Question

If the horizontal distance between a staff point and the point of observation is \( d \), the error due to the curvature of the earth is proportional to

• A. \( d \)
• B. \( \frac{1}{d} \)
• C. \( d^2 \)
• D. \( \frac{1}{d^2} \)

Hint:

When calculating errors due to the curvature of the earth, always use the squared distance formula for accuracy.

Answer 1

The Correct Option is C

The error due to the curvature of the earth is given by the formula:

\[ E = +0.0785d^2 \]

where \( E \) is the error and \( d \) is the horizontal distance between the staff point and the point of observation. From the formula, we can see that the error is proportional to \( d^2 \).

Thus, the correct answer is option (C).

The error due to curvature increases with the square of the distance. This is a key concept in geodesy and surveying.