Question

Bowditch rule for adjusting a closed traverse of perimeter ‘l’ is based on the assumption that the probable error is proportional to

• A. l
• B. √l
• C. l²
• D. 1/√l

Hint:

Bowditch rule adjusts for errors in a closed traverse by assuming that the probable error is proportional to the square root of the length of the traverse side (√l).

Answer 1

The Correct Option is B

The Bowditch rule (or compass rule) is used to adjust the measurements in a closed traverse. The rule assumes that the probable error in the linear measurement is proportional to the square root of the length of the traverse side (√l). This assumption helps in distributing the errors proportionally to the distance of the traverse. Step 1: Understanding the rule. Bowditch’s method assumes that the errors in measurement increase with the length of the traverse, but the relationship is proportional to the square root of the length of the line. This ensures that longer sides in the traverse receive a larger share of the adjustment to account for larger measurement errors. Step 2: Analyzing the options. - Option (A) is incorrect because the error is not directly proportional to the length of the traverse. - Option (B) is correct because Bowditch's rule assumes that the probable error is proportional to √l. - Option (C) is incorrect because the error is not proportional to the square of the length. - Option (D) is incorrect because the error is not inversely proportional to the square root of the length. Thus, the correct answer is (B).