Why does the statute mile have the length that it has?

Question

Why was our (statute) mile established as it was?

This happened in 1593, by the order of Elizabeth I which said:

"A Mile ſhall contain eight Furlongs, every Furlong forty Poles, and every Pole ſhall contain ſixteen Foot and an half." It was thus 1760 yards (5280 feet, about 1609 meters)

(Citation from Wikipedia). The question is why 8 furlongs? Why forty poles, etc.

I conjecture that this was based on some very crude measurement of the Earth circumference, and the mile was supposed to be 1' of the meridian.

Indeed, as late as in 1667 Newton thought that one degree =60 miles, and as a result, that the gravitational force inversely proportional to the square of the distance cannot alone explain the Moon's orbit. (Based on Wiston's recollections of conversations with Newton, cited in http://books.google.com/books?id=xIkn3eFNy20C&printsec=frontcover#v=onepage&q&f=false this book.

Nautical mile is indeed one minute of the meridian. And kilometer was originally defined as one "decimal minute" (400 degrees in a circle, 100 minutes in a degree).

I conclude that Elizabeth's statute was based on some very imprecise measurement of the meridian. Which measurement?

Remark. Is this not amazing that we are still using this mile established in XVI century on the basis of a wrong measurement?

Answer 1

The OED writes this:

"Originally: the Roman unit of distance of 1000 paces (mīlle passus or passuum), reckoned to have been about 1618 yards (approx. 1479 metres). Hence: a unit of distance derived from this used in the British Isles and in other English-speaking countries, and now equal to 1760 yards (approx. 1609 metres). Frequently with a prefixed numeral forming a phrase used attributively.The length of the mile has varied considerably at different periods and in different localities, chiefly owing to the influence of the agricultural system of measures with which the mile has been brought into relation (see furlong n.). It was fixed by statute at 1760 yards (viz. 8 furlongs of 40 poles, each pole being 16½ feet) in 1592 (Act 35 Eliz. I, c. 6, s. 8), and in Britain is also called a statute mile. This is also the legal mile in the United States. The obsolete Irish mile was 2240 yards (approx. 2048 metres), and the Scottish mile (obsolete by the late 19th century) was 1976 yards (approx. 1807 metres) although values probably varied according to time and place."

This suggests that the mile is originally a military term, a round counting of the paces of marching soldiers, and is not based on a calculation of the size of the earth. Educated Romans were presumably aware of Eratosthenes' rather accurate measurement of the earth's circumference, but it seems unlikely that this should have filtered down to military usage.

Answer 2

The question is why 8 furlongs? Why forty poles, etc.

Because furlongs and poles were already-standardized units that predated a c. 1300 measurement reform. These units couldn't be changed without screwing up everyone's property records.

The mile was not part of the Anglo-Saxon land-measuring system, but a borrowing from ancient Roman legions, that had used a mille passus (thousand paces) as a unit of distance. A “pace” is not naturally a constant, as it depends on a person's physical stature and health, as well as the condition of the road. But for practical purposes, a “mile” needed to be standardized. Choices based on the original “thousand paces” definition are:

• Define a “pace” as 5 Roman feet of 296 mm, resulting in a mile of 1480 m. (Incidentally, this is close to my average personal “pace” as I measured with my FitBit a few years ago.)
• Define a “pace” as 5 English feet of 304.8 mm, resulting in a mile of 1524 m.

The problem with such a “mile” is that, as I already mentioned, the furlong of 660 ft was a long-established unit, and it would be a lot more convenient if a mile were a whole number of furlongs. So the practical choice was either to round a mile down to 7 furlongs (1408 m) or up to 8 furlongs (1609 m). I suspect that 8 was chosen to allow a mile to easily divide into halves or quarters, in contrast to the inconveniently-prime 7.

Since the mile's definition was dependent on the furlong, your question then becomes why the furlong is the length it is (201.168 m). Conceptually, a furlong is a “furrow long”, i.e., the length of a furrow in an agricultural field, determined by the distance that a team of oxen could plow before they had to be rested and start a new furrow.

But why was a furlong standardized to be the length that it is? Could it have been meant as some convenient fraction of a meridian?

Earth's polar circumference has been measured as 40 007 863 meters. (Based on the original conceptual definition of the meter, it should be exactly 40 million, but the survey had an error of 197 PPM.) This works out to 198 877.868 furlongs (based on the International Yard and Pound Agreement of 1959).

To which you might point out, “Hey, that's really close to a nice round 200 000. Clearly that was intentional, and so a foot was supposed to be 1/132M of the Earth's circumference (303.09 mm).”

But by the same reasoning, you can point out that a Roman foot (pes) was almost exactly the length of a sheet of A4 paper. Does that mean that the Romans independently discovered ISO paper sizes, or is it just a coincidence?

Answer 3

Remark. Is this not amazing that we are still using this mile established in XVI century on the basis of a wrong measurement?

Not really, all measurements are arbitrary at their base so there are no "wrong measurements." All measurement simply come down to defining an arbitrary object as a reference against which all other objects are compared to. The point of measurement is to create a common reference for communication and memory. What the reference object actually is has no bearing on its utility. Our entire system could be based on length of a halibut caught 1272 and it would work just the same.

As long as everyone can and will use the same reference object, the system works. If we visited an alien world, we'd just ask for their reference object and we'd be good to go.

Evolved traditional systems have a better track record than designed "rational" systems. The meter was supposed to be all rational and derived from natural measurements, (ignoring the fact that people pushing the system at the time where lopping off heads right and left) but owing to simple error one of science history's epic bitter personality feuds, its was originally wildly off. Now it's just an arbitrary length. Even if it were based on an actual consistent physical phenomena, it wouldn't really matter.

It took more than a century for the metric system to really catch on despite being official in most of Europe since the Napoleonic era. The metric system relies on users having precise linear measurements as well as a need for intensive computations. We take such precision for grandted today but mass produced precision is a mid-to-industrial era phenomena at best.

A metal ruler made of the metals of any time up to the mid industrial era would expand and contract in length by several millimeters as the ambient temperature changed and in any case, manufacturing could not mass produce meter rulers to to less than than a 5mm tolerance at best. So every meter ruler in use could be off as much as 10mm from any other ruler in use. The same ruler would give different measurements at different times. That's a whole lot of accumulated error.

That's why the metric system was slow to catch on and mostly ended up being imposed by force officially and was used largely only by elites and military while artisans and manufactures continued to use traditional measures for a good century or more.

In Revolutionary and Napoleonic France the government issued specs and had shipwrights present plans in metric, and then the shipwrights went right back and used their traditional reference based tools. When the ships all came out slightly different sizes and clearly not based on metric measurements, the shipwrights just gave a gallic shrug and something like, "the ship she still floats and sails, yes?" (Funny story, the French official specification were based on mathematically flawed concept of a ship's meta center. Had the shipwrights actually follow official instructions, the ships would have been disastrously unstable. The snoots were so confident in their math they didn't bother to test it on real ships.)

Metric worked fine for elite computational intensive work like early 18th century astronomy or even surveying in most cases but good luck trying to reliably and repeatedly measure a 41.5cm length of wood for table day after day around the year with early linear measure made with 18th century metallurgy. (Even today it sucks for traditional woodworking. I was amazed to find out how many European woodworkers don't use metric for anything more complicated than cranking out the plywood boxes of the modern style.)

Lacking precise linear measurements, people in the past made precise measurements with angles instead. A compass/divider can be made of many different materials and be used under many different conditions of heat and humidity and still give the same consistent measurement of angle. Angular measurement dominated all measurement in all human cultures for thousands of years.

But converting angles to linear lengths is computationally expensive, especially when you don't have computers or even a handy sheet of paper, so instead, people used compass/dividers to take measures of lengths off local reference objects and then just made everything various multiple or divisions of those lengths.

The original "ruler" was block of stone whose dimensions where used as a references for all the measurements of a particular project e.g. a cathedral or castle. It was said to "rule" all the other dimensions. Later, "rulers" became standardized lengths of plain unmarked metal of various sizes and lengths made of alloys that did expand or contract to much in temperature changes. Only in the late 1800s were gradation marks made on them and engineers still use old reference rulers in some cases.

The phrase "rule of thumb" means to use one's thumb as a reference object. Since the length of people's thumbs vary, it means that measurement with a lot of potential for variation but which will serve for an immediate purpose, if you use the same thumb.

Other traditional measurements evolved to meet local needs and which could be made with local tools and reference objects. An acre was originally defined as the amount of land that could plowed by a team of oxen in a set number of hours in particular types of soil. Sounds silly to modern ears but for taxation and figuring work back at the time, it was a very useful measure. The original concept of acre included the amount of food a unit of land could produce per man hours per year. It allowed for the convertibility between units of poor and good land. A simple modern numerical measurement of area like hectare would have told them nothing useful.

In theory, the best unit of measurement on the earth's surface is the nautical mile, because it can be in theory be derived from solar observation. Of course, since the earth is not actually round and its axis wobbles, the nautical mile is always off as well. But since it is based on an angular measurement, its very easy to convert from sextant sightings and to make accurate measurements and calculation off charts without dragging out Dr. Babbage's difference engine.

We have an odd tendency to see lack of power in technology, in this case a lack of mass produced precision, with stupidity in our ancestors. In fact, they had fair less margin for error than we do and their solutions had to work well and reliably where and when they were needed. Smirk all you like but if they hadn't got things right consistently year after year, decade after decade, century after century, we wouldn't be sitting here all fat, happy, snug and smug.