The Hoppus Quarter-Girth Formula
A measurement designed to be wrong, by exactly the right amount.
Origin
Published by Edward Hoppus in Practical Measuring Made Easy in 1736, and adopted as the standard method for round timber throughout the British timber trade and its colonial extensions.
The catch
The formula underestimates the true volume of a log by about 21.5 per cent, and that is entirely deliberate. The shortfall is roughly the waste involved in squaring a round log into a usable baulk, so the buyer pays for the timber he can actually use rather than for the tree.
((Girth ÷ 4)² × Length) ÷ 144Girth is the circumference at the midpoint in inches; length is in feet. The result is hoppus feet. Divide by 50 for hoppus tons.
Worked examples
Hoppus solved a practical problem rather than a mathematical one. Timber merchants needed a figure they could reach with a tape and a mental calculation, in a yard, in the rain, with a seller watching. Squaring the quarter-girth achieves that, and the systematic error it introduces happens to correspond closely to what is lost when the log is squared for use. Whether Hoppus intended that correspondence or merely found it convenient is not entirely clear, but the trade adopted the method for two and a half centuries and it remains in use for tropical hardwoods in parts of the Commonwealth today.