Chain surveying errors – identifying a cumulative error (positive or negative) Among the following, which source of error in chaining is cumulative in nature and may be positive or negative depending on the direction of error?

Introduction / Context:
Errors in chaining are classified as cumulative or compensating. Cumulative errors add up systematically with each chain length, whereas compensating errors tend to cancel out partially due to randomness. Recognizing which errors are cumulative helps surveyors prioritize calibration and procedural controls. This question targets the classic cumulative error source in chain surveys.

Given Data / Assumptions:

• Standard chain or tape is used to measure multiple lengths.
• Some errors repeat at every application of the chain length.
• Others vary randomly with sign and magnitude.

Concept / Approach:

If the chain is too long or too short relative to its nominal length (due to wear, temperature, or manufacturing tolerance), every measured segment inherits a systematic bias. Over many applications, the total measured distance will be proportionally too small (if chain is long) or too large (if chain is short). Hence, chain-length error is cumulative and can be positive or negative depending on whether the error shortens or lengthens the actual standard relative to nominal.

Step-by-Step Solution:

Verification / Alternative check:

Field calibration against a standard base line reveals a constant ratio error that persists across measurements, confirming the cumulative character.

Why Other Options Are Wrong:

Bad ranging/straightening: predominantly compensating; signs vary with operator behavior and terrain, partially canceling out.

Sag: generally produces an excess length (tape sags), thus a consistent negative correction; while systematic, it is treated per span and not strictly “±” as asked.

Common Pitfalls:

Ignoring temperature corrections; failing to recalibrate worn chains, leading to large positional misclosures.

Final Answer:

Erroneous length of chain