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Principle applied in two-way linear measurement

Short answer

Measure the line forward and backward with the same tape and tension. Compute the difference and relative error; if within the permissible limit (e.g., 1/2000), adopt the mean. This provides an independent check, detects mistakes, and reduces accidental errors by averaging.

How do you apply the principle of surveying in two-way linear distance measurement? Explain.

A principle of surveying is that a quantity should be fixed by at least two independent measurements, and each measurement must be checked. In linear measurement this is done by measuring the line twice, in the forward and backward directions (two-way measurement).

Procedure

  1. Measure line AB from A to B with the tape, keeping it straight, level and under the same tension. Record L1L_1.
  2. Measure back from B to A in the same way. Record L2L_2.
  3. Find the difference d=∣L1−L2∣d = |L_1 - L_2| and compute the relative error =d/Lmean= d / L_{mean}.
  4. Compare it with the permissible error (e.g. 1/1000 to 1/2000 for ordinary chaining, 1/5000 or better for careful taping on level ground).
  5. If the error is within the limit, adopt the mean:
L=L1+L22L = \frac{L_1 + L_2}{2}
  1. If it is greater, find the cause (miscounted tape lengths, wrong reading, slack tape) and measure again.

Example

L1=150.42L_1 = 150.42 m and L2=150.38L_2 = 150.38 m. Difference =0.04= 0.04 m, relative error =0.04/150.4=1/3760= 0.04/150.4 = 1/3760. This is better than 1/2000, so it is acceptable for ordinary work (though not for precise taping to 1/5000), and L=150.40L = 150.40 m.

The backward measurement is independent of the forward one, so mistakes are detected and accidental errors are reduced by averaging.

✓ Answer checked by Claude Opus 5.5 (high effort)

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