We have found by the principle of equalizing backsight and foresight distances that if the level is placed exactly midway between two points and staff reading are taken to determine the difference of level, then the errors (due to inclined of collimation line, curvature and refraction) are automatically eliminated. But in the case of a river or valley, it is not possible to set up the level midway between the two points on opposite banks. In such case the method of reciprocal levelling is adopted, which involves reciprocal observation both banks of the river or valley.
In reciprocal leveling, the level is set up on the both banks of the river or valley and 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 true difference of level is equal to the mean of the true apparent differences of level.
. Suppose A and B are two points on the opposite banks of a river. The level is set up near A and after proper temporary adjustment, staff readings are taken at A and B. Suppose the readings are a₁ and b₁ (Fig. – L.23.a).
. The level is shifted and set up very near B and after proper adjustment, staff reading are taken at A and B. suppose the readings are a₂ and b₂ (Fig. – L.23.b).
Let h = true difference of level between A and B
e = combined error due curvature, refraction and collimation (The error may be positive or negative, here we assume positive)
In the first case,
Correct staff reading at A = a₁ (as the level very near A)
Correct staff reading at B = b₁ - e
True difference between A and B,
h = a₁ – (b₁ – e) (fall from B to A) ……. (1)
In the second case,
Correct staff reading at B = b₂ (as the level very near B)
Correct staff reading at A = a₂ - e
True difference of level,
h = (a₂ –e) - b₂ …….……. (2)
From (1) and (2),
2h = a₁ – (b₁ – e) + (a₂ – e) - b₂
= a₁ – b₁ + e + a₂ – e - b₂
h = [(a₁ – b₁)+(a₂ – b₂)]/2
It may be observed that the error is eliminated and that the true difference is equal to the mean of two apparent differences of level between A and B.
(Next post on “METHODS OF CALCULATION OF REDUCE LEVEL”)