Which is the following rule is used for balance the traverse when the angular measurements are most precise th

Question

Which is the following rule is used for balance the traverse when the angular measurements are most precise than the linear measurements.

Examoogle · Accepted Answer

Option D: Both A and C

Explanation & Concepts:
When angular measurements are more precise than linear measurements, the Transit Rule is used to balance the traverse. Under this rule, corrections are applied in proportion to the latitude or departure of the individual side rather than its length. Option A shows the mathematical formula for the Transit Rule, making both Option A and Option C correct, hence Option D is the correct choice.

Working Principle: The Transit Rule assumes that angular measurements are measured with greater precision compared to linear measurements. Corrections to latitude ($C_L$) and departure ($C_D$) are calculated by multiplying the total error in latitude ($\ me\Sigma L$) or departure ($\ me\Sigma D$) by the ratio of the latitude or departure of the specific line to the arithmetic sum of all latitudes or departures.

Key Formulas: $C_L = \Sigma L \ imes \ rac{L}{L_T}$ — Correction in latitude of a line; $C_D = \Sigma D \ imes \ rac{D}{D_T}$ — Correction in departure of a line

Key Points: Transit rule is preferred when angular measurements are more precise than linear measurements.; Bowditch (Compass) rule is used when angular and linear measurements are of equal precision.; In Transit rule, $L_T$ is the scalar arithmetic sum of all latitudes $(\Sigma |L|)$ and $D_T$ is the scalar arithmetic sum of all departures $(\Sigma |D|)$.

Advantages: Minimizes structural alteration of angle values when linear errors dominate.; Computationally simple to apply directly to individual latitudes and departures.

Disadvantages: Theoretical foundation is less statistically sound compared to Axis or Least Squares rules.; Can lead to disproportionate corrections if a line's latitude or departure approaches zero.

Applications: Traverse balancing when using modern precise theodolites paired with less precise chain/tape measurements.; Standard civil engineering survey problems in competitive exams.

Additional Info: Option B (Bowditch Rule) is incorrect because it is applied when linear and angular measurements have equal precision, where $C_L = \Sigma L \ imes \ rac{l}{\Sigma l}$.. Option A gives the correct mathematical formula of the Transit Rule, while Option C names the rule itself. Hence, Option D (Both A and C) is the correct choice.

Answer: D is correct — Option A represents the mathematical formula and Option C gives the name of the rule used when angular measurements are more precise than linear measurements.

Exam Tip: Remember: Bowditch = Equal precision (Length dependent), Transit = Angles more precise (Latitude/Departure dependent).

Examoogle · Answer

Option A: CLor CD=ΣL or ΣD ×L or DLT or DT

CLor CD=ΣL or ΣD ×L or DLT or DT

Examoogle · Answer

Option B: Bowditch rule

Examoogle · Answer

Option C: Transit rule

Feature	Transit Rule	Bowditch Rule
Precision Condition	Angular precision > Linear precision	Angular precision = Linear precision
Correction Proportion	Proportional to Latitude / Departure of line	Proportional to length of line ( $l$ )

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