reciprocal levelling

When obtaining the relative levels of two points on opposite side of a wide gap such as a river , it is impossible to keep the length of sights short and equal .

Collimation error , Earth curvature and refraction affect the longer sight much more than the shorter one . in order to minimize these effects, the method of reciprocal levelling is used , as illustrated in 

if the instrument near A observes a backsight onto A and a foresight onto B , the difference in elevation between A and B is :

this proves that the mean of the difference in level obtained with the instrument near A and then with the instrument near B is free from the errors due to curvature , refraction and collimation error . Random errors of observation will still be present , however .

Assumes , the value of refraction is equal in both cases , Refraction is a function of temperature and pressure and so varies with time . Thus refraction may change during the time taken to transport the instrument from side A to side B . To preclude this it is advisable to use two levels and take simultaneus reciprocal observations .

however . this procedure creates the problem of each instrument having a different residual collimation error . The instruments should therefore be interchanged and the hhole procedure repeated .

The instrument should therefore be interchanged and the whole procedure repeated . The mean of the values obtained will then give the most probable value for the difference in level between A and B .