For long sights and accurate levelling work, the effects of curvature of the earth and refraction of the line of sight shall have to be taken into consideration. Due to curvature, the points appear to be lower than they actually are; while due to refraction, they appear to be higher than they actually are.
Music Theory - Treble Clef (Understanding & Identifying Notes)
The effect of curvature being greater than that of refraction, the combined effect causes the points to appear to be lower than they actually are. 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.
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.
CBSE Guide Light Reflection and Refraction class 10 Notes
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:. Since BC is usually very small as compared with the diameter of the earth and its square will still be much smaller and may therefore be neglected in calculation:.
The effect of curvature is to increase the staff reading i. It is a well-established law of physics that rays of light passing through layers of different densities do not remain straight but are refracted or bent down towards the denser medium.
Consequently, the ray of light from the staff to the instrument is not straight as AB in fig. Under normal atmospheric conditions, arc AD may be taken as circular and of radius seven times that of the earth.
Hence the correction for refraction is additive to the staff reading. Since the effect of curvature is to increase the staff readings and that of refraction is to decrease them and also the effect of curvature is greater than that of refraction, the combined effect is therefore, to increase the staff readings, hence the combined correction is subtractive.
For ordinary lengths of sights, the error is very small and hence negligible. It may be well understood that for m length, it is only 0.
Therefore sights less than m in length, the effect may be neglected. The error due to curvature and refraction can be eliminated by equalising back sight and fore sight distances and also by the method of reciprocal levelling which is explained in the article.
Curvature and Refraction in Levelling , Levelling , Surveying.