The recent discovery that the principles of the metric system were proposed in England over a century before they were adopted in France seems to deserve comment on Metric Views.

An Australian, Pat Naughtin, has recently drawn attention to a book by John Wilkins published in 1668. Wilkins was Oliver Cromwell’s brother-in-law, and his distinguished career included being Warden of Wadham College Oxford, Master of Trinity College Cambridge just before the arrival of the youthful Newton, Secretary of the Royal Society, Dean of Ripon and finally Bishop of Chester.

In his book, “An essay towards a real character, and a philosophical language”, Wilkins discusses the nature and variety of language and languages, and includes a short chapter on measurement, entitled, “Of measure”.

The first section of this chapter concerns number. Having considered division by eight, he concludes, “But because general custom hath already agreed upon the decimal way, therefore I shall not insist upon the change of it.” Not exactly a ringing endorsement of decimal systems, but the arguments for non-decimal systems, which continue to this day, seem already to have been lost three centuries ago.

The second section of the chapter looks at measurement of length, and volume, which Wilkins calls collectively, “magnitude”. The first issue he raises is the absence of a universal system of measurement. He says, “The several Nations of the World do not more differ in their Languages, than in the various kinds and proportions of these Measures. And it is not without great difficulty, that the measures observed by all those nations who traffick together, are reduced to that which is commonly known and received by anyone of them; which labour would be much abbreviated, if they were all of them fixed to an one certain Standard.” He then proposes that this should be “some natural standard or universal measure”, and that this should be of length as “the other measures might easily be fixed from thence.”

So, as well as proposing the principles of the metric system, he seems also to have foreseen the need for agreed international standards for units of measurement.

For the natural standard of length, he looks first at the height of the column of mercury in a barometer, which he calls the quicksilver experiment, and he rejects this because of its uncertainty. Quite right! He then says, “Some have conceived that this might be better done by subdividing a Degree upon the Earth: But there would be so much difficulty and uncertainty in this way as would render it impracticable”. This was the method originally used to define the metre, but French surveyors engaged on the meridian surveys of the 1730’s and 1790’s would at times probably have agreed wholeheartedly with Dr Wilkins. Finally, he recommends the pendulum, “which was first suggested by Doctor Christopher Wren”. The pendulum was seriously considered by the founders of the metric system for their standard of length, but finally rejected when it was realized the variation in the earth’s gravity with latitude meant that this could not be the universal measure they sought. Quite by chance, the pendulum recommended by Wilkins, based on experiments carried out by the Dutch physicist, Christiaan Huygens, is 997 mm long.

Wilkins then goes on to recommend additional units for length by dividing and multiplying his standard by ten, a hundred and a thousand. Units for “capacity” follow naturally by cubing his standard length, with decimal multiples and sub divisions.

For the standard of weight, known nowadays as mass, he proposes the standard of capacity filled with “distilled rainwater”. So the relationship between mass and volume that was sought by the founders of the metric system is also in the ‘Wilkins system’.

Finally, he proposes decimal currency, which any readers of Metric Views who have reached this point in the article will be happy for me to pass without comment.

Hitherto, most historians have agreed that a French priest, Gabriel Mouton, was the ‘founding father’ of the metric system. He proposed a decimal system of measurement in 1670, two years after Wilkins. Mouton based his standard on the length of one minute of arc of a great circle of the Earth (now called a nautical mile, 1852 metres). He also proposed the swing-length of a pendulum with a frequency of one beat per second as the unit of length (about 25 cm). At that time, England and France enjoyed friendly relations, and it is possible Mouton could have learned of Wilkins’ work before making his proposals. Or this may be another example, like the miners’ safety lamp or the incandescent light bulb, of two people putting forward similar proposals at almost the same time but quite independently.

Clearly, Wilkins’ proposals, like those of Mouton, include the essential principles of the original metric system:

A universal standard of length

A simple relationship between length and volume

A simple relationship between volume and mass

Decimal multiplication and division of the standard units to give further units

Wilkins did not, of course, see the adoption of his proposals – he died in 1672 – and he might have been disappointed to learn they would be taken up and developed by the French, not the British. However, the development of the metric system beyond his proposals has depended a great deal on international cooperation. He would be pleased to learn of significant British contributions in areas he never foresaw, such as the addition of electrical units to the metric system as proposed by the British Association for the Advancement of Science in 1874. And he would probably be delighted that the simple and logical system he proposed has now become almost universal.

Further details of John Wilkins can be found at http://www.cl.cam.ac.uk/~rja14/wilkins/wilkins.html

The relevant pages of Wilkins’ book can be found at Pat Naughtin’s web site at: http://www.metricationmatters.com/docs/Wilkins_translation_2007-07-14.pdf

“Quite by chance, the pendulum recommended by Wilkins, based on experiments carried out by the Dutch physicist, Christiaan Huygens, is 997 mm long.”

I disagree with this. John Wilkins states that his “standard” (= metre) should be equal to 38 Rheinland Zoll (=inches) which is the same as 39.25 British inches. According to this website: http://home.fonline.de/fo0126/geschichte/groessen/mas7.htm, before 1816, the Rheinland Fuss was 0.31385 m. This means the Rheinland Zoll was 26.154 mm.

38 Rheinland Zoll x 26.154 mm/Zoll = 993.86 mm. 39.25 inches, using the post 1959 definition of 25.4 mm per inch yields 996.95 mm. The two values that John Wilkins assumed to be the same vary by 3.09 mm.

This brings a dilemma that results from assuming that a British inch of 2007 (post 1959) is the same length as the British inch of 1668. Do we know for sure how long a British inch was in 1668? Do we know how long a Rheinland inch was in 1668? Is John Wilkins correct in stating that 38 Rheinland inches was equal to 39.25 British inches in 1668? Maybe at that time that relation was true. But the interesting thing is, we don’t know today how much each inch changed since then. If we assume that John Wilkin’s “standard” of 1668 was indeed equal precisely to the metre of today (maybe he knew something the French didn’t know 120 years later and we still don’t know today that would have spared them the need to survey the meridian), then the Rheinland Zoll of 1668 was equal to 26.315 8 mm and the British inch of 1668 was equal to 25.477 mm.

This makes the Rheinland inch longer by 0.1618 mm in 1668 compared to 1816 and the British inch shorter by 0.077 mm from 1668 compared to today. Actually not much of a difference. But still it is just to point out that you can’t assume the inch of today was the exact same length in 1668 and that John Wilkin’s standard varied by 3 mm from the present metre.

I believe in 1668 the inch of London was defined as 3 Barley Corns round and dry. There is no way the Barley corn method could be precise and even a variation of 0.1 mm between Barley Corns would result in a 4 mm variation in 39 inches compared to one metre. This is enough to prove that it is impossible to say the “standard” proposed by John Wilkins is 997 mm. The best we could do is say it was the same as the present metre plus or minus a few millimetres here and there.

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Regardless of how close John Wilkin’s proposed “Standard” unit of length is to today’s metre, Pat Naughtin’s discovery is remarkable.

It rewrites the history of the metric system in the sense that John Wilkins as well as Gabriel Mouton are fathers of the system. Wilkins recognised three key things that are important for todays international system (SI):

a) the need to base units on a natural constant rather than an object

b) the need to use a single numeric base of the units

c) the need of international standardisation

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We must understand that Wilkins and probably Mouton two years later were looking at the philosophical implications of a coherent system of measurement rather than proposing an immediate plan of action. If we back-calculate WilkinsÃ¢â‚¬â„¢ proposed universal standard using the equation for the period of a pendulum, we can easily discover that:

1) The Ã¢â‚¬Å“vibrationÃ¢â‚¬? to which Wilkins referred was the time for the pendulum to swing from one extremity of its motion to the other extremity Ã¢â‚¬â€œ ie half of its period.

2) Using a value of 9.8118 m/sÃ‚Â² (the value for London), the length of such a pendulum would be 0.9941 m or 39.14 inches.

This gives us the clue that in his essay, Wilkins was looking at concepts rather than exact measurements, otherwise why would he have stated that the length of the pendulum would be 39Ã‚Â¼ inches? One should therefore resist the temptation to draw conclusions from calculations performed to micrometric accuracy.

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No matter which country thought of it first, we still can’t deny the fact that the imperial system was used by a majority of people in the UK for hundreds of years. Another fact that can’t be ignored is that a lot of people still use the imperial system, be it on the roads, or talking about their height and weight. Out of all the people I know, none of them tell me their height in metres.

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I think one of the most remarkable things about this story is the fact that two different approaches were used to define the unit of length. One used the gravity field of planet Earth, the other its physical size yet they produced results that differ by less than 1%

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Tabitha Jones Says:

“No matter which country thought of it first, we still canÃ¢â‚¬â„¢t deny the fact that the imperial system was used by a majority of people in the UK for hundreds of years.”

Wrong! Imperial came into existence in 1824. That is less then 200 years ago.

And so what if they did use some archaic mumbo-jumbo back then. They also rode in horses, took baths once a month, if that, couldn’t read & write, etc, and mostly lived in poverty. Most of us would not trade places with them.

We have progressed in every facet of life, including weights and measures.

“Another fact that canÃ¢â‚¬â„¢t be ignored is that a lot of people still use the imperial system, be it on the roads,”

Because they are FORCED to. Change the signs and see how fat imperial becomes either forgotten or confused. Why is it that those opposed to metric can only come up with road signs and pints in pubs as examples of Fred Flintstone units (FFU) still in use? People also use metric when buying petrol and thousands of products that are marked only in metric in the shops. If you work for a living their business will be metric and they will use it there.

“or talking about their height and weight. Out of all the people I know, none of them tell me their height in metres.”

I’m sure that people’s statistics are a constant source of talk. I can’t remember how long it has been since I was asked how tall I was or even bothered to ask someone. Since I use metric and have a feel for it (none for FFU), I can easily look at someone and tell their height precisely. I don’t have to ask.

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Martin Vlietstra Says:

“This gives us the clue that in his essay, Wilkins was looking at concepts rather than exact measurements, otherwise why would he have stated that the length of the pendulum would be 39Ã‚Â¼ inches? One should therefore resist the temptation to draw conclusions from calculations performed to micrometric accuracy. ”

Wilkins didn’t discuss the pendulum, but a string and a ball. From what he describes, the Standard (=metre) would = (L+r) + 0.4r^2/(L+r), where L is the length of the string, and r is the radius of the ball.

Using the method Wilkins mentioned, what would you calculateÃ‚Â the Standard (=metre) to be? Maybe much closer to 1.000……

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I wonder how many people actually think metric, but communicate in imperial for fear of being seen as “sellouts to the EU”…

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It seems Wilkins, Mouton and Leibnitz had the same idea at the same time. I just wonder how much this idea floated around before being put to print.

Gabriel Mouton

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Gabriel Mouton (1618 Ã¢â‚¬â€œ 28 September 1694) was a French abbot and scientist. He was a doctor of theology from Lyon, but was also interested in mathematics and astronomy.

His 1670 book, the Observationes diametrorum solis et lunae apparentium, came to form the basis of what was to become the metric system hundred years later. Based on the measurements of the size of the Earth conducted by Riccioli of Bologna (at 321,815 Bologna feet to the degree), Mouton proposed a decimal system of measurement based on the circumference of the Earth, explaining the advantages of a system based on nature.

His suggestion was a unit, milliare, that was defined as a minute of arc along a meridian. He then suggested a system of sub-units, dividing successively by factors of ten into the centuria, decuria, virga, virgula, decima, centesima, and millesima.

The base unit would be the virga, 1/1000 of a minute of arc, corresponding to 64.4 Bologna inches, or ~2.04 m. This was reasonably close to then current unit of length, the Parisian toise (~1.95 m) Ã¢â‚¬â€œ a feature which was meant to make acceptance of the new unit easier.

For practical reasons, Mouton suggested that the actual standard be based on pendulum movement, so that a pendulum located in Lyon of length one virgula (1/10 virga) would change direction 3959.2 times in half an hour. The resulting pendulum would have a length of ~20.54 cm.

His ideas attracted interest at the time, and were supported by Jean Picard as well as Huygens in 1673, and also studied at Royal Society in London. In 1673, Leibniz independently made proposals similar to those of Mouton.

It would be over a century later, however, that the French Academy of Sciences weights and measures committee suggested the decimal metric system that defined the meter as, at least initially, a division of the circumference of the Earth. The first official adoption of this system occurred in France in 1791.

By today’s measures, his milliare corresponds directly to a nautical mile, and his virga would by definition have been 1.852 m.

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Wilkins would have known that his standard length (derived by the pendulum method) was approximately a ten millionth of the distance between the north pole ant the equator because, in 1505, Duarte Pacho Pereiri had calculated the length of a degree of meridian arc with a 4% margin of error. Perhaps this influenced him to choose the seconds pendulum.

Today we define the period of oscillation of a pendulum as the time taken for it to swing from one extreme to the other AND BACK; Wilkins suggests one that takes a second to swing ONLY from one extreme to the other – ie has a period of two seconds. Maybe, in those days, it was conventional to define pendulums by how long they took to complete a half cycle (I don’t know) or perhaps Wilkins wanted his standard to be approximately a ten millionth of the distance between the N pole ant the equator.

Had he chosen a pendulum, whose period was one second, his standard would have been 0.249m instead of 0.994m (for pendulums in London).

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It’s fascinating that the circumference of the Earth was known, to within a few percent of its true value, as long ago as the 3rd century BC.

As Carl Sagan states, in this awe-inspiring clip from his 1980 TV documentary – Cosmos, “Eratosthenes’ only tools were sticks, eyes, feet and brains, … plus a zest for experiment”.

The fact that the Earth’s circumference has an easy-to-remember value of 40 000 kilometres is an extra bonus for viewers, that would have been lost if miles had been used.

Carl Sagan’s use of exclusively metric units throughout a popular TV series, even one targeted primarily for an American audience, still stands as an example for the producers of today’s TV documentaries.

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It seems Carl Sagan knew the correct pronunciation of kilometre. It’s unfortunate that the wrong pronunciation is taking over. With going in this direction, will centimetre and millimetre be pronounces as cen-tim-e-ter and mil-lem-e-ter?

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@Alex McDowell – the exact text used by Wilkins read “Let this ball be suspended by this string, being extended to such a length, that the space of every vibration may be equal to a second minute of time”. From this text it is clear that Wilkins was measuring what we today call “half-oscillations”. See https://www.google.co.uk/books/edition/An_Essay_Towards_a_Real_Character_and_a/BCCtZjBtiEYC?hl=en&gbpv=1, page 191.

I doubt that Wilkins had in mind the figure of one ten-millionth of the distance between the North Pole and the equator – if you read the rest of what he wrote on that page, you will see that he was looking for the most reproducible way available to man to replicate a standard unit of length.

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