Lautard doesn't mention how that was done.
If the "rattling" was done near the mouth of the bore simply holding a scale in place and reading the swing would work. Another way I can imagine would be to use a pair of dividers and keep opening them until their span matched the swing of the stick, then hold them against a scale. Remember, even a poor estimate of the swing will improve the estimate of the bore. A detailed error analysis would be a waste of time; if you really need to know the bore with high accuracy you'll use more sophisticated techniques.

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