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OUR METRE IS TOO SHORT: BLAME GRAVITY FOR IT
Abstract
In 1791 the French Academy of Sciences decided to have the size of the Earth measured once more, to a superior accuracy, hoping that perhaps the size of the Earth could be determined to some 10 metre accuracy. This would translate to the error of one metre etalon to be about 1 micrometer. The task of determining the size of the Earth was entrusted to a pair of geodesists/astronomers, P.F.A. M?chain and J.-B.J. Delambre, both highly regarded members of the Academy. Their task was to measure as accurately as possible the length of that part of the meridian that ran through Paris mostly on French territory, between Dunkerque and Barcelona which represents about 1 tenth of the Earth quadrant. Their result had to be expanded about 10-times to the length of the Earth quadrant which meant that the accuracy of the 1000 km long meridian segment was expected to be better than 1 metre, a very high accuracy of 1 part per million (? one ten thousandth of one percent) at the end of 18th century. From their measurements, combined with measurements of the geographical latitudes of Dunkerque fD and Barcelona fB were then used to determine the length of the Earth quadrant but, as a by-product, also the size of the Earth. The experiment had not turned out as well as expected; the length of the metre they determined - the metre that is still used today - is 0.2 mm, too short, i.e., 2 parts in ten thousand, way below the accuracy expected by the Academy. Careful re-evaluation of M?chain and Delambre?s results show that the error in their measurements was really only about 3.5 parts per million. The fact that the real error is about 200-times larger is due to the existence of the Earth gravity field the knowledge of which was almost non-existent, or very rudimentary up until the mid-nineteenth century.
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