# Reciprocal Levelling | Curvature and Refraction Correction

## Reciprocal levelling helps in compensating for the error due to curvature and refraction & also line of collimation errors in surveying.

In reciprocal levelling, the level is set up on both sides of the levels. Two sets of staff reading is taken. This helps in compensating for the error due to curvature and refraction & also line of collimation errors in surveying.

It is assumed that the atmospheric refraction remains at the same level when the instrument is shifted (Advisable to shift the instrument quickly!)

### Curvature and refraction error

• Curvature correction : Horizontal line is not a level line, because of which the staff reading is more than expected. Negative correction required.

• Refraction correction : Rays of light passing through the atmosphere of different density bends down. Positive correction to be applied.

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Let us say A and B are two points as shown in figure below.

• Instrument is setup near A and readings on the staff are noted (x1 and y1)

• Instrument is shifted near B and readings on staff are again noted (x2 and y2)

Let the curvature and refraction error be e, the calculation is as shown below