[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

Â» The difference in level between A and B

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

Â  Â  = 1.545 m

Error due to curvature = 0.07849 d2 m

= 0.07849 (1.53)2

= 0.184 m

âˆ´ When the level is at A, corrected staff reading on

B = 3.810 – (Cc – Cr) + C1

Where,

Cc = Correction due to curvature

Â  Â  = 0.184 m

Cr = Correction due to Refraction

C1 = Correction due to collimation

= (0.004/100) Ã— 1530

= 0.0612 m

âˆ´ Corrected staff reading on B

Â  Â  = 3.810 – (0.184 – Cr) + 0.0612

Â  Â  = 3.6872 + Cr

âˆ´ True difference in level between A and B

= (3.6872 + Cr – 2.165)

Â  Â  = (1.5222 + Cr)

But it is quual to 1.545

âˆ´ 1.5222 + Cr = 1.545

Cr = 1.545 – 1.5222

= 0.0228 â‰ƒ 0.023 m

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