# 39. The Shifting Standards of the Metre and the Imperial System

Updated: Jan 21

One consequence of Brexit is that the UK is no longer required to trade in metric units. An article in the Guardian newspaper states:

*Since 1995, goods sold in Europe have had to display metric weights and measurements. And since 2000 when the EU’s weights and measures directive came into force, traders have been legally required to use metric units for the sale by weight or measure of fresh produce, which became a recurring issue for Eurosceptics about Brussels’ supposed interference in British life.*

*While it is still legal to price goods in pounds and ounces, these have to be displayed alongside the price in grams and kilograms.(6)*

The article states that Boris Johnson, Prime Minister, “claimed that measuring in pounds and ounces was an “ancient liberty””. But just how ancient is this imperial system, and how independent is it from the Metric system?

The inch and the foot are lucky to have had great champions like John Michell One reason for their enthusiasm is that their research has found the English inch, foot and yard to be part of an extremely old and sophisticated system of measure, designed by people well versed in surveying and astronomy. The foot and the mile are widely acknowledged to be very old units of measure, derived from a reasonably accurate estimate of the circumference of the earth (“geodesic”). This is because the average of the polar and equatorial circumferences is very close to being 12 x 12 x 12 x 12 x 12/10 = 24,883.2 miles. Another researcher, Robin Heath, has suggested the equatorial circumference was divided by the number of days in a solar year, and that figure was then divided by 360,000, to produce one small unit of measurement, the foot. Hence, the equatorial circumference of the earth is 365.242199 x 360,000 =131,487,191.64 feet, or 24,902.877 miles 7. The exact distance around the equator is estimated today to be exactly 24,901.461 miles, and around the poles is 24,859.734 miles (producing an average of 24,880.5975 miles, which is very close to 24,883.2).

Another researcher, has found intriguing connections between the mile and the earth: Hugh Franklin’s insight about the link between the value of the circumference in miles and pi, the ratio between a circle’s circumference and diameter, is equally fascinating, and should be more widely known. In his article “Earth, Pi, Miles and the Barleycorn”, he points out that the number 24,902.31984, which is very close to the contemporary figure for the *equatorial* circumference of the earth in miles, is in fact √(π3 x 20,000,000). So if you have a circle with a circumference of 24,902.31984, and the diameter of this circle can also be the diagonal of a square. The square will have a side of 24,902.31984 /(√2x π), and the area of this square will be 10,000,000 π. This square would be equal in area to a circle with a diameter of 10,000,000. This would suggest that the equatorial circumference of our planet, via the geometries of the circle and the square, gave rise to the mile itself, as a unit of measure. The circumference of the earth as a value in miles is equated to a square with an area of 10,000,000 π. It’s worth noting that in this model, actual pi is used, not an approximation such as 22/7.

So, approximately,

one mile = earth’s equatorial circumference /( √(π3 x 20,000,000)

= √(10,000,000 π) x √2 x π /earth’s equatorial circumference

and the equatorial circumference of the earth

= 365.242199 x 360,000 =131,487,191.64 feet, or 24,902.877 miles

Astronomy plays a huge part in the history of measure. There is a link between the mile and the cycles of the sun and the moon also. One lunation in days, 29.53059, divided by the average difference in days between the lunar year and the solar year, 10.87512 days, multiplied by 7,000/36, is 5,279.996. There are of course 5,280 feet in a mile, so if you take this to be a value in feet, it’s very close to a mile.

5,280 x 10.87512 x 36 / 70,000 = 29.5306

** **And so one mile, in feet, can be defined as 70,000 lunations / (36 x the difference in days between solar and lunar years). Consequently, earth’s equatorial circumference in feet

= 70,000 lunations x (√(π3 x 20,000,000) / ( 36 x the difference in days between solar and lunar years)

= √(10,000,000 π) x √2 x π x 5,280

and the equatorial circumference of the earth in miles

= 365.242199 x 1,296 x the difference in days between solar and lunar years / 7 lunations

and the meridian circumference of the earth

= 1752 x 10,000,000 lunations / ( 3 x the difference in days between solar and lunar years x 176) inches

The imperial system of measure offers many intriguing possible connections to geodesy, geometry, and astronomy that are not easily dismissed.

and John Neal.

A once widespread and very old system of measurement which used imperial or English yards and feet and inches is now used only in a handful of places. While the language of the long-lost British Empire has remained ubiquitious and influential in the world, the system of measure that underpinned the empire's trade and engineering projects has largely been replaced by the system created by the great rival empire of the time. Nothing lasts for ever, especially not a basic unit of measure. The English yard and the French metre have slightly changed in size over the centuries, both in the length of their standards, and in the ratio between them.

Making an accurate, durable and stable standard of measure for a city, yet alone a whole country, is notoriously difficult. Standards shrink and expand, standards chip and bend, standards are stored in buildings that burn down, rust after shipwreck, or are sent across the great ocean on ships that are captured by pirates (yes, all these things have happened to measuring standards!). Is it any wonder scientists started falling back on lightwaves and other highly regular and predictable microscopic phenomena to define a standard by? But exactly what length of a beam of light's journey should you actually adopt to make a new standard? Do you take a unit already in wide use, even if it's from some totally different system of measure, to use as your guide?

That's exactly what seems to have happened when the imperial yard, foot and inch were defined in relation to the metre. This is despite a distinct lack of enthusiasm in the UK for the metre from the start. At the height of the French Revolution, Talleyrand wrote to a British MP, to see if Westminster would consider adopting this fantastic new measure of length the revolutionaries had come up with: the metre. One selling point was that it was derived from a fairly accurate measure of the Earth's meridian circumference. With the introduction of this new unit, finally all the old ways, with their corruption and confusion, could be left behind, in this brave new world that was being created. Also, this new metre wasn't so scary really, just a new and improved version of the old familiar yard of three French feet, just re-jigged into a brand new decimal system.

While in France it was ‘out with the old and in with the new’, strong conservative principles reigned on the other side of the Channel. The suggestion of adopting the metre was made in the British parliament, but the response was lukewarm, and the proposal soon forgotten. Replacing the imperial system must have seemed about as horrific as chopping off your king and queen’s heads. Napoleon’s expansionist policies did nothing to warm the British to the new metric project in the aftermath of the revolution. So how was it that, in a strange twist of fate, a couple of centuries later, the measures indigenous to the UK were actually redefined in relation to this same metre? The history of the inch and the foot had become forever intertwined with the history of the metre.

The problem seems simply to have been that the surviving standards for the yard and foot were not trustworthy. The physical standard for the imperial yard was a problem for a start because it was unstable. This was recognised in 1855 as a problem. As a result, in 1893, in the USA, the Mendenhall Order changed the fundamental standards of length and mass from the customary standards based on those of England to the metric standards. Soon after, the UK followed, and the imperial units were made *to *align the system to the metric, legalised in 1897 in the Weights and Measures Act mentioned above. With this whole new level of precision and durability, getting the correct ratio between inch and metre, whatever the criteria for that may be, would have been much easier. Should the most stable examples of the metre standards simply be measured and used to define the imperial yard, or should an ideal ratio between the two systems be chosen? If so, what should this ratio be?

The length chosen for the new stable metric standard was simply the old *mètre des archives*, and the reference to the meridian circumference of the earth was dropped. However there is quite a difference between the length, as measured in inches, of the first metre agreed upon, 39.3827", and the variations on this measure of the late nineteenth and early twentieth centuries, much closer to 39.37”. This last value for the metre, or something very close to it, became pivotal to the new, intertwined histories of the metre and the yard, not the first metre.

Scientists in the early twentieth century adjusted the length of the yard to a certain ratio of the French metre. In an article published by the Royal Society in **1928**, entitled "A New Determination of the Ratio of the Imperial Standard Yard to the International Prototype Metre", by J.E. Sears, W.H. Johnson and H.L.P. Jolly, the metre is defined as **39.370147 inches**. The method used involved a standard with graduations that approximated the yard and metre, "32 main intervals being closely equivalent to one yard and 35 to one metre."(3) While 36 inches divided by 32 and multiplied by 35 make 39.375 inches, this is quite a bit longer than the authors' proposed 39.370147 inches. The third smallest graduations on the standard are 0.125 inches, and so there are 288 of these 0.125" units in a yard and 315 of these in a 39.375" metre. Smaller subdivisions of 1/40 and 1/200 inches also divide perfecty into 36 and 37.375.

288/315, or 64/7, is the same ratio Mauss uses, as we will see.

To put that in context, from the **1897** Weights and Measures Act the definition of the metre in inches was **39.370113"**. Before that, in 1836, a book by Olinthus Gregory gives **39.37079** inches to the metre (7), and in 1816 Patrick Kelly defined the metre as **39.371** English inches (8).

By 1927, a year before the article for the Royal Society was published, the International Bureau of Weights and Measures had adopted the 1908 light-wave definition of the metre. And by **1930**, the British Standards Institution had adopted a different length for the inch altogether: an inch of 25.4 mm based on the metre, so a metre was worth 10,000/254 = **39.3700787402 inches**. The Commonwealth Science Congress confirmed this is 1946, acknowledging that the yard was now 1.7 millionths of an inch longer than the old imperial inch, and 2 millionths of an inch shorter than the old US inch. The revolutionary metric system had become the basis for the imperial system, and the imperial inch was allowed to grow in length slightly. The metre, conversely, had shrunk slightly since the work of Méchain and Delambre.

Originally, the metre was defined as **3 French feet and 11.296 lines **of the Toise of the Academy, in **1799,** and in relation to the English inch, it was a little longer than the current metre, at** 39.3827"**. We since have had various historical ratios between the metre and the yard, foot and inch (not including the US Survey inch and yards, which in any case are on their way out in two years time). Specifically, the metre has been valued at 39.3827", 39.370432144", 39.370147", 39.370113", and 1/254 = 39.3700787402", as well as 39.375". What is the ratio between inch and metre meant to be, in an ideal world, where standards don't shrink / expand / go up in flames / rust?

In Robert Hussey's **1836** article, "Essay on the Ancient Weights and Money", he writes the English foot is to the (metric) French foot (one third of a metre) as 10,000 to 10,659. He deduces this from the Mémoires de l'Institut, Base du Systeme Métrique, vol iii, p. 470. In this account by the creators of the metric system, the metre is clearly stated as **39.3827"**, being also 3.07861 French Feet, or 443.32 lines, or 0.513074 toises. One line is a 1/144th part of the French foot.

In a footnote in his Appendix on the Roman foot, __page 227__, Hussey writes:

As calculations in French measures often occur here, it will be well to state at once the proportion between the French and English. The English foot is to the French as 10000 to 10659. This is deduced from Mem. de l'Institut, Base du Systeme Metrique, vol. iii. p. 470, where the English foot is compared with the metre, and the latter is proved to be equal to39.3827English inches, or 3.2818916, &c. English feet. In the same vol. p. 557, the metre is reckoned equal to 443.32 lines, the line being the 1/144th part of a French foot. Hence the metre is equal to 3.07861 &c. French feet; from which the proportion above given follows. Eisenschmidt (p. 94.) gives the proportion 1000 to 1066 : De Romé de l'lsle 10000 to 10646. In 1742 a comparison between the two feet was made, and the proportion settled as 10000 to 10654. See Philosoph. Trans. 1742. p. 105. But in 1768. Maskelyne (then Astronomer Royal) entertaining some doubts about the correctness of this proportion, caused a new comparison to be made : and the result was that the toise was found to be equal to 76.734 inches of the brass standard of the Royal Society, at the temperature 620 Fahrenheit. This gives the proportion between the feet 10000 to 10657, differing but .0002 from that of the French calculators, which is taken here. See Philosoph. Trans. 1768. p. 326.

This note gives a good idea of the amount of change that occurs between two recent and well-documented units such as the English and French feet.

Hussey also quotes the ratios of other researchers between the English and French feet. De Romé de l'Isle has 10000 to 10,646; Maskelyne has 1 toise = 76.734" (**1768**), so the ratio is 10,00 to 10,657. Le Pere, cited by Hussey, has 239.7 lines = 17.74278576". Henry James gives 3 English feet as 0.914391792 metres, which means a metre of **39.370432144** inches.

.

An article by C. Mauss (1), over half a century later, gives an English yard worth 914.2857 mm and a foot of 304.7616 mm. It follows that he is using a conversion of 1 metre = 39.3750393752" for the foot, and 39.375" for the yard. He was probably using **39.375"** for both, and rounded the value for the foot slightly, or even made a typo, as a third of the yard value Mauss uses should read 304.76190476 mm.

Curiously, the authors of the 1927 Royal Society article, metioned above, also pre-suppose a 39.375" ideal measure or the French metre as a starting point, despite their settling on a different figure after careful analysis of various physical standards. This is apparent from their method, in that they used a ruler with 32 intervals of 1 1/8th inch on the yard and 35 of these intervals in a metre of 39.375", which is taken to be "a length closely equal to one metre, the difference of approximately 0.004 inch being conveniently measurable by the direct use of an ordinary comparator microscope with a micrometer eyepiece".

I have not been able to find any other references to an ideal 39.375" value for the metre, apart from in the work of Mauss, the Royal Society article of 1927, a reference to Cagnazzi by Hussey, as we shall see below, and Berriman (as well as in research by Jim Alison, David Kenworthy, and others). Where did it come from? There is no mention of it in the work on the determination of the metre by Delambre and Méchain, which contains two chapters on the comparison between the metre and the English measures in Volume 3. It is a very appealing ratio, in that it offers lots of nice connections between the metre and the English inch.

It appears that for Mauss, the English yard is one seventh of 6.4 metres. A value of 6.4 metres relates to the yard (of 36 inches) as 16/90. While Mauss connects the English yard and foot to Persian measures, he might also have connected them to the French, and said that this same yard was 1 metre (of the 39.375" kind, which he was using), x 9/10 x 64/63. In fact 36, the number of inches in a yard, is 40 x 9/10, and if there are 40 x 9/10 inches in a yard which itself is 9/10 x 64/63 metres, it follows there are 40 inches in 64/63 metres (of the 39.375" kind). While the modern metre is valued at 10,000/254 inches, this conversion used by Mauss, of 39.375" per metre, is 63/64 x 40 inches. Curiously, 64/63 is a ratio associated with Ancient Egypt: the Eye of Horus. This is according to a theory by Egyptologist Georg Möller, who took the various components of the symbol to be fractions of a hekat, with just 63/64 left as a remainder.

What might a seventh of 6.4 metres be? 36 inches multiplied by 7 are also an Egyptian Royal Cubit of 20.625" x 144/55 x 14/3. The fraction 144/55 is an approximation of Phi squared using Fibonacci numbers. Alternatively, using a value of 20.6181818" for the Egyptian Royal Cubit, and a different approximation of Phi squared with other Fibonacci numbers, 55/21, then 7 yards are 20.618181818 x 55/21 x 14/3.

What is this 14/3? An Egyptian Royal Cubit of 20.625", usually thought of as 20 digits of 0.7291666667" x an approximation of root 2, which is 99/70; but it is also 132 digits of 0.7291666667" multiplied by 3/14. Therefore the 14/3 fraction can be written in terms of this approximation of root 2, so 14/3 = 66/10 x 70/99. So 7 yards can be written as the Egyptian Royal cubit x Phi squared divided by root 2 x 66/10, using 144/55 for a 20.625" value and 55/21 for a 20.618181818" value for the cubit. Or simply, 7 yards are 132 digits x Phi squared (using 144/55 and 0.729166666").

Since a 39.375" metre multiplied by 55/21 and 2/10 is the 20.625" Egyptian Royal Cubit, 7 yards are a 39.375" metre multiplied by Phi squared, 28/30, and Phi squared again, with one value for Phi squared at 144/55 and the other 55/21. Another way to put it is 270 inches divided by these two kinds of Phi squared approximations make a metre. The 20.618181818" Royal Eygptian Cubit is a yard and a half, or 54 inches, multiplied by 21/55, and the 20.625" Egyptian Royal Cubit is 54 inches x 55/144.

One of the raisons d'etre of a 39.375" ideal metre is that it contains 54 Roman/Egyptian digits, each valued at 0.729166667". This digit goes 2,160,000,000 times into a particular value of the circumference of the earth (the polar circumference of 24,857.95454545 miles to be exact), 45 times into a Megalithic Yard of 32.8125", 20 times into the remen of 14.583333", 18 times into the Northern foot of 13.125", and 16 times into the Roman foot of 11.66666". What's not to like? Of course, the digit could be made to fit a contemporary metre of 39.37007874022", a 54th part being 0.7290755322259" fitting 2,160,000 000 times into an ideal 40,000 km polar radius. (40,000 km was the initial division of the polar circumference from which the metre was derived, but in fact now the circumference is estimated to be slightly bigger, at 40,007.863 km, according to Wikipedia. (You might ask, however, as Benoit Mandelbrot did when he developed his concept of fractals by observing jagged coastlines in potentially ever greater degrees of magnification: "How do we measure such a thing?". Is there not also a huge array of possible measurements of the circumference of the planet, depending on how the measurement is taken? But such a question is not going to enlighten us on the question of the metre and yard's relationship. If we think about it too long, we will be left with an infinity of yards and metres and ratios between them, and will need to take a long walk.)

Even the 20.625" Egyptian Royal cubit works with a 0.7291666666" digit, if you apply 99/70 as an approximation of the square root of 2. Or even, the Royal Egyptian cubit and the digit, as 20.625" and 0.729166667", can be linked like this: cubit x 49,500 / 1,400,000 x 9,800/9,801 = digit. The Neal / Michell value for the Egyptian Royal Cubit of 20.618181818", can be thought of as 25,920 x 54 x 0.7291666667 / 49,500 = 20.6181818181. (This is because the link between these two Egyptian Royal cubits, the 20.6181818" one and the 20.625" one, is 9,801/9800 x 4,375/4,374.) So we could define the digit of 0.7291666667" as simply 25,920 ancient metres divided by 49,500, and multiplied by 4,375/4,374 (ragisma) and 9,801/9,800. Or, to adjust it slightly, the same but with modern metres.

Another, purely theoretical, link between the metre and inch could be this: a square with sides of 21/55 x 21/55 x 55/144 = 0.0556818181 inches has a diagonal of 2 millimetres of the 39.375" metre. i.e. 0.7875". Here all the approximations are used instead of Phi squared and the square root of two. in the same way, we could think of the remen as 100 x 21/55 x 21/55 inches, and the Egyptian royal cubit is the remen times 99/70.

There are many ways in which a 39.375" metre can relate geometrically to the imperial system.

When you `read a page from a historical book on historical metrology, all these variations become a bit of a headache. These are the values Hussey gives for the Roman foot, in relation to the English foot of his day. He also alludes to changes in the value for the foot since Greaves's time. If you look at the figure Gosselin gives for the Roman foot, it seems to fit well with a 0.729166666" digit, if you take his 0.296296296 metres, with a 39.375" metre: multiply Gosselin's figure by 39.375, divide by 16 (there are 16 digits in a Roman foot) and there's your digit of 0.7291666666". But Gosselin's Roman foot is given as 0.9724 decimal parts of the English foot, so that the Roman foot is here, in inches, 12 x 0.9724 = 1.6688, and the digit 0.7293". However, the value given in metres for Cagnazzi is 0.29624, which converts using Hussey's 39.3827" rate to the metre to 11.666731048 inches.

Taking the 16 digits of a Roman foot against the 12 inches of an English foot, 0.72916666667 x 16 / 12 = 0.972222222. Cagnazzi's Roman foot is 0.9722 parts of an English foot. 0.9722 x 12 = 11.6664 and 0.972222222 x 12 = 11.666666666. Who is Cagnazzi? I could find no trace of him online at first, and Hussey says the same, he could find no text by him, he only had a quotation in Barthold Georg Niebuhr's work on Roman history. But while Hussey didn't have Wikipedia or Google Books. we do. I found Cagnazzi, who seems to have only a chapter on measures in a book of statistics of his, from 1808. See __here__.

Just for interest, these are the pages from the brief chapter on measure, and the cover page of the book.

The conversion rate of 39.375 inches for a metre is full of possibilities, and seems to appear in Cagnazzi's analysis, yet it does not seem to ever have been an official rate. With it, the metric system, the imperial system, as well as various ancient measures such as the Persian and Egyptian, at least according to Mauss, seem to come together into one system. Despite all these interesting connections between the English system and the metre, provided by 39.375" for the metre, another value was picked, which we have still today. With the new ratio between inch and metre, these theoretical connections created by a 39.375" metre vanish. In a passage on the Olympic Greek measures in ancient Egypt, Letronne reminds us that we need to be careful about jumping to conclusions in metrology.

Can we be justified in allowing connections to be made between the metric and imperial systems, such as 20 mm of a 39.375" metre are a nice tidy 7.875" which, when multiplied by Phi squared, especially a nice approximation such as 144/55 or 55/21, give us the Egyptian royal cubit, which is also a metre multiplied by pi (again a nice approximation such as 22/7 works well) and then divided by 6. Or 0.8 yards being related to a Persian cubit of 28.8 inches or 5.12 / 7 mm, as Mauss claims? Where there have been so many historical fluctuations in the absolute values of these measures, not to mention their ratios, how much precision can we hold on to in historical metrology? Does anything go? Can we really read much into the ratios between units from different parts of the world and diferent times? I think that we can cautiously look at the history of measure as the evolution of one or several interconnected systems that have been broken up and modified over time, either because of a lack of political and economic unity, or because of problems with standards. there is a lot we don't know about the origins of current measuring systems, such as imperial, and how it is geodesic when, officially, our planet was only successfully measured in recent centuries. Looking for connections between measures from different times and locations can be very interesting.

Even though the 10 000/254 inch metre (the current one) isn't quite as nice, in that respect, as the 39.375" metre, it does also offer some nice theoretical connections. For example, we could look for a meaningful comparison to the cycles of the moon and sun. 254 years are approximately 1000 lunations. While this isn't useful astronomically, it does offer a very nice connection to the moon and the sun, a sort of calendrical coincidence.

Jim Wakefield has found very intriguing connections between imperial and metric in the dimensions of the glass pyramid at the Louvre. In a blog post, he wrote:

Many people believe there is no relationship re metric and imperial measure. I certainly thought that until I found quite by accident two measures and this may be only a coincidence but worth recording.

The solar year and the lunar year. 365.25 days and lunar 354.3 days.

If you can imagine a solar year being a circle 365.25 days find the diameter = 116.2626 and call this feet.

116.2626 feet = 35.4368 metres.

And we know this is accurate as 35.4368 / 12 = 2.95306 and that is pretty good 29.53 days in a synodic month really 29.5306

With pleasure I wish to add a remarkable fact re the dimensions of this glass pyramid and to the cleverness of its architects. This may be common knowledge anong architects but for me it was a discovery.

Length of base given in drawing 35.42 metres. I am not sure if these figures are absolutely correct so if anyone knows then let me knows please.

Height 21.64 metres.

I asked myself why the odd numbers? Why not just 35 metres? for the base and 21 for the height.

Then I looked at the number 35.42 and thought about the closeness of this number to that of a moon based year.

A synodic month = 29.53059 days x 12 months 354.36 days close to the number given 35.42. Ok that is easily shaken off as a coincidence but look.

As in the drawing the length given is 35.42 metres now remember Pei the architect is an American and as I have been informed was living in his Manhattan home in January 2016 he turns 100 on the 27th April this year 2017. I looked at this odd number and converted to feet 35.42m = 116.20734 feet and I saw it straight away.

A circle inscribed into the base of the pyramid at the Louvre measures 365.076 feet 365 the number of days in a year.

By switching from metric to Imperial the architect has given the lengths for a lunar and solar year. 354 and 365. Interesting that the metre allows this??

And not only that he has done it again in the height as he has doubled his base length 35.42 x 2 = 70.84 and named this number FEET.

70.84 FEET = 21.6m. Not sure exactly which value for pi he used but so clever.

(5)

Twelve synodic months of 29.53059 days make a lunar year of 354.36708 days.

Convert a value of 35.436708 metres to imperial feet, so multiply by 10,000/(254 x 12), the result is 116.26216535 feet. Multiply by pi, top convert this measure, as the diameter of a circle, to obtain the circumference, the result is 365.24836 feet.

I think Jim has found something very curious about the relation between metric and imperial, which could well explain to a certain extent why, after scientists busied themselves for so long with microscopes measuring the inch in relation to the metre and vice versa, with various standards at various temperatures, in the end a seemingly random 10,000/254 rate was chosen. Take 365.242199 feet as the circumference of a circle, then divide by pi to find the diameter, convert to modern metres, you will get 35.4361098 m. there are 365.242199 days in an average solar year and 354.36708 days in an average lunar year (of 12 synodic months). In other words a circle representing ten years in imperial feet will have a diameter of one lunar year in metres. The 10,000/254 ratio works here perfectly because a circle representing 254 years will have a dimension of 1,000 lunar months. This could be the reason why this ratio was chosen. The imperial foot becomes associated with the sun, and the metre with the moon. At any rate, the connections provided by this ratio, and Jim's insightfulness, are a reminder that if we don't try and look for connections between units in metrological systems, we won't find them. And also, it's a reminder that we don't always need to be looking for whole numbers of units in when we try and make sense of structures through their dimensions, as Petrie claims in his introduction to *Inductive Metrology*. If Jim's analysis is right, then we can't underestimate the importance of the astronomical cycles in analysing measures that have been used in designs in prominent, symbolic places.

Jim Wakefield has found some amazing connections to various astronomical cycles at Giza, and he helped me come up with this interpretation of the Giza rectangle, for example.

The moon's cycles seem to be present in metres. I think the metre may well have long associations with the moon, which have been carried on to this day.

When Méchain and Delambre were busy measuring the meridian between Dunkerque and Barcelona, to determine the length of the new metre, they were closely supervised by Laplace. This is clear from reading Delambre's account Laplace seems to act as a head scientist (his name is mentioned by Delambre in relation to refraction, the detremination of the latitude of the Pantheon in Paris, and tables) but also as a supervisor. (see Base du système métrique décimal, ou mesure de l'arc du méridien compris entre les parallèles de Dunkerque et Barcelone, executée en 1792 et années suivantes : suite des Mémoires de l'Institut. 2 - Google Play Books) Laplace was an exceptional man, an aristocrat of Napoleon's empire, a leader who managed not to get his head chopped off in the revolution, a politician, an astronomer, a phyisicist, a philosopher, and a mathematician. In the end, perhaps he was looking for Méchain and Delambre to find something he already knew, that fitted in a system he wanted to use as a basis. But then why did he not allow a 10,000 / 254 inch metre to be fixed from the start, assuming he knew of this 254 year and 1000 lunation connection with a circle? I don't know. It does seem that the endeavours of Méchain and Delambre were genuinely motivated by science, to a very high level of exactness, not to serve a foregiven conclusion. Yet, despite all their efforts, and all the efforts of their successors in determining the length of the new metre, in the end it was fixed over a century later to an easy fraction, reflecting this calendrical quirk of sun and moon.

Perhaps those who fear the imperial yard and foot are in danger of extinction have nothing to fear: maybe the metric and imperial systems are designed to co-exist, in a dual system that mimics the eyes of Horus, that is, the sun and the moon. (And perhaps this also means we don't have to worry about how to measure the earth anymore, with all the fractal headaches it will create!)

Notes

Mauss, C. 1892, "L'ÉGLISE DE SAINT-JÉRÉMIE A ABOU-GOSCH OBSERVATIONS SUR PLUSIEURS MESURES DE L'ANTIQUITÉ (Suite)", in Revue Archéologique Troisième Série, T. 20 (JUILLET-DÉCEMBRE 1892), pp. 232-253 (22 pages) Published by:

__Presses Universitaires de France__3. Sears, J. E., et al. “A New Determination of the Ratio of the Imperial Standard Yard to the International Prolotype Metre.” Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, vol. 227, 1928, pp. 281–315. JSTOR, http://www.jstor.org/stable/91218. Accessed 30 May 2022.

4. Ibid. See A New Determination of the Ratio of the Imperial Standard Yard to the International Prolotype Metre on JSTOR

Jim Wakefield- Reconciliation - History of Metrology. (tapatalk.com)

“Boris Johnson to reportedly bring back imperial measurements to mark platinum jubilee”, Nadeem Badshah, Sat 28 May 2022, The Guardian

7. Olinthus, Gregory, 1836, Mathematics for practical men: being a common-place book of principles, theorems, rules, and tables, in various departments of pure and mixed mathematics, with their application; especially to the pursuits of surveyors, architects, mechanics, and civil engineers, Philadelphia, E. L. Carey and A. Hart

8. Kelly, P. 1816, METROLOGY, OR , AN EXPOSITION OF WEIGHTS AND MEASURES ,CHIEFLY THOSE OF GREAT BRITAIN AND FRANCE : COMPRISING Tables of Comparison , AND VIEWS OF VARIOUS STANDARDS ; WITH AN ACCOUNT OF LAWS AND LOCAL CUSTOMS , Parliamentary Reports ,London