The correct answer is: C. error due to both curvature and re-fraction.
The error due to curvature is caused by the fact that the Earth is not a flat surface, but is curved. This means that when you sight a level from one station to another, the line of sight is actually curved. This can cause an error in the measurement, which can be significant for long distances.
The error due to refraction is caused by the fact that light bends as it passes through the atmosphere. This bending is caused by the difference in temperature and pressure in the atmosphere. This can also cause an error in the measurement, which can be significant for long distances.
By setting the level midway between the two stations, you can reduce the effect of both the curvature and refraction errors. This is because the line of sight from the level to each station is now shorter, and the effect of the curvature and refraction is therefore less.
A. error due to curvature only
This is not the correct answer because the error due to refraction is also present.
B. error due to refraction only
This is not the correct answer because the error due to curvature is also present.
D. none of the above
This is not the correct answer because the error due to both curvature and refraction can be neutralised by setting the level midway between the two stations.