Measuring the quadrant
Obviously it would be impossible to survey the distance between the North Pole and the equator, the whole 90°. No one had ever been to the North Pole. But if one could measure a significant piece of a meridian, the rest could be calculated. The two ends of the line to be measured had to be at sea level, and somewhere near the middle of the pole-to-equator quadrant. As it happens, there is only one such meridian on earth: from Dunkirk to Barcelona, which covers about a tenth of the distance from the pole to the equator. The distance lies almost entirely in France, which did not escape the French, nor indeed such impartial observers as Thomas Jefferson.
The survey was put in the hands of P. F. A. Méchain and J. B. J. Delambre. (See map; caution, 1.05 MB file.) In the summer of 1792, Delambre began working his way south from the coast near Dunkirk, while Méchain started north from the Mediterranean. They would meet at Rodez, 300 miles south of Paris. Méchain's share was shorter, but more difficult, for it crossed the Pyrenees Mountains that separate Spain and France. In September the Republic was declared.
The French revolution was soon in full swing. Within a few months France was at war with Great Britain, Austria, Prussia, Holland and Spain; Louis XVI had been executed, and Parisian mobs were massacring various groups. The Terror was not far off. In such a climate the surveyors were regularly arrested. The flags on their survey poles were whitethe color of the royalists! They were from Paris. All they had going for them was that their storywe are measuring the distance from Dunkirk to Barcelonawas so unbelievable in the midst of war and revolution that no real spy would have used it.
Once when Delambre was seized his captors compelled him to make his explanations in the most republican way, to an audience of volunteers on their way to the war. The troops did not find the trigonometry lecture entertaining. Delambre was saved from the crowd by an official who took him into protective custody, and was eventually released only because the National Convention ordered it.
On August 8, 1793, the National Convention abolished the Academy of Sciences as unrepublican. The Committee of Public Safety, however, remained intent on doing away with the old feudal measures and needed the help of the Academicians to do it, so it persuaded the Convention to create a new, independent temporary commission (Commission temporaire des poids et mesures républicains) with the same members. In November Lavoisier was arrested; the commission asked for his release; the Committee of Public Safety responded by kicking five more members off the commission, including Delambre. Seeing which way the wind blew, the commission then devoted itself to preparing revolutionary denunciations of the old weights and measures. Delambre thought they should kill the whole meridian-measuring project and just accept the provisional meter.
But war requires maps. A military cartographer who was also a Jacobin was put in charge of map-making. Needing trained people, he brought Delambre and Méchain back to Paris. (Méchain had prudently withdrawn to Genoa, narrowly escaping pirates.)
On April 7, 1795 an order establishing the names now in use (meter, liter, gram) also reestablished the commission (except for Lavoisier, who had been guillotined the previous year) and ordered resumption of the survey.
Delambre finished his portion in the fall of 1797. But Méchain had yet to reach Rodez. Sick, with winter coming, he wrote to his colleague, I will sacrifice everything, give up everything, rather than return without completing my part. And so the survey stalled. But Méchain recovered and resumed work; in September 1798 he reached Rodez.
To this point, except for the sides of two triangles, only angles had been measured, the angles of contiguous triangles stretching all the way from Dunkirk to Barcelona. If any side of only one of these triangles were known, the dimensions of all the others could be calculated, and from them the distance along the meridian. While Mechain labored in the south, Delambre measured one of the baselines with a special ruler. It took him 33 days.
On November 28, 1798, the French convened an international meeting of experts from friendly powers and puppet states. One of the meeting's committees consisted of four persons, each of whom independently calculated the length of the meter from the measurements made by Delambre and Méchain (and from certain assumptions about the shape of the earth). Their calculations agreed. The meter was established at 0.144 lignes of the toise de Perou shorter than than the provisional meter.
Today the length of the earth's quadrant can be measured relatively easily by the use of satellites. Such measurements show that the meter is actually about 1/5 of a millimeter shorter than one ten-millionth of the earth's quadrant. The startling thing about this fact is not that the meter does not conform to its original conception, but that two 18th century surveyors should have come so close.
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