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In this paper we have proved that the assertion on the existence of residual motion of the Earth rotation axis within the Earth is a result of erroneous interpretation of the zenith distance (angle) measurements with instruments using as a reference the plumb-in line or artificial horizon. The functional relationship between the plumb-in line deviation and Moon's perigee position has been established for an arbitrary point on the rotating Earth surface. This relationship manifests itself as variations in the gravitational acceleration vector direction and magnitude at the observation point or, in other words, as periodical deviations of the plumb-in line (local vertical). The results of our work show that it is necessary to revise some postulates of metrology, gravimetry, astronomy, geophysics and satellite navigation.