The difference between the last reduced level and the first reduced level is equal to:
Correct Answer: C. difference between the sum of back sights and foresights
📚 Detailed Explanation: Difference Between Last RL and First RL = Difference Between Sum of BS and FS
Why C (difference between the sum of back sights and foresights) is correct: This is the fundamental arithmetic check (closure check) in levelling: the algebraic sum of all Back Sights minus all Fore Sights must equal the difference between the last Reduced Level and the first Reduced Level. This check validates all HI calculations.
Arithmetic check (applicable to all levelling methods):
ΣBS – ΣFS = Last RL – First RL
ΣBS – ΣFS = Last RL – First RL
Derivation (simple example with 2 setups):
HI₁ = RL₁ + BS₁
RL₂ = HI₁ – FS₁ = RL₁ + BS₁ – FS₁
HI₂ = RL₂ + BS₂ = RL₁ + BS₁ – FS₁ + BS₂
RL₃ = HI₂ – FS₂ = RL₁ + BS₁ – FS₁ + BS₂ – FS₂
= RL₁ + (BS₁ + BS₂) – (FS₁ + FS₂)
= RL₁ + ΣBS – ΣFS
Therefore: RL₃ – RL₁ = ΣBS – ΣFS ✓
Summary of Arithmetic Checks
| Method | Check Formula |
|---|---|
| HI method | ΣBS − ΣFS = Last RL − First RL |
| Rise and Fall method | ΣBS − ΣFS = Last RL − First RL AND ΣRise − ΣFall = Last RL − First RL |
- Arithmetic check: ΣBS − ΣFS = Last RL − First RL.
- This check verifies all HI and RL calculations but does not check IS in the HI method.
- Intermediate sights do NOT appear in this formula (they cancel out in the derivation).