The rise and fall method of levelling provides a complete arithmetic check on:
Correct Answer: D. Back sights, intermediate sights, and fore sights
📚 Detailed Explanation: Rise and Fall Method Checks BS, IS, and FS
Why D (Back sights, intermediate sights, and fore sights) is correct: The rise and fall method provides the most complete arithmetic check of all three categories of staff readings — BS, IS, and FS. This is its defining advantage over the Height of Instrument (HI) method, which only checks BS and FS arithmetically and does not detect errors in IS readings.
Rise and Fall Method: Complete Worked Example
| Station | BS | IS | FS | Rise | Fall | RL |
|---|---|---|---|---|---|---|
| BM | 1.855 | 100.000 | ||||
| A | 2.410 | 0.555 | 99.445 | |||
| B | 1.280 | 1.130 | 100.575 | |||
| CP1 | 2.165 | 0.995 | 0.285 | 100.860 | ||
| C | 1.720 | 0.445 | 100.415 | |||
| Sums | 4.020 | 2.715 | 1.415 | 1.000 |
Three arithmetic checks:
(1) ΣBS – ΣFS = 4.020 – 2.715 = 1.305 ✓
(2) ΣRise – ΣFall = 1.415 – 1.000 = 0.415…
(1) ΣBS – ΣFS = 4.020 – 2.715 = 1.305 ✓
(2) ΣRise – ΣFall = 1.415 – 1.000 = 0.415…
Wait – the IS readings (A, B) contribute to rise/fall:
A: IS=2.410 vs BS=1.855 → Fall of 0.555 → RL(A) = 100.000 – 0.555 = 99.445
B: IS=1.280 vs IS=2.410 → Rise of 1.130 → RL(B) = 99.445 + 1.130 = 100.575
CP1 FS=0.995 vs IS=1.280 → Rise of 0.285 → RL(CP1) = 100.575 + 0.285 = 100.860
C FS=1.720 vs BS(CP1)=2.165 → Fall of 0.445 → RL(C) = 100.860 – 0.445 = 100.415
ΣRise – ΣFall = (1.130+0.285) – (0.555+0.445) = 1.415 – 1.000 = 0.415
Last RL – First RL = 100.415 – 100.000 = 0.415 ✓
All IS readings are captured in the Rise/Fall column — errors in IS ARE detected.
- Rise and fall checks: Back Sights + Intermediate Sights + Fore Sights (all readings).
- HI method checks: BS + FS only; IS errors go undetected.
- For surveys with many IS readings, R&F is the more reliable check.