Q.A 30 chain, was tested before the commencement of the day’s work and found 5 cm too long. After chaining a distance of 1600 m, it was checked again and found 10 cm too long. At the end of days work, after chaining 3000 m, the chain was found to be 18 cm. too long. Find the true distance measured.
Solution:
For first 1600 metres:
Average error e₁=(5+10)/2 = 7.5 cm
= 0.075 m, too long.
Incorrect length of chain
L1=30+0.075 = 30.075 m
True length
= L1 = L₁/L*ML₁
= ( 30.075 / 30 ) x1600
= 1604 m
For next 1400 metres:
Average error = e2
10+18/2 = 14cm 0.14 m, too long.
Incorrect length of chain
L2= 30+0.14 =30.14m
True length = L=( L’2/L)x ML2
= 30.14/30 * 1400 = 1406.53 m
Total True length of line =L= L1 + L2
= 1604 +1406.53
= 3010.53
Q. The surveyor measured the distance between two stations on a plan drawn to a scale of 10 m to 1 cm and the result was 686 m. Later, however, it was discovered that he used a scale of 20 m to 1 cm. Find the true distance between the station s.
Solution:
Distance between two points measured with a scale of
1cm to 20m = 686/20 = 34.3cm
Actual scale of the plan is 1cm = 10 m
True distance between the points = 34.3 x 10 =343 m