[30 Marks] Two points A and B are 1530 m apart across a wide river

Question:

Two points A and B are 1530 m apart across a wide river. The following reciprocal levels are taken with one level.

Level at	Reading on A	Reading on B
A	2.165	3.810
B	0.910	2.355

The error in the collimation adjustments of the levels is -0.004 m in 100 m. Calculate the true difference of level between A and B and the refraction.

Solution for Two points A and B are 1530 m apart across a wide river

» The difference in level between A and B

    = [(3.810 – 2.165) + (2.355 – 0.910)]/2

    = 1.545 m

Error due to curvature = 0.07849 d² m

    = 0.07849 (1.53)² 

    = 0.184 m

∴ When the level is at A, corrected staff reading on

    B = 3.810 – (Cc – Cr) + C1

Where, 

Cc = Correction due to curvature

    = 0.184 m

Cr = Correction due to Refraction

C1 = Correction due to collimation

    = (0.004/100) × 1530 

    = 0.0612 m

∴ Corrected staff reading on B

    = 3.810 – (0.184 – Cr) + 0.0612

    = 3.6872 + Cr

∴ True difference in level between A and B

    = (3.6872 + Cr – 2.165)

    = (1.5222 + Cr)

But it is quual to 1.545

∴ 1.5222 + Cr = 1.545

Cr = 1.545 – 1.5222

    = 0.0228 ≃ 0.023 m