Answer :
To determine the Reduced Level (RL) of point B using the method of reciprocal levelling, we can follow these steps:
### Given Data:
- At instrument position 1, 5 m from A:
- Reading on staff at A ([tex]\( \text{reading}_{A1} \)[/tex]) = 1.396
- Reading on staff at B ([tex]\( \text{reading}_{B1} \)[/tex]) = 1.387
- At instrument position 2, 5 m from B:
- Reading on staff at A ([tex]\( \text{reading}_{A2} \)[/tex]) = 1.837
- Reading on staff at B ([tex]\( \text{reading}_{B2} \)[/tex]) = 1.842
- RL of A ([tex]\( \text{RL}_A \)[/tex]) = 10.000 m
### Solution:
1. Calculate the True Difference in Level ([tex]\( \Delta H \)[/tex])
The true difference in level considering reciprocal levelling is calculated using the formula:
[tex]\[ \Delta H = \frac{(\text{Reading on A from position 1} + \text{Reading on B from position 2}) - (\text{Reading on B from position 1} + \text{Reading on A from position 2})}{2} \][/tex]
Substituting the given readings, we get:
[tex]\[ \Delta H = \frac{(1.396 + 1.842) - (1.387 + 1.837)}{2} \][/tex]
[tex]\[ \Delta H = \frac{(3.238) - (3.224)}{2} \][/tex]
[tex]\[ \Delta H = \frac{0.014}{2} \][/tex]
[tex]\[ \Delta H = 0.007 \text{ m} \][/tex]
2. Calculate the RL of point B ([tex]\( \text{RL}_B \)[/tex])
The RL of point B with respect to the RL of point A can be calculated as:
[tex]\[ \text{RL}_B = \text{RL}_A + \Delta H \][/tex]
Given [tex]\(\text{RL}_A = 10.000 \text{ m}\)[/tex] and [tex]\( \Delta H = 0.007 \text{ m} \)[/tex], we have:
[tex]\[ \text{RL}_B = 10.000 + 0.007 \][/tex]
[tex]\[ \text{RL}_B = 10.007 \text{ m} \][/tex]
### Conclusion:
The Reduced Level (RL) of point B is [tex]\(10.007 \text{ m}\)[/tex].
### Given Data:
- At instrument position 1, 5 m from A:
- Reading on staff at A ([tex]\( \text{reading}_{A1} \)[/tex]) = 1.396
- Reading on staff at B ([tex]\( \text{reading}_{B1} \)[/tex]) = 1.387
- At instrument position 2, 5 m from B:
- Reading on staff at A ([tex]\( \text{reading}_{A2} \)[/tex]) = 1.837
- Reading on staff at B ([tex]\( \text{reading}_{B2} \)[/tex]) = 1.842
- RL of A ([tex]\( \text{RL}_A \)[/tex]) = 10.000 m
### Solution:
1. Calculate the True Difference in Level ([tex]\( \Delta H \)[/tex])
The true difference in level considering reciprocal levelling is calculated using the formula:
[tex]\[ \Delta H = \frac{(\text{Reading on A from position 1} + \text{Reading on B from position 2}) - (\text{Reading on B from position 1} + \text{Reading on A from position 2})}{2} \][/tex]
Substituting the given readings, we get:
[tex]\[ \Delta H = \frac{(1.396 + 1.842) - (1.387 + 1.837)}{2} \][/tex]
[tex]\[ \Delta H = \frac{(3.238) - (3.224)}{2} \][/tex]
[tex]\[ \Delta H = \frac{0.014}{2} \][/tex]
[tex]\[ \Delta H = 0.007 \text{ m} \][/tex]
2. Calculate the RL of point B ([tex]\( \text{RL}_B \)[/tex])
The RL of point B with respect to the RL of point A can be calculated as:
[tex]\[ \text{RL}_B = \text{RL}_A + \Delta H \][/tex]
Given [tex]\(\text{RL}_A = 10.000 \text{ m}\)[/tex] and [tex]\( \Delta H = 0.007 \text{ m} \)[/tex], we have:
[tex]\[ \text{RL}_B = 10.000 + 0.007 \][/tex]
[tex]\[ \text{RL}_B = 10.007 \text{ m} \][/tex]
### Conclusion:
The Reduced Level (RL) of point B is [tex]\(10.007 \text{ m}\)[/tex].
