The rise and fall method of booking levelling field readings provides an arithmetic check on:
Correct Answer: C. Both back sights and fore sights
📚 Detailed Explanation: Rise and Fall Method Checks Both BS and FS (and IS)
Why C (both BS and FS) is correct: The Rise and Fall (R&F) method provides a built-in arithmetic check on every reading — backsights, intermediate sights, and foresights. This is its main advantage over the HI (Height of Instrument) method, which does NOT check intermediate sights arithmetically.
Arithmetic Checks in Rise and Fall Method
| Check | Rise and Fall Method | HI (Collimation) Method |
|---|---|---|
| Sum of rises − sum of falls | = Last RL − First RL ✓ | Not applicable |
| Sum of BS − sum of FS | = Last RL − First RL ✓ | = Last RL − First RL ✓ |
| Checks intermediate sights (IS) | YES — included in rise/fall column | NO — IS errors are not caught |
| Mathematical certainty | High (3 independent checks) | Lower (only 1 definitive check) |
Rise and Fall arithmetic checks (3 checks):
(1) ΣBS – ΣFS = Last RL – First RL
(2) ΣRise – ΣFall = Last RL – First RL
(3) ΣBS – ΣFS = ΣRise – ΣFall
(1) ΣBS – ΣFS = Last RL – First RL
(2) ΣRise – ΣFall = Last RL – First RL
(3) ΣBS – ΣFS = ΣRise – ΣFall
All three must agree. If any check fails, an error exists somewhere in the field book.
- Rise and Fall method checks BS, IS, and FS readings arithmetically.
- HI method only checks BS and FS; intermediate sight errors go undetected.
- R&F is preferred when there are many IS readings and high accuracy is needed.