Having rejected the physical surface of the Earth as a computational surface, one is instinctively drawn to a consideration of a mean sea level surface. This is not surprising, as 70% of the Earth’s surface is ocean. If these oceans were imagined to flow in interconnecting channels throughout the land masses, then, ignoring the effects of friction, tides, wind stress, etc., an equipotential surface, approximately at MSL would be formed. An equipotential surface is one on which the gravitational potential is the same at all points.
It is a level surface and like contours on a map which never cross, equipotential surfaces never intersect, they lie one within another as in Figure Such a surface at MSL is called the ‘geoid’. It is a physical reality and its shape can be measured. Although the gravity potential is everywhere the same the value of gravity is not. The magnitude of the gravity vector at any point is the rate of change of the gravity potential at that point. The surface of the geoid is smoother than the physical surface of the Earth but it still contains many small irregularities which render it unsuitable for the mathematical location of planimetric position. These irregularities are due to mass anomalies throughout the Earth. In spite of this, the geoid remains important to the surveyor as it is the surface to which all terrestrial measurements are related.
As the direction of the gravity vector (termed the ‘vertical’) is everywhere normal to the geoid, it defines the direction of the surveyor’s plumb-bob line. Thus any instrument which is made horizontal by means of a spirit bubble will be referenced to the equipotential surface passing through the instrument. Elevations in Great Britain, as described in Chapter 2, are related to the equipotential surface passing through MSL, as defined at Newlyn, Cornwall. Such elevations or heights are called orthometric heights (H) and are the linear distances measured along the gravity vector from a point on the surface to the equipotential surface used as a reference datum. As such, the geoid is the equipotential surface that best fits MSL.
and the heights in question, referred to as heights above or below MSL. It can be seen from this that orthometric heights are datum dependent. Therefore, elevations related to the Newlyn datum cannot be related to elevations that are relative to other datums established for use in other countries. The global MSL varies from the geoid by as much as 3 m at the poles and the equator, largely because the density of sea water changes with its temperature, and hence it is not possible to have all countries on the same datum.