Short note: sources of error in levelling

Errors in levelling are classified as instrumental, natural, and personal errors.

1. Instrumental errors

• Collimation error: the line of collimation is not parallel to the axis of the bubble tube; removed by balancing sights or by permanent adjustment (two-peg test).
• Bubble tube not adjusted, sluggish bubble.
• Staff not correctly graduated; wear and tear of the staff foot, bent staff, or loose joint (telescopic staff).
• Parallax due to improper focusing.

2. Natural errors

• Curvature of the earth: makes the staff readings too high, $C_c = 0.0785\,d^2$ (d in km, correction in m).
• Refraction: bends the line of sight downward, so readings are too low, $C_r = \dfrac{1}{7}C_c$.
• Temperature changes causing unequal expansion of the instrument and heat shimmer; wind causing vibration; settlement of the tripod or of the staff in soft ground.

3. Personal errors

• Bubble not centred at the time of reading.
• Staff not held vertical; wrong reading (e.g. reading 1.234 as 1.324) or inverted figures; wrong booking.
• Staff not held on the same point at the change point.
• Mistakes in calculation (wrong addition or subtraction, wrong sign).
• Wrong focusing or sighting in a hurry.

Minimising the errors: balance the sights, test and adjust the level, keep the sights short (about 60–100 m), hold the staff vertical, avoid the lowest part of the staff, and apply the arithmetic checks.