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60. As It Toise

Updated: Dec 11, 2023

Long ago, there was a unit in France named the toise, of six French feet, or pieds de roi. That's about the length of an adult's outstretched arms, and in fact that's where the word toise comes from, the Latin being tensa brachia. The six pieds of the toise also equalled 72 pouces (thumbs, or inches) or 864 lignes. This pied was said to have come from the east, and to have been adopted by Charlemagne. By the time of the French revolution, the toise seemed to embody almost a thousand years of continuity. So why was the official toise changed twice before it was finally discarded? Despite its connection to the Middle East, had the pied de roi been used in Europe long before Charlemagne?


When the metre came into being, the toise was retrospectively valued at 1,949.03632 mm (1866), just shy of two metres. By then, the metric system had long since guillotined not only heads, but pieds and pouces too, in order to make space for the new unit that was supposed to be precisely derived from the meridian circumference of the Earth. But was the toise was already geodectic - a sixteenth of a second of a meridian degree? If so, why did these Banshee of Inisherin-style metrological amputations have to take place?




The long prelude to the metre

The French revolution was about changing the world, starting afresh. Everything was reconsidered, the constitution, religion, and all aspects of cultural life, from fashion to the names of the months of the year. So, naturally, the way time and space were counted and divied up had to be reviewed. The old units of linear measure were completely re-evaluated. In fact, change in relation to units of length and weight had been discussed for a very long time prior to the revolution, and these discussions had nothing to do with the winds of political change. The new political order simply provided the opportunity to implement a new nation-wide system.

While the proponents of the metre took advantage of the social and political chaos, the toise had already been tweaked twice in the century or so before the king's execution. The first time had resulted in a return to a previous standard, deemed to be more correct, under pretext of a warped iron bar which served as the main national standard. The second had been part of the 18th century rise of science. A standard that could be reproduced exactly and precisely was essential to the scientific community, so that measurements made by scientists could be part of a single system. In the early 18th century, this was not yet possible. The national standard was a rough iron bar attached to an outdoor wall in Paris. A scientist, who later went on to become the president of the Royal Academy of Science of Paris, had the best copies he could get made. He was in need of a carefully made ruler that could be replicated exactly, for a scientific prject, not a crude iron bar. He had two perfectly identical rulers made, and much later on, one of them became the new standard for the scientific community, known as the toise de l'Académie.

The scientific project that motivated this approach was the attempt to prove Newton right and Cassini wrong about the shape of the earth. Newton predicted it would be found to be slightly flattened at the poles. To find out, two teams set off from Paris to measure a meridian degree at the equator and at the arctic circle. In fact, Newton's work on gravity also relied on a good knowledge of the size of the earth, and these expeditions were going to be able to help improve on the best estimates. It was essential the two teams should work with identical rulers in order to be able to precisely compare the results. Even the slightest difference in the standards of measure used by each team could seriously undermine their efforts. This work started the demand for ever more precisely determined units of measure for scientific research wehich went on till the twentieth century.

Also heading for the chop was the sexagesimal or duodecimal system (thinking in 6s and 12s), that had characterised many of the old systems of measure, to be replaced by a decimal system. Many considerations were taken: should the new system of measure be geodectic, that is, should it be defined in relation to some division of the the Earth's circumference or radius? Should the new unit be derived from a measure on the ground, a particular degree of latitude, or a measure of a pendulum for a particular time period, related to the Earth's motion, which would also depend on a particular latitude? If so, what degree of latitude should prevail? It was even suggested that each country should adopt a slightly different length as their standard unit of measure, based on one system but adapted to the local length of a meridian degree of latitude, a bit like the way our time zones work, but depending on latitude rather than longitude. So if you were heading to southern Europe from northern Europe, you might expect to be served a slightly larger pint.



The measure of a degree of latitude, not at the equator, nor at France's latitude, but simply a mean division of a meridian won the day. In 1739, Lacaille and Cassini had discussed measuring a degree at a latitude of 45 degrees instead, and this resulted in the famous measurement of the distance between Dunkerque and Barcelona. However, in March 1790, the discussions around a new unit of measure were centered not on a division of the earth's circumference, but on the idea of a seconds pendulum at 45 degrees latitude. These discussions were kickstarted by the Bishop of Autun, Charles Maurice de Talleyrand-Périgord (1754 -1838). His proposals were in the same vein as those of the abbé Mouton en 1670, and of Christiaan Huygens. Mouton had suggested a linear measure in connection with a trigonometric survey of the earth, based on a minute of a degree devided decimally. Cassini proposed a geometric foot which was to be six 1000ths of a minute of a great circle, or a fathom being ten 1000 000ths of half the diameter of the earth. Writing in 1864, John Taylor summed up the long prelude to the invention of the metre by observing that "the merit, if it be one, of suggesting the base of the metrical system belongs to the old monarchy of France, and not to the Revolution, as modern Frenchmen are fond of declaring!"(1) The metre was indeed the culmination of decades of scientific discussion, but also a return to the ancient idea of a unit of measure that should be precisely geodectic.

When it was agreed to use the length of a seconds pendulum at Paris's latitude, with a length of 440,5593 lines of the toise du Pérou, or 993,8263 mm, envoys were sent to share the new unit with neighbouring countries. But then there was a change of opinion. England and the United States, though favourable at first to this seconds pendulum, decided against it by the end of 1790. A new commission then drew up plans for the unit to be a degree of a meridian of the planet. There was obviously an importance to consulting the United Kingdom and the United States, and agreeing on a system that suited everyone, even though, ironically, these two nations never adopted this metre. It can however be surmised that the metre had to fit in within certain unknown international parameters.

In 1791, the metre was officially defined as the ten millionth part of a quarter of a meridian, and it was shortly after that that the Académie des Sciences sent surveyors to measure the meridian between Dunkerque and Barcelona. However, by 1793, the king having been beheaded, his pied had to be cut too. The implementation of the metre became a highly politically symbolic statement. At the moment the will was there for change, the long hoped for new product was't ready, and a substitute had to be found. So by August of that year, a provisional metre was officially adopted, even though the surveyors who'd set out to measure a the length of a degree at France's latitude, risking life and limb, were still painstakingly measuring away. The provisional metre was based on measures made during scientific expeditions, in 1735 to Peru, and in 1740 to Lapland, set into a decimal system, as well as on the measure of the meridian of France conducted in 1740. The provisional metre was adopted after a report by the Academy of Science on the 29th May 1793, enacted in law on the 1st August 1793, and the 18 Germinal year III (& April 1795), based on a value of 5132430 toises de Paris. However the definitive metre was based on Delambre and Méchain’s measure of this same meridian, which was eventually finished in 1798. In 1799 the metre was defined to be exactly 443.296 lignes or 13 853 ⁄ 27 000 toises, with the hope that the metre should equal 1⁄10 000 000 of the distance from the pole to the equator.

The metre might have had a brand new name, but it was, both in length and spirit, not so different from the old toises, and the culmination of decades of research and debate rooted in the old kingdom, and which had already resulted in slight changes to the official pied de roi. Based on the 1799 definition, the pied de roi, being a sixth part of the toise, would be 0.3248394 metres, or 12.788952 inches. It seems the French foot was officially slightly re-evaluated several times, giving rise to different toises. The oldest is associated with Charlemagne, and was referred to after 1668 as the Toise de l'Ecritoire. The second, the Toise du Chatelet, was introduced after the main standard became warped, and the third, the Toise du Pérou, was basically just a copy of the Toise du Chatelet but made in such a way as to lend itself to precise replication and scientific work, in preparation for a scientific trip to South America.


Why the need for a new French national standard in the mid 18th century?


The importance of having a precisely defined and replicable toise was outlined by La Condamine in an address to the Royal Academy of Science of Paris on the 29th July 1758 . He was in favour of the Academy adopting what he called the Toise de l'Équateur (i.e. the Toise du Pérou, which later became known as the Toise de l'Académie, or the Toise de Paris). His speech captured the reality of the situation France found itself in as an aspiring world leader in science. France desperately needed to improve certain aspects of its infrastructure, most notably access to a precise and reliable system of measure. While the country had dozens of different regional units, a single national unit wasn't required yet. All that was needed was a single, carefully made standard, that scientists could use and replicate precisely.

Charles Marie de La Condamine was a man of action, an explorer, a scientist, who was a vital part of the French Enlightenment. He had fought in the war against Spain, spent ten years on the scientific expedition to South America, where among other things he discovered rubber, and had also travelled to the Levant, and to Rome in order to precisely determine the length of a Roman foot. He was instrumental in arguing in favour of vaccinations, and treating malaria with quinine. While in South America, he also studied Inca architecture first hand. He became president of the Acdemy of Science of Paris, and was a friend of Voltaire's.

By the time of La Condamine's address to the Academy in 1758, the official standard of measure in France, the Toise du Châtelet, was an old iron bar in a courtyard, and the standard used by Picard to measure a meridian had disappeared. Nobody knew where it was, or at least nobody at the observatory, where it was supposed to be officially kept, would let anyone see it. Worse still, the toise du Chatelet had been re-defined less than a century before, but in such a rough and imprecise way that scientists had been left with no choice but to use their own initiative and come up with something to work with. La Condamine began his address with these words:

It would be easy for me to prove that the toise of the Châtelet, if by that name one meant some particular fixed measure, has never existed; but what is sufficient for the present case, and what everyone tends to agree on, is that it no longer exists today. M. Mairan on 24 May last, warns the Academy that the iron bar fixed to the wall at the foot of the stairway of the Châtelet to serve as a standard for the toise, was altered and distorted, and that its length had changed. He added that the Magistrates by whom the inspection is made had agreed with him to rely on the Academy for restoration of this public measure.
It must be confessed that a standard that seems intended only for legal verification of ordinary toises of masons, carpenters, or, if you will, architects, does not appear to require very scrupulous precautions. In measuring buildings lignes are neglected; sometimes even pouces are of no consequence. But since the Academy is consulted on fixing the new standard, doubtless one expects an accuracy worthy of it.
To fulfill these views, you must first agree what is the toise used by the Academy in the measurement of the degrees of Earth, and clarification does not permit the slightest negligence. The slightest mistake on the length of the toise is multiplied nearly sixty thousand times in the length of the Degree of the Meridian. A hundredth of a ligne—if our senses, helped by the most perfect instruments, can reach that far—is not to be willingly neglected in the seconds pendulum, when it is possible to take it into account. It leads to some differences in the shape of the Earth and in the theory of gravitation, important problems in celestial physics.
Astronomy, geography and navigation are therefore interested in fixing the length of the Academy's toise. It is above all a question of noting the differences, if any, between the different toises that have been used for the measurements of the various degrees, and to report the various degrees, and to relate everything to the same measure. (2)

It's clear from La Condamine's speech to the Academy that there was an urgent need for change, and that in order to get it exactly right, it wasn't enough to simply agree on a good approximation of what the toise du Chatelet or the toise de l'Ecritoire once might have been. The unit needed by science could almost be arbitrary, since obtaining a perfectly accurate geodesic measure wasn't yet possible. In order to know the precise size and shape of the earth, in order to actually, further down the line, create a geodesic unit, some kind of unit had to be agred upon, and it had to be able to lend itself to precision to the order of a "hundredth of a ligne". Also, without knowledge of the precise length of the standard toise, how could anyone interpret precisely the work that had already been done in measuring a degree of latitude in France and beyond? Looking for "the precise length of the toise with which the French meridians had been measured", La Condamine said, was essential to uniting all the work that had been done at the equator and in the Arctic circle too.

It is above all a question of noting the differences, if any, between the different toises that have been used for the measurements of the various degrees, and to report the various degrees, and to relate everything to the same measure. (2)

Not only was it essential to use a single precisely evaluated measure of the toise to understand precisely the shape and dimensions of the earth, it would soon also become essential to understand the toise itself in relation to the size of the earth. The speech given by La Condamine paints a bleak picture of the situation France found itself in. Some of the blame seems to fall on Picard. Jean Picard was a French astronomer and priest, who'd attempted to measure the size of the earth in 1669–70, by measuring a degree on the Paris meridian between Paris and Amiens. The standard of the toise Picard had used had not only been designed in a slipshot way, according to La Condamine, it had gone missing. These were the conditions under which the top scientists of the day were supposed to advance human knowledge on the size and shape of the earth, and prove Newton right and Cassini wrong along the way. La Condamine went on to say in his address:

If the toise used 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 this toise, and the doubts which have arisen since then on the true length of the base of M. Picard's toise would have been promptly cleared up. But Mr. Picard's toise no 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 a toise when one tests it there, were never polished nor filed square and parallel with one other. No wonder the toises calibrated at different times and by different people on this defective original, are not perfectly equal to each other.

La Condamine was dismissive of the official toise of the day, the toise du Chatelet, and was clearly not interested in simply getting the academy to agree on restoring it, to a good approximation, or restoring the older toise de l'Ecritoire, for the sake of historic continuity, or trade. The fact was nobody knew the precise dimensions of the toise Picard had used in his work. urthermore, La Condamine was scathing of Picard's work, whom he associated with the creation of the toise du Chatelet, the year before Picard's work measure of the earth started. La Condamine seems to want to encourage the academy to consign the whole toise du Chatelet episode to history. He accuses Picard of having made several errors in his work, stating:

He [Picard] found that the measure of the seconds pendulum, in Paris, was 36 pouceslignes of his toise, and this length, very different from the true one, is incompatible with the number of toises that he gives to his base. It is thus necessary to agree that M. Picard was mistaken, either by assigning two fifths of a ligne too much to his pendulum, if his toise was good, or by employing a toise which was too short by more than four fifths of a ligne, if the measure of his pendulum is exact.

After the long and arduous expeditions to South America and Lapland, La Condamine was not prepared to let those efforts be wasted by shoddy administration and imprecise, flawed science. La Condamine noted the existence of several scientific endeavours that depended on some version of the Toise du Chatelet, and that some of these versions were different from the others.

The other toises known to the Academy, and different from that of M. Picard, are 1. that which Messrs. Godin , Bouguer and I, carried to Peru in 1735, and which served us in measuring the three Degrees of the meridian nearest the Equator; 2. the toise with which Messrs. de Maupertuis , Clairaut , Camus and le Monnier measured, in 1736 and 1737, the Degree of the meridian which intersects the Arctic Circle in Lapland; 3. the toise that M. Cassini de Thury and Abbé de Lacaille made use in 1739 and 1740, for the verification of the Meridian of Paris; 4. the toise employed by Abbé de Lacaille in his measurement of the 34th and 35th degree of southern latitude, at the Cape of Good Hope in 1752; 5. M. de Mairan's toise, with which he made his experiments with the pendulum, in 1735.
All these toises originally had for their model that of the Châtelet, which no longer exists: one supposed them all equal. If their equality were perfect, there would be no choice to be made, or this choice would be indifferent. But in the last comparison, which was made in 1756 on the occasion of the new measurement of the base of Villejuive, some differences between these various toises were recognized, and the precision that we seek here does not allow us to ignore them.

La Condamine himself had had two of these standards he mentions made, by the same craftsman, to a high standard. One of them went to Peru, the other, intended for Paris as backup, was in fact taken to Lapland by Maupertuis. It was these two standards, or rather the one that went to Peru, the other having been involved in a shipwreck and gone rusty, that La Condamine put forward in his address for the new standard of the Academy. It seemed to still be, at the time of his address, the most carefully built standard available in Paris.

He tells the story here:

“We had taken with us in 1735: a polished iron rule, seventeen lignes wide, by four and a half lignes thick. Mr. Godin, assisted by a skilled artist (Mr. Langlois), had put all his attention into adjusting the length of this ruler to that of the standard toise, which had been fixed in 1668, at the foot of the staircase of the Grand Châtelet of Paris. I foresaw that this old standard, made rather roughly, and moreover exposed to the shocks, the insults of the air, the rust, the contact of all the measures which are presented there, and to the malignity even of any ill-intentioned person, would be hardly suitable to verify in the future the toise which was going to be used for the measurement of the Earth, nor to become the original to which the other toises were to be compared. It therefore seemed to me very necessary, while taking a well verified toise, to leave in Paris another one of the same material and of the same shape, to which one could have recourse if some accident happened to ours during such a long journey. I took upon myself the care of having such a one made. This second toise was built by the same workman, and with the same precautions as the first. The two toises were compared together in one of our Assemblies, and one of the two remained in deposit at the Academy. It is the same one which has since been carried to Lappland by M. de Maupertuis, and which has been used for all the operations of the Academicians sent to the Arctic Circle.”
[15] When I wrote the above in 1748, and which I transcribe literally from my Measure of the Meridian, I believed that this iron rule, which I call our toise, was still in Quito in the hands of Mr. Godin. I did not know that it had been in Paris for several months. M. le Comte de Maurepas, then Minister of the Academy, had written in 1747 to M. Joseph de Jussieu, our traveling companion who remained in Quito, and had charged him, at my request, to retrieve from M. Godin a copy of his observations, our toise and the Academy's other instruments, and to bring everything back to France, since M. Godin was called to Lima in 1747 by the Viceroy of Peru, and seemed to have already settled in the service of the King of Spain. The letter of the Minister reached M. de Jussieu at the beginning of 1748, when he was fifty lieues from Quito, in the province of Canelos, ready to embark to return to France by the Amazon River. He retraced his steps to Quito, which he left as soon as possible to go to Lima, with the intention of carrying out the orders of the Minister ³. He found Mr. Godin preparing to return to Europe. Both took the road to Buénos Aires by land, after having placed on the ship le Condé, ready to sail for France, a portable geodetic quadrant and our toise enclosed in its case. These instruments arrived at the end of 1748, or towards the beginning of 1749, at the address of M. le Comte de Maurepas, and were carried without my knowledge to the Academy's cabinet of machines, and transported some years later to the Royal Botanical Garden. M. Bouguer, having known about it, withdrew only the portable geodetic quadrant that was part of the shipment, which was the one he had always used during the trip. Three years and more passed, from that time on, without my hearing anything about our toise, until in 1752 I eagerly asked Mr. Godin for news of it on his arrival from America. I was surprised to learn that the toise had been in France for nearly four years. I took all the necessary care to search for it; finally it was found in the storage room of the Royal Garden, in good condition, enclosed in a wooden case, solid and lined with serge, where it had always been kept. I did not want to withdraw it; I only repeated my request for the verification of the toise of Messrs. Cassini, preserved at the Observatory, and for its comparison with ours.*
* This toise of Peru is in the cabinet of the Academy (April 1776). Mémoires de l'Académie, 1772. Part II.

This is why, once back in Paris, the ruler that had travelled half way across the world to the Americas and back became the standard, and the new unit used across France was called the toise du Pérou. and became the standard for the Academy and all scientific work.


It is known that the ship on which it was embarked, on its return, was shipwrecked in the Gulf of Bothnia. The toise was wet with seawater; it is especially at the ends and edges of a filed iron that rust attaches. This rust could not be removed without the toise losing some of its length; it must therefore necessarily be a little shorter today than it was in 1735, when it was compared to ours. It is indeed, and this is a new proof of their original equality; but the change which occurred to the North toise, occurred after all the operations made in Lapland; the base of 7000 toises which served as their foundation, was thus measured with a toise equal to ours; the length of the North Degree, and that of our three Degrees close to the Equator, were thus determined by a common measure.

La Condamine's proposals were eventually accepted. As time went on, not even the standard that was created in 1799 was considered sufficiently precise for scientific work. By 1860, a new movement had begun to rethink the definition of the metre, and the process of requiring ever more precisely determined standards to use in science continued until, ultimately, the speed of light was chosen to define this measure. It was La Condamine who kickstarted this move to define in the most precise terms possible the standard of measure for science, and by extension, or a country, or group of countries.

The toise du Pérou or toise de l'Équateur


The loi du 19 frimaire an VIII (Law of 10 December 1799) stated that one decimal metre was exactly 443.296 French lines, or 3 pieds 11.296 lignes de la "Toise du Pérou". This Toise du Pérou, was created as a reliable and precise standard against the standard of the Toise du Chatelet, which was rough and exposed to the elements. Until a new generation had had time to grow up with the metre, the toise du Pérou remained in use, if only by name, until 1812 when it was redefined as 2 metres exactly. This last generation of the toise survived until 1840.


Extract of the Resolution passed by the Minister of the Interior, 28th March 1812, for the execution of the foregoing Decree . ART . I. It is permitted to employ for the use of commerce , 1. A measure of length equal to 2 mètres, which shall be called toise, and be divided into 6 feet .
2. A measure equal to of the metre, or of the toise, which shall be called foot ( pied ), shall be divided into 12 inches (pouce), and the inch into 12 lines .
II . Each of these measures shall bear on one side the corresponding divisions of the metre, that is, the toise, 2 metres divided into decimetres, and the first decimetre into millimetres, and the foot 31 decimetres divided into centimetres and millimetres; in all 333 millimetres. (1)

The toise du Pérou, the national standard, was not a division of the meridian degree at the equator. Rather than being the result of the expedition, it was one of the tools that enabled it from the beginning. It was simply a precisely and carefully made copy of the toise du Chatelet standard, which itself was a rough piece of iron, exposed to the elements and other potential sources of damage, and the result of unsatisfactory scientific work. After the expedition to America and theLapland trip, it was deducted that the earth was indeed an oblate speroid, proving Cassini wrong, and Newton right. The flattening at the poles was estimated to be de 1/179, though in fact this was too much, as it is now estimated at 1/298.3. The story of the expedition to South America is part of the story of the toise, partly because the work done there contributed to the long debate about a new unit, which culminated in the metre, and partly because the measuring rule that was taken on the trip became the French scientific standard until the metre took over, and was known as the toise de l'Académie. The main purpose of the expedition, organised by the Royal Academy of Science of Paris, was to measure the length of a degree there. Pierre-Louis de Maupertuis, wanting to know if Newton's theories on the shape of the planet were correct, had persuaded the king to organise this expedition. The following year, Maupertuis was sent by the Academy to the Arctic circle, in Lapland, to measure the length of a degree there.

The meridian in France had already been measured, by Picard in 1672, though as we've seen there were issues with his data as the standard he'd used had gone missing. Also, Cassini de Thury, son of Jacques Cassini, had attempted to provide a more correct measure of the meridian, publishing La méridienne de l’Observatoire Royal de Paris in 1744.

The expedition left La Rochelle, in France, on the 16th May 1735, on the Portefaix. Charles-Marie de La Condamine, there as a chemist and geographer, and two other members of the Académie, Louis Godin, an astronomer, and Pierre Bouguer, a mathematicien and physician, were chosen to lead the expedition. It was the first ever scientific expedition to the New World. In many ways it was a successful one. The measures they arrived at were considered accurate even two centuries later. Many discoveries and advances in knowledge were made. In the end, the expedition took ten years. The observations were eventually finished in 1743. La Condamine remarqued in his account that when they set off they thought they'd be gone for four years at the most. Just getting to Quito took thirteen months. As a matter of fact, La Condamine didn't get along with some of his crew mates, and as soon as they reached land on the other side of the Atlantic, he set off on his own to Quito, going his own way, through the Amazon, making him the first modern European scientist to sail up the Amazon.

The difficulties the expedition team faced were considerable. From the start there were personality clashes, notably between La Condamine and Godin, there were scorpion stings and illnesses, several earthquakes, ongoing money problems, there were the physical difficulties of negotiating the steep slopes of the Andes, added to the cultural and political clashes with the locals, which resulted in the locals dismantling their equipment. The Spanish in Peru were generally hostile to them. There were the climate difficulties, the high altitude and the extremes of heat and cold which broke the springs in everybody's watches, and which, La Condamine says, affected his hearing for the rest of his life. It seems not every member of the crew on the way over was guaranteed a ticket home. Eleven years after the Portefaix had set sail, some of the team were still in Peru. Some members of the team never got home again. The astronomer Granjean de Fouchy died suddenly. The 1746 earthquake in Lima killed the clockmaker and marine engineer Hugot, who was, crushed by a wall while trying to fix a clock. Louis Godin, an astronomer and member of the French Academy of Sciences, who'd stayed on in Lima, survived the earthquake. He was able to make valuable seismological observations and be of assistance. He had started teaching astronomy and mathematics in order to pay for his return to Europe. By chance, he was subsequently unlucky enough to be in Cadiz at the time the massive Lisbon earthquake in 1755. The assistant geographer Jacques Couplet-Viguier, the youngest on the team, died of malaria in 1736. Morainville, a natural history artist, died after a fall from scaffolding, during the reconstruction of the Church of Nuestra Señora de Sicalpa in Riobamba in 1764 or 1765.

Perhaps the most gruesome death was the surgeon Séniergue's, who was fatally injured during some fiestas centered around bull racing in Cuenca (south of Quito) in 1739. The story is told by La Condamine. Séniergue had got himself involved in a local feud. A man had broken up with his fiancée to marry another, and had failed to pay the compensation owed to her. Séniergue, having treated the girl's father as a patient, had taken the girl and her father's side, and had come to blows with the man. During the fiestas, Séniergue had failed to keep a low profile, and was attacked, not just by the man he had previously challenged, but by the whole crowd, on the instuctions of the highest ranking official there, the Alcalde, who was heard shouting to the mob "kill him!".

Jean Godin des Odonais, cousin of Louis Godin, also stayed, but to become a professor of astronomy and natural science at the College of Quito, in 1739. He studied the Indian languages and the flora of Ecuador. He was lucky enough to marry an heiress, Isabel Gramesón, which allowed him to resign from his post in 1743, and give his whole time to natural science and learning the Indian language. He explored Ecuador and the northern provinces of Peru, and collected an herbarium containing more than 4,000 species of plants. He also made drawings of over 800 species of animals. However, having lost the greater part of his wife's dowry in speculations, he decided to try his fortune in Cayenne, where he arrived in May, 1750, and settled on the banks of the river Oyapok. As a French citizen, he was refused permission by the Spanish and Portuguese authorities to return to his family. For fifteen years he explored Cayenne and the Brazilian Guiana, north of the Amazon, and collected nearly 7,000 species of plants. From 1765 till 1773 he explored the Amazon. Eventually, his wife decided to travel to him, to bring him home. For some reason, she brought all her children and many servants on this dangerous 3000 mile journey to the Amazon. Her expedition sunk in the Amazon, those who survived got lost in the forest, and everyone but her died of yellow fever or smallpox. She did finally find her husband and they eventually set off to live in France.

Joseph de Jussieu, a botanist, didn't return to Europe until 1771, having stayed on to continue his studies and work as a doctor in South America for thirty-six years, but returned sick, unable to write his memoirs. In his illnesss, he was sent home without his botanical collections and manuscripts, which were then lost forever. He is credited with discovering rubber and the coca plant (though a Spanish explorer, Nicolas Monardés, had already described the coca plant in the 1580s and La Condamine is also credited with discovering rubber.)

La Condamine tells the story about how, after he himself had returned to France, he asked the minister of the Academy to request that the standard that he had had made, and taken to Peru, be sent back to France. He did not know till he got back to Paris that the second copy of the rule he'd had made had gone to Lapland, and then been damaged, so he badly needed the one in America back. He was probably kicking himself he hadn't had three made. It seems La Condamine asked the minister to order Jussieu to do this, even though the standard had been entrusted to Godin. La Condamine says Jussieu had already left for France and was travelling to the place he might embark on a ship to France. La Condamine wrote:


M. le Comte de Maurepas, then Minister of the Academy, had written in 1747 to M. Joseph de Jussieu, our traveling companion who remained in Quito, and had charged him, at my request, to retrieve from M. Godin a copy of his observations, our toise and the Academy's other instruments, and to bring everything back to France, since M. Godin was called to Lima in 1747 by the Viceroy of Peru, and seemed to have already settled in the service of the King of Spain. The letter of the Minister reached M. de Jussieu at the beginning of 1748, when he was fifty lieues from Quito, in the province of Canelos, ready to embark to return to France by the Amazon River. He retraced his steps to Quito, which he left as soon as possible to go to Lima, with the intention of carrying out the orders of the Minister. He found Mr. Godin preparing to return to Europe. Both took the road to Buénos Aires by land, after having placed on the ship le Condé, ready to sail for France, a portable geodetic quadrant and our toise enclosed in its case. These instruments arrived at the end of 1748, or towards the beginning of 1749, at the address of M. le Comte de Maurepas, and were carried without my knowledge to the Academy's cabinet of machines, and transported some years later to the Royal Botanical Garden. M. Bouguer, having known about it, withdrew only the portable geodetic quadrant that was part of the shipment, which was the one he had always used during the trip. Three years and more passed, from that time on, without my hearing anything about our toise, until in 1752 I eagerly asked Mr. Godin for news of it on his arrival from America. I was surprised to learn that the toise had been in France for nearly four years. I took all the necessary care to search for it; finally it was found in the storage room of the Royal Garden, in good condition, enclosed in a wooden case, solid and lined with serge, where it had always been kept. I did not want to withdraw it; I only repeated my request for the verification of the toise of Messrs. Cassini, preserved at the Observatory, and for its comparison with ours.*
* This toise of Peru is in the cabinet of the Academy (April 1776). Mémoires de l'Académie, 1772. Part II.

It seems that Jussieu missed his boat as a result, as he had to go back and get the standard from Godin, and place it on another ship, though it seems he himself had no place on board. And there was no need to ask Jussieu to do this at it so happend Godin was on his way home to France ayway. Was he stranded in the Americas as a result? It's not clear. Perhaps he had paid for his passage on the boat he was heading for when the letter from France arrived and then lost his money. The minister sent the instructions in 1747, and Jussieu didn't get back to France until 1771. So it could well be that the order to go back and get the standard cost Jussieu twenty four years delay. And after all that, the precious standard arived in Paris and was placed in storage, and La Condamine waited four years to be told of this.


La Toise du Châtelet


The toise du Chatelet was problematic. In 1668 the national standard was damaged and a new one issued, that owas different in length. La Condamine writes:

Mr. Picard in his Latin treatise On 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 five lignes in 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 twelve pieds wide. Half of that length [six pied] became the new standard of the toise, which proved shorter than the old by five lignes. (2)

The toise du Châtelet seems to have been deliebrately shortened. Why? And what did La Condamine mean when he stated in is 1758 address to the Academy that "the toise of the Châtelet, if by that name one meant some particular fixed measure, has never existed"?

La Condamine wrote:

We know neither in what season of the year, nor by whom the new Châtelet standard was set. If Mr. Picard had presided over it, the circumstance of the season seems too important for him to have neglected to inform us. Everything seems to indicate that this care was left to some worker, or at least to some unintelligent subordinate. It is therefore possible that the standard was, from the time it was installed, longer than the toise that 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 new toises, gauged to this standard for twenty-five or thirty years; are longer than that of Mr. Picard, and consequently that one would have found fewer toises than he in the measurement of the base between Villejuîve and Juvify (Mém. De l'Acad. year 1754, p. 172). (2)

The toise du Châtelet didn't match the instruments which Parisian artisans and builders used. The change was not popular, but the minister in charge, Colbert, stuck to his guns and demanded that it be adhered to. Was this stuborness rooted in a fear of undermining his authority, or in a belief that the new toise was in some way better, more authentic? The Abbé Picard wrote: “Parisius, anno 1668, facta est reformatio, quorum sexpeda veram excedebat lineis 5.”(3) (In Paris, in the year 1668, there was a reformation of the foot of latoms, whose six feet exceeded the true by 5 lines.) According to La Hire, the old French foot of the architects and "maçons", or builders, was 1 line longer than the Toise du Chatelet.


Picard said in his Mesure de le terre that the original toise du Châtelet had been “newly re-established”. In 1714, La Hire said that the reformation of the pied des maçons in 1668 had been contemporary with the toise du Châtelet. Guillermoz tells us this was not quite true.

This is what happened according to Guillermoz. The standard of the pied de roi was the toise of 6 pieds, and had been in the Chatelet in Paris since 1394, perhaps it could have ben replaced at some point but no one knows. In the middle of the 17th century, this standard was fixed to a stone pillar in the courtyard. Sometime after 1755, it was stolen. Around 1667 part of the stone pillar moved and the iron bar was left misshapen. A new standard was then stuck to the courtyard wall, under an archway, and this was used till 1758, at which time the iron bar was again distorted because of movement in the stone pillar. There was another standard kept in the Ecritoire aux maçons. This was the greffe des maitres jurés des oeuvres de maçonneries et charpenterie de la ville de Paris, and this measure was what Picard referred to as the pied des maçons. It was more often called the pied de l’écritoire. For a time, the maçons continued to use their standard, even though it didn’t agree with the official toise, which was at the Châtelet. La Reynie, who was lieutenant de police du prévot de Paris, working for Colbert, banned the use of the toise des maçons. The maitre genéral des oeuvres des bâtiments du roi, a man named Bricart, was called to state the difference between the two measures in front of the procureur du roi and master masons. The gallery of the Louvre was measured twice: first with the toise du Châtelet, then with the toise de l’Ecritoire. The first result was 220 toises, 1 pied, 2 pouces 7 lignes, or a total of 190 255 lignes, and the second result was 219 toises 9 pouces 7 lignes, or 189 331 lignes. This means the ancient pied was 0.7028 new lines longer than the new pied, and so the ancienne toise was 4.2166 lignes longer than the new. On the 9th January 1668 Charles Perrault (of fairy tale fame) gave the results to Colbert, and the order was then given to the masons to change their measure to match the standard at the Châtelet. Guillermoz informs us that this measure was mostly ignored, especially outside Paris, and the old, pre-1668 measures continued to be used. Outside of Paris, measures were often expressed in terms of pied de roi but they weren’t actually derived from the standard at the Châtelet.

There was another important standard kept in Paris: the aune de Paris. This was kept at the Bureau de la corporation des merciers. When it was measured in 1736 by a member of the Académie des Sciences, Du Fay, and again in 1745 by Hellot and Camus, it was found to be 526 lignes 10 points long. It was dated to 1554. The 1540 law stated that the aune de Paris was to be 524 lignes long. This meant that the old pied de Paris related to the new (from the toise du Châtelet) as 526 5/6 to 524, or 3161 to 3144, if this aune des merciers was exact. In any case, as we’ve seen the iron bar standard at the Châtelet was a crude one, so it’s hard to know with much precision.

It is possible that those in charge wanted to preserve a certain ratio between the French foot and another unit, perhaps the English foot, or the Roman, or the Arab. If the ratio between the English foot and the French was considered to be 15/16, then the French foot should measure 12.8 English inches. One French foot based on the toise du Châtelet would be worth 12.78895 English inches. With the Toise du Châtelet valued at 1,949.03632 mm, and with six feet to the toise, twelve pouces to the foot and twelve lines to the pouce, the old foot, prior to the Châtelet, must therefore have been:

1949.03632 / 6 = 324.839386 mm. If 144 lines are 324.839386 mm, 145 lines are 327.0952157 mm, which are 12.8778 and 12.8794 inches respectively, with a 39.375 metre, or 12.788952 and 12.877764 with the modern metre. This agrees with William Hallock's value: "The French foot was longer than the English foot, being equal to 12.79 inches of the latter".(4)

(Curiously this measure of 0.32328 m is close to being 20 cm x Phi.)

To find out more we need to go back to the Renaissance and the time of King François Ier, and the aune de Paris, and to the time of Charlemagne and the last days of the Roman Empire. (Next post)


Base du système métrique décimal, ou mesure de l'arc du méridien compris entre les parallèles de Dunkerque et Barcelone: executée en 1792 et années suivantes : suite des Mémoires de l'Institut.



Mesure de la meridienne, Mechain et Delambre, Vol 3






Did the the French toise originate in the Middle East?




Conclusion


The toise was both a unit derived from the earth and a unit designed to measure the earth.

The study of historical metrology, as well as cutting edge scientific research were the twin drivers behind these changes tha eventually produced the metre, one a nod to the past and the other to the future. The metre was in some ways the last incarnation of a unit that had been in doing a lot of soul searching over recent centuries. But the change was mostly driven by the need for precision, in response to the new scientific importance of the age.


The trouble with units of measure, historically, has not just been the problem of implementing standards for wide areas and facilitating trade, perhaps across a country, or an entire region. It's true of course that the many regions of France had their own variations on the foot and the toise, and that this was a huge problem for trade. But this is only half the problem. The units of length, upon which the units of mass and volume depended, were highly symbolic, politically and culturally. They were not immune to a certain fluidity that belied their metallic and wooden alter egos, not just at grassroots level, but at the very upper echelons. There seems to have been a need to periodically validate the central unit of length, which seems to have been independent from the need to enforce a common system in a given jurisdiction. This seems to have been rooted in a need to comply with some ancient standard, perhaps Roman, perhaps biblical, in order to give the entire system a legitimacy and a parentage. The next post will explore the re-defining of the pied de roi under the authority of King Francis I, and Charlemagne.



Notes


1 Taylor, John, 1864, The Battle of the Standards: the Ancient, Of Four Thousand Years, Against The Modern, Of The Last Fifty Years, The Less Perfect Of The TwoThe battle of the standards: the ancient, of four thousand ... - Page 62


2. Condamine, Charles Marie de la , 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.


3. Mémoires de l’Académie des sciences depuis 1666 jusqu’a 1699, VI, p 536, quoted by Guillermoz.

We need to bear in mind that Guillermoz is using a different ratio between the metre and the English inch than today's. He says the yard is 0.914391792 metres. This means for him a metre is 39.370432144 inches. This ratio was also used by Henry James.




This table of Picard suggests that he was found of rounding things, at the expense of accuracy. For Picard, 1 second of a degree of a meridian is 16 toises. 16 x 60 is not 951, and he seems to be using a value of 15.85 toises per second, and rounding everything to integers.

Bibliography


Aviler, Charles Augustin d', 1730, Dictionnaire d'architecture, Dictionnaire d'architecture, ou Explication de tous les


Berriman, A, Historical Metrology

Kelly, P. 1816, Metrology, or and Exposition of Weights and Measures, Chiefly those of Great Britain and France, Paliamentary Reports, London


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


Hallock, William, 1857, Outlines of the evolution of weights and measures and the metric system, the Macmillan company, New York


Fourcaud, Louis de, 1872, Evaluation des poids et mesures anciennement en usage dans la province de Franche-Comté ou au Comté de Bourgogne


Guilhiermoz, P, 1913, De l'équivalence des anciennes mesures. A propos d'une publication récente, Bibliothèque de l'École des chartes Année 1913 74 pp. 267-328


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.


La Condamine, Charle Marie, 1739, Lettre a Madame *** sur l'emeute populaire excitée en la ville de Cuenca au Perou, le 29. d'août 1739. : Contre les Académiciens des sciences, envoyés pour la mesure de la terre, Publication date 1746, Lettre a Madame *** sur l'emeute populaire excitée en la ville de Cuenca au Perou, le 29. d'août 1739. : Contre les Académiciens des sciences, envoyés pour la mesure de la terre : La Condamine, Charles-Marie de, 1701-1774 : Free Download, Borrow, and Streaming : Internet Archive


Méchain, P & Delambre, J-B, 1810, Base du système métrique décimal, ou mesure de l'arc du méridien compris entre les parallèles de Dunkerque et Barcelone: executée en 1792 et années suivantes : suite des Mémoires de l'Institut, Volume 3 ·


Neal, J, Arabic & Egyptian Geodesy, Arabic Measures-3 | John Neal - Academia.edu


Taylor, John, 1864, The Battle of the standards of the Ancient,




Zupko, Ronald Edward, 1985, Dictionary of Weights and Measures for the British Isles

The Middle Ages to the Twentieth Century


Grand vocabulaire français : contenant l'explication de chaque mot dans ses diverses acceptions grammaticales (…), Par Guyot (Joseph Nicolas, M.), Sébastien-Roch-Nicolas Chamfort, Ferdinand Camille Duchemin de la Chesnaye ; Ed. C. Panckoucke, 1768 ; Voir l'article Louveterie.





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