Reciprocal levelling is a method of levelling used to eliminate errors caused by the curvature and refraction of the earth's surface. The following are the details explaining why option 'D' is the correct answer:

Elimination of Curvature Error:
Curvature error occurs when the earth's surface is not flat, and the line of sight between the instrument and the staff is not straight. As a result, the measured height of the staff is affected by the curvature of the earth's surface. In reciprocal levelling, two points are measured in both forward and backward directions, and the difference in the readings is taken to eliminate the curvature error.

Elimination of Refraction Error:
Refraction error occurs when the light rays passing through the atmosphere deviate from their straight path due to the variation in the density of the medium. This deviation causes the staff to appear higher or lower than its actual height. In reciprocal levelling, the errors due to refraction are minimized by taking readings in both forward and backward directions, and the average of the readings is taken to eliminate the refraction error.

Partially Elimination of Refraction Error:
Although reciprocal levelling helps to minimize the refraction error, it cannot fully eliminate it. This is because the variation in the density of the atmosphere cannot be accurately measured, and thus, the exact amount of deviation in the light rays cannot be determined. Therefore, it is said that reciprocal levelling can eliminate the curvature error fully and the refraction error partly.

In conclusion, reciprocal levelling is a useful method of levelling that helps to eliminate errors caused by the curvature and refraction of the earth's surface. While it can fully eliminate the curvature error, it can only partially eliminate the refraction error.