Question

Reciprocal levelling is performed for points P and Q by placing the same levelling instrument at A and B. The observations of staff readings are tabulated as below. 

If the Reduced Level (RL) of P is 115.246 m, then the true RL of Q, in m, is _______ (rounded off to 3 decimal places)
 

Hint:

In reciprocal levelling, the average of staff intercept differences at both instrument locations gives the true difference in levels between the two points.

Answer 1

Step 1: Compute the difference in readings at instrument A and B.
The staff intercepts at A and B for stations P and Q are given as:
At A, Staff reading for P = 1.512 m, and for Q = 2.100 m.
At B, Staff reading for P = 0.680 m, and for Q = 1.302 m.
The difference in staff readings for stations P and Q at A and B is: \[ \Delta h_A = 2.100 - 1.512 = 0.588 \, {m} \] \[ \Delta h_B = 1.302 - 0.680 = 0.622 \, {m} \] Step 2: Calculate the difference in the reduced levels between stations P and Q.
The difference in reduced levels is the average of the differences in readings at A and B: \[ \Delta h = \frac{\Delta h_A + \Delta h_B}{2} = \frac{0.588 + 0.622}{2} = 0.605 \, {m} \] Step 3: Determine the true Reduced Level (RL) of Q.
The RL of station P is given as 115.246 m. To find the RL of Q, subtract the difference in height from station P's RL: \[ {RL of Q} = 115.246 - 0.605 = 115.136 \, {m} \] Thus, the true RL of Q is \(\boxed{115.136 \, {m}}\).