We know that earth flattens in the polar direction and this curvature of earth is responsible for the departure of horizontal line from a level surface. To counter this error, orthometric corrections is applied.
This departure in feet, Cf is calculated as
Cf= 0.667M2=0.0239F2
This departure in meters, Cm is calculated
Cm =0.0785K 2
where M = distances in miles from the point of tangency to the earth.
F= distances in thousands of feet from the point of tangency to the earth.
K = distances in kilometers from the point of tangency to the earth.
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This is NOT the orthometric correction. The equation and discussion are for earth curvature – how much a spherical surface departs from a tangential straight line as distance increases.
The orthometric correction an elevation correction due to the effect of gravity and centrifugal force on equipotential surfaces. These surfaces are flattened at the poles and expanded at the equator. A “constant” elevation is an equipotential surfaces. The physical distance between two elevations gets shorter as we approach the poles. The amount it shortens, which depends on the distance surveyed, is the orthometric correction.