Miles, yards, feet and inches, pints, pounds and stones. Yes, fifty years after the UK embarked on the metric transition, we still need to be familiar with some of those old units. In this article, Ronnie Cohen looks at some of the less well known and largely forgotten features of the imperial system.

Readers may ask why Metric Views is discussing the measurement ‘system’ that the UK almost, but not quite, succeeded in abandoning a generation ago. Is this an attempt to kill it by kindness?

It is clear that many who profess enthusiasm for imperial measures know little about them. Would their enthusiasm be less, if they knew more? Alas, they are unlikely to come clean. But our readers may have an opinion. So please, take a look at some of the questions that follow and let us know if you think there is a place for such information in our campaign.

Do you know, for example, that there are two systems of pounds and ounces: troy and avoirdupois? The troy pound ceased to be legal for trade in 1879, and the troy ounce is now restricted to trade in precious metals. There are 12 troy ounces (31.3 g) in a troy pound , but 16 avoirdupois ounces (28.3 g) in an avoirdupois pound. When you see quotes of prices for precious metal per troy ounce, this is not the ounce on your kitchen scales.

Do you know that the British Empire and the US used different definitions of the yard until after WW2. As a result of problems with incompatible equipment, the US and Commonwealth countries agreed in 1959 on common definitions: one yard is equal to 0.9144 metres exactly and one avoirdupois pound is equal to 0.453 592 37 kg. In the UK, these definitions were incorporated into law in 1963.

Do you know that the imperial gallon was introduced in 1824, replacing several different gallons then in use? It was defined then as the space occupied by 10 pounds of distilled water weighed in air with brass weights with the barometer standing at 30 inches of mercury and at a temperature of 62 degrees Fahrenheit. In 1985, it was redefined as 4.546 09 litres exactly.

Do you know that the Americans have two versions of each of the fluid ounce, pint and gallon, namely ‘dry’ and ‘liquid’, and that these differ from the imperial units? As well as the US customary fluid ounce (29.6 mL), the Americans also use a nutrition fluid ounce (exactly 30 mL). The imperial fluid ounce is approximately 28.4 mL.

Do you know that there are several types of ton? As well as the short or US ton (2000 lb) and long or imperial ton (2240 lb or about 1016 kg), there is also the water ton (a unit of volume of exactly 224 imperial gallons), the freight ton (40 cubic feet) and the register ton (100 cubic feet). None of these should be confused with the tun (spelled with a “u”, not an “o”), an old English volume measurement for measuring alcoholic drinks and other commodities. The tun varied in volume between 800 and 1000 litres, depending on the commodity being measured. By contrast, the metric system has one tonne (known in the US as the “metric ton”) equal to 1000 kg.

Do you know that an acre is based on an Anglo-Saxon strip field? Acre is a similar word to the modern German Acker or Dutch akker, both words for cultivated fields. The acre is the area that a yoke of oxen could plough in a day and is often visualised as a rectangular area, one furlong by one chain (220 yards by 22 yards), equivalent to 4840 square yards or about 4047 square metres. The acre and the closely related rood (a quarter of an acre) do not fit well with the use of square feet and square yards. A square that is the size of an acre would be 69 yards 1 foot 8½ inches on each side.

Do you know that stones of different sizes were once used for weighing different commodities? Historically, the number of pounds in a stone depended on the commodity being weighed and, in some cases, the area. The 1862 Report on weights and measures reported the use of “about 10 different stones; a stone of wool at Darlington is 18 lbs.; a stone of flax at Downpatrick is 24 lbs.; a stone of flax at Belfast is only 16 3/4 lbs.; but it is also at Belfast 24 1/2 lbs., having in one place two values.” The imperial stone is 14 pounds, about 6.35 kg.

Do you know that miles, feet and inches, pounds and ounces were once used throughout continental Europe? These old, pre-metric measurements differed from country to country, sometimes widely, and in some parts of Europe from region to region. They all differed from the English versions.

Do you know that the units names “inch” and “ounce” are derived from the same Latin word *uncia*, meaning a twelfth part? The names reflect the use of the Roman duodecimal systems of the 12-inch foot and 12-ounce pound. The 12-ounce pound is used in the troy system of weights.

Do you know that there were two types of chain used for surveying: the Ramsden chain with 100 links each of one foot, and the Gunter chain, 22 yards long, also with 100 links.

Do you know that the mile was originally divided into 1000 units? The mile was originally defined by the Romans and was the length of 1000 paces of a Roman legionary. Each pace was a double step. Clearly, the Romans saw the benefits of using powers of 10 for units of distance long before the invention of the metric system. This unit name is derived from the Latin word for a thousand.

Do you know that different miles are used on land and for sea and air transport? The statute mile is so-called because it was fixed by Parliament at 5280 feet, to settle disputes and confusion about the length of the mile and to replace the various miles that were in use at that time. The mile for sea and air transport is called the nautical mile and for many years was defined as 6080 feet. In 1970, the UK adopted the international nautical mile of 1852 metres. Speed at sea is measured in knots, that is nautical miles per hour.

Do you know that Britain had a different set of unit lengths for measurements at sea, namely fathoms, cables and nautical miles. A fathom is 6 feet, there are 100 fathoms to a cable and 10 cables are equal to about one nautical mile. Clearly, mariners saw the benefits of using units based on powers of 10.

Do you know that the imperial system has units for weight and volume for medical recipes? These form the apothecaries’ system, replaced in pharmacies in 1969 by the metric system. Although the apothecary pound weighs the same as the troy pound (373.2 g), the subdivisions of the pound differ from the subdivisions of the troy pound, and include drachms and scruples. The apothecaries’ system also contains subdivisions of the fluid ounce including fluid drachms and minims.

Do you know that the oil barrel is neither an imperial unit nor a physical container but a unit of volume equal to 42 US gallons (about 159 litres) or just under 35 imperial gallons. It is doubtful if oil was ever stored in 42 gallon barrels.

Do you know that there are different imperial units for thermal and mechanical energy and power. For thermal energy there is the British thermal unit, and for mechanical power there is the horsepower. Metric uses the same units for thermal, mechanical and electrical energy and power, namely the joule and the watt (yes, both named after Britons!)

And finally, do you know that by 2010, all imperial measures had ceased to be legally authorised in the UK, other than:

* those required by international treaties relating to transport,

* the *mile*, *yard*, *foot* and *inch* for road traffic signs, distance and speed,

* the *pint* for draught beer and cider, and doorstep milk, and

* the *troy ounce* for trading in precious metals.

So what does this tell us about the UK measurement muddle?

Imperial measures may be an interesting area of study for historians, but they are not a coherent system – they are a collection of separate, stand-alone systems that developed independently for unrelated purposes. This is not surprising. Many of these sets of measures are application-specific (e.g. drachms for dispensing medicines, troy weights for precious metals) while some were adopted for general use (e.g. avoirdupois system of weight). For length, there are the general units such as the inch, foot, yard and mile, but there were also maritime units and survey units, as noted above. And so on for area, volume, energy and power.

That said, is any of this likely to influence the imperial enthusiasts?

Happily, no country now has to tolerate a measurement muddle, which, as we know only too well, increases costs, confuses shoppers, leads to serious misunderstandings, causes accidents, wastes children’s education, impairs numeracy and handicaps efforts to compete in global markets. All countries have the option of using just one unit for each physical quantity with one definition, accepted internationally, and all wrapped up in *a single, simple, logical, coherent and universal measurement system*. Most have taken this option. How long before the UK does so is anyone’s guess.

I seem to remember the late Pat Naughtin produced something on the lines that there were over 1000 separate and incompatible non-metric units of measure either currently in use or relatively recently defunct around the world - and all capable of being replaced by just six metric units.

Advanced nations that were already not metric nations have made the switch, encompassing 95% of the world's population (only very occasionally does the odd non-metric unit survive). These nations now enjoy the fruits of that switch, by being the most economically active countries in the world, and enjoying seamless trade with like-minded countries. Britain also enjoys more-or-less seamless trade with the rest of the world - but only because its industries HAVE in general made the switch, even if the general population still lags behind. As I postulated in an article a few months ago, the opposition of the DfT and a number of politicians to completing the conversion on our roads to metric units costs this country dear.

I spent the first thirty years of my life in the Netherlands (where they went fully metric in 1870) and there some old units remained in name only. There are still common phrases that refer to the "duim" (thumb) which used to be a measure and words such as "pond" (pound) and "ons" (ounce) are still used everyday when buying groceries. The only difference being that a "pond" is officially 500 grams (two "pond" to a kilogram) and an "ons" is officially 100 grams. At a butcher you'd order two "ons" of ham and he would slice 200 grams for you.

Did you know the the metric system is so backward you can't even divide a metre by 3? With imperial we can use fractions and divide anything to exactitude...We can also decimalise any imperial unit (a practise in use way before the arrival of metric), so what on earth is the advantage of using metric. Cutting added functionality I guess is a good thing according to your average metric hobbit.

What's the best system ? One that disallows fractions (as metric is strictly base ten, nothing else) or one that you can decimalise, fractionalise which comes with mathematically divisible units such as 12 or 16 to boot? Seem obvious to anyone with a even modicum of mathematical knowledge.

I'm a press toolmaker/precision engineer of 20 years since leaving school..know metric and imperial like the back of my hand (as if us imperial users don't know don't know what a troy oz is...come on. Most of the stuff written in the above article I knew when I was around 23). In my job I almost exclusively use imperial, finding it much more practical and logical. As opposed to metric, the system is mathematically based, so it's a no brainer really. If a costumer brings in a drawing made to metric spec., I charge a conversion fee...and the great thing is, they're learning! Metric drawings are becoming an increasingly rare site around my make shift office!

Did you know that the calculation for the metre is wrong? The quadrant they measured from equator to north pole running through Paris is around 40,000 metres out. Why? Because they failed to learn Newtonian physics...they thought the Earth was actually elongated at the poles!

@Matthew John

Good grief!

So I cannot dived a metre by 3, now that has brought my life to a sudden end (well it almost gave me a heart attack anyway). Now why should I need to divide by 3 any more than by any other number? 10/3 is the same no mater if it is meters feet or cubits. Yes, metric 10/3 who said we can't use it? In which branch of scientific mathematics is the 'divisor ' line banned? Do please let me know then I can stop using it. I would also love to know the branch of Imperial mathematics that can resolve 'any fraction to exactitude' try 22/7, otherwise known as pi.

Again to those that love to use 12's and 16's (and 14, 22, 20, 112, 8 ... and all the others), please, please remember they are all numbers to the base 10, base 10 is with us forever.

Of course we all know the original measure of the metre was wrong, nowhere near as precise as the length of a barley corn, eh? Or of that yard stick, nor the lump of rock for stone, nor the handful of wheat for the pound. It is amazing the USA could land a man on the moon using a barleycorn as the base measurement; it did not work so well when they tried to land on Mars though, it ran out of precision. It is, I understand called progress. Science moves on, and with it the way of doing things. The Imperial system ran out of steam when they discovered electricity.

"Did you know the the metric system is so backward you can’t even divide a metre by 3?"

So what? You can't divide imperial mass units by 3 either. You can't divide the yard into 5 but you can the metre. Take your choice.

"With imperial we can use fractions and divide anything to exactitude…"

As a precision engineer Matthew you should know that when it comes to practical measurement there is no such thing as "exactitude". They are always subject to finite tolerances. If you need to, you can divide the metre (or any other metric unit) into any fraction you like for any specified precision. The range of uncertainty is far easier to express in decimal form than in fractions.

In any case what is all this fuss about divisibility? The divisibility of any one unit can only be an issue if the measurement itself happens to be an integral number units.

I'll never understand why people like you are so crazy about imperial units. The arguments that are typically made suggest a poor understanding of measurement and the practical implications.

If ever I needed the services of a precision engineer I would studiously avoid people like you Matthew.

@Matthew John

You may wish to read the Wikipedia article on meridian arc. The modern length assigned in the WGS84 ellipsoid (the model used in GPS) is 10 001 965.729 m. Thus the original French value was in error by less than 2 km in 10000 km, not 40 km as you suggest. You will also learn that:

1) Newton had proved the earth was approximately an oblate ellipsoid in 1687, although his flattening value was in error.

2) There was a period of time in the early 18th century when it was thought to be prolate, as you say.

3) This was resolved by French expeditions to measure the radius of curvature at several other latitudes and the earth was well-understood to be oblate by late in the 18th century. The best values for equatorial radius and flattening continued to vex geodesists until the GPS era.

Finally, while the intent was to use that value to define the meter, it was recognized to be an impractical measurement, and the first official definition of the meter was the prototype bar at Paris.

Have you considered that perhaps customers who want metric parts have gone elsewhere? As long as you have enough work, perhaps it doesn't matter.

The "not divisible by 3" argument has been going on since the 1790's. The following is taken from the Wikipedia article at https://en.wikipedia.org/wiki/History_of_the_metric_system:

"In response to Tallyrand's proposal of 1790, the Assemblée set up a new committee under the auspices of the Académie to investigate weights and measures. The members were five of the most able scientists of the day—Jean-Charles de Borda, Joseph-Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge and Condorcet. The committee, having decided that counting and weights and measures should use the same radix, debated the use of the duodecimal system as an alternative to the decimal system. Eventually the committee decided that the advantages of divisibility by three and four was outweighed by the complications of introducing a duodecimal system [of counting]."

@Matthew John

Any length, area, volume, weight or mass, can be divided by 3 into three parts.

A length a metre long, can be divided into 3 parts, and the parts can be measured with divisors of the metre unit, or with Imperial units, the foot, the inch, or the divisors of those units, and any other units of measure.

But the metre length, or any length or distance, or any area, volume, weight, or mass, cannot be divided into 3 exactly equal parts. That is because there is alway some uncertainty in any measurement. If the metre length was measured in inches (39.370 0787 4 inches), it still cannot be divided into 3 exact parts. Irrespective of whether metric or Imperial units are used to measure, measurements are never exact.

The astronomers who attempted to measure the Paris meridian, were never going to get an exact measurement. Considering, for example, the political instability occurring in France at that time, the use of 18th century instruments, the difficulty of determining the latitude of Barcelona by astronomical observations, and not knowing the exact shape of the earth, it is surprising is that the error was so small.

The GPS systems of today, are centuries in advance of the instruments used in the 18th century, but still need to be re-calibrated every 24 hours to compensate for clock error and clock drift.

Measurements are never exact, but numbers are exact.

Numbers are used to record measurements, but are not measurements.

@Matthew John, my original reaction to this was that it is a spoof post from the 'other lot' just to wind us all up. Either way, let’s play along.

It would also be interesting to know what precision instruments you use to measure these values in fractions of an inch. I use the iconic Moore and Wright 1 inch micrometer (1961) that is calibrated in 'thou, 0.001 of an inch, not decimal? Not using unit 10? Lets throw in the 25 'thou to the revoloution scale just for fun, Now how do you measure in fractions? My American callipers are calibrated in 1/1000" (and 1/20 mm), using a 1/100" inch main scale and x10 vernier scales. I also still use feeler gauges in 'thou. I have no need to spend on metric replacements as I seldom use them; valve and point’s gaps are a thing of the past. So leaving that aside it makes little difference except the need to translate metric to imperial and back. Precision is limited to practical factors, not mathematical ones. Maybe the use of these instruments would make using imperial a little more practical physically, but the conversions would soon get me buying metric instruments, maybe I get me a laser one. The world is metric, not imperial.

Another thing is that the metric system allows for the use of modules. This has been a feature from the beginning. Measuring sticks, a series of weights or capacity measures were often in series of 1/4, 1/2, 1 and 2 m, kg or L. One very common module is the 300 mm one, found in millions of rulers. It is in fact the foot surviving and assuming a new role in a metric environment. However, never, ever should modules be given unit names. The 300 mm module is highly divisible of course.

I concede that divisiblity is convenient and practical; the metric system gives ease of calculation because of its strictly decimal structure, and divisibility by allowing the use of modules. Metric offers the best of two worlds.

On the other hand, decimalisation of US/UK units is irrational. Where 3.648 km is equal to 3648 m, in a measurement of 3.648 miles the decimal part is utterly meaningless and forces one to make a difficult conversion if the number of feet or yards is required.

Last, but not least: I would never use the services of Matthew John.

At present I am on a Hurtigruten ship off the Norwegian coast and I wish everybody a Merry Christmas and a very happy and fruitful New Year.