RECIPROCAL LEVELLING

• Reciprocal leveling is used to determine the correct difference of elevations of the two points which are quite far apart and when it is not possible to set up the instrument mid-way between the two points to balance the fore sight and back sight.
• This reciprocal leveling is usually used to determine the difference of elevations of two points on the opposite banks of a river or a deep gorge.
• Reciprocal levelling eliminates the error due to curvature and refraction.

In Figure, let A and B be the two points on opposite banks of a river. The following procedure is used:

• Drive pegs at A and B. Set up the instrument at L₁ near peg A. Take readings ‘a’ and ‘b’ on staffs held at A and B respectively
• Shift instrument to L₂ near peg B. Take readings ‘a₁’ and ‘b₁’ on staffs held at A and B respectively.
• Find the correct difference in elevations between A and B as per the procedure given below:

Let B is at higher elevation than A and e be the total error.

When instrument is at L₁

Apparent difference of levels, h’ = a – b

Since A is very near to L₁, the error in a is not significant.

Thus, correct staff reading at A = a

Correct staff reading at B = b – e

Correct difference of levels, h = a – (b – e)

When instrument is at L₂

Apparent difference of levels, h” = a1 – b1

Correct staff reading at B = b₁

Thus, correct staff reading at A = a₁ – e

Correct difference of levels, h = (a1 – e) – b1

Adding Eqs. (a) and (b),

2h = a – (b – e) + (a1 – e) – b1

h = [(a₁ – b₁) + (a – b)]/2

h = (h’ + h”)/2