WHY USED CORRECTION FOR CURVATURE AND REFRACTION IN LEVELING

Levelline:- A level line is a line on the surface . It is normal to the plumb line at all
points.

Line of collimation:- The line joining the intersection of the cross-hairs to
the optical -hairs to the optical center of the object glass and its continuation.
It is called the line of sight.

Curvature Correction:- In the long sighting the horizontal line is not level line due to the
level line being curved and parallel to the mean spheroidal surface of the earth.But the
line of sight is horizontal . In the long sight affects the staff reading due to curvature of
the earth, the leveling staff appear lower than real .The vertical distance between line of
collimation to the level line is called curvature correction.

In the above picture

PO= D=Horizontal distance in KM.

OQ= Cc =Curvature correction.

QC=PC= R=Radius of earth

QQ’= Diametre =12742 km

In ⊿ POC

⇒OC²=PC²+PO²

⇒(R+Cc)²=R²+D²

⇒ R²+Cc²+2RCc=R²+D²

⇒ Cc2R =D² (NoteCc² is neglected it is very small comparison to diameter of the

earth)

⇒ Cc = D²÷2R

⇒ D²×1000÷12742

⇒ 0.0785D² (negative)

True staff reading= Observed staff reading-Curvature Correction

2. Refraction correction :- When the long sites are taken the line of sight refracted towards
the surface of earth in curved path. The radius of earth is seven times that of the earth in
normal atmospheric condition.Due this effect object appears higher than really .

⇒ Cr =1/7× D²/2R

⇒ Cr=1/7× 0.0785D² m (positive)

⇒ 0.0112D² m (positive)

True staff reading = observed staff reading- Refraction correction

3. Combined correction= Curvature correction+refraction correction

- 0.0785D²+ 0.0112D²

- 0.0673 D²

True staff reading = observed staff reading- Combined correction