The unit revolution

To find the universal measurement of a metre, French scientists struggled through seven years of trials and tribulations during the French Revolution.

Illustration by Chehehe

Illustration by Chehehe

If I asked you what a metre was, could you tell me? What exactly is it?

My Dad dropped this casually into conversation recently and I had to (blushingly) acknowledge that I didn’t know. And yet our world runs on the implicit agreement and trust that a metre is a metre, and a kilogram is a kilogram. Without this trust in the metric system, manufacturing and trade would be impossible.

Of course, it wasn’t always the case. In 18th century Europe, weights and measures often varied from village to village. During France’s Ancien Régime it’s estimated there were over 250,000 different units of measurements, many using the same names to mean different amounts. Drowning in units, they wanted to implement a system that was methodical, decimalised, and not at the mercy of a ruler's whim. 

Which is how the metre came to be defined: as one ten millionth of a quarter of a meridian — the distance from the equator to a pole.

It may seem completely arbitrary, and in some ways it is. But according to Prof Ken Alder from Northwestern University, who has researched the origin of the metric system, this is because “they wanted to make it the same for everyone, everywhere in the world, so they decided to base it on the size of the Earth.”

Why is a metre, a metre?

The Academy of Science knew they wanted the length of the metre to come out to around the size we have now, similar to an old unit called the aune. An aune was the distance from the tip of your nose to your outstretched fingertips, and was used all over France for measuring cloth. They knew that if they took a quarter of the Earth’s meridian, and divided it by ten million, it would get pretty close to that.

As Prof Alder noted: “It’s a beautiful mix of things that are very exact and very precise, and on some levels completely arbitrary to make it come out to what they wanted.”

But in order to find one ten millionth of a quarter of the Earth’s meridian, they had to physically measure at least part of it.

A metre could then theoretically be determined anywhere. But being that the French Academy of Sciences proposed the idea, they chose to measure the meridian that goes through Paris. The project was expected to take about a year. No-one could have predicted it would take seven.

While the measurement itself was tricky, the slow pace of the project was also due to the strange set of political circumstances at the time. France was a country in turmoil during the French Revolution, meaning the scientists had to deal with being accused of spying, running out of money due to inflation, the Reign of Terror, and being captured by the Spanish.

In some ways this was the only time it could be done. According to Prof Alder, “something that fundamental — such as weights and measures — really only changes at times of revolution and huge political upheaval. It was the French Revolution with its dreams of utopian renewal that allowed people to think that they could take this old system of weights and measures everywhere and get rid of it ... Start over.”

Measuring a meridian

The task fell to two men. Both were French astronomers with experience in surveying. Their job was to use triangulation to measure the distance from Dunkirk to Barcelona. Jean Baptiste Delambre headed north from Paris to Dunkirk, while Pierre Méchain headed south. Delambre had the lion’s share of country to measure — 666 km; with Méchain only surveying about 333 km, albeit this was the uncharted (or at least, unmeasured) territory over the Pyrenees and into Spain.

Triangulation — the science of surveying large distances using trigonometry — had already been around for centuries at this time. The method of triangulation involved “using sighting devices to create a series of imaginary triangles over the surface of the Earth,” which are “connected one to the other in a sort of lattice of triangles,” Prof Alder explained.

 
This map of New England, USA, shows the use of the triangulation method, which determines distances overland using the angles of giant imaginary triangles and the location of known points as a guide. NOAA/Wikimedia Commons (public domain)

This map of New England, USA, shows the use of the triangulation method, which determines distances overland using the angles of giant imaginary triangles and the location of known points as a guide. NOAA/Wikimedia Commons (public domain)

 

Most of the triangles they were using had sides approximately 40-50 km across, as this is about as far as you can accurately see from the church towers and mountaintops they used as triangulation points. Stationed at one of these points, you need to see at least three other points to accurately measure the angles of these imaginary triangles.

“So if you measure nothing but angles, except for one base … by simple geometry you then have the size of that triangle, and therefore the size of the adjacent triangle,” explained Prof Alder. This creates a “method of triangulation that allows you to measure vast distances along a line.”

But they still had to physically measure one of the triangle bases along the ground. They chose a small one: only 10km, which they measured hand-over-hand with a set of four specially made sticks of precise length. End to end for ten kilometres in a straight line. 

This took a month.

And being so concerned with accuracy, they did this twice. Or rather Delambre did this twice as Méchain was busy being imprisoned. Though Delambre didn’t get off scot-free. He was attacked by wild dogs when he measured the second base, which I can imagine is quite distracting when you are painstakingly laying these sticks out in a very, very straight line.  

 

Diagram explaining how a Borda repeating circle is used to measure vast distances using trigonometry. The repeating circle was invented in the 18th century to measure the angles between two points with greater precision than ever before. Author provided.

 

The duo employed the use of a repeating circle (similar to a sextant). New technology for the time, a repeating circle consists of two telescopes on the same axis. Pointing one to each of the triangulation points, it is possible to calculate the angle between them with a high level of precision.

As measuring the whole arc would be next to impossible, Delambre and Méchain needed to find the latitude of both the northern and southernmost points. To do this, they measured the transit of stars across the meridian utilising the repeating circle. While aiming one scope along the horizon, the other points towards a circumpolar star, such as Polaris, which marks the north celestial pole. Measuring the angle between these gives your latitudinal position.

It has to be said that what they were doing wasn’t entirely new. Cassini (the fourth in a familial line of cartographers) had already measured the meridian from London to Paris a few years earlier. And along with data collected by his father and grandfather, Cassini created maps of France that were so accurate, the roads they recorded matched those on satellite pictures 200 years later.

Delambre and Méchain thought this would make their task relatively fast, as most of the meridian had already been measured, so they could use the same triangles, and the same sighting towers and high places (church towers and mountaintops) as the previous expedition. But their plans didn’t allow for the French revolution.

 
A 12 inch repeating circle. Used in geodetic surveying, these instruments allowed Delambre and Méchain to measure the angles of triangulation with greater precision than ever before. WUS National Oceanic and Atmospheric Administration/Wikimedia Commons (public domain)

A 12 inch repeating circle. Used in geodetic surveying, these instruments allowed Delambre and Méchain to measure the angles of triangulation with greater precision than ever before. WUS National Oceanic and Atmospheric Administration/Wikimedia Commons (public domain)

Sharing the burden

 

Delambre, who was measuring the north section, supposedly had the easier job. He was simply re-measuring the section Cassini had worked on, and because this was seasonal work (heaven forbid working in winter), he returned to Paris every winter to do calculations, play at politics and work on other scientific projects. But because the countryside was in upheaval, he was constantly held up at barricades by local militia. The revolutionaries also tore down many of the cathedrals that had been used to sight regions, so he had to change the positions of his triangles.

Méchain, on the other hand, had the southern portion. This was a slightly harder task as not only was it the unmapped portion — Cassini’s map only went to France’s southern border — but the unmapped region was in the Kingdom of Spain. Méchain’s section took him through the Pyrenees all the way to Barcelona, and unlike Delambre, he didn't get the option of returning home for winter. In fact, he didn’t return to Paris for seven years, which is partly why the experiment took so long.

But it wasn’t really his fault. As Prof Alder put it, for Méchain: “Everything that could go wrong, goes wrong.”

And he’s not putting it lightly. In 1793, when war breaks out between Spain and France over the famous execution of Louis XVI, Méchain is stuck in Spain. When he first went to Barcelona he worked very closely with Spanish Enlightenment figures, who supplied his expedition to map the Catalonian section through the Pyrenees. This mountainous terrain had never been surveyed before, and the crests of the Pyrenees served as the official border between the two kingdoms. Both sides wanted the border to be defined more scientifically, so it could be policed and taxed accordingly — not that the Catalonians were particularly fond of either the French or Spanish. This section — while only 80 miles — turned out to be particularly treacherous. Full of bears in summer and wolves in winter, Méchain also narrowly avoided an ambush in his first year. He was then imprisoned by the Spanish for years. When he was finally released, he wasn't allowed to return to France.

But they got there in the end. After seven years of hard-work, the metre was born.

The platinum standard

Once they were done, in 1799 a platinum bar was created to be the official metre, the ‘Mètre des Archives’, which was held in Paris and remained the prototype for 90 years. After a series of more precise standards, the metre is now defined as the distance light travels in a vacuum in 1/299,792,458 of a second, making time the universal unit. Although, it could be said that this figure is still an arbitrary number. "We picked that unit to match the historical metre,” said Prof Alder.

The irony was that even after all their careful measurements, they realised that one of their fundamental assumptions was wrong. The Earth isn’t exactly round. While they knew it was flat at the poles, they didn’t know how much. This showed up in their data as the curve of the meridian they were calculating didn’t change in a regular way. 

What they didn’t realise is that the length of the meridian that runs through Paris, is different than the length of the one that runs through Tokyo or New York. “The whole project was based on the assumption that the meridian of Paris would create a universal measure. But of course the meridian of Paris is unique now, they’re all different. The whole thing becomes arbitrary again,” Prof Alder noted.

It may have taken 200 years, and while there are still some holdouts (Liberia, Myanmar and the US), the metric system governs much of world. “That’s what the French Revolution wanted, they wanted to create global standards. And in that sense, they completely succeeded,” Prof Alder said. And while it may not have been necessary to measure the meridian from Dunkirk to Barcelona, or to carefully lay sticks end-to-end for those 10km sections, it’s a feat of great science. To this day, their measurement was only 0.16mm out for each metre — meaning the distance from pole to equator isn't an even ten million, but rather, 10,002,290 metres.

Edited by Bryonie Scott