Question

Mathematical check for the computation of R.L. by rise and fall method is given by

• A. $\Sigma$ FS - $\Sigma$ BS = RL of last station point – RL of first station point = $\Sigma$ Fall - $\Sigma$ Rise
• B. $\Sigma$ BS - $\Sigma$ FS = RL of first station point – RL of last station point = $\Sigma$ Fall - $\Sigma$ Rise
• C. $\Sigma$ BS - $\Sigma$ FS = RL of last station point – RL of first station point = $\Sigma$ Rise - $\Sigma$ Fall
• D. $\Sigma$ BS - $\Sigma$ FS = RL of first station point – RL of last station point = $\Sigma$ Rise - $\Sigma$ Fall

Hint:

Always remember: for rise and fall method, the change in elevation equals the total rise minus total fall.

Answer 1

The Correct Option is C

In the rise and fall method of levelling, the correctness of the reduced levels (RLs) is verified using a mathematical check. The sum of the back sights (BS) minus the sum of the fore sights (FS) should be equal to the difference in RL between the last and first station points. Additionally, the difference in total rise and total fall should match the same value. Hence, the valid check is: \[ \Sigma \text{BS} - \Sigma \text{FS} = \text{RL}_{\text{last}} - \text{RL}_{\text{first}} = \Sigma \text{Rise} - \Sigma \text{Fall} \]