Which of the following expressions is correct to calculate the correction for curvature (Cc) in levelling? Where, d is the distance sighted (measured in km).

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  1. Cc = 0.6782d2 m
  2. C= 0.5459d2​ m
  3. C= 0.07849d2​ m
  4. Cc = 0.02498d2​ m

Answer (Detailed Solution Below)

Option 3 : C= 0.07849d2​ m
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Detailed Solution

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Explanation:

We know Correction for the curvature is given by

  

Where

d = distance between points under consideration

R is the Radius of earth = 6370 km

It is always negative 

Correction due to curvature

C

Cc = - 0.0785 d2

Important Points 

Correction due to refraction (CR) is given by 1/7th of correction due to curvature.

 

But it is a positive correction.

Corrections due to refraction

CR = + 0.0112 d2

Composite correction

C = - 0.0785 d+ 0.0112 d2

C = - 0.0673 d2 

where d is the distance between the staff and the instrument in km, and C is in m.

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