# Incorrect Chaining in Surveying – Error & Correction

If the chain that is employed for measuring length is not equal to the true length, then the length measured won’t be correct. This measurement hence requires correction.

A chain that is very long, gives a distance that is lesser in value. This means the error is negative and the correction is positive. A chain that is short, gives larger distance value. In this case, the error is positive and the correction is negative.

If,

L = True length or designated length of the chain or tape

L’ = Incorrect or Actual Length of the chain or tape used

The correction for length, area and volume can be given by the following formulas.

## 1. Correction to Measured Length

If ‘l’ is the actual or true length of the line and l’ is the measured length of the line then,

True length of the line = Measured length x [L’/L]

** l = l’ x (L’/L) ** Eq.1

## 2. Correction to Area

If ‘A’ is the actual or the true area of the ground and A’ is the measured or the calculated area of the ground, then

True Area = Measured Area x Square of [L’/L]

Also,

L’/L = [(L +dL) / L] = 1 + (dL /L) Eq.3

dL = Error in the length of chain;

Let dL/L =e;

Eq.3 becomes,

**L’/L = 1+e**

Therefore,

A= (1+e)(1+e) . A’

A=[ 1+2e+ (e.e)] A’

If e is very small, then

### A = (1 +2e)A’

## 3. Correction to Volume

If V is the actual or the true volume and V’ is the measured or the computed volume, then

True volume = Measured Volume x cube of [L’/L]

Also,

L’/L = [(L +dL) / L] = 1 + (dL /L) Eq.5

dL = Error in the length of chain;

Let dL/L =e; Therefore Eq.5. becomes

**L’/L = 1+e**

Eq.5 becomes,

V = (1+e)(1+e)(1+e).V;

By solving,