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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.
Contents:
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,
V = (1+3e)V'
Also Read: Errors in Chaining -Causes and Types
