(a) Determine from first principles the approximate distance at which correction for curvature and refraction in levelling amounts to 3 mm, assuming that the effect of refraction is one seventh that of the Earth's curvature and that the Earth is a sphere of 12740 km diameter.
(b) Two survey stations A and B on opposite sides of a river are 780 m apart, and reciprocal levels have been taken between them with the following results:
Compute the ratio of refraction correction to curvature correction, and the difference in level between A and B.