Natural Units

Who ever thinks about units of measure?  They are a classic example of things we presume are always there, known and dependable.  (And, in the case of English versus metric measurements, eternally at war.)

However, it was not always so.  In 1788 it was estimated there were 2000 different units in use in France alone.  The pound (livre) of peas you bought in one town wouldn’t weigh or cost the same as the pound you bought in the next town.

The endless confusion that this caused had finally reached the point where the government determined to do something about it.  In the fine old bureaucratic tradition, they formed a committee to look into the problem.  But what a committee!  The membership of the Commission of Weights and Measures included Condorcet, Lavoisier, Coulomb, Laplace, and Legendre.

This august group decided that they would have to start from scratch, as none of the existing units related to any others and, more importantly, none were “natural.”  Their idea was to remove the old “length of the king’s forearm” units and establish a set that would be forever fixed by being based on some natural, repeatable fact or phenomenon, such as basing the temperature scale on the boiling and freezing points of water.  The weight unit, in turn, could be based on the weight the amount of water in a volume of the new unit of length.  And the unit of length…

Hmmm…

This was not so easy.  Finding some natural phenomenon with an invariant physical datum for their new metre (based on the Greek word metron – to measure) turned out to be quite a challenge.

Way back in 1657, Christiaan Huygens invented the pendulum clock by noting that the period of a pendulum was dependent on the pendulum’s length alone, independent of its weight.  He suggested that this fact could be used to establish a “natural” unit of length: since the time unit, the second, was clearly an invariant natural unit (which it is…more or less), then the length of a pendulum with a period of exactly one second would be the perfect natural unit.

Although several governments, including Britain and the United States, had accepted the idea that the pendulum would indeed form the perfect natural unit of length (bringing up the dizzying prospect of everyone using the same units), there were problems.  By 1790, when the committee began to look at the problem, it was pretty well known that gravity varied from place to place on the earth’s surface.  Hence the period of a pendulum varied with location.  Since measuring gravity independent of weight was a nasty problem, creating a natural unit based on the pendulum was a practical non-starter.

The reason that they gave so much thought to the pendulum idea was that the second place proposal was so daunting: base the new standard on the earth itself.  Specifically, on the distance from the north pole to the equator.  The earth was obviously invariant, but the theoretical calculations of that quadrant’s length were widely at variance.  Real, honest-to-goodness empirical data would have to be gathered.  Obviously, no one was going to physically measure the whole distance, but a substantial fraction would have to be arduously surveyed to give the necessary accuracy.  The measured line would have to begin and end at sea level and lie more or less on a meridian.  A line from Dunkirk, passing through Paris (but of course!) and ending at Barcelona fit the bill nicely.

Karma can be a terrible thing.  I have no idea what sins Pierre Méchain and Jean Delambre committed in a previous life, but they must have been doozies.  These two worthy astronomers were tasked with the job of surveying the Dunkirk to Barcelona line, one starting in Dunkirk and the other from Barcelona.

Tough, but doable.  However, timing, they say, is everything.  And these gentlemen had the worst timing imaginable.

The weights and measures problem was officially identified in 1788.  The Commission was established in 1790.  In between, a little thing called the French Revolution had begun.  The Commission was actually started under the signature of Louis XVI but reported to the new National Assembly.  The Assembly voted that the new unit, the metre, would be officially defined as 1 ten-millionth of the distance from the pole to the equator on a meridian passing through Paris.  Then they sent out our two hapless surveyors to measure the line.

It wasn’t until 1792 that the actual survey work began.  By then France was in a turmoil of an ever-spreading revolution, about to declare herself a Republic, and Louis XVI had about a year to live.  On September 5, 1793, the Reign of Terror began.

There were many reasons for the Terror.  Fundamentally, though, the Terror was all about fear: fear of a royalist counter-revolution, fear of attack by foreign kingdoms (a war with Spain actually began in March, 1793), and a pervasive fear of spies, royalist and foreign.

It was not, then, the most propitious time for two highly educated savants from Paris to venture out to the provinces, equipped with their telescopes and white flags (the color of French royalty).  It was not a good time to climb onto landmarks like hills and spires and watchtowers and engage in mysterious observations, note-taking, and calculations.  Above all, it was not a good time to try to sell the completely unbelievable idea that you were trying to create a new unit called the metre by measuring the distance from the pole to the equator.  One can only imagine how the suspicious peasants of rural France reacted to that happy alibi.

What we do know is that poor Méchain and Delambre were followed and harassed.  We know that when they wanted help to cut down trees that blocked their lines of sight, they were met with sullen refusals.  Finally, we know that they were arrested…more than once.  Ironically, it appears as if they were saved by the fact that their explanation was so dumb that no real spy would ever have used it.

The work took six years and even included painstakingly measuring two reference baselines 12 kilometers long using four platinum rulers (the measurements took many weeks).  Finally, in 1798, a meeting of international experts (less the British and other countries with whom France was then at war) gathered to consider the results and calculate the new unit.

All honor to Méchain and Delambre:  The meter they established, considering the technology of the day and the oblateness of the earth’s true meridian (not to mention all those peasants), was astonishing accurate.  Today, the official meter, based on a number of wavelengths of Krypton 86, differs from their’s by just .2mm, or about 8 thousandths of an inch.

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