Ex15-1 In order to transfer reduced level across a canyon, a reciprocal leveling campaign was conducted. Simultaneous readings were observed using two levels one at each side of the canyon. Each of the levels are having same magnifying power and sensitiveness of level tube. With instruments interchanged during leveling operation yielded the following average readings:
Instrument station |
Average near readings, meter |
Average distant, readings, meter |
R.L of X = 101.345 m Distance, XY = 1.025Km e curvature = 0.0785 XY 2 |
X |
1.780 |
2.345 |
|
Y |
2.435 |
1.870 |
Find out the R.L. of unknown point. Comment on the errors associated with observations.
Solution :
The difference in elevation between X and Y is
= 0.565 m (Y lower than X)
R.L. of Y (unknown Point) = R.L. of X - Dh = 101.345 - 0.565 = 100.780 m
Since two leveling rods are used and the elapsed time between reading in a set observation is little, the error due to change in atmospheric condition can be neglected. Moreover, since readings were taken with instruments interchanged, instrumental errors get cancelled between different set of observation. As the observations are repeated and averages of the readings have been considered for further calculation, it is expected that error associated with observation is minimized thus removed. Only error present in the observation is that associated with the curvature of the earth.