Question

Explain reciprocal levelling with neat sketch. 

Answer 1

Reciprocal levelling is adopted

i) To find the difference in level accurately Between the two points considerably apart.

ii) When it is not possible to set up the level in between the two points due to river or pond etc.

In this error due to curvature and refraction, collimation errors, error in instrument adjustment are eliminated.

Procedure: Let A and B be the two points on opposite banks of the river. Let it is required to find out the level difference between A and B

Step 1) Case I:Set up the level very near to A and with bubble in centre take the readings on the staff held at A and B Let these reading are a1and b1

2) Case II: Shift the level and set up very near to B and with bubble in center take the readings on the staff held at A and B, these reading are a2 and b

 

3) Let d=true difference of level between A and B

Let e= Total error ( error due to curvature and refraction , imperfect adjustment)

In Case I, The correct reading on B = b1-e

In case II , the correct reading on A = a2- e

From A, the true difference of level between A and B, d = ( b1-e)-a1

Or d= (b1-a1)-e equation 1

From B, the true difference of level between A and B , d= b2-(a2-e)

= (b2-a2)+e equation 2

To eliminate total error e adding equation 1 and 2

2d= (b1-a1) –e + (b2- a2) +e

d = (( b1-a1) + (b2-a2))/2

The error is eliminated and the true difference is equal to the mean of the two apparent differences of level between A and B