Combined correction for curvature and refraction formula
Answers
Curvature:
Earth has a curved face which is assumed to be a level surface but the line of sight as furnished by the levelling instrument is horizontal and not the level line. Therefore, all points on the line of sight are not equidistant from the surface of the earth and consequently the points read on the staff are not strictly at the same level as horizontal hair of the diagram.
The level line falls away from the horizontal line of sight and the vertical distance between the horizontal line and the level line denotes the effect of curvature of the earth.
In Fig., 7.24. A’ is the instrument station and P the point where the staff is held. On looking through the telescope, we sight along AB, the horizontal line of sight, and take the staff reading PB. The point B is consider to be at the same level as A, but actually the points C and A are at the same level. The true reading is, therefore, PC.
The difference BC between the observed and true staff readings denotes the error due to curvature of the earth, which may be determined as follows: