Traverse adjustment—Transit Rule: If the arithmetic sum of the latitudes of a closed traverse is ∑Lat and the closing error in latitude is denoted by dx, what is the correction (to be applied to latitude) for a side whose computed latitude is l according to the Transit Rule?

Introduction / Context:

Traverse adjustment distributes small misclosures so that the final figure satisfies ΣDeparture = 0 and ΣLatitude = 0. When angular work is relatively more precise than linear, the Transit Rule is preferred over Bowditch's rule, because it allocates corrections in proportion to the computed departures and latitudes themselves, not to side lengths.

Given Data / Assumptions:

• Closed traverse with known closing error in latitude: dx.
• Arithmetic sum (taken without sign convention issues for scaling) denoted as ∑Lat.
• A particular side has computed latitude l (algebraic).

Concept / Approach:

The Transit Rule prescribes that corrections be proportional to the magnitudes of the components: C_latitude,i = − (l_i/∑Lat) × dx and C_departure,i = − (D_i/∑Dep) × dy. The negative sign ensures that the applied corrections act opposite to the misclosure so that the adjusted sums become zero. This contrasts with Bowditch, which uses side length as the weighting parameter.

Step-by-Step Solution:

Verification / Alternative check:

Check that ΣC_L = −dx. If satisfied, the latitude misclosure has been fully compensated by the distributed corrections.

Why Other Options Are Wrong:

• Positive sign would increase the misclosure.
• Using |l| or l² is not part of the Transit Rule definition.
• None of these is incorrect because the standard formula exists.

Common Pitfalls:

• Confusing Transit Rule with Bowditch (length-proportional) adjustments.
• Mixing sign conventions; maintain consistent quadrants when computing l.

Final Answer:

− (l / ∑Lat) × dx