Level book with missing data, RL 1249.260

Method. In the rise and fall method each rise or fall is the difference between two consecutive staff readings taken from the same set-up (previous reading $-$ present reading: positive is a rise, negative a fall), and RL $=$ previous RL $\pm$ rise or fall. A change point has an FS (from the old set-up) and a BS (from the new set-up). The missing values are found in order, then checked with $\Sigma BS = 12.795$.

Finding the missing values

1. B (FS): fall of 0.750 from A, so FS $= 3.250 + 0.750 = 4.000$. RL of B $= 1249.260 - 0.750 = 1248.510$.
2. C (fall): BS at B is 1.755 (new set-up), IS at C is 1.950: fall $= 1.950 - 1.755 = 0.195$; RL of C $= 1248.510 - 0.195 = 1248.315$.
3. D (rise): FS at D 1.920 against IS at C 1.950: rise $= 1.950 - 1.920 = 0.030$; RL of D $= 1248.345$.
4. D (BS): E is in the next set-up with D as BS: rise at E $= BS_D - 2.340 = 1.500$, so BS at D $= 2.340 + 1.500 = 3.840$; RL of E $= 1249.845$.
5. F (IS): rise at F is 1.000 from E: IS at F $= 2.340 - 1.000 = 1.340$; RL of F $= 1250.845$.
6. G (fall): FS at G 2.185 against IS at F 1.340: fall $= 2.185 - 1.340 = 0.845$; RL of G $= 1250.000$.
7. H (rise): BS at G 1.850 and IS at H $-1.575$: rise $= 1.850 - (-1.575) = 3.425$; RL of H $= 1253.425$.
8. I (IS): fall of 2.820 from H: IS at I $= -1.575 + 2.820 = 1.245$; RL of I $= 1250.605$.
9. J (fall): FS at J 1.895 against IS at I 1.245: fall $= 1.895 - 1.245 = 0.650$; RL of J $= 1249.955$.
10. J (BS): $\Sigma BS = 12.795$, so BS at J $= 12.795 - (3.250 + 1.755 + 3.840 + 1.850) = 2.100$.
11. K (rise): BS at J 2.100 and FS at K $-1.350$: rise $= 2.100 - (-1.350) = 3.450$; RL of K $= 1253.405$.

Completed level book

Check

$\Sigma FS = 4.000 + 1.920 + 2.185 + 1.895 - 1.350 = 8.650$, so $\Sigma BS - \Sigma FS = 12.795 - 8.650 = 4.145$.

$\Sigma \text{Rise} - \Sigma \text{Fall} = 9.405 - 5.260 = 4.145$.

Last RL $-$ first RL $= 1253.405 - 1249.260 = 4.145$. All three are equal, so the book is correct.

Answer: RLs: A 1249.260, B 1248.510, C 1248.315, D 1248.345, E 1249.845, F 1250.845, G 1250.000, H 1253.425, I 1250.605, J 1249.955, K 1253.405 m. Missing data: FS(B) = 4.000, Fall(C) = 0.195, Rise(D) = 0.030, BS(D) = 3.840, IS(F) = 1.340, Fall(G) = 0.845, Rise(H) = 3.425, IS(I) = 1.245, Fall(J) = 0.650, BS(J) = 2.100, Rise(K) = 3.450.