Surveying Reciprocal leveling done

In the case of an obstacle like river valley, it is not possible to set the up the level midway between two points on the opposite banks. In such cases the method of reciprocal leveling is adopted, which involv3es reciprocal observations from both banks of the river or valley. Two sets of staff readings are taken by holding the staff on both banks. In this case it is found that the errors are completely eliminated and the true difference of level is equal to the mean of the two apparent differences of level. The principle is explained as follows.

up very near a and after proper temporary adjustment , staff readings are taken at A and B. Suppose the readings are a1 and b1.

The level is shifted and set up very near B and after proper adjustment , staff readings are taken aat A and B .Suppose the readings are a2 and b2.

Let  h = true difference of level between A and B

e = Combined error due to curvature , refraction and collimation