For scientists, units are like money: a few people obsess about them, but the less you have to think about units, the better. And, like switching a bank account, changing your units is usually tiresome and complicated for little real advantage. But spare a thought for the many units that have been lost to the inexorable march of scientific advance, and for the few that are still in regular use.
A typical adult horse is 13 to 18 hands tall, a hand being 4 inches and representing a children’s shoe size of 0. The shaftment – the width of a hand with the thumb outstretched, later defined to be six inches – is one-and-a-half hands. For measuring rods, it is a useful rough-and-ready unit: grasp the rod in your fist and place your thumb on it in a thumbs-up gesture. This is one shaftment. European and Imperial shoe sizes coincide in their use of thirds of standard length units. A third of an inch – a barleycorn – is only a few millimetres longer than a Paris point, or two thirds of a centimetre, which forms the basis of European shoe sizes.
Chains – 66 feet; 80 per mile – survive as the base unit for linear distance along British railways, and as the distance between the stumps in cricket. An acre is ten square chains or 160 square rods. This 66 ft chain is properly known as Gunter’s chain, while Ramsden’s chain – 100 feet – corresponds to an actual chain used by Jesse Ramsden in the eigtheenth-century Anglo-French Survey, which provided the relative locations of the Greenwich and Paris observatories. Tensioned at a constant weight, with thermal expansion reckoned explicitly, it gave a measurement error of only three inches in five miles.
A furlong is the distance that a furrow is long. If, in medieval England, you had one acre, you had a narrow rectangle that was 10 chains or forty rods in length and one chain in width. Thus, your furrows measured forty rods, ten chains, or 1/8 of a mile. Now used chiefly in horse racing, the furlong also appears in mile markers in Burma, and in the layout of Phoenix, Arizona; Salt Lake City and Logan, Utah; and parts of Melbourne. Highway exits from Interstate 10 in Phoenix are one mile apart and numbered in furlongs: 35th, 43rd, 51st, matching the city’s grid layout.
A league is the distance a person can walk in an hour, traditionally varying depending on the quality and difficulty of the road in question. The English convention is that a league measures three miles, and thus a ‘nautical’ league is three nautical miles. The French league varied from three to five kilometres, but after the advent of the metric system, it finally was standardised for a time to 4 kilometres. Thus, Twenty Thousand Leagues Under the Sea refers to a submarine journey of 80,000 linear kilometres. (It does not refer to a journey to a depth of 80,000 km, which would be 40 times the radius of the earth, under a water pressure of nearly 800 billion Pascals, a hundredfold excess of the manufacturing pressure of artificial diamonds. The greatest depth mentioned in the book is four leagues – half again as deep as the Mariana trench – perhaps an excusable flight of the nineteenth-century imagination.)
We use the SI system because it uses only a small set of base units, and because it allows convenient conversions from the very small to the very large. But pre-industrial workers had no need to calculate forces from distances, for example, or to work across scales of more than two orders of magnitude. In that setting, units which correspond to intuitive demarcations of the accessible world are a vital interpretive tool, and consistency between their representations provides no advantage.
So: next time you have to describe a quantity, go the extra 80 chains and pick the best unit.
