Setting the standard for a new unit of measurement can be tedious and even hazardous

A small essay for your amusement: I am reading a book about how some of today’s most fundamental units of measurement were defined and calibrated.

The more precision one requires, the harder a measurement becomes (this was an known adagium even before Heisenberg): in 1790 a new length unit was proposed: the meter. It would consist of 1/1000 of 1/10,000 of the distance from the equator to the poles. It only remained to measure that distance as precise as possible.

The French took the lead here, and thus the requirements for which meridian to use as a base line was stated as: “the one with the longest stretch over land, being well charted territory, which ends at both sides at sea level”. By sheer coincidence this happened to be in France.

France.



So what was needed was to measure the total distance between both ends (near Dunkirk and Barcelona) by triangulation, and measure the length of one side of one of those triangles  in terms of a provisional meter (using a platinum bar, compensating for temperature at each position, and for the curvature of the road).

Two expeditions, one headed by Delambre, the other by Méchain, were formed to do the triangulation first, then measure the exact latitude of the end-points. They were to report findings within a year. I would take six years to arrive at acceptable results.

The triangulation itself took several months, as many mountains lay on the path. One of numerous perils encountered was an angry mob in Paris. People discovered the esoteric instruments the team carried in their baggage, and suspicion arose these might be spying tools, to aid reactionary forces opposing the Revolution. An angry mob gathered and demanded an explanation. That explanation would better not meet deaf ears, because at that time a mob, when in doubt, tended to regard the guillotine the safer option. Fortunately the team leader was an experienced teacher, so he knew how to balance between saying too little, and saying too much (and thus lose most of the audience), but the ‘trial’ still lasted for many hours.

After the triangulation was done all that remained was getting the exact positioning of the end points. An new device, called the Borda Circle (with two telescopes) made it possible to determine the angle between two stars with twice as much precision as before. All that remained was to repeat the measurement 10,000 times to reduce the human reading error by averaging the outcomes.

Unfortunately the expedition leader suffered an almost fatal accident and recovery took months, in which the expedition could not travel, so the team settled down in a place just 2 (provisional) kilometers away from the end-point of the meridian: biding their time they took it upon themselves to repeat the initial measurements and do another batch of 10,000. To their dismay the two averages diverged noticeably. They knew of the imperfect curvature of the earth, (Earth radius to the equator is 6400 km, 64 km more than the radius at the poles) [3]. What they didn’t know yet (and which brought them to despair) was that every meridian has a different length, as the earth’s curvature isn’t even uniform for every place at the same latitude. It took years to get this sorted out.


Tien verdwenen dagen

This story came from an excellent book by Michiel van Straten, called “Tien verdwenen dagen” (“Ten lost days”, alas in Dutch only), about humanities’ struggle to define good units of measurement.

There is a story about the difficult transition from Julian to Gregorian calendar (which has still not been completed as this Wikipedia chart shows);

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a story about how before the invention of time zones not only every town had their own unique time, but with the emergence of railroads different railroad companies used a different time for the same town (and we think planning a trip with stop-overs today is time consuming), a story about Napoleons new metric calendar, and how the Catholic Church made him retract it after several years (10-day weeks with only one day off didn’t help either), stories about long debates to establish which meridian to make the Prime Meridian, and where to draw the international date line, and many more.

 

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