Section 4: Soil and Water Conservation Engineering
Surveying and Levelling
Subtopic: The Theodolite traversing
Question Statement:
Which of the following geometric and computational conditions are true for a mathematically closed polygon traverse in surveying?
Options:
(A) The algebraic sum of latitudes must equal zero ($\sum L = 0$)
(B) The algebraic sum of departures must equal zero ($\sum D = 0$)
(C) The linear closing error $e$ is given by $e = \sqrt{(\sum L)^2 + (\sum D)^2}$
(D) Bowditch's rule balances traverse errors assuming linear and angular errors are equally proportional to the square root of line length
Answer Key:
A, B, C, D
Step-by-Step Solution & Explanation
All four statements are foundational principles in closed traverse computation:
- A & B: For a polygon returning to the starting station, total net displacement in Northing/Southing (Latitude) and Easting/Westing (Departure) is strictly zero.
- C: Resultant linear misclosure vector magnitude is $e = \sqrt{(\sum L)^2 + (\sum D)^2}$.
- D: Bowditch (compass rule) assumes linear errors $\propto \sqrt{l}$ and angular errors $\propto 1/\sqrt{l}$, distributing corrections proportional to length: $C_L = -\sum L \frac{l}{\sum l}$.