Which of the following errors in linear measurement by chains or tapes will always be negative?

📝 Detailed Explanation: Understanding the Sign of Surveying Errors

In surveying, an 'error' is defined as the Measured Value minus the True Value. Understanding whether an error is positive or negative is key to applying the correct correction.

Why 'Chain length too long' Causes a Negative Error

This is the correct answer. Here's the logic:

• If your measuring chain is physically longer than its stated value (e.g., a 30 m chain is actually 30.1 m), you are using a "stretched" ruler.
• When you measure a distance, you will lay the chain down fewer times than you would with a correct chain.
• This leads to a recorded or measured distance being shorter than the true distance. (e.g., you might record 299 m when the true distance is 300 m).
• Therefore, the error, calculated as (Measured Distance - True Distance), will always be a negative value (e.g., 299 m - 300 m = -1 m).

Analysis of Other Options

• (a) Sag in chain: When a chain sags between two points, it follows a curved path (a catenary), which is longer than the straight horizontal distance. This always results in a measured distance that is too long, making the error positive.
• (b) Temperature variation: This can be positive or negative. If the temperature is higher than standard, the chain expands and becomes too long (negative error). If the temperature is lower, the chain contracts and becomes too short (positive error). It is not always negative.
• (d) Bad ranging: This occurs when the chain is not aligned in a straight line between two points. The measured path along the crooked line will always be longer than the true straight-line distance, resulting in a positive error.

Summary of Common Errors in Chaining

This table provides a list of various errors that can occur in chain and tape measurements and classifies their nature and sign.

Case / Action	Error Type	Sign of Error (+/-)
When the length of the chain/tape is too long	Cumulative	Negative (–)
When the length of the chain/tape is too short	Cumulative	Positive (+)
Wrong alignment (Bad Ranging)	Cumulative	Positive (+)
Sag in the chain/tape	Cumulative	Positive (+)
Not stretching the tape or chain fully	Cumulative	Positive (+)
Temperature being different from standard	Cumulative	Positive (+) or Negative (–)
Applying more or less force (pull) than standard	Compensating	Positive (+) or Negative (–)
Reading the wrong mark on the chain	Compensating	Positive (+) or Negative (–)