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Level book, RL of 4th point 562.50

Short answer

Using rise and fall and HI methods with instrument shifts after the 4th and 7th readings, the RLs of points 1 to 9 are 563.825, 563.688, 563.479, 562.500, 561.977, 562.570, 562.298, 561.707, and 561.000 m. Checks confirm ΣBS − ΣFS = −2.825 m equals last RL minus first RL.

The following readings were successively taken with a level: 0.35, 0.487, 0.696, 1.675, 1.893, 2.416, 1.823, 0.487, 0.759, 1.350 and 2.057. The instrument was shifted after the fourth and seventh readings. Prepare a level book and calculate the RLs of different points if the RL of the 4th point is 562.50 m. Use both the methods.

Assumptions: 11 readings; the instrument is shifted after the 4th and 7th readings, so the 4th and 7th readings are foresights on change points and the 5th and 8th readings are backsights on the same points. Hence there are 9 points (numbered 1 to 9). Set-ups: (0.350, 0.487, 0.696, 1.675), (1.893, 2.416, 1.823), (0.487, 0.759, 1.350, 2.057). RL of point 4 = 562.500 m.

(a) Rise and fall method

PointBSISFSRiseFallRL (m)
10.350563.825
20.4870.137563.688
30.6960.209563.479
41.8931.6750.979562.500
52.4160.523561.977
60.4871.8230.593562.570
70.7590.272562.298
81.3500.591561.707
92.0570.707561.000

(b) Height of instrument (HI) method

HI of set-up 1 = RL of point 4 + FS(4) = 562.500 + 1.675 = 564.175 m, so RL of point 1 = 564.175 - 0.350 = 563.825 m.

PointBSISFSHIRL = HI - reading (m)
10.350564.175563.825
20.487563.688
30.696563.479
41.8931.675564.393562.500
52.416561.977
60.4871.823563.057562.570
70.759562.298
81.350561.707
92.057561.000

Both methods give the same RLs.

Checks

ΣBS−ΣFS=2.730−5.555=−2.825ΣRise−ΣFall=0.593−3.418=−2.825Last RL−first RL=561.000−563.825=−2.825\begin{aligned} \Sigma BS - \Sigma FS &= 2.730 - 5.555 = -2.825\\ \Sigma \text{Rise} - \Sigma \text{Fall} &= 0.593 - 3.418 = -2.825\\ \text{Last RL} - \text{first RL} &= 561.000 - 563.825 = -2.825 \end{aligned}

Answer: RLs of points 1 to 9 = 563.825, 563.688, 563.479, 562.500, 561.977, 562.570, 562.298, 561.707, 561.000 m.

✓ Answer checked by Claude Opus 5.5 (high effort)

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