For rapid leveling or leveling in rolling ground or for inaccessible points, trigonometric method of leveling is being used. In this method, theodolite (an instrument which can measure angle) is being generally used as an instrument for taking different measurements.
Let us consider two stations T and X on rolling ground whose difference in elevation is required to be determined (Figure 15.2) by trigonometric method of leveling. At T, a theodolite instrument is set up. TT ' is the height of the instrument above the point T (to be recorded at the time of observation). A leveling staff is held at X. At the vertical angle of elevation of the actual line of sight a, let x1 is the observed staff reading. The difference in level between T and X is given by
where xt' xh is deviation of the horizontal line of sight due to curvature of the earth and refraction of light (given by 0.0675 T' x h2 ). xh x1 is T' x1 sina or T' x h tana , T' x1 is the inclined distance from the instrument to the staff and T' xh is the horizontal distance between the points, x1 X is the staff reading at X.