In the surveys, the slope correction applied to the base line is:
Correct Answer:
A. Always cumulative
📈 Understanding Cumulative and Compensating Errors
In surveying, errors are unavoidable. They are broadly classified into two types based on how they affect the final measurement.
- Cumulative Errors: These errors occur in the same direction and tend to accumulate with each measurement. The total error is the sum of all individual errors. They are systematic and can often be corrected if the conditions causing them are known.
- Compensating Errors: These errors are random and can be either positive or negative. Over a series of measurements, they tend to cancel each other out. They are accidental and follow the laws of probability.
🔬 Detailed Analysis: Why Slope Correction is Cumulative
The slope correction is required because the distance measured along a slope is always greater than the true horizontal distance. The correction formula itself, \(C = -h^2 / 2L\), shows that the correction is always negative (subtractive).
Because the error from measuring on a slope always makes the measured length too long, the correction is always applied in the same direction (subtraction). This one-directional nature means that with every sloped measurement, the error adds up. Therefore, the slope correction is always cumulative.
📊 Summary of Error Types in Chaining
| Error Type | Nature | Examples |
|---|---|---|
| Cumulative | Systematic, always in the same direction (+ or -). Errors add up. |
|
| Compensating | Random, can be positive or negative. Errors tend to cancel out. |
|