# Shapes and Sizes of the Earth

## and Lengths of the Metre

An assumption that the Earth is a perfect sphere was the only one that could be made by early Earth measurers. When standing on extensive deserts or riverine flood-plains, the land clearly fell away uniformly in all directions from wherever you were. So, with a measured North to South distance, and angles obtained through sun shadows of vertical pillars, or sun sightings, remarkably accurate values of the size of the Earth were made. From such measures performed by earlier civilisations, the Greek Geodesic Foot of 12·15 inches was obtained, 6000 of which equalled a minute on a great circle arc. There were thus 6075 modern feet to the minute, which compares favourably with the 6080 feet in our present geographic mile.

Surveys and reduction of results to determine the distance along the Paris meridian from Pole to Equator were undertaken by triangulation but, despite sophisticated equipment, with scarcely any greater accuracy.
By then the Earth was known to be an oblate spheroid due to inflation of the equatorial region by centrifugal forces, but the resulting ellipticity - (equatorial - polar radii)/equatorial radius was not known with certainty. A choice of distances for a range of ellipticities was submitted in a report of April 1799, and listed in reference 1.

From these, the meridian distance for an ellipticity of 1/334 was selected for division into ten million parts, so the length of the metre became 0·5 130 740 740 Toise, which were six Pieds du Roi or Paris feet. Satellite measures now put the ellipticity at 1/298·4, which means that the metre is 0·2 millimetres shorter than intended.

It has been noted that, almost perversely, the metre does not quite render any important physical constant into a whole number. Earth gravity acceleration is now defined as 9·81 metres per second per second, often rounded up to ten with potentially disastrous consequences. The fundamental constant for the entire Cosmos is the velocity of light, which could be expected to appear as an integral figure in a truly scientific system of measures, instead of the 299 792 458 metres per second which we use. Within the range of uncertainty, a meridian length could have been selected that allowed the usual approximation of 3 x 108 to be exact, if this was known at the time. A metre length of 2·9979/3 = 0.9993 of its established value, ie., 0·7 mm shorter would be required

Alas, such a modification would be in addition to the discrepancy noted earlier. However, the metre is not now claimed to be any more than a distance between the two end faces of a platinum alloy bar held in a vault at Sèvres near Paris, which can now be specified to within the diameter of an atom! Bearing in mind that this length was deduced from an actual survey of only one tenth of the full distance , and over mountainous terrain, the chances of repeating the results accurately would be very small.

The latest, and, proudly, final definition of the metre is the light-metre; the distance travelled by light in 1/299792458 ... seconds, or 0·000 000 003 334 200 4 ... s in its full decimalised glory, since time can now be measured with far greater accuracy than space. Perhaps they have fallen into a pit of their own making, since there is talk now of a nano light-foot. Conversion of metres to feet involves the factor 0·3048, so, multiplying the light-metre time by this helps to simplify the row of figures. Thus a foot is the distance traversed by light in one nano-second, 10-9s. 1·01626 nano-s to be more precise, but closer than the 3·0000 x 10-9 accepted for integrality of the light-metre time.

Nevertheless we are now saddled with a measuring system that has no justification in fact or a physical meaning, whose un-ergonomic units are too small or too large for ordinary use and do not provide a suitable perspective on the world around us so necessary to its understanding.
Moreover, they are embedded in a rigid arithmetical framework that distorts relationships for mathematical, scientific and social requirements into un-natural forms by suppression of the simple proportions by which most things are arranged.

1. H W Chisholm. On the Science of Weighing and Measuring and the Standards of Weights and Measures. Nature. Vol. VIII (1875) pp 386 et seq.
2. M. Danlous Dumesnils. Esprit et Bon Usage du Systeme Metrique, pp 48 - 54. Librairie Polytechnique Beranger, Paris, 1965. English version by Athlone Press.
3. Prof. R D Connor. The Weights and Measures of England, Appendix C pp 334 - 357. H.M.S.O 1978.