Chaining Error – Effect of a Too-Short Chain on Measured Distance If a 30 m chain is actually 0.01 m too short (i.e., its true length is 29.99 m) and is used for chaining, what type of error is introduced in the measured distance over a long line?

Introduction:
Instrumental length errors in chains or tapes create systematic bias in measured distances. Recognizing the sign and nature (cumulative vs compensating) of such errors is essential for applying corrections in traverse calculations and setting out.

Given Data / Assumptions:

• Nominal chain length = 30.00 m; actual chain length = 29.99 m (too short by 0.01 m).
• Chaining is done by counting full chain lengths along a line.
• No slope or temperature corrections are applied in this conceptual question.

Concept / Approach:

With a too-short chain, each counted '30 m' segment on the ground is truly only 29.99 m. To cover the same true distance, more chain lengths are counted, so the reported distance (count × 30) becomes larger than the true distance. The bias adds up with every application, hence it is a positive cumulative error.

Step-by-Step Solution:

Verification / Alternative check:

Apply the standard correction formula: corrected length = measured length × (actual/nominal) = Lm × (29.99/30) < Lm, confirming measured is too large.

Why Other Options Are Wrong:

Compensating errors change sign and can cancel; here the bias is one-sided. 'Negative cumulative' is the opposite of what occurs. Personal errors are separate from instrumental bias.

Common Pitfalls:

Misremembering which sign applies for too-long vs too-short chains; forgetting to scale the entire measured line by the length ratio.

Final Answer:

Positive cumulative error