Saturday, January 22, 2011

The Measure of All Things

Two hundred years ago, the only standard measure was time, with the day divided into two 12 hour halves, the hours into 60 minutes each and the minutes into 60 seconds each. The circle was also divided into 360 degrees with each degree further divided into 60 minutes and each minute into 60 seconds. Beyond that, every country, county, town and village seemed to have its own units of length, weight and volume. The units may even have had the same names in places but the actual amounts varied. This worked well in local markets but made trade very difficult.

In 1792, two Frenchmen, Delambre and Mechain set out from Paris to measure with extreme accurately the length of the meridian which ran from Dunkirk to Barcelona through Paris. The French Academy of Science, fired by revolutionary zeal intended to create the perfect system of measurements based on the earth itself which all people of all nations would adopt. The meter was to be exactly one 10 millionth of the distance from the North Pole to the Equator. Units of length, volume and weight would be all linked together related to the meter. The decimal system and Latin suffixes completed the new Metric system.

While the meridian had been measured some 40 or 50 years before, a new and very accurate instrument, the Borda repeating circle, meant it could be measured much more exactly. It took them seven years. The difficulties of actually doing the survey in the middle of the French Revolution, the Reign of Terror, wars with Spain, Prussia and England and the rise of Napoleon merely compounded the physical difficulties. Prior to the age of satellites, distances were measured by triangulation. If the three angles of a triangle are known and the length of one side, the other two sides can be calculated. So a series of triangles stretching the length of the distance to be measured, connected by common sides can be calculated by measuring one side of one triangle.

Delambre was a pragmatist and finished his half of the meridian first. Mechain was a perfectionist and it eventually killed him. He started in Barcelona, Spain in late 1792 and was to work his way north. He got into the Pyrenees and was stopped by the war, ending up back in Barcelona for the winter of 1793-4. Not knowing to leave well enough alone, he redid one of his measurements and found it to be very different from the one before (simplified version). He buried the error and it haunted him. He felt he had failed. His depression slowed his work and he almost did not complete it. He finally went back to Barcelona to try to find the error, caught malaria and died.

Delambre had to sort out Mechain’s papers which were a deliberate mess. Mechain had suppressed and doctored a lot of data but he had done so to make himself look more precise and was very careful to keep his doctored data from affecting the final calculations. Delambre sorted it out, recalculated everything and published the data. He did not expose Mechain’s deliberate cover ups and called the Barcelona error a discovery.

The work of these two men while not very relevant to the precision of the metric system, as it turned out, did advance the cause of science and mathematics. Error was found to be a normal part of any measurements and could be split into errors in precision and accuracy. Precision is an indication of the repeatability of results while accuracy is how close the results are to the “right” answer. The statistical method of “Least Squares” was developed using their data.

The promo on the cover and the other reviews I have read make a big deal of Mechain’s error, which may have contributed to the meter being 0.2mm short. (The satellite confirmed distance is actually 10,002,290 meters). The author, and indeed Delambre, realized the error was irrelevant as setting the meter at one 10 millionth of the quarter was arbitrary to start with. What was critical was that the length be standardized and the system adopted.

The metric system replace the systems of the Ancien Regimes country by country in the 19th and 20th centuries in most cases in times of political and social upset – war, revolution, independence – when the government could forcibly “ram it down the throats” of the people. France herself where metric was invented, didn’t officially adopt it till the middle of the 19th century and for decades after the old systems were still in use in the towns and villages. Britain and several of the other Commonwealth countries adopted the metric system last.

My take-away lesson from this book is that while Canada adopted the metric system 40 years ago, it may be another 60 years or more, if ever, before it totally supplants the British Imperial System in all things. Systems of weights and measures are not just impersonal methods of uniform description. They are part of our very culture.

In a footnote, as it were, I will add that in 1884, along with the 24 hour clock and standard time zones, the brain-children of Canadian Sir Sandford Fleming, the meridian of 0º longitude was established as running through Greenwich England, leaving the Paris meridian some 2º20’ to the east.


  1. Very educational and interesting. People take standardized weights, measures and such systems for granted. We'd be sunk without them.

    As for Canadians (and us yanks, too) soldiering on despite all the calls and rational arguments for going metric, I dunno. I keep thinking, give 'em an inch and they'll take a kilometer. ;)

  2. And ever since, we've been trying to measure up to an inaccurate measure.

    There is no justice!

  3. All construction, carpentry and woodworking continues in inches (2x4, anyone?). At least in the west, the roads are surveyed in miles and land in sections (640 acres). You can drive on the highway in kilometers but as soon as you leave it for country roads, it is miles. Grain is measured in bushels (volume) for storage but sold in tonnes. Because of our trade with USA (and because cattle people are the slowest to adopt anything new) cattle are still bought and sold in pounds.
    Units of measure are built into our way of life so solidly that change does not come easy.

  4. I have an older relative where the only good thing he has to say about St. Ronnie of Reagan is that he kept us from converting to the metric system. I on the other hand think it's stupid to have to deal with two different measuring systems.

    None of the measuring systems are totally accurate, they are all based on someone saying this is a foot, yard, or meter and then standardizing that measurement.

  5. I have no problem with thinking in inches or in centimemters. Either think fractionally or in decimals. Of course it would make sense for everyone to be on the same page. But where would be the fun in that?

  6. Kulkuri, Systems of measurement are arbitrary. As you said "someone said" this is a foot and this is a meter. The one 10 millionth business was just to lend some kind of authority to the arbitrary length. The key is that it (foot or meter) is ALWAYS the same length and that EVERYONE uses the same system.
    Mike, I can switch back and forth to a point in most things. Especially working internationally in agriculture, I have to switch constantly to adapt North American information for clients in other countries.


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