Horizontal Stadia Sights 2

PROBLEM:
A dumpy level with an interval focusing telescope was set up on the left bank of a river and the rod reading tabulated below were taken on a stadia rod held successively at the left and right water edges, if the K is 95.50m and stadia constant is 0.30m. Determine with of the river.

Rod Position Hair Readings
U (a) M (c) L (b)
Rod Held @ LWE 2.189m 2.172m 2.155m
Rod Held @ RWE 2.277m 2.173m 2.069m

Wherein:
S = stadia sight observed @ LWE
S2 = stadia sight observed @ RWE
d = horizontal distance from the level of the rod @ LWE
d2 = horizontal distance from the level of the rod @ RWE
w = width of the river

Formula:
S = (a - b)
S2 = (a2 – b2)
d = Ks + C
d2 = Ks2 + C
w = d + d2

Given:
K = 95.50m
C = 0.30m

Solution:
S = (a - b)
= (2.189 – 2.155)
= 0.034m
S2 = (a2 – b2)
= (2.277 – 2.069)
= 0.208 / 0.21m
d = Ks + C
= 95.5 (0.034) + 0.3
= 3.247 + 0.3
= 3.55m
d2 = Ks2 + C
= 95.5 (0.21) + 0.3
= 95.5 (0.21) + 0.3
= 20.36m
w = d + d2
= 3.55m + 20.36m
= 23.91m