Sur l'histoire de la notion du potentiel

Summary Huygens undoubtedly used the notion of the potential in his well-known work “Discours de la cause de la pesanteur” (Leyden, 1690), investigating the Earth's figure by means of Newton's famous canals. Maupertuis used this notion in a similar work published in London in 1733. The notion of potential was used by Clairaut in the “Théorie de la figure de la Terre” (Paris, 1743) and by D'Alembert in many articles (1752, 1761, 1768, 1773, 1780). Euler used it also in many of his works since 1736. These examples of application of the potential were not noticed because of peculiarities of terminology.      

Constant part of the Earth tides in the Earth figure theory

Journal of Geodesy - It is recommended not to reduce measured geodetic values by the constant part of the tidal influence. For this case there is shown an exact solution of the tasks of the theory...     

On The Determination Of The Earth's Model – The Mean Equipotential Surface

The sea surface cannot be used as reference for Major Vertical Datum definition because its deviations from the ideal equipotential surface are very large compared to rms in the observed quantities. The quasigeoid is not quite suitable as the surface representing the most accurate Earth's model without some additional conditions, because it depends on the reference field. The normal Earth's model represented by the rotational level ellipsoid can be defined by the geocentric gravitational constant, the difference in the principal Earth's inertia moments, by the angular velocity of the Earth's rotation and by the semimajor axis or by the potential (U ₀ ) on the surface of the level ellipsoid. After determining the geopotential at the gauge stations defining Vertical Datums, gravity anomalies and heights should be transformed into the unique vertical system (Major Vertical Datum). This makes it possible to apply Brovar's (1995) idea of determining the reference ellipsoid by minimizing the integral, introduced by Riemann as the Dirichlet principle, to reach a minimum rms anomalous gravity field. Since the semimajor axis depends on tidal effects, potential U ₀ should be adopted as the fourth primary fundamental geodetic constant. The equipotential surface, the actual geopotential of which is equal to U ₀ , can be adopted as reference for realizing the Major Vertical Datum.