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 context of the rise and fall method for calculating the reduced level (R.L.) in surveying, we need to establish the check condition which ensures accuracy. The correct mathematical relationship is expressed as:

$\Sigma$ BS - $\Sigma$ FS

= RL of last station point – RL of first station point

= $\Sigma$ Rise - $\Sigma$ Fall

Explanation:

• $\Sigma$ BS: Sum of back sights. These are the readings taken on a leveling staff when the instrument is moved to a new station and the staff is placed on a point of known or assumed R.L.
• $\Sigma$ FS: Sum of fore sights. These are the readings taken on a leveling staff when it is placed on a new point, and the R.L. at this point is to be determined.
• The expression $\Sigma$ BS - $\Sigma$ FS represents the change in elevation across all measured points, correlating the cumulative changes observed (rises and falls) to the differences in R.L. between the first and last points.

The verification involves ensuring that the difference in the sum of back sights and fore sights equals the difference between the R.L. of the last and first station points and also equals the net change computed as the total rise minus the total fall.