Levelling · Geomatics Engineering Or Surveying · GATE CE

If the horizontal distance between a staff point and the point of observation is $d$, the error due to the curvature of earth is proportional to

In levelling between two points A and B on the opposite banks of a river, the readings are taken by setting the instrument both at $A$ and $B$, as shown in the table. If the $R L$ of $A$ is 150.000 m , the $R L$ of $B$ (in m ) is __________ (rounded off to 3 decimal places).

Level position	Staff readings
	A	B
A	1.800	1.350
B	1.450	0.950

Trigonometric levelling was carried out from two stations P and Q to find the reduced level (R. L.) of the top of hillock, as shown in the table. The distance between Stations P and Q is 55 m. Assume Stations P and Q, and the hillock are in the same vertical plane. The R. L. of the top of the hillock (in m) is ____________ (round off to three decimal places).

$$ \begin{array}{|c|c|c|c|} \hline \text { Station } & \begin{array}{c} \text { Vertical } \\ \text { angle of } \\ \text { the top of } \\ \text { hillock } \end{array} & \begin{array}{c} \text { Staff } \\ \text { reading on } \\ \text { benchmark } \end{array} & \begin{array}{c} \text { R.L. of } \\ \text { bench } \\ \text { mark } \end{array} \\ \hline \mathrm{P} & 18^{\circ} 45^{\prime} & 2.340 \mathrm{~m} & \begin{array}{c} 100.000 \\ \mathrm{~m} \end{array} \\ \hline \mathrm{Q} & 12^{\circ} 45^{\prime} & 1.660 \mathrm{~m} & \\ \hline \end{array} $$