Reciprocal Leveling is also used when it is not possible to set up a level instrument.
fig 1.
PROCEDURE Let A and B be the two points whose difference is to be determined.
i. Set the level instrument near A. Complete temporary adjustment and takes reading staff A and B. Write the reading like as a1 and b1. shown in fig. 1
fig 2.
ii Transfer the instrument to B and set up near to B. Make a temporary adjustment. Take the staff reading as a2 and b2.
d= the true difference of level between A and B. e= the total error due to curvature, refraction, and imperfect collimation adjustment.
The correct staff reading in fig.1= b1-e.
The correct staff reading in fig.2= a2-e.
In the fig.1 the true difference of level between A and B (true fall from A to B) d= (b1-e)-a1
or d= (b1-a1)-e ....................................equation F
In the fig.2 the true difference of level between A and B (true fall from A to B)
d= b2-(a2-e) or (b2-a2) +e ............................................equation G
Adding the equation Fand G to eliminate e, we get
d= (b1-a1)+(b2-a2)/2
Two values gives the true difference of elevation between two points free from all errors, like error due to curvature of the earth, refraction error and error of collimation error.