The arithmetical check for the computation of R.L. by "rise and fa...
Two arithmetic checks in collimation method
∑ Backsight - ∑ Foresight = Last RL - First RL
Three arithmetic checks in Rise and Fall Method.
∑ Backsight - ∑ Foresight = Last RL - First RL = ∑ Rise - ∑ Fall
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The arithmetical check for the computation of R.L. by "rise and fa...
The arithmetical check for the computation of R.L. (Reduced Level) by the rise and fall method is given by option 'C': B.S. (Backsight) - F.S. (Foresight) = R.L. (Reduced Level) of the last station point - R.L. of the first station point = Rise - Fall. Let's break down the explanation:
Backsight (B.S.) and Foresight (F.S.)
- Backsight (B.S.) is the reading taken on a staff held at a previously established point of known reduced level.
- Foresight (F.S.) is the reading taken on a staff held at the next point where the reduced level is to be determined.
Reduced Level (R.L.)
- Reduced Level (R.L.) is the vertical distance of a point above or below a reference level, usually mean sea level or a benchmark.
- In the context of the rise and fall method, the reduced level is calculated by comparing the backsight and foresight readings.
Rise and Fall
- Rise is the algebraic sum of the differences between the backsight and foresight readings when moving from one station to the next.
- Fall is the algebraic sum of the differences between the foresight and backsight readings when moving from one station to the next.
Arithmetical Check
The arithmetical check is used to verify the accuracy of the computation of the reduced levels. It involves comparing the differences between the backsight and foresight readings with the differences between the R.L. of the last station point and the R.L. of the first station point.
- The formula in option 'C' states that the difference between the backsight and foresight readings (B.S. - F.S.) is equal to the difference between the R.L. of the last station point and the R.L. of the first station point (R.L. of last station point - R.L. of first station point).
- Furthermore, it states that this difference is equal to the algebraic sum of the rise and fall (Rise - Fall).
Explanation of Correct Option (Option 'C')
- This option is correct because it correctly represents the arithmetical check for the computation of R.L. by the rise and fall method.
- It ensures that the difference between the backsight and foresight readings is consistent with the difference between the R.L. of the last station point and the R.L. of the first station point.
- By comparing the rise and fall with the difference in R.L., any errors or mistakes in the calculations can be identified.
Other Options
- Option 'A' is incorrect because it incorrectly equates the difference between the backsight and foresight readings (F.S. - B.S.) with the difference between the fall and rise.
- Option 'B' is incorrect because it incorrectly equates the difference between the backsight and foresight readings (B.S. - F.S.) with the difference between the rise and fall.
- Option 'D' is incorrect because it incorrectly equates the difference between the backsight and foresight readings (B.S. - F.S.) with the sum of the rise and fall, rather than the difference between the R.L. of the first and last station points.
Overall,