Measure for measure

The Brexit vote in the UK has produced a bizarre collection of desires of those Leavers eager to escape the poisonous grasp of the Brussels’ bureaucrats. At the top of their list is a return of the death penalty, a piece of errant stupidity that I shall leave largely uncommented here. Not far behind is the wish to abandon the metric system and to return to selling fruit and vegetables in pounds and ounces. This is particularly strange for a number of reasons. Firstly the UK went metric in 1965, six years before it joined the EU. Secondly EU regulations actually allows countries to use other systems of weights and measures parallel to the metric system, so there is nothing in EU law stopping greengrocers selling you a pound of carrots or bananas. Thirdly the country having gone metric in 1965, anybody in the UK under the age of about fifty is going to have a very hard time knowing what exactly pounds and ounces are.

Most readers of this blog will have now gathered that I have spent more than half my life living in Germany. Germany is of course one of the founding states of the EU and as such has been part of it from the very beginning in 1957. The various states that now constitute Germany also went metric at various points in the nineteenth century, the earliest in 1806-15, and the latest in 1868. However the Germans are a very pragmatic folk and I can and do buy my vegetables on the market place in Erlangen in pounds and half pounds. The Germans like most Europeans used variation of the predecessors to the so-called Imperial system of weights and measures and simple re-designated the pound (Pfund in German) to be half a kilo. The Imperial pound is actually approximately 454 grams and for practical purposes when buying potatoes or apples the 46-gram difference if negligible. Apparently the British are either too stupid or too inflexible to adopt such a pragmatic solution.

At the beginning of the month Tory dingbat and wanna be journalist Simon Heffer wrote an article in The Telegraph with the glorious title, Now that we are to be a sovereign nation again, we must bring back imperial units. I haven’t actually read it because one has to register in order to do so and I would rather drink bleach than register with the Torygraph. I shall also not link to the offending article, as it will only encourage them. Heffer charges into the fray thus:

But I know from my postbag that there is another infliction from the decades of our EU membership that many would like to be shot of, and that was the imposition of the metric system on large parts of our life. 

Consumer resistance ensured that our beer is still served in pints (though not in half-pint and pint bottles when bought in supermarkets: brewers please note), and that our signposts are still marked in miles.

As pointed out above it was not the EU who imposed the metric system on British lives but the British government before the UK joined the EU. According to EU regulations you can serve drinks in any quantities you like just as long as the glasses are calibrated, so keeping the traditional pint glasses and mugs in British pubs was never a problem. Alcohol is sold in Germany in a bewildering range of different size glasses depending on the local traditions. My beer drinking German friends (the Germans invented the stuff, you know) particularly like pints of beer because they say that they contain a mouthful more beer that a half litre glass. Sadly many bars in Franconia have gone over to selling beer in 0.4litre glasses to increase their profits, but I digress.

UK signposts are still marked in miles because the government could not afford the cost of replacing all of them when the UK went metric. Expediency not national pride was the motivation here.

Just before Heffer’s diatribe disappears behind the registration wall he spouts the following:

But we have been forced on to the Celsius temperature scale, which is less precise than Fahrenheit

When I read this statement I went back to check if the article had been published on 1 April, it hadn’t! Is the international scientific community aware of the fact that they have been conned into using an inaccurate temperature scale? (I know that scientist actually use the Kelvin temperature scale but it’s the same as the Celsius scale with a different zero point, so I assume by Heffer’s logic(!) it suffers from the same inaccuracy). Will all of those zillions of experiments and research programmes carried out using the Celsius/Kelvin scale have to be repeated with the accurate Fahrenheit scale? Does Simon Heffer actually get paid for writing this crap?


Anders Celcius Portrait by Olof Arenius Source: Wikimedia Commons


Daniel Gabriel Fahrenheit

Like myself on being confronted with the bring back imperial weights and measures madness lots of commentators pointed out that the UK went metric in 1965 but is this true? No, it isn’t! The UK actually went metric, by act of parliament over one hundred years earlier in 1864! The nineteenth century contains some pretty stirring history concerning the struggles between the metric and imperial systems and we will now take a brief look at them.

As soon as it became in someway necessary for humans to measure things in their environment it was fairly obvious that they would use parts of their body to do so. If we want a quick approximate measure of something we still pace it out or measure it with the length of an arm or the span of our fingers. So it was natural that parts of the body became the units of measurement, the foot, the forearm, the arm span and so on and so forth. This system of course suffers from the fact that we are not all the same size. My foot is shorter than yours; my forearm is longer than my partners. This led cultures with a strong central bureaucracy to develop standard feet and forearms. The various Fertile Crescent cultures developed sophisticated weights and measures systems, as did the Roman Empire and it is the latter that is the forefather of the imperial system. The Roman foot was between 29.5 and 30 cm, the pace was 2.5 feet and the Roman mile was 5000 feet. The word mile comes from the Latin for thousand, mille. The Roman military, which was very standardised, carried the Roman system of weights and measures to large parts of Europe thus establishing their standards overall.

With the collapse of the Roman Empire their standardised system of weights and measures slowly degenerated and whilst the names were retained their dimensions varied from district to district and from town to town. In the eighth and ninth centuries Karl der Große (that’s Charlemagne for the Brits) succeeded in uniting a substantial part of Europe under his rule. Although he was uneducated and illiterate he was a strong supporter of education and what passed at the time for science and amongst his reforms he introduced a unified system of weights and measures for his entire empire, another forefather of the imperial system. Things are looking quite grim for the anti-European supporters of the imperial system; it was born in Rome the birthplace of the EU and was reborn at the hands of a German, nothing very British here.

Karl’s attempt to impose a unified system of weights and measures on his empire was not a great success and soon after his death each district and town went back to their own local standards, if they ever left them. Throughout the Middle Ages and deep into the Early Modern Period traders had to live with the fact that a foot in Liège was not the same as a foot in Venice and a pound in Copenhagen was not a pound in Vienna.

This chaos provided work for the reckoning masters producing tables of conversions or actually doing the conversions for the traders, as well as running reckoning schools for the apprentice traders where they taught the arithmetic and algebra necessary to do the conversions, writing the textbooks for the tuition as well. The lack of unity in currency and mensuration in medieval Europe was a major driving force in the development algebra – the rule of three ruled supreme.

At the beginning of the seventeenth century Simon Stevin and Christoph Clavius introduced decimal fractions and the decimal point into European mathematics, necessary requirements for a decimal based metric system of mensuration. Already in the middle of the seventeenth century just such a system emerged and not from the dastardly French but from a true blue English man, who was an Anglican bishop to boot, polymath, science supporter, communicator, founding member of the Royal Society and one of its first secretaries, John Wilkins (1614–1672).

Greenhill, John, c.1649-1676; John Wilkins (1614-1672), Warden (1648-1659)

Greenhill, John; John Wilkins (1614-1672), Warden (1648-1659); Wadham College, University of Oxford;

Asked by the society to devise a universal standard of measure he devoted four pages of his monumental An Essay towards a Real Character and a Philosophical Language (1668) to the subject.


Title Page Source: Wikimedia Commons

He proposed a decimal system of measure based on a universal measure derived from nature for use between ‘learned men’ of various nations. He considered atmospheric pressure, the earth’s meridian and the pendulum as his universal measure, rejecting the first as susceptible to variation, the second as immeasurable and settled on the length of the second pendulum as his measure of length. Volume should be the cubic of length and weight a cubic standard of water. To all extents and purposes he proposed the metric system. His proposal fell, however, on deaf ears.


European units of length in the first third of the 19th century Part 1


European units of length in the first third of the 19th century Part 2

As science developed throughout the seventeenth and eighteenth century it became obvious that some sort of universal system of measurement was a necessity and various people in various countries addressed to subject. In 1790 the revolutionary Assemblée in France commissioned the Académie to investigate the topic. A committee consisting of Jean-Charles de Borda, Joseph-Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge and Nicolas de Condorcet, all leading scientific figures, recommended the adoption of a decimal metric system based on one ten-millionth of one quarter of the Earth’s circumference. The proposal was accepted by the Assemblée on 30 March 1791. Actually determining the length of one quarter of the Earth circumference turned into a major project fraught with difficulties, which I can’t do justice to here in an already overlong blog post, but if you are interested then read Ken Adler’s excellent The Measure of All Things: The Seven-Year Odyssey That Transformed The World.


Standard meter on the left of the entrance of the french Ministère de la Justice, Paris, France. Source: Wikimedia Commons

However Britain needed a unified system of mensuration, as they still had the problem that every town had different local standards for foot, pound etc. John Herschel the rising leading scientific figure wanted a new decimal imperial system based on the second pendulum but in the end parliament decide to stick with the old imperial system taking a physical yard housed in the Houses of Parliament as the standard for the whole of the UK. Unfortunately disaster struck. The Houses of Parliament burnt down in 1834 and with it the official standard yard. It took the scientists several years to re-establish the length of the official yard and meanwhile a large number were still advocating for the adoption of the metric system.


The informal public imperial measurement standards erected at the Royal Observatory, Greenwich, London, in the 19th century: 1 British yard, 2 feet, 1 foot, 6 inches, and 3 inches. The inexact monument was designed to permit rods of the correct measure to fit snugly into its pins at an ambient temperature of 62 °F (16.66 °C) Source: Wikimedia Commons

The debate now took a scurrile turn with the introduction of pyramidology! An English writer, John Taylor, developed the thesis that the Great Pyramid was constructed using the imperial system and that the imperial system was somehow divine. Strangely his ideas were adopted and championed by Charles Piazzi Smyth the Astronomer Royal of Scotland and even received tacit and indirect support from John Herschel, who rejected the pyramidology aspect but saw Taylor’s pyramid inch as the natural standard of length.

However wiser heads prevailed and the leaders of the British Victorian scientific community made major contributions to the expansion of the metric system towards the SI system, used internationally by scientists today. They applied political pressure and in 1864 the politicians capitulated and parliament passed the Metric (Weights and Measures) Act. This permitted the use of weights and measures in Britain. Further acts followed in 1867, 1868, 1871 and 1873 extending the permitted use of the metre. However the metric system could be used for scientific purposes but not for business. For that, Britain would have to wait another one hundred and one years!

Interestingly, parallel to the discussion about systems of mensuration in the nineteenth century, a discussing took place about the adoption of a single prime meridian for cartographical, navigational, and time purposes. In the end the two main contenders were the observatories in Paris and Greenwich. Naturally neither Britain nor France was prepared to concede to the other. To try and solve the stalemate it was suggested that in exchange for Paris accepting Greenwich as the prime meridian London should adopt the metric system of measurement. By the end of the nineteenth century both countries had nominally agreed to the deal without a formal commitment. Although France fulfilled their half of this deal sometime early in the twentieth century, Britain took until 1965 before they fulfilled their half.

Should the Leavers get their wish and the UK returns to the imperial system of measurement then they will be joining an elite group consisting of the USA, Myanmar and Liberia, the only countries in the world that don’t have the metric system as their national system of measurement for all purposes.



Filed under History of Mathematics, History of Navigation, History of science, Uncategorized

18 responses to “Measure for measure

  1. 1965 … I remember learning the metric system in primary school in the early 70s, but it was only for school use. Outside school, everyone used imperial measures, and even when the “new money” came, a shilling (now transmogrified into 5 new pence) was called a “bob” by all the adults I knew, and 25 pence was therefore five bob. In the early 80s we were still buying sweets by the quarter pound from the corner shop. I wonder when all this changed?

  2. carlvehse

    “But we have been forced on to the Celsius temperature scale, which is less precise than Fahrenheit…”

    It’s a joke. It plays on the fact that one degree unit in the Fahrenheit scale is smaller than one degree unit in the Celsius scale. It’s like one unit of length in the inch scale is smaller than one unit of length in the meter scale. The smaller unit is more precise if one only measures in integer units. Of course, if one measures in fractional or decimal units, the scale used doesn’t make any difference.

    • araybold

      Well, it may be a joke to you and me, but I imagine that it is a serious matter to Simon Heffer, who probably considers rational numbers to be another continental contagion. Rational numbers! the very name is enough to turn a true Tory blue in the face. Did you notice how carefully Thony elided the nationalities of Simon Stevin and Christoph Clavius , the perpetrators of the decimal point? I think we can expect another Telegraph editorial from Mr. Heffer, demanding that Britain returns to integer-only arithmetic (and don’t mention Peano’s nationality!)

  3. carlvehse

    Since you discussed the history of some units of length, here’s a bit of history on temperature scales.

    Ole Christensen Rømer (1644-1710) was a contemporary (and friend) of Isaac Newton and best remembered for his discovery of the finite speed of light. However, Rømer was a most versatile person (with accomplishments covering more than a dozen different careers in his native Denmark!). But Ole had another under-recognized accomplishment.

    It was Rømer who designed and constructed his own more accurate thermometers and was the first to realize and use two fixed points (rather than one) to calibrate the scale of a thermometer. Rømer’s upper point was the boiling point of water, which he set as 60 d egrees. (Rømer apparently did not realize that water’s b.p. depended on atmospheric pressure.)

    Rømer’s lower calibration point has been the subject of some debate. Some have said that a 0 value was assigned to a mixture of water, ice, and ammonium chloride; others claimed Rømer used the melting point of snow (which he marked as 7.5 deg.). Because many of Rømer’s records were destroyed in a fire in Copenhagen in 1728, we may never know for sure. (BTW, 7.5 is one-eighth of 60, and accurately dividing a scale on a thermometer by powers of 2 is easily accomplished with simple tools of that day.)

    In 1708, the German physicist, Daniel Gabriel Fahrenheit, visited Ole Rømer in Copenhagen. Rømer showed him the two-point calibration system he had developed. Rømer was also testing small thermometers designed for meteorological use which had divisions marked from 0 to 22.5 deg. (normal blood temperature) using Rømer’s scale.

    Fahrenheit was so impressed with Rømer’s thermometers and the two-point
    calibration scale that he adopted them for use back in Germany. While it appears that Fahrenheit used the same lower calibration point as that of Rømer, it is clear (from a letter written by Fahrenheit to Boerhaave in 1729 and rediscovered in 1936) that Fahrenheit used Rømer’s 22.5 deg (“normal body temperature”) as the upper point. From a 1724 paper, Fahrenheit determined the upper point either in the mouth or under the armpit (the third alternative technique was not noted :-)). It is not
    clear whether Fahrenheit (or Rømer) distinguished a male or female body
    temperature (in his Latin paper Fahrenheit used the word “hominis“).

    Fahrenheit later multiplied Rømer’s scale numbers by four for easier reading. This made the melting point of ice 30 deg. and body temperature 90 deg.

    Eventually Fahrenheit adjusted the calibration points to 32 (ice melting point) and 96 (body temperature) to simplify marking the scale divisions (i.e., 64 divisions). Thus the boiling point of water would be measured experimentally near 212 deg. Later, the b.p. of water, at one atmosphere pressure, was used as the upper calibration point of 212, returning to Rømer’s initial calibration concept. (With these two
    calibration points, the experimentally determined temperature of a healthy person is now approximately 98.6 deg.)

    Thus, as noted by historian I.B. Cohen, Ole Rømer’s thermometer scale design is really the basis of the thermometer scale used by Daniel Gabriel Fahrenheit (1686-1736).

    For more information on Rømer, the thermometer, and his other accomplishments, see Roemer and the First Determination on the Velocity of Light, I. Bernard Cohen (Burndy Library, New York, 1944). Cohen’s short book has many references, mostly in Danish, French, German, or Latin; and mostly very old. Fahrenheit’s own acknowledgement of Rømer’s contribution is in a letter he wrote in 1729 and reprinted in Kon. Akad. Wet. Verhand., Vol. XVI, 1936, pp. 1-37. A more recent discussion of Rømer’s temperature scale was given by Robert H. Romer, “Temperature scales: Celsius, Fahrenheit, Kelvin, Reamur, and Romer”, The Physics Teacher, 20, Oct. 1982, pp. 450-454).

  4. I thought the ancient Egyptians invented beer.

    • jrkrideau

      You do realize where our estimated host resides?

      It is obvious that a group of Sun-worshipping travellers from a proto-Germanic tribe on the Lower Rhine introduced beer making to Egypt during one of their annual winter pilgrimages to the Temple of Ra on the coast of the Red Sea.

    • A drink made of fermented barley is even older than the ancient Egyptians but strictly it is ale and not beer, which as I said was invented by the Germans, so what’s the difference?

      • Jeb

        The next post citizen of nowhere makes the difference I think. Bell beaker complex. Booze is a classic example of the spread not of a particular people but of an idea and style which alters local social structure.

        It also alows an elite warrior arstocracy to develop that can further develop the idea of being German or Egyptian.

        I think it may be helpfull to look at it the other way round booze invented Egypt and Germany. In terms of modern nationalsim we are living with the mother of all hangovers.

  5. jrkrideau

    Thanks Thoney, a most interesting post.

    And, specifically, it answered a couple of questions about the 19th C evolution of the use of the Metric System that had been in the back of my mind for a couple of years.

    • I should point out that my post is only a rough outline of the developments in the nineteenth century, the full story is much more complicated.

      • jrkrideau

        Oh definitely, but your post touched on the exact couple of points that had been nagging at me, so thanks.

        P.S. Apologies for the typo in your name.

  6. Pingback: Whewell’s Gazette: Year 3, Vol. #36 | Whewell's Ghost

  7. DCA

    Three ironies from the United States:
    1. The US went on the metric system in 1866, in the sense that everything else was defined in terms of these units.
    2. There was a very slight difference between the US and Imperial inch, and (I think during WW II) the US inch became the global standard.
    3. In the late 1990’s California mandated that its highway department go metric (which meant that everyone who contracted with them would have had to do the same). A few years later (after they had spent a lot of money redrawing everything) the rule was reversed by none other than Arnold Schwarzenegger.

    And why does the US stick to non-metric units? Beats me.

  8. I am American and think in Imperial measurements for the most part. I don’t have strong opinions about which units to use except for temperature. I’m good at converting back and forth between miles and kilometers, feet and meters, ounces and milliliters, pounds and kilograms, but I prefer Fahrenheit, and I sympathize with the complaint that Celsius is too imprecise. Of course, we can measure the temperature to any precision that our thermometers allow using any unit, but to me the larger size of the Celsius degree makes a real difference in how useful Celsius is for describing my experience of temperature (which is presumably what Heffer meant; whether or not his statement about precision was precise is a different matter). Fahrenheit is just more human. Celsius degrees are too big. A difference of 5 degrees C is quite a lot, and 10 is huge. It makes giving round numbers more difficult in Celsius. “It’ll be 70-75 degrees” is just more how we like to talk about things than “It’ll be 20-23 degrees” or “21-24 degrees” or whatever. 0 degrees is “really flippin’ cold day” and 100 degrees is “really flippin’ hot day.” Those are nice human benchmarks. I’m OK at remembering some reference temperatures, but I think I’ll never be as comfortable with Celsius as with other metric units.

  9. houinkyouma

    Well as a moderate Brexiter I don’t think I know anyone who thinks bringing back the death penalty is a good idea. Strictly for the pub bores. But if you can name a Brexit mp that supports this I’m genuinely interested.

    On weights and measures I’m probably of the generation that was the last to learn imperial. I regret it’s passing greatly. But people younger than me would rather saw off their, er, left foot than go back so that boat has sailed too.

    And so has the Celsius boat. But actually I do think Fahrenheit (which is all I can think in) has objective superiority here at least when discussing the weather. Celsius is too compact. With Fahrenheit you can say, arg, tomorrow it’s going to be in the nineties. Or it was a lovely day, mid seventies and it actually means something. But gone forever I fear.
    I take your point about metrication though. The EU should have outlawed martyring the metric martyrs then Brexit would never have happened!
    Love the blog!

  10. I had a physics prof who, for one assignment, had us turn in answers using the FCF system: furlong-hundredweight-fortnight. As I recall, we had to express G and h in these units.

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