CompuServe Messages

Here begineth the lesson on datums: In the beginning was the *topography*, which was up and down all over the place, and not describable mathematically. And the topography was without form and mightily vexatious for surveyors, because it interfered with their measurements. And lo! the surveyors invented the *geoid*. The geoid took the form of the earth from which all the topography had been removed. And the *geoid* was an imaginary equipotential surface corresponding to the location of mean sea level if the earth was covered with a frictionless, limitless, tideless sea. And the surveyors called the geoid *geoid* because this word means *earth-shaped*. And the surveyors enlisted the assistance of the tribe of the rockhounds, to realise the dream of the geoid by chipping little bits of the topography away until, in the fullness of time, the geoid will become a real surface. And the shape of the geoid is like unto a pear, if one stretches the imagination a bit. But the surveyors found that lo! although this surface contained fewer lumps than the topography, it was still a bitch to calculate on. And it came to pass that eventually the great prophets at the DMA constructed a gravitational model of the geoid with 18,000 coefficients which was a representation of the geoid of that type known as *pretty fair*. This model was constructed to feed the appetite of the arcane beast known as SDI, but the great prophet in the White House forbade the release to the surveyors of more than the first few coefficients in this series, fearful as he was that any other prophet may be able to pinpoint the true location of the White House to a few metres and thus destroy his abode with accurately targeted fire and brimstone. Lacking enough of the wisdom of IBM, Amdahl and Cray, the surveyors were mightily vexed to find that a model containing even the first few coefficients despatched unto the people by the miserly and secretive prophets of the DMA was still a bitch to calculate, and so returned to a surface used for computational purposes by many previous generations of surveyors. And the name of this surface was *ellipsoid* also known unto certain brethren as *spheroid*, and many of the sons and daughters of the surveyors used the two terms interchangeably without perceptible problems. And the ellipsoid was without form and void, until some smart cookie created it by rotating the form of an ellipse about it's minor axis. Oh joy! This surface was found to be easy to calculate with in the grade of *dead cinch*. And the ellipsoid was completely defined by an axis of the type called *semi-major*, and a value called *eccentricity*. And the distance between two points on the ellipsoid was found to be calculatable using only the most basic spherical trigonometry of doubly curved surfaces. And the surveyors surveyed it, and were glad, for the mysteries of div, grad and curl, not to mention the calculus of tensors, were well beyond the capacity of most of them, for otherwise they would have been of the tribe of astrophysicists. And the joy of the surveyors, at first as sweet as the good wines of Lebanon, turned to dust in their mouths when they realised that the shape of this ellipsoid bore only passing resemblance to the shape of the geoid, and it's facility of calculation was therefore of the type known as *effectively useless*. And so the tribe of the surveyors fragmented across the globe. Prophets arose in each location. And each prophet measured the shape of the earth in his own location and derived an ellipsoid which closely modelled the shape of the geoid around the location of that prophet. And the sizes of these ellipsoids, and their eccentricities, were all different. And none of the ellipsoids had the same location in space, for all were designed to fit the geoid at a particular location and nowhere else. ….. To be continued!!! Rob