Errors and Adjustment

Repeat any measurement and the answers scatter — not from carelessness but because measurement is a physical process with limits. The readings fall in a normal distribution: small errors common, large ones rare, positive and negative equally likely.

So the question is never what the value *is*, but how confident we are and over what range. Every survey specification is written in that language.

A systematic error is the dangerous one: repetition narrows the scatter without moving the centre, so you become more confident about a wrong answer. That is why precision and accuracy are kept as separate words.

• Standardise the tape against a known length — calibration.
• Equalise sight distances — cancels curvature, refraction and collimation at once.
• Observe on both faces — cancels the three instrument axis errors.
• Reciprocal observations — cancels what the others cannot reach.

The elegant part is that none of these procedures measures the error. They arrange for it to cancel, which is why survey procedure looks fussy and is not.

A survey with exactly enough observations has no check — every answer is consistent by construction, including a wrong one. Deliberate over-observation creates redundancy, and redundancy is what lets measurements disagree visibly. That is why a traverse is closed and a level run is run back.

Least squares then finds the coordinates minimising the weighted sum of squared residuals, honouring a precise observation more than a rough one — and reporting the precision of every adjusted point as a by-product. Bowditch and the transit rule are special cases with the weights assumed.

A stated tolerance of ±10 mm usually means 95% confidence, or two standard errors. So an occasional reading outside tolerance is expected — one in twenty, by construction — and discarding outliers requires a stated rule rather than judgement.