Example of Random or Accidental Errors:

A 30 m chain was found to be 3 cm too long after chaining 1800 m. The similar chain was observed to be 5 cm too long after chaining the total distance of 3600 m. assuming in which the chain was correct at the commencement of work, search the true length of the total distance chained.

Solution

(a) During chaining from 0 m to 1800 m:

Initial length of chain at commencement of work = 30.0 m Final length of chain at end of chaining up to 1800 = 30.03 m Average true length of chain during this exercise

= 30.03 + 30.00/2 = 30.015 m

True distance of measured distance 1800 m =L'/L× 1800                                ...(i)

= 30.015 /30.00× 1800 = 1800.90 m

 (b)      During measurements from 1800 to 3600 m:

Initial length of chain = 30.03 m

Final length of chain = 30.05 m

Average true length of chain during this measurement

= 30.03 + 30.05/2 = 30.04 m

Measured distance = 3600 - 1800 = 1800 m

True measured distance = 30.04 × 1800/30.00 = 1802.40 m                              . . . (ii)

Total true distance chained = 1800.90 + 1802.40 = 3603.30 m.