The old French foot, of which 6 made the toise de Paris, was said to have been brought in by Charlemagne, the 8th-9th century Emperor of the Franks. This foot, or* pied royal Carolingien *was estimated by French historian and metrologist Paul Guilhiermoz in 1919, to have been 0.31448 metre, or 12.3811023 inches, at the time of Charlemagne, so on that basis, a toise of six pieds de roi should have been 1.88688 metres long. Yet, the toise that was in place when king Louis XVI was guillotined was valued at 1.94903631 metres, and a foot at 0.324839 metres, or 12.78895217 inches. The French foot was referred to variously as *pied de roi* or *pied du roy*, the old spelling for the word "king" having been with a "y" between 1694 and 1740 according to the *Académie française**, *and probably before that also. The difference between a *pied de roi* (using the most recent spelling, in this article) at the time of Charlemagne and at the time of Louis XVI was over a centimetre, which is quite a lot for a foot. Was Guilhiermoz correct, and if so, how was Charlemagne's *pied *allowed to grow so much? What is the history of the French foot?

## 1667: The Toise du Châtelet is warped

There had already been some chopping and changing of the French national standard of length, the Paris foot or king's foot, in the run up to the design and implementation of the metre, originally defined in 1791. Well over a century earlier, in 1667, the main standard for the toise, a stout iron bar in a Parisien courtyard, was bent out of shape when the wall it was attached to shifted. Rather than replacing it with another iron bar, as close as possible in size to the original, a new standard, with a slightly different length, was defined for the country, based on some idea of what the toise ought to have been. It seems the opportunity was taken by the authorities to correct the *pied de roi*. Presumably, some kind of error had been perceived to have crept in. Since at least 1394, the earliest mention of it in a document, the standard for the toise of Paris had been this - or some - iron bar embedded in the wall of the Grand Châtelet. No one really knows if the iron bar that was bent in 1667 was the same that was there in 1394.

Was this when the *pied de roi* grew? No. On this occasion, it was actually shrunk, only very slightly but enough to cause a stir. Despite the uproar, a new toise, named *Toise du Châtelet*, was imposed by law, at least in Paris, in 1668 - although beyond the capital, people didn't seem to take much notice. It's not known for sure how the new *Toise du Châtelet* was designed, in 1667, or why the authorities wanted to make it shorter. The whole process is shrouded in mystery.

Many years later, the French scientist and explorer La Condamine related the story of the change of standard in Paris as follows:

Mr. Picard in his Latin treatiseOn Measures, inserted in Volume VI of the old memoirs of the Academy, says with his usual concision;“the old Masons toise was reformed and shortened by fivelignesin 1668”,without informing us of any other circumstances. One learns only through oral tradition, that to give the new standard the true length it ought to have, they measured the width of the arcade or inner door of the large house that serves as the entrance to the old Louvre, the side on rue Fromenteau. According to the [builder's] plan this opening was to be twelvepiedswide. Half of that length [six pieds] became the new standard of thetoise, which proved shorter than the old by fivelignes. (9)

To come up with a new length for the *pied de roi*, in 1667, the doorway of a house was measured. How old was this house? It stands to reason it must have built at a time when the *pied de roi*, according to some unkown parameter, was considered by the French authorities in 1667 to have been correct, and that the measure provided by the iron bar at the Châtelet was considered faulty in some way. The bar could have been less than a century old, or could have been hundreds of years old. Even though Paris was at the heart of a vast empire, and a huge trading network used its units of measure, one of its most important of units of measure was considered worth changing slightly, for reasons unknown. Imagine if someone in Paris or London today decided the metre or foot must absolutely be shortened by 5%, because for the last hundred years it had been the wrong length, and with no further explanation for the change!

This rue Fromenteau, and the house on it, have long since gone. The road ran along the western side of the Louvre, which was completely remodelled in the 1850s during the Second Empire, and is now called the Pavillon de l'Horloge. This pavilion was originally built between 1624 and about 1645, so not that long before 1667, but perhaps the large house there mentioned by La Condomine was much older than that. Whatever period this house had been built in must surely have held a special appeal for the authorities. What period this was is anyone's guess. The Louvre was originally built as a castle in 1190 and has seen many changes since then. We can imagine that this house was one of the beautiful *hôtels* that would have lined the road at the time, and that the plans of its construction had survived, and been chosen as evidence for the 'correct' length of the *pied de roi*.

M. de la Hire, in a 1714 *Mémoire* (1) tells us that *before* the 1668 redesign of the pied de roi, which he refers to as the *pied des Massons*, another foot was used which was one line longer than the pied of the toise du Châtelet. La Hire is certain this foot was the same as the one from the fathom or cubit of the emperor Charles (Charlemagne, 8th-9th c.), a view which is in contradiction with Guilhiermoz's.

## The pied de l'écritoire

There was another standard kept in Paris, at the "Ecritoire aux maçons", a registry of the "master jurors of the works of masonry and carpentry of the city of Paris”. Picard called this the *pied des maçons*, and it was commonly used in Paris, also going by the name *pied de l'Ecritoire*. Builders and carpenters continued to use this foot until the authorities put a stop to it. La Reynie, *lieutenant de police du prévôt de Paris*, forbade masons to use any measure other than the one in the Châtelet in March 1667. However, he must have listened to the complaints, because he asked Bricart, master general of the works of royal buildings, to ascertain, in the presence of the royal prosecutor and sworn master masons, the difference that existed between the two measures, old and new. On October 12th, 1667, the results were recorded. The length of the gallery of the Louvre was measured twice, first with a measurement taken with the *toise of the Châtelet*, then with a measurement taken with the *toise de l'Ecritoire*. The first result was 220 toises 1 pied 2 pouces 7 lignes, or 190,255 lines, and, the second, 219 toises 9 pouces 7 lignes, or 189,331 lines, which gives the old foot 0.7028 of a line more than new foot, and consequently the old toise 4,2166 lines more than the new toise. The difference was clear. In the end, however, the new toise was made compulsory anyway, in 1668. The *ma**ç**ons* clearly had a case, but the reasons their protests were dismissed are unclear.

Unfortunately, this gallery in the Louvre has since that time been shortened, so it's impossible to re-measure it now as it was.

## A scientific awakening

The standard for the toise du Châtelet was bent right in the middle of a period of important mathematical and scientific advances taking place in Paris, and beyond. The Copernican revolution was well underway. The abbé Mouton published his *Observationes diametrorum solis et lunae apparentium* ("Observations of the apparent diameters of the Sun and Moon") in 1670, in which he put forward the idea of a new unit of measure, based on a decimal system, and the dimensions of the earth, for the purpose of science, internationally. While the authorities were looking to the past to change French measures, the Academy of Sciences held its gaze firmly towards the future.

The Paris meridian was defined on the 21st June 1667 by mathematicians of the Academy of Science of Paris, and on that day they traced along the ground the line of the meridian exactly where the future Observatory of Paris would be. In 1669, the Abbé Picard measured the meridian, in order to measure the size of the earth, and in order to properly map France. In 1672, Jean-Dominique Cassini was in charge of a team of astronomers trying to determine the distance of the earth from the sun. Yet, despite all these advances in science, there was not yet any single, precise, readily available standard of unit for the pied de roi in France. Scientists would have their own rulers made by the craftsmen of their choice, presumably based on that rough old iron bar at the Châtelet. Even if the standard at the Châtelet hadn't been bent out of shape, it wouldn't have been good enough for precise scientific work, being roughly made and exposed to the weather for years, perhaps centuries. As La Condamine remarked, the bar was so roughly made that it would be very unlikely that two measurements taken of it would be the same, even if taken by the same person. In fact, this raises the question of what standard the authorities themselves were using, in order to so preciely reduce the length of the toise in 1667-68. By the time of La Condamine's trip to Peru, whatever standards had been used by various teams of scientists in the past, including Picard's, had vanished. Without precise knowledge of Picard's particular reading of the post-1668 Paris foot, how could anyone correctly interpret his attempt to measure the earth? La Condamine said, in 1758:

If thetoiseused by M. Picard had remained on deposit at the Academy or at the Observatory, where M. Picard formally says that it will be carefully preserved, one would not have failed to make it serve in all the measurements of Degrees subsequent to his; they would have all been related to thistoise, and the doubts which have arisen since then on the true length of the base of M. Picard'stoisewould have been promptly cleared up. But Mr. Picard'stoiseno longer exists, and we have no authentic monument, from his time, other than an iron bar sealed in the wall at the foot of the staircase of the Grand Châtelet, ending in two projections or steps at right angles, and which served as a standard for public measurements. This standard had been roughly built; its angles had become dull, and the interior faces of the two steps which must fit atoisewhen one tests it there, were never polished nor filed square and parallel with one other. No wonder thetoisescalibrated at different times and by different people on this defective original, are not perfectly equal to each other. (9)

Because to this day no one knows exactly how long Picard's *pied de roi *was, it is still difficult to interpret Picard's work. As La Condamine wrote:

It is therefore possible that the standard was, from the time it was installed, longer than thetoisethat Mr. Picard took to measure his degree, or that it had lengthened since by striking with a hammer the nails which attached it to the wall; moreover the two projections must have been worn by rust, by the continual rubbing of the measures being gauged, and perhaps by polishing them; it is thus very apparent that the distance between them increased. It would not be astonishing in this case that the newtoises, gauged to this standard for twenty-five or thirty years; are longer than that of Mr. Picard, and consequently that one would have found fewertoisesthan he found in the measurement of the base between Villejuîve and Juvify (Mém. De l'Acad. year 1754, p. 172). (9)

Picard's foot is the foot that Newton refers to in his work *De mundi systemate* (*The System of the World*), published posthumously in 1728, but written in 1685, in passages such as this:

Suppose the circumference of the earth to be 123 249 600 Paris feet; as has been determined by the late mensurationof the French (vide p. 406); then the same body, deprived of its circular motion, and falling by the impulse of the same centripetal force as before, would, in one second of time, describe 15 ¹/¹² Paris feet.

This we infer by a calculus formed upon Prop. XXXVI, and it agrees withwhat we observe in all bodies about the earth. For by the experiments of pendulums, and a computation raised thereon, Mr. Huygens has demonstrated that bodies falling by all that centripetal force with which (of whatever nature it is) they are impelled near the surface of the earth, do, in one second of time, describe 15¹/¹² Paris feet. (10)

How long exactly was this foot used by Picard, Huygens and Newton? Were they even referring to precisely the same value, or to a generic French foot for which they all had a slightly different length? It is hard to be certain. Perhaps Newton or Huygens was able to take a precise reading of Picard's standard.

There is an important clue however given to us by Newton in this passage, referencing the work of Huygens. If we use the modern value for the acceleration due to gravity to deduce the length of the Paris foot, and assume Huygens had calculated correctly, we might be able to determine the length of the Paris foot he used. The figure provided by Huygens and quoted by Newton states that bodies falling under the centripetal force near the surface of the Earth cover a distance of 15¹/¹² Paris feet in one second of time. Today, the equation for distance covered in free fall is: d = 0.5 * a * t². Given that the distance covered, d, is 15¹/¹² Paris feet and the time, t, is 1 second, we have the equation:

15¹/¹² Paris feet = 0.5 * a * (1 second)². If we use the modern acceleration due to gravity value, approximately 9.80665 m/s², for "a", we have:

15¹/¹² Paris feet = 0.5 * (9.80665 m/s²) * (1 second)²

This gives the length of the Paris Foot (L) as:

L = 15¹/¹² Paris feet / (0.5 * 9.80665 m/s² * 1 second²)

L = 0.3250823

So if Huygens was correct in his estimation, the Paris foot he used would have been 0.325082 metres or 12.798517 inches long.

If the measure of the earth was estimated as 123 249 600 Paris feet by Picard, then this same value for the pied de roi gives a figure of 1 577 412 044 inches, or 40 066 266 metres. Either Picard's measurement was off, by 60 or so kilometres, or the precise value of the foot he used to measure the earth was not in fact the same as Huygens used in the calculation above. La Condamine observed:

It is fair to look for all that can excuse this famous Academician [Picard], who does not deserve to be condemned lightly; but it must be admitted that the previous conjecture cannot save the error recognized in the base of Villejuive, unless to attribute another error to M. Picard, since he himself has left us the means of verifying the length of histoise, by attaching it, these are his terms, to an original, which being drawn from Nature itself, must be invariable and universal. He found that the measure of the seconds pendulum, in Paris, was 36pouces8½lignesof histoise, and this length, very different from the true one, is incompatible with the number oftoisesthat he gives to his base. It is thus necessary to agree that M. Picard was mistaken, either by assigning two fifths of alignetoo much to his pendulum, if histoisewas good, or by employing atoisewhich was too short by more than four fifths of aligne, if the measure of his pendulum is exact. (9)

If the toise used by Picard was indeed too short by 4/5 of a *ligne* (about 1079/1080), it might explain why his figure for the polar circumference of the earth seems too long, by around 701 / 700, based on a correct estimation of the polar circumference.

It's clear that the precision required for the work of Picard, Huygens and Newton was not available, due to the lack of a French reliable and precisely made standard of measure, or some other international reliable unit, and the scientific and political will to design and implement it. We can also see just how important it would be in the following century when the attempt to determine the size and shape of the earth was made, to use a single unit of measure, the length of which didn't matter, but which had to be fit for purpose, and unchanging, upon which later generations of scientists could also rely.

## The Toise du Pérou

A few decades after the 1668 debacle, when the pied de roi was changed, scientists wishing to measure the earth precisely, and working as a team, required very carefully made, identical, portable rules on which to base their work. In 1735, La Condamine, a member of the* Académie des Sciences de Paris*, organised this himself, but had only two made (why not three?). One accompanied him on his trip to South America, the other, he left in Paris as back up. However, his good friend Maupertuis, rather than having his own copy made, cheekily borrowed it for his expedition to the Arctic circle. It was after all imperative that both teams, one measuring the earth at the equator, the other near the north pole, should use the same standard of measure. Unfortunately, the ruler taken to Lapland was shipwrecked on its return, and though recovered, it was damaged by rust. So that the only standard of measure either team had as a reference was the one that had been left behind in South America, which eventually made its way back to Paris. This precious artefact, on which years of scientific work already depended, and without which would become practically worthless, was then used as standard by the Academy of Sciences for all scientific work, and was called the *Toise du Pérou, Toise de Paris *or *Toise de l'Académie*.

In 1766, eighty copies were then made and sent out to the various regions of France, and so this became the new national standard, which had been made simply to allow for more precision, and had not departed much in length from the toise du Ch*â*telet, imposed on the *ma**ç**ons*. The idea behind it had simply been to create a precise, user-friendly standard which was valid for scientific work. The next change in national standard of measure that was coming, just around the corner, was the metre. So if Charlemagne's pied de roi did grow, it must have been well before 1668.

## The Roman foot casts a long shadow

There were other standards of measure relating to the* pied de roi* in Paris at the time of the toise du Châtelet's creation, including the *aune de Paris, *which was kept in the* bureau de la corporation des merciers,* headquarters of the cloth merchants, rue Quincampoix. The *aune* is an ancient measure of usually two, sometimes four feet, or even three feet (Edward I's *ulna *of three feet is the present English yard). An *aune *is the equivalent of the anglo-saxon *oln*, the gothic *aleina*, the old German *elina*. In Latin, an *ulna* is the equivalent Roman length, meaning the forearm, and in Italian, it's a *braccio, *meaning arm*. *The aune of Paris was a double aune of 4 feet. On one side, this cloth merchant's aune was divided into 1/2, 1/4, 1/8, and 1/48 , and on the other side into 1/3, 1/6, etc. For two centuries it was used as the basis for trade in Paris. This standard was measured in 1736 by a member of the *Academie des Sciences*, Du Fay, and again in 1745 by two other members of the Academy, Hellot and Camus, and the aune de Paris was found to be 526 lines and 10 points long (or 526 ⁵/⁶ lines). Interestingly, this ruler bore a date: 1554, a time when the king was *François Ier* (Francis I).

A 1540 law declared the aune de Paris must be 524 lines long, which works out as four 16th century Paris feet of 131 lines, a surprising number as 131 is a prime (you would expect a multiple of 6 or 12). 524 lines are 3 *pieds*, 7 *pouces *and 8 *lignes *of the* Pied du roi (*3 pieds of 144 lines + 7 pouces of 12 lines + 8 lines*) * Why didn't the law simply make 4 pieds de roi, or even 4 x 11/12 pieds, an aune?

This tells us two things. Firstly, that the old foot of Paris (16th century) was to the new one (17th & 18th centuries, culminating in the 1667 saga) as 526 ⁵/⁶ to 524, so the old toise (16th century) was 4.6718 (18th century) lines longer, the new foot 0.7786 lines. As Guilhiermoz notes, the ratio between the 16th and 18th century pieds is 3144 / 3161. The* pied de roi* was defined as 0.324 839 metres with Delambre's definition of the metre, so we can guess the *pied de roi* that the aune de Paris was based on measured 0.326 5954 metres, or 12.858088 inches. However, this is based on just one example of a 16th century aune de Paris rule, and it's impossible to be sure how precisely it was made, or how closely it corresponded to other standards of the *pied in Paris* at that time. Standards varied slightly according to the manufacturer. The* toise du Châtelet* iron bar was so crudely made it was impossible to get a single precise value for the length it had been made to represent, but the toise de l'Académie, while based on this old bar, offered much more precision. Still, the aune des merciers de Paris gives a good indication of the size of the old 16th century *pied de roi*.

If we go back to the Grand Gallery of the Louvre measurement in 1668, and recall the foot was shrunk slightly (by 0.70276667 lines), it seems clear that this corresponds almost exactly to the amount by which the foot of Paris *grew* between the 16th and 18th centuries. We can begin to understand the mysterious behaviour of the authorities a little better if we think of their actions as an attempt to return to the 16th century value of the *pied de roi*. This would imply that to the 18th century Parisien authorities, the 16th century foot was in some way superior, and to regain the old length they thought nothing of shrinking the new. Why?

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 defined a little differently to today's value, at 39.3827 inches**. **We know from Delambre's definition that 5 130 740 toises de Paris were equal to 10 000 000 metres, so the 18th century pied de roi would measure 0.324 839 metres, or 12.788937 inches according to today's value of the metre in inches, or 12.793037 inches according to the 1799 value. We know from 19th century reports that the *pied de roi *was still being valued retrospectively as 0.324839 metres. This would give the 16th century *pied de roi* 0.326 596 metres, or 12.85811 inches.

Alternatively, using the 190 255 : 189 331 ratio established after the gallery of the Louvre was measured in both toise de l'Ecritoire and toise du Châtelet, in 1667, this would give a *pied du roi *prior to 1667, based on the masons' *toise de l'Ecritoire*, of 0.3264 metres, or 12.85039 inches.

The second thing the 16th century *aune *law tells us is that some unit other than the *pied de roi *was being used to make up an aune de Paris, and then translated into *pieds de roi* of the time (16th century French feet). It's unlikely that François Ier believed in an earthly authority greater than himself, so if his own royal foot was second in importance to some other foot, it must mean that this other foot was in wider use and had a popular legitimacy of its own. François Ier's son, Henri II, also defined the *Aune des Merciers* at Paris in 1557 to be 3 feet, 7 pouces, and 8 lines of the pied de roi, so this was clearly correct at the time. The 16th century law defined the aune de Paris as 4 x 131 lines. A French foot having 144 lines, 131 such lines would work out as 0.2971111 metres, or 11.6972888 inches. As we have seen, if the *aune de Paris* had been defined in relation to the *pied de roi*, or at least 11 pouces of the *pied de roi*, the aune would have matched 132 lines of the *pied de roi*, not 131.

According to Guilhiermoz, this aune de Paris was an attempt to revive the old Roman foot, or at least, *an* old Roman foot, and the aune de Paris was supposed to correspond to 4 such feet. Even in the 16th century the fall of the Roman Empire had happend well over a thousand years before. So, if four Roman feet made an *aune de Paris*, why would King François I enshrine in law a Roman measure? Was it simply out of respect for the ancient world, a royal figure seeking validation from a long lost world of emperors? Or was it because the Roman units of measure had never really gone away? It's not certain if the authorities were trying to impose anything on the people, as with the 1667 episode, or whether they were simply trying to eliminate any confusion there may have been over the size of an aune.

It is perhaps more likely that the 17th century law wasn't trying to revive anything, but simply clearly defining the length of a measure which happened to be very close to a multiple of Roman feet, that had been in continuous use for a very long time. For some reason, whether the calculations were right or wrong, the 1667-68 change to the *pied de roi* was considered reasonable enough to justify disrupting trade and construction projects, and angering Parisiens, seemingly in order to bring back a precise unit of length, the *pied de roi*, that had been defined against a Roman foot, a relic of the Roman Empire. Guilhiermoz reckoned that in 1667, the* pied de roi *was modified in order to have it correspond to the correct ratio with the Roman foot. There must have been a moment of realisation that the Roman foot was a certain length, and that France had got it all wrong for at least a century or two. The French government of 1667 might be accused of what we might call today a lack of transparency, but it can't be accused of not being interested in precision, when it came to standards of length - Roman or royal. The real mystery is why they didn't take the opportunity to create precisely made, easily reproducible standards at that time, to enforce the use of the new length and prevent the very errors that had crept in before from creeping in again. The story also shows that despite the crude appearance of the toise's standard at the Chatelet, the French authorities were perfectly capable of great precision, and interested in implementing correct measures, motivated not necessarily by easing trade or building, but by historical fact.

When it is said that the metre had to be invented because the toise was somehow insufficient, unregulated, or imprecise, a closer loook at the story of the French *pied* shows that this was not the case. The authorities and the trades people were very much interested in precision, and worked to very precise standards, as is shown by the 16th centry *aune de Paris *law, and by the clash between trades people, principally the builders and masons, and the authorities in the late 17th century. We might even say that, with his own reading of the toise du Chatelet, and creation of his own ruler,which eventually resulted in the toise de l'Academie, La Condamine had managed to provide a solution to the problem of designing and using a precise standard of measure, at least in the world of science. Perhaps it is not quite right to say that the creation of the metre was about replacing a shoddy product, a response to a French foot which had created too many messy footprints. What does become apparent in the story of the French *pied*, however, starting with the correction of the standard in 1667, and the way the situation was handled by the government, the lack of dialogue, of information given, and then the failure to implement the new standard correctly by distributing correct and precise rulers around Paris and further afield, is that the problem was the government itself. It comes across as having been autocratic, heavy-handed, dismissive of people's concerns, and incapable of facilitating such a simple thing as a precise national standard accessible to all. The French foot was tarred with the same brush. What the *Académie des Sciences *ended up doing, almost a century after the 1667 episode, creating multiple copies of a precisely made standard, the goverment could have done decades earlier if the political will had been there. The failure by the authorities to make available to all a well-made standard of the national unit, and to make precise standards available to all, borders on contempt towards the people. The story of the French *pied *suggests that it was not the king's foot which had to be axed, but the authorities themselves.

After all, in 1667, someone in a position of authority believed the iron bar in the Châtelet represented the wrong length of measure, and was prepared to stand up to all of Paris on the issue, without however explaining why publicly. This person (perhaps it was Colbert, the First Minister of State, perhaps it was Louis XIV, the Sun King), must have believed instead in a historical ideal, and a correct length of measure, that must be regained, no matter the consequences. Whether the number of lines to the *pied *was correct or not, it is hard to understand how the authorities could prioritise regaining a correct French foot defined in terms of a Roman measure, over facilitating trade and construction.(13) Long before this, King Edward III of England had presented a sack of wool to the Chancellor of the Exchequer to sit upon, as a reminder that trade was the "seat of power and the true foundation of the prosperity of the country". While trade was of paramount importance, it seems the authority of the state and bureaucracy came first in 17th and 18th century France. And yet, this powerful state could have chosen to impose an entirely new measure of their own making on the people, a* pied de roi* based on whatever standard seemed desirable to them. The 17th century state chose to enforce a unit of length, which was in popular use all around the country, albeit in various guises and slightly different values. In imposing the 16th century pied de roi derived from the *aune de Paris* on Paris and the rest of the country (if this is indeed what happened), the state was in all its grandeur and importance only imposing on the people what was already, or had been once, in popular use, and had, in a sense, already been imposed on the state. Perhaps this can be best understood as a form of Hegelian dialectic between master and slave. This was not about defining the *pied *against the value of the Roman foot from the time of, say, Julius Cesar, thereby acheiving some sort of Roman endorsement of a French ruler. Rather, it was the 16th century version of the Roman foot was what that was required.

What was the exact length of the Roman foot considered to be in the 16th century? We can work it out by looking at the length of the 16th century *aune de Paris*. The 16th century *pied de roi* was 0.326 596 metre, or 12.85811 inches long, and was divided into 144 lines, so 131 lines of this foot would be 11.697308 inches, or 0.2971116 metre. This seems a little bit long for a Roman foot. Indeed Guilhiermoz writes that various copies of the Roman foot were slightly shorter:

It is known that there are quite a large number of old copies of the Roman foot; several of them, measured from the time of the Renaissance, made it possible to note that the Roman foot had a length very close to 131 lines of Paris, i.e. between 295 and 296 millimeters. (18)

Fréret, in 1756, valued "le pied d'Angleterre" as a sixteenth part shorter than the "pied de France". (3).This suggests the correct ratio between the English and French feet would produce a French foot of 12.8 English inches. If we take 12.8 inches for the value of the 16th century pied de roi, and look for the value of 131 lines of this foot, we would get 11.644425 inches, which is a good approximation of the Roman foot according to Raper (11.64 inches) and Berriman (11.664 inches, or 11.6666667 inches). And if we use Berriman's value for the Roman foot as 11.664, and the 144 and 131 line ratio, then the French foot would measure 12.821496 inches, or with 11.66667 inches, the corresponding French foot would be 12.82442748 inches. This is a little on the big side.

A length of 192 inches is made up of 16 feet of 12 inches, or 15 feet of 12.8 inches. A length of 422.4 inches, or 32 Saxon / Sumerian feet of 13.2 inches would be equivalent to 33 feet of 12.8 inches (theoretical *pied de roi *rounded to one decimal place). Such a length would also be equivalent to 2¹¹ / 100 Egyptian royal cubits of 20.625 inches. Another possible connection for a foot of around 12.8 inches would be x 10/11 to approximate a Roman foot.

## The pied de roi measured by various people in imperial / English inches and Rhineland inches (17th to 19th centuries)

To get a good idea of the size of the pied de roi at various periods, it's useful to look at how it was defined in other units Here are a some measurements of the French foot referred to in the 17th, 18th and 19th centuries in imperial inches mostly, and in Rhineland inches too. As we've just seen, Fréret suggests 12.8 inches for the *pied de roi*.

The estimate for the *aune de Paris*, provided by William Hallock in the mid 19th century is this:

There was also the aune or ell, which, originally a double cubit, became adopted as a unit of linear measure for cloth, and survived until displaced by the meter. A standard Aune des Marchands, Merciers et Grossiers, 1554, divided into halves, quarters, thirds, sixths, etc., was preserved by that guild, and was the basis of this unit. The aune of Paris corresponded to 46 17/20 Eng. inches, but it was never adopted in the latter country to any considerable extent or authorized by law, though a cloth aune or ell of 45 in. is found marked on the standard yard of Queen Elizabeth. (2)

Hallock's estimate would imply a foot of 11.7125 inches or 0.2974975 metre. However, it's not clear which ratio between the metre and the inch Hallock was using. His 46.85 inches for the aune, converted to metres, not with the modern ratio but with a mid 19th century one, say Robert Hussey's 39.3827 inches per metre, divided by the number of lines in the *aune de Paris* as it was in the 18th century, 526 + 10/12 lines, multiplied by 144, gives a foot of 0.32515718 metres, or 12.8014638 inches. This is comparable to the 0.324 839 metres obtained using Delambre's 5 130 740 toises de Paris being the equivalent of 10 000 000 metres (although it might imply instead that Hallock was using a ratio of 39.42128 inches per metre).

Frank Skinner relates this story of the imperial yard having been made more accurate for the purposes of scientific measurement, just as the toise had had to be upgraded in France:

In 1742 the Royal Society of London, requiring a more accurately sub-divided linear measure than that of Queen Elizabeth, for scientific purposes commissioned Mr. George Graham (1673-1751) to undertake the work with the assistance of Mr. Sisson the London instrument maker. This was done on two finely engraved flat brass bars 42" long, I" wide and 1" thick on each of which were carefully marked off the lengths of the existing Tower Standard Yard made by Mr. Rowley in 1720, and Elizabeth's Exchequer Standard Yard of 1588. The two bars were sent to France to the "Academie Royale des Sciences" at Paris where M. Du Fay and the Abbe Nollet marked on the rods the French half-Toise of three Pied du Roi (3 x 12.789"); one bar was retained in Paris and the other returned to the Royal Society in London; both have been carefully kept for reference. Graham's Royal Society Yard of 1742 is now at the Science Museum, London, lent by the Royal Society for exhibition. (5)

This tells us the* pied de roi* was 12.789 inches long. However, since these measures were made by both the academies for science, and since the inch has not changed since that time, it must be one of the more reliable values for the *pied de roi*, as it was in the 18th century. This is also the length of the Quebec foot in Canada today.

In 1760, Matthew Raper wrote about the *pied de roi*:

The Paris foot is one sixth part of the toise in the Chatelet; which was renewed in the year 1668, and the new standard has continued in use ever since. In the year 1742, the Royal Academy of Sciences of Paris, at the request of the Royal Society of London, sent over a measure of half a toise of the Chatelet, from which Mr. Graham determined the proportion of the Paris foot to that of London to be as 1065.41²/³ to 1000. Mons. le Monnier, of the Royal Academy of Sciences, from the same originals, found their proportion as 864 to 811, or as 1065.351 to 1000. (6)

Graham's determination of the *pied de roi* can be valued as 12.79292 inches. Le Monnier's determination can be valued as 12.784212 inches. Raper also compares pre-1668 meaures of various Roman feet in London feet and Paris feet, taken by Greaves and Auzout, Snellius, Desgodetz and Hardy. His conclusion is that before 1668, the Paris foot contained 1065.4 parts to 1000 of the London foot, giving a value of 12.7848 inches to the Paris foot. Raper reminds the reader that the Great Fire of London in 1666 destroyed part of the Guildhall, and the old standard of the foot was destroyed. Just as the following year in France, when the iron bar which served as the standard was destroyed, a replacement was created. The new London standard was also slightly different, though probably not intentionally. However, Elizabeth's Exchequer Standard Yard of 1588 did still exist. It's important to consider these changes when comparing measures in London or Paris feet, before and after 1666 and 1667. The London foot which Greaves and others used before this being slightly different in size than its successor, the problem is to ascertain by how much. To find out how long the London foot must have been before the fire, Raper writes “we have nothing left whereby to discover its true magnitude, but the measures others have taken of it, and those which have since been taken of such magnitudes as Greaves had compared with his copy of it”. (5)

The measure of the Paris foot, which Greaves received from Mons. Hardy, was taken from the old standard in the Chatelet and contained 1068 such parts as his London foot contained 1000. These numbers are in the proportion of 1065.4 to 997.57; therefore, if the new standard did not differ from the old one (and no such difference appears to have been intended), Greave’s London foot must have been 2.43 parts in 1000 shorter than Graham’s. All these comparisons shew Greaves’s measure of the London foot to have been shorter than Graham’s. (...) The three more immediate comparisons of Greaves’s measure with the Paris foot, are by the measures of Auzout, Desgodetz and Hardy, which afford as clear a proof as can well be expected in this matter, that his measure of the iron standard was about 2 parts in 1000 deficient of Graham’s London foot.(6)

This means that in modern inches, the pre-Great Fire of London foot measured 12 - (12 x 2.43 / 1000) = 11.97084 inches, or more conservatively, using the 2 parts in 1000 instead of 2.43, 11.976 inches. The pre-Great fire of London foot was slightly smaller than the modern foot. So to convert to pre-1666 values, the English foot can be multiplied by 0.998. Taking the Paris foot used by Desgodetz to measure various things in order to ascertain the Roman foot's length, Raper estimates his Paris foot to be 1065.4 parts to 1000 of the London foot, whch gives it a value of 12.7848 inches. This can be multiplied by 0.998 to obtain 12.7592304 modern inches. Greaves visited the Great Pyramid of Egypt and he left marks on the wall of the King's Chamber with the exact dimensions of this pre-1666 London foot. So if his markings are correct, then that is the only known imprint of the length of the pre-Fire of London foot that was derived from the standard in the Guildhall.

There are many tables comparing units of measure between the French and British systems. This one dates from 1834. The conversion used is 39.37079 inches to the metre, slightly different to today's 39.3700787402. A *pied de roi* is 0.324839 metre, or 12.789168 inches according to this historical ratio (12.788937 inches according to today's ratio).

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 thisfrom the Mémoires de l'Institut, Base du Systeme Métrique. In this account by the creators of the metric system, the metre is clearly stated as 39.3827 inches,** **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 *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 Système Métrique, vol. iii. p. 470, where the English foot is compared with the metre, and the latter is proved to be equal to 39.3827 English 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 the1/144th 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 com- parison 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.(14)

With Hussey's first ratio, according to the definition of the metre, the French foot is 12.7908 inches, and his last ratio, linked to the Royal Society, gives a French foot of 12.7884 inches. In 1768, 1 toise was worth 76.734 inches, so a French foot was 12.789 inches.

Fréret writes: "Le pied d'Angleterre est d'un seizième plus court que le pied de France" (16), which translates as the English foot being one sixteenth shorter than the French foot, implying 12.8 English inches for the French foot. This could be a simplified ratio for practical purposes, or an ideal scenario. Fréret also gives us a ratio between the pied de roi of Picard's time and the Rhineland foot. We've seen that a *pied de roi* is made up of 144 lines. The Rhineland foot was measured by Picard as 139.2 such lines, as Fréret tells us: "pied de Léide ou de Rhinland; ce pied contient 1392 dixièmes de ligne, felon la mesure qu'en prit M. Picard, lors de fon voyage d'Uranibourg". (16) This is useful information because the metal rod for the Rhineland foot in Leiden still exists, in a staircase at the city hall. The Rhenish foot is 0.314 metres, or 12.3622 inches, long. Twelve feet make a Rhenish Rod. The wall has a rod etched into the wall with foot and thumb markings, there is also a metal rod that is exactly 1 Rhenish foot long. This means Picard's foot would have been in the region of 12.78848 inches.

Flinders Petrie gives a value for the pied de roi in his 1911 article, 1 *pied de roi* is 12.7892 inches. However, elsewhere in the same article he rounds this up to 12.8 inches. His value for the old English mile of 79 200 inches ("10 not 8 furlongs") is 2000 x 22/7x 12.6 inches. (8)

If Guilhiermoz is correct about the length of Charlemagne's foot, the pied de roi grew progressively smaller from at least 1540 until the revolution, yet this foot of Charlemagne's was shorter than the foot of the toise du Châtelet. What was going on? The *pied de roi* must have grown in size some time between the reigns of Charlemagne and François Ier. The graph below illustrates what Guilhiermoz proposes. Is Guilhiermoz correct, or was there no change in the length of the pied de roi since the time of Charlemagne?

The graph below illustrates Guilhiermoz's values for the *pied de roi*. Is it possible that the French foot changed so drastically after the time of Charlemagne?

## An 11-pouce pied?

The aune de Paris was based on something close to 4 pieds of 11 pouces of the pied de roi, not 12. However, this 11 pouce pied was slightly under 11 pouces de roi, by about a quarter of a line, because the 16th century aune de Paris was defined by law as 131 x 4 lines, not 132 x 4 lines, with 132 being 11 x 12. It's clear that even in the 16th century, 11 pouces de roi (132 lines) did not exactly match whatever kind of Roman foot was being used, and that an 11:12 ratio between this Roman foot and the 12 pouce pied de roi was only approximate. The Roman foot derived from the 16th century aune de Paris law was slightly too short to properly match 11 pouces of the pied de roi.

Perhaps a 9/10 ratio would work better. The 16th century foot deduced from the aune de Paris of 12.858088 inches multiplied by 9/10 would give 11.5722792 inches. The foot of the toise de l'écritoire, as deduced from the measurement of the gallery of the Louvre, of 11.565351 inches, would in this way give 11.565351 inches.

In 1759, Matthew Raper gave a value of 970 parts to 1000 of the English foot, which gives 11.64 inches, and closely matches estimates by many other metrologists, but also another value of 965 parts, which makes it 11.58 inches.

Titus Caesar Vespasianus was Emperor from 79 to 81, Lucius Septimius Severus was Roman Emperor from 193 to 211, and Diocletian was Roman Emperor from 284 until his abdication in 305. If we take a value of 20.625 inches for the Egyptian royal cubit, multiply it by 9 / 8 and then divide by 2, we get a foot which is within Raper's parameters, 11.6015625 inches. With 20.6181818 for the Egyptian cubit we get 11.597727 inches, and with 20.614 inches, we get 11.595375 inches.

John Neal suggests a value of 0.96768 feet (11.61216 inches, or 0.29494886 metres) for the Roman Cossutian foot (which he classifies as "standard canonical"). This value multiplied by 11 / 10 is 12.773376 inches, which gives a value close to the pied de roi, as John Neal, and Stecchini observe. (15) Neal writes:

Pélagaud noted that the interior of a Roman aqueduct in Bologna was scored with lines in increments of 295mm on one side and 413mm on the other. This is a foot of the Standard Canonical of .96768 feet and an Etruscan cubit (Assyrian) of 1.35752 feet “Notice sur la découverte d’un métrage en pieds romains dans un acqueduc, à Bologne, suivi des observations de M. E. Desjardins.” P 155 E Pélagaud 1879 (15)

A foot of 0.295 metres (11.61417 inches) is within Raper's two values.

There was indeed a widely used foot of somewhere in the region of 11 pouces in the kingdom of France, right up until the implementation of the metre. According to Guilhiermoz, this 11 pouce foot was in fact the most widely used in all of France, more so than the 12 inch pied de roi. Guilhiermoz gives many examples of this 11 pouce pied, for example, there was a toise of Bazas, and others in the Languedoc region, which measured 5 ¹/² pieds de roi, which is the same as 6 pieds of 11 pouces (a toise being 6 pieds) (4). Guilhiermoz finds these examples of French feet that are very similar to this ancient Roman length: the foot of Hainaut, the standard for which was found in Mons, was measured as 0.293 43 metre (11.55236 inches), the foot of Trêves, evaluated as 0.293 754 m (11.565118 inches), the feet of Noyon and Bar-le-Duc, 0.294 386 metre (11.590 inches), the foot of Saint-Hubert de Liège, 0.294 698 metres (11.60228 inches), the foot of Saint-Lambert de Namur, 0.294 763 metre (11.60484 inches), the foot of Strasbourg, 0.294 95 metre (11.6122 inches), this last one being just about 11/12ths of the pied de roi. These examples are all within a close margin of the later Roman foot given by Raper of 11.58 inches, and also close to the earlier 11.64 inch value. However, while even the biggest of these values fall short of 12.8 x 11 / 12, they are all very close to Raper's two values for a Roman foot, 11.58 and 11.64 inches. It's probable that these regional French feet are simply Roman feet, that have been changed slightly over the centuries. The slight variations between them are exactly what you'd expect in the aftermath of the collapse of an empire, during which no single power succeeded in implementing and enforcing a precise, universal unit of measure for a long time.

In *Historical Metrology*, Berriman gives 11.664 inches or 11.6666667 inches for the Roman foot. By contrast, an 11th part of Berriman's Roman foot multiplied by 12 would give a pied de roi of 0.3231988 m or 0.323272727 m, which is 12.724363 or 12.72727272 inches. These values are slightly shorter than the 12.788937 and 12.85811 inch values we have seen. It could be that the 11/12 ratio between this Roman foot and the pied de roi isn't set in stone and merely works as a rough guide, or perhaps if there was originally such a precise ratio between them, over time, as standards have ebbed and flowed in their relative lengths, this ratio remains a little elusive now. In his article, Guilhiermoz goes looking for a foot which would actually fit, in terms of the aune de Paris, and finds a late Roman foot that fits quite well.

## The palmo architettonico

According to Guilhiermoz, the 11/12 ratio works only with a particular variant on the Roman foot, used in construction and surveying, found (unsurprisingly) in Rome, called the *palmo architettonico. *This unit was measured in 1811, when Napoleon invaded Rome, as 99.042 lines of Paris (0.223422 metre, 8.79614 inches). The *palmo* (Italian) or *pan* (French) was equivalent to half a cubit. Therefore, the *palmo architettonico* of Rome supposes a foot (x 4/3) of 132.056 Paris lines equal to 0.297 896 metres, or 11.72819 inches. As 144 lines were 12 *pouces*, 132 lines were 11 *pouces*. These 132.056 Paris lines are very close to an exact 11:12 ratio to the *pied de roi*, and to a properly 11 pouce long French foot. There are several theoretical scenarios, each with a slightly different value for the digit, 16 of which make up the Roman foot and 18 the Saxon foot. According to the first, and 11.72819 x 12 / 11 = 12.794389 inches being a good approximation for the *pied de roi, *if this foot is divided into 16 smaller units or digits, of 0.733011875 inches, and then multiplied by 18, we get 13.19421375 inches, which is almost exactly the 13.2 inch Saxon foot. And so if the Saxon foot was indeed the Roman foot of 18 inches (as opposed to 16 inches) then there is a clear and simple link between the *palmo architettonico,* the Saxon / Sumerian foot, and the pied de roi.

11.728489x 12/11 = 12.794389

11.728189 x 18/16 = 13.19421375

A second set of theoretical values involves 13.125 inches for the Saxon foot, 11.66667 inches for the Roman foot, 12.727272 inches for the pied de roi.

The third, still keeping with the same ratios between them, has 16 digits of 0.7333333 English inches, which would make 11.7333333 inches, which, multiplied by 12/11 would give a 12 pouce French pied of 12.8 English inches exactly. By this logic, a pied of 12.788937 inches would match a digit of 0.7326995 inches, and a pied of 12.85811 inches would match a digit of 0.73666255 inches. If 16 x 0.733333, then 18 x 0.733333 is 13.2, the Saxon foot. Also, 270 digits of 0.733333 inches exactly give a rod of 198 inches, and 54 digits give a Saxon wand of 39.6 inches. Such a digit is close to the way Flinders Petrie described the Egyptian digit: if the royal cubit was 20.6 inches, and the half diagonal of this was the remen, of 14.6 inches, this was made up of 20 digits of 0.73 inches. According to Jim Alison, the Egyptian and Roman digits are equal in length, and so this digit of 0.73 inches would work also for the Roman measures. (20)

Guilhiermoz observes that a fourth part of the aune de Paris, 131 lines of the 16th century French foot, is very close to the 132.056 18th century Paris lines contained in the foot of the Roman palmo architettonico. The assumption is that the 1540 aune de Paris was 4 neo-Roman feet long. Using the foot of the Roman palmo architettonico measure as a guide, which we know measured 0.297 896 metres (11.728189 inches), three such feet would be 1.191584 metres (46.9127559 inches), and a toise of six of these feet would be 1.787376 metres (70.369134 inches) long. This is quite a bit shorter than the toise de Paris was 1.94903631 metres, which, divided by 6, gives a pied of 0.324839385 metres, which, multiplied by 11/12 to obtain the 11 pouce foot value, would give a very similar to the *palmo *0.2977694 metres. We saw that the 18th century pied de roi was 0.324 839 metres, the one before that, the pied du roi prior to 1667, corresponding also to the masons' *toise de l'Ecritoire*, was 0.3264 metres, and the 16th century *pied de roi *based on the *aune de Paris* was somewhere in the region of 0.326 596 metres. If a foot of 11 pouces instead of 12 were deducted from these three pieds, they would measure 0.2977691 metres, 0.2992 metres, and 0.2993797 metres respectively, and the closest to the neo-Roman foot, is the one the authorities cobbled together after the iron bar was damaged in 1667, the foot of the Châtelet, imposed on Paris despite popular outrage. Guilhiermoz 's theory that in the 18th century the toise du Châtelet provided an oportunity to recalibrate the national standard against the neo-Roman foot, with an 11:12 ratio, *because it was believed to be the correct ratio*, seems spot on.

As for the actual historical ratio, well, who knows? Perhaps, for example, there was a unit of 22 Roman feet that was subsequently divided into 20 feet, which became the French foot. There were various* perches*, one of 18 *pieds de roi*, in Paris, and a *perche royale et forestiere* of 22 *pieds de roi*, which might have been equivalent to 24 Roman feet, and a *perche moyenne* of 20 pieds de roi, which could have been equivalent at some time to 22 Roman feet. Or perhaps the French pied was never defined in relation to the Roman foot at all.

In historical metrology, the same unit name can have different guises, which makes things complicated. Hides, for example, did not always have the same number of poles, poles did not always have the same number of feet, and feet didn't always have the same number of digits or inches. The *arpent *of Paris shows that the ratio 9:10 had been adopted between the Roman foot and the foot of 18 digits, because it had once been made up of 20 Roman feet, had become a pole of 18 feet of 18 digits; only, instead of modifying the length of the pole to make up exactly 18 feet of 18 digits; the foot of 18 digits was adjusted to make it fit exactly into what had originaly been a 20 foot pole, with feet of 16 digits, and this explains why the pied de roi, while historically an 18 digit foot, was however, even before the reform it underwent in the seventeenth century, quite noticeably shorter.

In Champagne and Burgandy, in the Middle Ages, the official foot was the foot of 18 digits, and the royal perch was of 22 feet of 18 digits. In theory, a digit of 0.72 inches x 18 x 18 is equal to 20 feet of 11.664 inches. What Guilhiermoz does is to equate the the foot of 18 Roman digits to the Royal Babylonian cubit.

## A 16/15 ratio between the English and French feet?

If the French pied had at any time corresponded to exactly 12.8 English / imperial inches, and this is what Fréret suggests, this would have given a nice neat 16/15 ratio between the French and English feet; that is, 16 English feet would be equivalent to 15 French feet. Guilhiermoz states that a royal Carolingian pole (from the time of Charlemagne) was made up of 15 royal Carolingian feet, also equivalent to 16 ancient Roman feet. This would have implications for the English foot of the time of Charlemagne, as it would make it equivalent to whatever kind of Roman foot was contained 16 times in this royal pole.

Moreover, according to Guilhiermoz, the English royal perch was at one time the same as the Carolingian royal perch, and it was divided into 16¹/² feet when the "Norman ducal foot" was adopted, with William the Conqueror. A rod being 198 inches, this would imply a Norman ducal foot of 12 inches, i.e. the modern English foot. However, we can't be certain this rod was 198 inches long before the Battle of Hastings, and it is also thought by some researchers that the Norman invaders didn't try to impose foreign measures in England and other conquered lands. It's difficult to know for sure if what Guilhiermoz is suggesting here is true.

According to Jim Alison:

The odd length of 16.5 English feet or 5.5 English yards for the rod was chosen to equal the length of the rod of 15 Northern feet, or 5 Northern yards, or 6 megalithic yards, or 270 digits, or 300 shusi, or 150 Indus Valley inches, or 15 x 12 = 180 Northern inches, times 11/10 = 198 English inches = 16.5 English feet. (20)

The English yard is now 3 feet, or 36 inches, and the old ulna of Edward I was also specifically defined as 3 feet. But 4 old English feet of some sort were once also 1 yard ¹/⁴, or 45 inches (the cloth ell, mentioned earlier by Hallock), If these 45 inches are today's inches, which is uncertain, but probable, 1 foot would have been 15 of our present English inches It follows that there was more than one type of foot around in England, and that the present English foot would be to that older foot (a fourth part of 45 inches) as 4 is to 5. However, perhaps these 45 inches were in relation to a 12th division of the foot at a much earlier time. A 45 inch ell divided into 4 feet assumes a foot of 11.25 inches. Two such feet make up the 22.5 inch measure Flinders Petrie found at Stonehenge. And 7 such feet make 2 metres of 39.375 inches (which multiplied by 144/550 gives an Egyptian royal cubit of 20.6181818 inches). 16 feet of 11.25 metres make up 180 inches, which is also the equivalent of 15 feet of 12 inches.

The 15/16 ratio can be used twice, firstly to link a hypothetical 11.25 inch foot to the 12 inch modern foot, and secondly to link this 12 inch foot to a slightly rounded 12.8 inch French foot. The 12 inch foot was certainly in used at the time of Edward I (king of England from 1272 to 1307):

From Edward I's time, at least, there were 12 inches to the foot, 36 inches to the ulna, which is also three feet to the ulna, and 5.5 ulna to the rod, which makes 198 inches. Since 5.5 is an unusual number to multiply units by, it might be reasoned that it is half of 11, a number which might suggest a link to the approximation of pi as 22/7, or to the square root of 2, as 99/70, or to Phi squared as 144/55. The 198 inches in a rod are also 22 times 9 inches, 20 times 9.9 inches (Welsh foot), or 18 feet of 11 inches, 16 feet of 12.375 inches, or 15 Saxon / Northern feet of 13.2 inches. A rod would be the equivalent of the diagonal of a square with sides of 140 inches.

The number 7 was also an important number of units found in ancient measuring systems, for example an Egyptian royal cubit consisted of 7 palms, and there are still bronze weights embossed with the Plantagenet arms from the time of Edward III with denominations of 7, 14, 28, and 56 lb. Skinner informs us that "these weights (weighed in 1927), are on an ounce basis of 437 grains, with a 16 ounce pound of 6,992 grains, compared with the current avoirdupois ounce of 437-5 grains and its pound of 7,000 grain". (5) Still today, 1 Pound =16 ounces = 7,000 grains.

The 12.85811 inch value derived from the aune de Paris is almost exactly the English foot x 15/14, and this same 12.85811 inch unit x 7 is very interesting as it's 90.00677 inches, which is twice a 45 inch cloth ell, and 4 times the 22.5 inch unit that Flinders Petrie found at Stonehenge. (12) It is also very close to 90 / 7 inches. In relation to a Saxon / Sumerian foot of 13.2 inches, a Paris foot of 12.8 inches would have a ratio of 33/32.

## Rhineland Foot

For Guilhiermoz, the old Carolingian French foot measured 0.31448 metres, or 12.3811024 inches. This is very close in length to the old Rhineland foot, and several other feet that existed in northern Europe before the metre was adopted, around 0.314 metres, or 12.362205 inches, in length. did Guilhiermoz confuse the old Rhineland foot with the old Carolingian foot?

A Royal Egyptian cubit of 20.625 inches multiplied by 56 x 2.6181818 / 100 is an Aragon vara, estimated by C. Mauss as 0.768 metres are 30.24 inches (with a 39.375 inch conversion), also equivalent to 4 feet of 0.192 metres, or 756 inches, 1000 of which make an Olympic stadium, and also 7/6 of an Assyrian / Persian foot. The Aragon vara is 11.55 inches multiplied by 144/55 as Phi squared approximated. One interpretation of the Egyptian royal cubit is that is is pi/6 metres long, that is to say that a circle with a diameter of 1 metre would have a circumference of 6 Egyptian royal cubits. For Guilhiermoz the old Carolingian French foot measured 0.31448 metres or 12.3811024 inches, and this is basically the length of the Rhineland foot, or Leiden foot, roughly equivalent to pi/10 metres = 12.368475 inches.

Moreover, pi/10 metres = 12.368475 inches translates as almost exactly the number of lunations in a year: 365.242199 / 29.53059 = 12.368266.

The relation between the solar and lunar years could define the relation between the metre and the inch. But perhaps it could also be a way to understand the various feet of old Europe, at least in theory. However, the evidence that the foot of Charlemagne was indeed either closer to 12.8 inches or 12.38 inches is quite elusive. It seems from the dimensions of his chapel at Aachen, or Aix-La-Chapelle, that Charlemagne did indeed use the Rhineland foot. The height of the dome is given as 31.40 metres, which suggests pi and the use of the metre in relation to a circle, and also suggests the Rhineland foot. Also, it's worth noting that the height of the windows at Charlemagne's chapel at Aachen are 26 metres high, which could be 80 *pieds de roi*. (27) It may be too simplistic to think in terms of a single unit of measure for this ancient building.

12.36847 = Rhineland foot

12.36847 x 16/15 = 13.19304 Saxon foot

12.36847 x 15/16 = 11.595445 Roman foot

12.36847 x 32/33 = 11.9936727 English foot

12.36847 x 33/32 = 12.7549899 French foot

12.36847 x 8/9 = 10.9942 (11 inches)

12.36847 x 10/6 = 20.614125 Egyptian cubit

20 metres x 365.242199/(12 x 29.53059)x 6/10 = 12.36847

C. Mauss writes about a Persian foot of 330 mm (and another of 350 mm), and compares this to the size of tiles found in the south of France from the 10th century which measure 33cm. He suggests that a similar 329.142 mm length could in fact be half a Persian / Assyrian royal cubit of 658.285 mm (that is, 4,608 / 7 mm), or 25.92 inches. (25.92 is 6⁴ x 2)

A find of a metal ruler from Roman times in Mâcon, in France, made by Daniel Barthèlemy and Stéphane Dubois, provides an interesting link between the old measures and the Saxon foot, the Rhineland foot, the French foot, as well as the metre, though the authors of the article limit themselves to a comparison of their findings to Hultsch's Druisian foot of 33.27cm. (19) The half "inch" on this metal rod measures 1.39 cm, which would give an "inch" of 2.78 cm (or 1.094488 inches). 12 such units of 2.78 cm, perhaps we can call them Mâcon inches, would make up 33.36 cm, or 13.13385827 inches, which is indeed very close to the Druisian foot and Saxon foot. 36 Mâcon inches would make up something close to a metre, 100.08 cm or 39.40157 inches. And a Mâcon inch is also close to 3/2 of a digit of 0.729166667 inches, associated with the Roman and Egyptian feet. 10 Mâcon inches measure 10.94488 inches, and multiplied by 7/6, this gives 12.7690266667, a measure very similar to some of the estimates of the French foot. If we start off with the digit of 0.72916666 inches, 16 of which make up a Roman foot of 11.666667 inches, and multiply it by 10, 3/2 and then 7/6, we obtain 12.7604166667 inches.

A pied of 0.31435 could be explained as 10/9 x 6/5 , 11/12 x 1/8 inches, or as a 14.85 inches remen, divided by 12 x 10 = 12.375 inches, = 0.314325 m

or 1 metre x pi /10 x 33/32

11 x 9/8 x 6/5 x 10/12 x 1/39.3700787402 = 0.314325

A 12 inch foot = 39.375 x 22/7 x 32/33

If we take a foot of 12.375 inches, we obtain an English foot by multiplying it by 32/33, and a French foot by multiplying it by 33/32. A circle with a diameter of 1 metre gives a circumference of 6 Egyptian royal cubits, and a circle with a diameter of 1 metre also gives 10 x 12.375 in its circumference.

## Charlemagne's foot

John Neal has written about Charlemagne's relationship to the *pied de roi*:

As the spread of Islam into Europe from the east had been halted by the Eastern Roman Empire in the form of Byzantium — so the incursions from Iberia in the west had been halted by Charles Martell —the grandfather of the ﬁrst Frankish emperor, Charlemagne. Within 50 years of this victory of the Franks at Poitiers it became expedient that the enlightened Harun-al-Rashid made peace with Charlemagne. He posted permanent envoys at the Frankish court where as part of the reforms of 785 AD that were instituted by Charlemagne at the termination of the Saxon wars, the Franks adopted the Hashimi cubit as their standard.The foot of this cubit may therefore be exactly expressed as 1.064448 feet and this was the original“pied de roi”that survived as the standard for a millennium (though problematically) until the Revolutionary metrication in 1790.

The original *pied de roi* is here defined as 0.32444375 or 12.773376 inches. This is only slightly shorter than the final incarnation of the* pied de roi*, and not at all as short as Guilhiermoz's value for the orignal pied at Charlemagne's time. Neal believes the *pied de roi* was used long before Charlemagne, as far back as Roman times, and says that Stecchini believed it had been "used in harness unidecimally with the Roman foot", by which he refers to the Cossutian foot of 11.61216 inches, or 0.29494886 metres. This is interesting as these two lengths are in 10:11 ratio exactly, just as the English foot of 12 inches is to the Saxon of 13.2 inches. The ratio between 144 and 131 lines is close to 1.1, similar to the ratio between the English foot and the Saxon foot of 13.2 inches. 131 lines x 16/18 = 116.4444 lines. If we go back to the Mâcon inch of 1.094488 inches or 2.78 cm, it's clear that it fits in well with this foot that was perhaps imported by Charlemagne from the Middle East, as 12.773376 x 6/70 is 1.0948608, very close to a Mâcon inch. However, the Mâcon inch was from Roman times, so much earlier than Charlemagne. While this doesn't prove that a 12.773376 inch foot existed in France before Charlemagne, it does prove that a unit that was simply and directly related to it did. And 11.61216 inches is 12⁴ x 7 x 8 / 100 000 inches.

John Neal has suggested the Hashimi cubit which became the French pied de roi at the time of Charlemagne was 12.773376 inches, or 1.064448 feet long. He writes of Charlemagne:

He posted permanent envoys at the Frankish court where as part of the reforms of 785 AD that were instituted by Charlemagne at the terminationon the Saxon wars, the Franks adopted the Hashimi cubit as their standard.The foot of this cubit may therefore be exactly expressed as 1.064448 ft and this was the original.

We can see that this is very close, in fact almost identical to the *pied de roi* that existed in 18th century France.

Flinders Petrie wrote in his 1911 article:

the Alexandrian talent of Festus, 12,000 denarii, is the same talent again. It is believed that this mina ± 12 unciae by the Romans is the origin of the Arabic ratl of 12 ukiyas, or 5500 grains (33), which is said to have been sent by Harun al-Rashid to Charlemagne, and so to have originated the French monetary pound of 5666 grains. But, as this is probably the same as the English monetary pound, or tower pound of 5400, which was in use earlier (see Saxon coins), it seems more likely that this pound (which is common in Roman weights) was directly inherited from the Roman civilization. (29)

The Hashimi cubit has been estimated at 0.65 metres, or 25.59055 inches, and half of this is 0.325 metres, or 12.7952756 inches. According to Mark Stone:

In 1916, during the last years of Ottoman Empire and during WWI, the German Assyriologist Eckhard Unger found a copper-alloy bar during excavation at Nippur from c. 2650 BCE. He claimed it to be a measurement standard. This bar, irregular in shape and irregularly marked, was claimed to be a Sumerian cubit of about 518.5 mm or 20.4 inches. A 30-digit cubit has been identified from the 2nd millennium BCE with a digit length of about 17.28 mm (slightly more than 0.68 inch). The Arabic Hashimi cubit of about 650.2 mm (25.6 inches) is considered to measure two French feet. Since the established ratio between the French and English foot is about 16 to 15, it produces the following ratios: 5 Hashimi cubits≈10 French feet≈128 English inches. Also, the length of 256 Roman cubits and the length of 175 Hashimi cubits are nearly equivalent. (28)

## A Pre-Roman Pied de Roi

Neal writes:

The antiquity of the pied de roi in France is further evidenced by the ﬁndings of the archaeologist Jacques Dassié. He has specialised in interpreting distances between the cities of Gaul from the information given on the Roman milliary columns and from theTabula Peutingeriana(a mediaeval copy of a Roman map of the whole empire) and has identiﬁed many instances of leagues (7500 feet or 1 ½ miles) given in a variant of the Pied de roi. Dassié records that the earliest researches into these distances in Gaul, were conducted by Bourguignon d’ Anville in 1760, who calculated from the distances between the cities of Gaul a Roman league that equates to 2211 metres. TheStandard Canonicalvalue of the Roman foot is 0.96768 feet and 7500 of them equal 2212 metres. Pistollet de Saint-Ferjeux, in 1858 becomes the ﬁrst to propose a longer league of pre Roman origin. He is stated to have calculated the league as 2415 metres,and one and a half English miles is 2414 metres.Therefore the basic foot of this league may be stated to have been 1.056 feet - which is the Root Canonical value of the Persian foot and directly related to the original pied de roi by a ratio of 1:1.008.

The longer league is almost identical to one and a half English miles, which works out as 7920 feet, or 95,040 inches. Taking a rounded value of the pied de roi at 12.8 inches, there would be 7425 such feet in one and a half English miles, which is also 18 x 256 Egyptian royal cubits of 20.625 inches. The 1.056 foot value given by Neal to the Persian foot (12.672 inches) multiplied by 1.008 gives 12.773376 inches. If this is multiplied once more by 1.008, the result is 12.77292857 inches.

Neal and Stecchini both believe the French foot goes back farther in time than Charlemagne, with good reason. What if the French foot were much older than even the very idea of France? And what if this French foot could also be found in ancient Britain and Ireland?

Two very interesting researchers have found evidence that the* pied de roi* may well go back to pre-Roman times. Geoff Bath's work on megalithic stone circles reveals the presence of such a unit on the circumference of many circles in Britain and Ireland. And Jacques Dassié's work documenting ancient long-distance measures such as leagues, in France, suggests that such a foot existed before the arrival of the Romans in Gaul, and therefore should not only be associated with French rulers since Charlemagne.

Jacques Dassié has specialised during his career in aerial archaeology, having studied the Charente-Maritime area of France by plane, in relation to Roman maps and measures. He has made many important discoveries, and in particlular has examined the distances laid out in leagues. According to Jacques Dassié:

A recent measure, but prior to the metric system, is the Paris fathom = 1.949 metres [toise de Paris]. There are 6 feet to the fathom, hence 1 Paris foot (or pied de Roy) = 0.3248m. If we calculate a league from this Paris foot, with the same ratio as for the Gallic foot, we obtain: 1 league = 0.3248333 x 7500 = 2436 m. This is one of the values of the Gallic league most frequently encountered. We can therefore reasonably suppose that the Paris foot is just the continuation of a Gallic foot which would have lasted until the modern era. (21) The Great Gallic League

Over many surveys, Jacques Dassié has found a clear connection between long distance measures in this region of France and the French (or Paris, or Gallic) foot. This discovery is in fact referred to by Geoff Bath, who found a length compatible with the *pied de roi *in stone circles in Britain and Ireland. Together, these two discoveries put in doubt the claim that the *pied de ro*i originated in the Middle East, to be adopted in western Europe only in the 8th century, by Charlemagne. The *pied de roi* could still have originated in the Middle East, but if it did, this would have been at a much earlier date, long before recorded history, or it could have come from elsewhere altogether. It could also simply have originated from western Europe. Most likely, it is part of the ancient system of measures that is to be found in many ancient places all around the world. Therefore the fact that the Hashimi cubit corresponds to two French feet makes sense even with these pre-Roman connections to the unit in Fance, Britain and Ireland.

In his analysis of hundreds of stone circles over the British Isles and Ireland, over a period of 50 years, Geoff Bath has produced an important body of work. In particular, a unit of 12.8 inches has been found consistently in stone circles, which have been evenly divided into different sections, and this length is, very close in value to the *pied de roi*. Two things are noteworthy, the first is that a unit associated with France should be found much further to the north of Europe, and the second that it should be found so very far back in time, during the late Stone Age.

The megalithic yard (MY) is associated with stone circles in Britain and France, and was initially found, through extensive surveys, by Professor Thom. According to Geoff Bath, the megalithic yard appears on stone circle diameters "as a consequence of there being a common unit present on circumferences (effectively, MY can be calculated as a circumferential length of 2.6m divided by pi)." (22). This analysis produces a circumferential unit of 2.6m, which Geoff Bath divides into 16 parts, or "perimetric units", a division that must also be applied to the megalithic yard. As a result, Bath's work has found that a whole number of "perimetric units" on a circumference will result in fractions of a megalithic yard on the diameter of a stone circle. As a result of extensive surveying across Britain and Ireland, Geoff Bath has found that such a perimetric unit may vary by "up to two percent either side of the mean MY (829mm, which is also the median and mode). Such variance would therefore distort calculations using Thom's mean megalithic yard."(22)

Geoff Bath develops this idea with the study of several circles as examples in particular:

An indication of a potential common circumferential unit is provided by six equally-spaced circles in Scotland, England and central Ireland. The attraction and advantage of equally-spaced circles is that the circumference divided by the number of stones, timbers or pits should provide a fairly reliable mean gapsize. The data for circles in Scotland and England (the Aubrey Holes circle) is provided in Table 1.

Geoff Bath notes:

The mean circumferential unit common to all five circles would thus be 325.7mm (12.8 inches). However, it should be appreciated that there must logically be a common unit on the diameter that is the circumferential unit divided by π. In this case, the length would be 103.67mm (4.08 inches) which happens to be one-eighth of a Megalithic Yard. Thence, it can be appreciated by calculation that all the diameters are multiples of half a Megalithic Yard and, thus, all the radii will be multiples of one-quarter of a Megalithic Yard.

Machrie Moor V on the Isle of Arran (at row 4 in Table 1) has two concentric circles (Fig. 1). The ratio between the dimensions is, perhaps significantly, 11:7 with the inner circle having eight equal divisions. The diameter of this circle at 11.6m would produce a circumference of 8 x 14 perimetric units as in the table. However, assuming that the outer circle has the same unit of measure results in a half unit suggesting that all the values might be doubled.This then suggests an overall perimetric unit of 162.8mm (6.4 inches), and analysis of stone circles further afield, including Ireland, appears to bear this out. (11)

Indeed, a circle with a diameter of 1 megalithic yard of 2.72 feet or 32.64 inches would have a circumference of 8.011 x 12.8 inches, or 8 x 12.817698 inches. A circumference of 8 units of 12.8 inches would imply a diameter of 32.5949 inches, or 2.721624167 feet. There are, however, variations on the MY, both according to Thom, and to other researchers.

There may also be a link between divisions of the Megalithic yard, found on the diameter of a stone circle, and a cubit of 20.412 inches, as such a length is 1 Megalithic Yard taken as 20.7216 feet, divided by 1.6. A cubit of 20.412 inches is also almost exactly 5 x 12.8 / pi, and

20.412 x 1.6 = 32.6592, a good value for the MY in inches.

By analysing not just the dimensions of the diameters and circumferences of the circles, but also the number of stones present on the circumferences, and the measure of the gaps between them, Geoff Bath has arrived at the conclusion that the key to understanding the metrology of these megalithic sites is in the circles themselves, and the divisions on the circmferences. In a post online, Geoff Bath wrote:

Can a common unit be deduced from the sizes of the gaps? Aubrey Ring, 105MY, 56 gaps @ 1.875MY x pi Stenness, 37.5MY, 12 gaps @ 3.125 MY x pi Stanton Drew N, 36MY, 8 gaps @ 4.5MY x pi Machrie Moor V, 14MY, 8 gaps @ 1.75MY x pi Balbirnie, 12.5MY, 10 gaps @ 1.25MY x pi Cullerlie, 12MY, 8 gaps @ 1.5MY x pi So, mathematically, isn’t it staring us in the face? The unit common to all the gaps is 1MY/8 x pi! So, given Thom’s 2.72 feet, the unit common to these circles across England and Scotland is essentially 12.8 inches. Then, take a look at all other circles with a diameter in whole numbers of MY. The same unit appears in the gaps even when the circumference is not equally divided. Inspection reveals that every circle with a diameter in megalithic yards will actually have gaps in multiples of (1MY/16 x pi). Not surprisingly, perhaps, diameters will be found to be measured in eighths of a megalithic yard, but from my surveys and analysis the megalithic yard has a range of 2.66 to 2.77 feet. It’s the division of the circumference that provides the size of the site megalithic yard. (...) the circumferential unit could be seen to be half the French Pied de Roi of 12.8 inches (ref. Hashimi Cubit) - the French archaeologist Jacques Dassié maintains that the unit predates Charlemagne and the Roman occupation of Gaul. Furthermore, the circumferential unit in Germany appears to be half the Northern Foot of 13.2 inches. Thus, the European Iron Age units of measure may have been Bronze Age units on the circumference, which is probably where we should be looking.(23)

(10-Apr-20 by gjb)

A length close in length to the French *pied de roi*, therefore, appears as a circumferential or perimetric unit in stone circles, that relates to the megalithic yard by a factor of pi, as the MY is associated with the diameter. Geoff Bath has shown that the megalith builders used a unit of about 2.6m on the circumference of a circle, relating to the diameter, via pi, to produce the MY there. Because of the preponderance of divisions by 8 or multiples of 8 on the circumference, the 2.6 metre unit produces a unit of 2.6/8 = 0.325 metres, 12.79527559 inches, a pied de roi. A diameter of 1 MY produces 8 pieds de roi on the circumference. Geoff Bath for example has found that the gaps between the Aubrey Holes at Stonehenge would be 15 *pieds de roi*.

It's worth noting briely here that another unit of measure associated with the Romans, amongst otrher cultures, is the Northern or Saxon foot. Three such feet make up a unit of close to a metre, and Geoff Bath has found this foot on the perimeters of stone circles in Germany, a find backed up by the dimensions of the Nebra Sky Disk, also German, which has a diameter of 32cm and, thus, a circumference of just over a metre, which is three Northern Feet. Geoff Bath also observes that "the Trundholm sun disk has a major diametric division that generates a circumference of two Northern Feet. So, might the Northern Foot be a Bronze Age perimetric unit having an equivalent diametric megalithic yard of 854mm (that is, eight Northern Feet divided by pi)?" (23)
A unit of 32 cm has a presence in the Middle East, as the Arab foot, just as the *pied de roi* corresponds closely to the Hashimi cubit. Also, a circle with a diameter of a metre would have a circumference of a Rhineland (or Prussian / Danish / Leiden foot), which is the length that Guilhiermoz associates with the original Carolingian royal foot - rightly or wrongly. Indeed Geoff Bath notes:

Thus, it might be that European megalithic perimetric units existed that equate to ancient measures known as far east as the Indus Valley / Persia, and that these units continued into historical times. (23)

## The Pied de Roi as Astronomical Device

Various researchers, from Jim Wakefield to Dennis Payne, Richard and Robin Heath to Howard Crowhurst, and others, have noticed that when the dimensions of an ancient site are read in English inches, certain key values connected to astronomical time cycles appear. It seems that the inch is in fact a way of encoding cycles derived from observing the movemement of the heavens, into stone structures on the ground. This applies to units as much as to measured lengths derived from sites. For example Jim Wakefield has found that 9 metres of 39.3700787 inches give a length of 354.3307 inches, which is very close to the number of days in a lunar year (354.36708 days). As another example, at Giza, the width of the rectangle formed by the three major pyramids is, in inches, the equivalent of four lunar years.

In particular, Richard Heath has written about the connections between the inch and time, and about a harmonic matrix to model celestial resonances, and "all the celestial relationships in different parts of such a matrix act as a whole to maintain the pattern." (25) Heath has identified Plato's tuning theory as a key revealing "in ancient monuments and textual allusions a pattern of just intonation in the heavens that corresponds to our knowledge of these same atronomical invariants today an actual music of the spheres." (17). Having identified the 125/128 ratio as a key astronomical and musical constant, Heath connects the eclipse year of 346.62 days to the lunar year by this ratio. Could the 12.8 inches associated with the French foot (approximately) be connected to this ratio, through the number 128? What's more the 15/16 ratio identified as linking the English and French feet is also key to linking the Saturn synod of 378.09 days with the lunar year.

Perhaps we could add that a draconic month of 27.2122 days, when divided by the ratio between the solar and lunar years, 1.0306888, gives 26.40197, which is just over twice the value of a Northern / Saxon foot in inches, 13.2. And this would have a connection to the east, in that John Greaves identified a unit of 26.4 inches as the Turkish Pike at Constantinople. And this same Northern foot divided by the solar/lunar year ratio gives 12.806969 inches, which is compatible with the pied de roi.

Another curious possible link to the French foot was identified by Jim Wakefield, and also Robert Carl, in a series of __posts__ on the GHMB forum. The Sothic cycle or Canicular period is a period of 1,461 Egyptian civil years of 365 days each or 1,460 Julian years averaging 365¼ days each. It works on the basis that 365 x 1461 is equal to 365.24 x 1460. As it happens, the product of these sums multiplied by 24 / 1 000 000 is 12.79836, a value which is close to the length of a *pied de roi* in inches. Expressing the lunar month in metres, we might also say 29.53059 x 39.3700787 x pi/10 x 1460 x 24/1 000 000 also equates to 12.7983. Perhaps we could also make a tentative link to the digit of 0.729 or 0.73 inches. 0.729² x 24 = 12.754584, which could also be expressed as (9/10)⁶ x 24. Or if we use a digit of 0.729166667 inches instead of 0.729 inches we obtain 12.760416667. We can express a year of 365.25 days as 1 000 000 x 12.79808 / (24 x 1460), and a year of 365 days as (0.73 x 1000)² / 1460. The 364 day year, as used or example in the *Book of Enoch* can then be expressed as (0.729 x 1000)² / 1460 days.

Another possible way to understand the value of the pied de roi in inches in an astronomical context might be as part of a Metonic cycle, of 19 years, or 223 lunar months. A circumference with 223 markers on the circumference would have, for 223 x 12.780506 inches as the value of the circumference, a diameter of 70 x 12.96. A foot of 12.96 inches can be found in the Middle East.

There is another lunar connection. Quentin Leplat has remarked (30) that the *pied de roi* expressed in metres multiplied by 100/11 is close to the number of days in a lunation. So if we take 12.789, or more precisely, 12.788838 inches, and convert to metres, and then divide by 11, we obtain 29.53059. Another way of expressing this is that a pied de roi expressed in iches, as 12.78883 inches, divided by 29.53059 and 11, and multiplied by 1 000 gives exactly 1 metre.

## Conclusion

It seems the French foot has a very long history, and is probably just as old as the English foot. Because of the evidence of the very great age of the French foot, it's possible that Guilhiermoz had simply confused two units, the French foot and the Rhineland foot, measures that for Charlemagne perhaps could be used together. There are possible astronomical connections that can be derived from the length of the French foot, expressed in inches. The history of this foot as part of megalithic stone circles is perhaps just as surprising as its more recent history within the context of the three or four centuries leading up to the French revolution. The French foot itself was a sound measure with a long history, but unfortunately due to its being named "foot of the king" it did not fit within the revolutionary new post-1789 world. If it had simply been called Paris foot, or foot, it may have had stood a chance of surviving. Its association with autocratic authority and incompetence probably did nothing to help its image.

The connection between the French foot and the megalithic yard is compelling, and tracing the long history of this foot shines a little bit of light on to an ancient measuring system.

"All things that live long are gradually so saturated with reason that their origin in unreason thereby becomes improbable. Does not almost every precise history of an origination impress our feelings as paradoxical and wantonly offensive? Does the good historian not, at bottom, constantly contradict?" (26)

## Notes

2. Hallock, William, 1857, Outlines of the Evolution of Weights and Measures in the Metric System, __Outlines of the evolution of weights and measures and the metric system__,

3. Fréret, M, 1756, Essai, sur les Mesures Longues des anciens, Histoire de l'Academie Royale des Inscriptions et Belles-Lettres, depuis son establissement jusqu'à présent, avec les Mémoires de Littérature tires des registres de cette Académie, depuis son renouvellement jusqu'en MDCCX, Volume 24, l'Imprimerie Royale. Histoire de l'Academie Royale des Inscriptions et Belles-Lettres, depuis son ... - Google Books

4. Guilhiermoz, Paul, 1913, De l'équivalence des anciennes mesures. A propos d'une publication récente, Bibliothèque de l'École des chartes Année 191374 pp. 267-328, De l'équivalence des anciennes mesures. A propos d'une publication récente - Persée (persee.fr)

5. Skinner, F. G. 1952, The English Yard and Pound Weight. *Bulletin of the British Society for the History of Science*, *1*(7), 179–187. __http://www.jstor.org/stable/4024847__

6. Raper, Matthew, 1760, "Inquiry into the measure of the Roman foot", Phil. Transaction Roy Soc Vol 51 p 774/825

8. Flinders Petrie, W. M. , 1911, "Weights and Measures", Encyclopeadia Britannica, Weights and Measures - LoveToKnow 1911 (archive.org)

9. La Condamine, Charles Marie de , 1758, Remarks on the Toise-Standard of the Châtelet, and on the diverse Toises employed in measuring Degrees of the Meridian and on that of the Seconds Pendulum.

10. Newton, Isaac, 1685, A Treatise of the System of the World, printed in English and in Latin (1728) under the titles Treatise of the System of the World and De mundi Systemate

11. Bath, Geoff, 2023, Stonehenge as an Integrated Plan Based on Unit, Number and Geometry, (4) Stonehenge as an Integrated Plan Based on Unit, Number and Geometry | Geoff Bath - Academia.edu

12. See Flinders Petrie, W. M. , 1911, "Weights and Measures", Encyclopeadia Britannica, Weights and Measures - LoveToKnow 1911 (archive.org), and also Inductive Metrology

Or, the Recovery of Ancient Measures from the Monuments, first published in 1877

13. Colbert was also behind trade policies which hindered trade according to a British report:

"Louis XIV in 1664 introduced a sort of Navigation Act in order to engage builders and merchants to construct French vessels by which he levied a tax of 50 sous per ton on all foreign ships which being much cheaper than French vessels had taken possession of the trade In 1667 further restrictions were introduced and in 1687 the exclusive policy was established in its full rigour to Thus France became the country which adopted and still exhibits the consequences of a protecting system on a large scale Its introduction may be traced or rather its extension as far as possible to Colbert a minister to whose name and administration a great portion of applause has been given but whose system of encouragement was based on a complete ignorance of the true principles of commercial legislation How small an amount of manufacturing prosperity Colbert produced and how great an amount of agricultural commercial and manufacturing wealth he either destroyed or checked in its natural progress will be obvious any observer who looks at the immense natural resources and the active intelligence of France It may be safely asserted that the whole of the bounties by which he induced adventurers to enter into remote speculations as well as the excessive duties which he imposed on cheaper foreign articles were almost uncompensated sacrifices while on the other hand of the manufactures which he transplanted into France and which he protected by the exclusion of rival productions scarcely one took permanent root and of those which still exist and which he intended to support there is perhaps none which would not have been more prosperous and extensive but for those regulations with which his zeal encumbered the early march of manufacturing industry The popularity in France of Colbert's commercial legislation and the erroneous deductions drawn from the consequences of his interference have produced a most prejudicial effect on the minds of a large portion of the French public Colbert's system was a vain attempt to force capital in new directions Thus in order to compel the establishment of a trade with the West Indies he made the French people pay a premium of thirty francs upon every ton of goods exported and of fifty francs for every ton of goods imported independently of other encouragements In the same spirit he incited manufacturing settlers by large rewards to establish themselves in different parts of France and boasted of his having set up more than 40,000 looms whose produce was protected by legal enactments and no one was found to estimate the counterbalance of loss while the most flattering pictures were drawn of enormous gain He began in miscalculation he brought the most despotic interference to support his errors and if their consequences be faithfully traced they will be found little creditable to his own sagacity while greatly ruinous to the nation for whose benefit they were intended The French Revolution broke down many of the absurd and pernicious regulations which Colbert had introduced but the vestiges of others remain and although they have become habitual they interfere with improvement and give superiority to countries where the action of industry and capital is unfettered. "

THE SESSIONAL PAPERS 1834 Vol 29 HOUSE OF LORDS 1st Report on commercial relations with France & supplementary Report

14. Hussey, Robert, 1836, * An Essay on the Ancient Weights and Money, and the Roman and Greekliquid measures, with an appendix on the Roman and Greek foot,*

S. Collingwood, Oxford.

An essayon the ancient weights and money, and the Roman and Greek liquid measures, with an appendix on the Roman andGreek foot : Hussey, Robert, 1801-1856 : Free Download, Borrow, and Streaming : Internet Archive

15. Neal, John, "Arabic Measures", (12) Arabic Measures-3 | John Neal - Academia.edu

16. ** **Fréret, M, 1756, Essai, sur les Mesures Longues des anciens, Histoire de l'Academie Royale des Inscriptions et Belles-Lettres, depuis son establissement jusqu'à présent, avec les Mémoires de Littérature tires des registres de cette Académie, depuis son renouvellement jusqu'en MDCCX, Volume 24, l'Imprimerie Royale. __Histoire de l'Academie Royale des Inscriptions et Belles-Lettres, depuis son ... - Google Books__

17. Heath, Richard, & Heath, Robin, 2010, The Origins of Megalithic AstronomyThe Origins of Megalithic Astronomy as found at Le Manio, Based on a Theodolite Survey of Le Manio, Carnac, Brittany ,22nd to 25th March 2010, in associationwith ACEM

18. Guilhiermoz, Paul, 1913, De l'équivalence des anciennes mesures. A propos d'une publication récente, Bibliothèque de l'École des chartes Année 191374 pp. 267-328, De l'équivalence des anciennes mesures. A propos d'une publication récente - Persée (persee.fr)

19. Barthèlemy, Daniel & Dubois, Stéphane Dubois, 2007, Métrologie Antique: Une Tige Métallique Graduée Découverte à Mâcon, Revue Archéologique de l’Est, t. 56-2007, p. 371-379 © SAE 2007

20. Alison, Jim, 2021, Measurement Systems Related to the Digit, digit.pdf (hiwaay.net)

21. Dassié, Jacques, "The Great Gallic League, Metric of the ancient ways. Methodological appro26. ach." Archéologie aérienne J. Dassie aerial archaeology archeo136 (archaero.com)

22. Bath, Geoff, Megalithic Metrology and Design, An Alternative Route to the Megalithic Yard, An Alternative Route to the Megalithic Yard (gjbath.com)

23. Bath, Geoff, "The Stones Divide the Circumference, not the Diameter!", April 10, 2020 03:11AM, Graham Hancock Message Board

24. Mark H. Stone, "The Cubit: A History and Measurement Commentary", *Journal of Anthropology*, vol. 2014, Article ID 489757, 11 pages, 2014. __https://doi.org/10.1155/2014/489757__

25. Heath, Richard, 2014, *The Harmonic Origins of the World: Sacred Number at the Source of Creation*, Inner Traditions

26. Nietzsche, Friedrich; Clark, Maudemarie; Leiter, Brian; Hollingdale, R.J. 1997. Daybreak: Thoughts on the Prejudices of Morality. Cambridge, U.K.: Cambridge University Press. pp. 8–9

28. Stone, Mark J., "The Cubit: A History and Measurement Commentary", *Journal of Anthropology*, vol. 2014, Article ID 489757, 11 pages, 2014. __https://doi.org/10.1155/2014/489757__

29. Flinders Petrie, W. M. , 1911, "Weights and Measures", Encyclopeadia Britannica, Weights and Measures - LoveToKnow 1911 (archive.org)

30. Private correspondence with Quentin.

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