).
• We assume the standard attribution of the stadia method to James Watt.
• Four century-spaced distractors are provided.

Concept / Approach:

James Watt lived from 1736 to 1819, with principal engineering activity in the mid-to-late 18th century. Stadia tacheometry is documented as a late-1700s development; thus 1770 is the historically consistent year among the options provided. Later dates (19th–20th century) correspond to the era of more advanced optical instruments but not the original introduction of stadia principles.

Step-by-Step Solution:

Verification / Alternative check:

Surveying histories agree that the stadia concept emerged in the latter half of the 18th century; 1770 is widely cited in traditional question banks as the answer linked to Watt.

Why Other Options Are Wrong:

1670 predates Watt’s lifetime and the industrial context; 1870 and 1900 are too late for the method’s introduction; 1736 is his birth year, not the stadia milestone.

Common Pitfalls:

Confusing the advent of stadia with later refinements such as anallatic telescopes or EDM; memorizing only Watt’s birth/death dates.

Final Answer:

1770