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\begin{document}
\author{J.M. Ferr\'andiz\thanks{Escuela Polit\'ecnica Superior, Universidad
de Alicante, E-03080 Alicante, Spain}, Y. Barkin\footnotemark[1]
and J. Getino\thanks{Grupo de Mec\'anica Celeste, Departamento de
Matem\'atica Aplicada Fundamental,
Facultad de Ciencias, Universidad de Valladolid, E-47005 Valladolid, Spain.}}
\title{On the tidal variation of the inner potential of the Earth mantle}
\maketitle
\begin{abstract}
In this paper the temporal variations of the mantle gravitational potential
for its internal domain are defined. We take into account only the
deformation of the mantle caused by tidal influence of the Moon and the Sun.
The procedure of Takeuchi (1950) for the tidal deformation of the mantle is
used in our investigation. The analytical expressions for tidal variations
of the coefficients of the internal mantle potential are obtained in
trigonometrical form as conditionally periodic functions using the method
developed by Ferr\'andiz and Getino method (1993) to study the temporal
variations of the external Earth's gravitational field. Numerical
calculations and tables which show the periodic variations of the
coefficients of the internal mantle potential have been obtained for two
rheological Earth models, 1066A and 1066B of Gilbert and Dziewonski
(1975). The results of this paper are very important for the study of the
celestial--mechanical aspects of the motion of the internal and external
cores of the Earth.
\end{abstract}
\begin{thebibliography}{9}
\bibitem{} Ferr\'andiz, J.M. and Getino, J.: 1993, {\it Celes. Mech.},
{\bf 57}, 279--292.
\bibitem{} Gilbert, F. and Dziewonski, A.M.: 1975, {\it Phil. Trans. R. Soc.},
{\bf 278A}, 187--269.
\bibitem{} Takeuchi, H.: 1950, {\it Trans. Am. Geophys. Union}, {\bf 31},
651--689.
\end{thebibliography}
\end{document}
