LOCAL ATTRACTIONS AND THEIR INFLUENCE ON THE DETERMINATION OF HEIGHTS ABOVE MEAN SEA LEVEL

Abstract

The Mythical Spheroid.—The preceding article dealt with the fact that the spheroid of reference is a myth and that, even if it were not, we could not get hold of it at any given place. In order to apply corrections to observed quantities or, more generally, to operate upon them mathematically, we must make some assumption such as that of the spheroidal level surface. Probably a lot of harm has been done by attaching the notion of too concrete a thing to the spheroid. Disputes and misconceptions have arisen. People talk of“putting the spheroid down at a point” and imagine that the obedient thing is still at their feet when they get to another point, perhaps distant, in their system of triangulation or what not. Actually the spheroid may be disobedient not only as regards the direction of the vertical but also because it is above their heads or below their feet. What happens is that at each point afresh the computer treats the observations as if they were made there on the surface of a spheroid. In the same way, but travelling still farther along the road of hypothesis, he may treat observations for astronomical positions as if the compensation for visible elevations were uniformly distributed as a deficiency of density down to a depth of 122·2 kilometres. That was the depth which happened to give the smallest sum of squares of residuals in a certain restricted area, but nobody imagines that it corresponds with a physical reality, especially the ·2! It was a convenient mathematical instrument which, once the theory was to be given a trial, had to be fashioned out of some assumption or another. All this has little to do with geodetic levelling but is meant to try to banish the spheroid out of the reader's mind or at least to the back of his mind. In what follows we shall be compelled to make a certain amount of use of the family of spheroids but always with the above strictures in view.