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The Meter: The Measure of a Man

Wednesday, July 09, 2014 - 01:34 PM

About six and a half billion people use the metric system every single day.  That's more than the citizens of any single nation, the followers of any single religion or the speakers of any single language.  Sociologist Hector Vera has called the metric system “more popular than Jesus.”

In our “≤ kg” episode, we told a bit of its epic history.  How it dates back to revolutionary-era France, where over 250,000 measures were in regular use. How the hungry and angry French peasants demanded a unified set of weights and measures. And how the revolutionary government wanted their system to be natural and timeless, and thus based it on the most fundamental physical object they could think of: the earth.  As Napoleon later said, “It was not enough for them to make the forty million people [of France] happy, they wanted to sign up the whole universe.” 

No historian has told this story better than Ken Alder.

Free Press/Simon and Schuster

Alder’s book The Measure of All Things zooms in on the two astronomers who were enlisted to survey the world.  We couldn't squeeze their story into our episode, but it’s a doozy — so we figured we'd give you a small taste of it here.

As Alder explains, the duo set out in opposite directions from Paris - in tricked-out carriages, carrying the most advanced scientific equipment of their day - hoping to measure the fraction of the meridian between Dunkerque, France and Barcelona, Spain.  

(This map shows the triangulation of the Paris meridian during the expedition of 1792‒98. Map by Chris Robinson and Ken Alder.)

From their measurements, the French Academy of Sciences could extrapolate an exceedingly precise length: one ten-millionth of the distance between the equator and the north pole.  They’d consecrate this distance as the meter.

For all the sophisticated surveying tactics and all the noble utopian idealism, the expedition - conducted in a time of revolution and war - turned out to be a bit of a farce.  As the men climbed church steeples and peered through their instruments, angry mobs fingered them as spies. They were hauled before local officials, only to present papers signed by the now-deposed King.  They were repeatedly detained. “At every turn,” Alder writes, “they encountered suspicion and obstruction.”

Of the two, the South-going astronomer — a short and obsessive man named Pierre-François-André Méchain — fared worse.  

Pierre Mechain

Once he arrived in Barcelona, Méchain took 10,000 readings to get the precise latitude, and mailed it off to Paris. Before he had a chance to return to France, however, he suffered a freak accident, taking a blow to the chest so hard it left him in a coma for three days. In another twist, war broke out between France and Spain, and, as an enemy national, the convalescing Méchain was under house arrest.  In his hotel room jail cell, with nothing better to do, Méchain re-did the 10,000 latitude readings.  

He found, to his horror, a discrepancy. The reading didn’t match the prior reading he had already dispatched to Paris.   Admittedly, the error was slight - approximately the size of two football fields over the entire length of France - yet it was enough to make a difference in the standard meter bar that was already being forged back in Paris.  Méchain decided to keep the second set of calculations a secret.  Alder quotes from his letters at length, allowing us to see how guilty Méchain felt after being showered with his colleagues' accolades "which they presumed I deserved." 

A few years later, Méchain returned to Spain to try once more to straighten out his erroneous calculations.  Again, forces beyond his control seemed to conspire against him.  War began anew between Spain and France. Yellow Fever epidemics broke out up and down the coast.  A fog settled, preventing him from making any observations. He contracted malaria in Valencia, writing to his friend:

“Though I do not seek death, I am far from fearing it … Never, no never … have I found myself in a situation so hopeless, so terrifying, so wrenching. This dreadful commission, whose success appears so far off and so improbable, will more than likely be the end of me.”

Soon after, as a result of his attempt to correct himself, Méchain died. 

As a result of Méchain’s error - compounded by errors made in extrapolation back in Paris - the platinum meter bar is not one ten-millionth of the distance between the equator and the north pole.  It’s off by about 0.2mm, the width of two sheets of paper.  Crazy, right?!

By the time the world discovered this tiny error, it was too late. Everybody was already using the measures that were slightly "off."  By the Metric Convention of 1875, the European powers that be decided that it was too difficult and too costly to recalibrate all the world’s metric measures, and that instead, they’d just reset the standard from “one ten-millionth of the distance from the equator to the north pole” to “the length of this metal bar, right here.”  A new platinum meter bar was fashioned - the precise length of the old one - to be the true standard bearer.  In this new bar, Méchain’s error was immortalized. It remains built in to the meter (and, as a result, the kilogram) to this very day.

Alder’s history renders a seemingly objective and rational system of measure into a human and flawed one.  But, still, we didn’t quite know what to make of it.  What are the implications for measurement in general? Is it impossible to draw a standard from the physical world? Is the metric system one giant conspiracy?!

Alder's take on all this surprised us. 

“I’ll say this,” he told us. “measurement conventions are conventions. They’re what we all agree to … They’re agreements that we strike as an individual culture, as a global society. And the metric system is an incredibly successful global agreement of what measurement can and should be.  It has, in a sense, made it possible to communicate over the whole world.”

In the end, Méchain’s error didn’t matter one lick. The only thing that did matter was that we all agreed to use the meter, even the USA who was one of the signatories way back in 1875.  A standard is a standard is a standard. As long as we all agree to it, it’ll continue to help us - however quietly - communicate with one another, across borders, across cultures, across ages. And that seems like something worth agreeing to. 


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Comments [6]

West Slope Charlie from W Sierra-Cascade E Nevada

Isn't the earth in constant and dynamic flux as it hurtles it's molten core at unimaginable speed in many different tidal directions at once? If so, the meter would be only correct at the exact moment it was calculated (even if that were exactly the distance, it would change within moments)? As we near Apogee with the sun, moon, other planets; as we speed up and slow down as we cross the solar plane does not our surface 'bend' and 'bow' to accommodate these tidal forces, forcing towns apart my mm.'s then drawing them back together by mm.'s? Raising them by mm and smashing them back down by mm.s? The seas and oceans are not the only things which are affected by tidal forces. Had those engineers who designed the Mars lander that hit too fast had quick rather than methodical minds, they could have blamed the accumulation of these errors by extrapolating them over vast distances. The mere fact that one team worked in say Florida which being of sand and water would flux more than say the Rocky Mountains, at that precise moment of calculation (I presume they calculate at STP) -- how were they to know that dispute their apparent height, Florida was closer to Mars at that moment than barometric pressure and temperature would lead them to believe. It wasn't about calculating in SAE vs Metric units, it was either Florida was closer to mars, or global warming had expanded the rocks of the Rocky Mountains, causing them too, to be closer, the combined errors adding up mile after hundred million mile, until SMASH(!!!) goes the lander. But being Engineers, they marked it all up to SAE v Metrics and someone lost their job, when no job had to be lost, all they had to do was cover it up, say OH MY! and next time do it right! After all if Florida AND the Rocky Mountains were closer than calculated, the space craft WOULD have hit with FAR more velocity than calculated for. In fact, wouldn't having more carbon dioxide in the air throw off ALL STP calculations??? There would be FAR more carbon in the air than nitrogen, making air heavier, and ALL barometric readings just plain wrong. This might not have mattered when using slip-sticks, but with modern day computers with 100% more calculating power built in to the boot-up system would never have noticed this difference. Now MY question is: will we all be crushed by our own atmosphere before anything NEAR global warming has done many of you in? (Me? I plan to ride out this entire confusion in my GOOD mine tunnel(Get Out Of Dodge)where we are virtually immune from the crushing atmospheric pressure felt on the surface of this planet. We plan on digging a hole closer to the center of the earth, where gravity will negate the pressure of the atmosphere along with the extra weight being suspended in the air.)

Jul. 24 2014 03:42 PM
Susan from Maryland

Re: Bob's comment.

Since the circumference of the earth as measured through the poles is four times the distance between a pole and the equator (assuming a sufficiently symmetric earth), 1/10,000,000 the distance from a pole to an equator = 1/40.000,000 the circumference of the earth as measured through the poles. So, I think you've answered your own question: if your source is accurate, the standard meter is too short.

Jul. 23 2014 02:28 AM
christineU from Berkeley, CA

I can't read the story because I'm too hung up on Méchain's fantastic embroidered coat. I just Googled the hell out of his name to find it, and German Wikipedia states it was a posthumous portrait taken from an engraving. Now I'm left to wonder forever whether he really wore that coat, or if it was an artistic addition.

Jul. 22 2014 06:34 PM
cuvtixo from Boston

An interesting addition to the story of the meter is that the 17th General Conference on Weights and Measures in 1983 re-defined the meter as that distance that makes the speed of light in a vacuum equal to exactly 299,792,458 meters per second. Another reason Méchain’s error doesn't matter anymore.
I've read that the error was made in correcting for the flattening caused by the Earth's rotation. That seems like a pretty significant detail to leave out of the story. Is this wrong?

Jul. 20 2014 02:22 PM
BOB from Wichita

Wonderful article. However, I am having trouble finding the time period when these events occurred. Since Machain died in 1804, I suspect these events occurred around the turn of the 19th century. Also, is the standard meter 0.2 mm too long or too short to be 1/10,000,000 the distance between a pole and the equator? Perhaps that was in the article and I missed it. I was able to find that the standard meter would need to be lengthened by 0.196575 mm in order to be exactly 1/40,000,000 the circumference of the earth (the "geoid") as measured through the poles.

Jul. 20 2014 07:56 AM
Duane from Boulder CO

For what it's worth, Latif is utterly precise in his assessment of Alder's book. It is a great story and a great read.

Jul. 09 2014 10:19 PM

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