Abstract
Abstract In modern first-order geodetic work it is customary to measure horizontal and vertical angles, spatial distances and astronomic azimuths, latitudes and longitudes. These are projected onto an ellipsoid of reference and are then adjusted to yield positional co-ordinates on that ellipsoid. The results of spirit-levelling, which yield heights above the geoid, are commonly adjusted as a separate entity. Thus the classical method produces two distinct sets of unrelated quantities. A method for rigorously incorporating the results of spirit-levelling into a three-dimensional Cartesian frame of reference is presented. The use of the geoid and of an ellipsoid is avoided.
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