Which is the following rule is used for removing closing error that when the angles and distances are measured

Question

Which is the following rule is used for removing closing error that when the angles and distances are measured with the same precision.

Examoogle · Accepted Answer

Option D: Both A and B

Explanation & Concepts:
The Bowditch rule (also known as the Compass rule) is used to balance a closed traverse when both linear and angular measurements are made with equal precision. Under this rule, the correction applied to the latitude (or departure) of any line is directly proportional to the length of that line.

Working Principle: The principle assumes that accidental errors in linear measurements are proportional to $\sqrt{l}$ (where $l$ is the length of a line) and accidental errors in angular measurements are inversely proportional to $\sqrt{l}$. Based on this error distribution, the total closing error in latitude ($ mega L$) or departure ($ mega D$) is distributed among the traverse lines proportionally to their individual lengths relative to the total perimeter of the traverse.

Key Formulas: $C_L = \Sigma L 	imes \frac{l}{\Sigma l}$ — Correction to latitude of a line; $C_D = \Sigma D 	imes \frac{l}{\Sigma l}$ — Correction to departure of a line; $e = \sqrt{(\Sigma L)^2 + (\Sigma D)^2}$ — Total closing error

Key Points: Used when angular and linear measurements are made with equal precision.; Correction to latitude/departure of a side is directly proportional to the length of that side.; The linear error is assumed to be proportional to $\sqrt{l}$ and angular error inversely proportional to $\sqrt{l}$.

Advantages: Simple to compute and widely applied in routine engineering surveying.; Effectively distributes errors without altering the overall shape of the traverse drastically.

Disadvantages: Assumes equal precision for both linear and angular measurements, which may not hold true if superior instruments (like total stations) are used.; Not theoretically rigorous compared to the Least Squares method.

Applications: Balancing closed compass traverses.; Adjusting land and boundary survey measurements where precision of linear and angular equipment is comparable.

Additional Info: Option A shows the mathematical expression for Bowditch rule: $C_L 	ext{ or } C_D = \Sigma L 	ext{ or } \Sigma D 	imes \frac{l}{\Sigma l}$.. Option B explicitly names the Bowditch rule.. Because Option A states the mathematical formula and Option B names the rule, both options describe the same method, making Option D correct.

Answer: D is correct — Both Option A (the mathematical formula for correcting latitude/departure) and Option B (the name 'Bowditch rule') represent the required method.

Exam Tip: Remember: Bowditch rule is used when angular and linear measurements are equally precise ($C \propto l$), whereas Transit rule is used when angular measurements are more precise than linear measurements ($C_L \propto L$ and $C_D \propto D$).

Examoogle · Answer

Option A: $C_L 	ext{ or } C_D = (\Sigma L 	ext{ or } \Sigma D) 	imes \frac{l}{\Sigma l}$

Examoogle · Answer

Option B: Bowditch rule

Examoogle · Answer

Option C: Transit rule

Feature	Bowditch Rule	Transit Rule
Precision Assumption	Linear and angular measurements have equal precision	Angular measurements are more precise than linear measurements
Correction Proportional To	Length of the line ( $l$ )	Latitude or departure of the line ( $L$ or $D$ )

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