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## About the choice of the meridian

As we have remarked in Section 4, the Rapport sur le choix d'une unité de mesure[2] shows a certain degree of naïveness. For example, let us take the preference of the meridian over the equator, justified in terms of ease of measurement and of universality with respect to all nations of Earth.

Let us start from the latter point, that we called `democratic'. The sentence ``it is possible to state that every people belongs to one of the Earth's meridian, while only a group of people live along the equator'' is not more than a slogan. It is self-evident that every point on the Earth surface belongs to a meridian. A different question is to measure it in order to reproduce the meter with the accuracy required to exchange the results of precise measurements in different places of the globe. Even assuming that every people had the proper technology to perform the measurements, the country should be extended enough along the longitude in order the required measurements to be performed. Moreover, since Earth is flattened at the poles, at least two measurements of arc of meridian at two distant latitudes are needed, in order to infer the Earth ellipticity. Therefore, also the sentence ``The operations that are necessary to establish the latter could be carried out only in countries that are too far from ours'', referred to the equator, applies also to the meridian, with even a complication for the latter: while the determination of the equator requires only one campaign of triangulation, because (apart from small mass dishomogeneity) the circularity of the equator comes from symmetry arguments, determining the meridian requires necessarily, as it had already been done in the middle of the 18th century, several campaigns at different latitudes.

Frankly, we find that naïveness acquires an unintentional humorous vein at page 8 of the document [2], when, after having claimed a few pages earlier that the choice of the meridian is `democratic', the Paris meridian going from Dunkerque to Barcelona is presented as almost unique to perform the proposed measurement:37

One cannot find neither in Europe nor in any other part of the world, unless to measure a much wider angle, a portion of meridian that satisfies at the same time the condition to have the extreme points at sea level, and that of crossing the forty-fifth parallel, if one does not take the line that we propose, or as well another more western meridian from the French coast, until the Spanish one. (Ref. [2], p. 8)
(Their precise Swiss neighbors would have no chance to reproduce the meter standard in their country!) As a matter of fact, the choice of the meridian appeared to other countries, especially Great Britain and USA, as a imposition of the Paris meridian. All previous attempts of cooperation towards an international standard of length were frustrated, and still now we suffer of communication problems.38

Let us come now to the concept of `naturalness', about which we have already expressed some caveat above. Once chosen Earth as reference object upon which the scale of lengths has to be based, which of its parameters is the most natural? For simplicity, let us consider a sphere. To a mathematician or a physicist the natural parameter of the sphere is the radius (that was basically the reason of Cassini's proposal mentioned in section 4). However, for a engineer the natural parameter is the diameter, because that is what he directly measures with a gauge in the workshop. The diameter is also the convenient parameter for a sphere seen from very far (as it could be a planet). But if we take a soccer ball, neither of the above two parameters is `natural'. It is not by chance that the FIFA laws establish the ball size by its circumference [``of not more than 70 cm (28 inches) and not less than 68 cm (27 inches)''[45]], for it can be easily checked with a tape-measure.

The situation is a bit more complicated for a sphere as large as the Earth, and on which we live. It is a matter of fact that at that time it was practically impossible to make immediate measurements of any of the lengths related to the dimensions of Earth. One could only perform local measurements and extend the results to the quantity of interest, assuming a geometrical model of Earth. However, once a geometrical model is defined, it becomes of practical irrelevance which parameter is considered as unit, that could be the meridian, the equator or the distance between poles and center of Earth.39

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Giulio D'Agostini 2005-01-25