No. 1728:
The Meter Stick
Audio

Today, what do you do when your meter sticks?. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

My wife and I like to watch the TV series Star Gate, SG-1. It's about visiting alien worlds through an adjustable wormhole. In one episode, two characters guess a distance on some far planet. One thinks it's six hundred yards -- the other, six hundred meters. The joke, of course, is that meters and yards are almost the same. The difference is only nine percent.

We're told that the English yard is arbitrary, while the metric system is rational and self-consistent. Well, maybe. Let's see how it works.

The meter was defined as one ten-millionth of the distance from either pole to the equator. The gram was the mass of pure water that fills a cube one hundredth of a meter on each side. English and metric time were both defined by Earth's rotation.

The French Revolutionary government put the metric system in place. Then it was rescinded by Napoleon. The French finally readopted it in the mid-nineteenth century.

To use the metric system, you have to know the exact pole-to-equator distance, and historian Ken Alder tells the checkered history of that measurement. The Revolutionary government sent two fine astronomers out to determine the distance. One was Delambre, low-key and easy-going. The other, Méchain, was concentrated and intense. First they determined a precise distance between Orleans, France, and Barcelona, Spain. Then astronomical data revealed what fraction that was of the total from pole-to-equator distance.

By 1799, the effort yielded a standard platinum meter stick. But Méchain had found an inconsistency in his data, and he was terrified. Lavoisier had told him, "You ... are carrying out the most important mission that any man has ever been charged with." Mëchain took that very seriously.

For years, Méchain kept trying to get consistent results. He told only Delambre about the problem. Finally, after Méchain died of Malaria in Valencia, Delambre realized what Méchain had not. Earth is not a perfect sphere. The data would always be flawed. He published the results, but sealed the fact that Méchain had been covering up inconsistencies. By then, the method of least squares had been created to get information from scattered results, and Delambre used it to get a best estimate from Méchain's data.

We now know that it takes ten million, plus another two thousand, of those meters to get from pole to equator. The standard platinum meter is short by about twice the thickness of paper.

Today we define the meter as the distance light travels in a certain small fraction of a second. That doesn't match any pole-to-equator distance, for there is no such consistent distance. Rather, it simply reflects Delambre's and Mëchain's two-century-old flawed measurement. And the standard meter remains as arbitrary as the distance from my nose to my outstretched fingers.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)

Alder, K., The Mis-Measure of All Things. Invention & Technology, Fall 2002, Vol. 18, pp 38-44.

For more on units and dimensions, see Episodes 260 and 1363.

Some units of measurement, from J. H. Lienhard IV and J. H. Lienhard V, A Heat Transfer Textbook, 5th ed., Dover Pubs. Inc., Mineola, NY, 2019. You can easily download the entire book, free of charge, at https://ahtt.mit.edu/.