  Proper motions and radial velocities of luminous infrared stars in the
galactic center have provided strong evidence for a dark mass of 2.5 million
solar masses in the central 0.05 pc of the galaxy. The leading hypothesis for
this mass is a black hole. High angular resolution measurements at radio
wavelengths find a compact radio source, Sagittarius (Sgr) A*, that is either
the faint glow from a small amount of material accreting onto the hole with low
radiative efficiency or a miniature AGN core-jet system.
  We provide in this paper a full report on the first program that has measured
the apparent proper motion of Sgr A* with respect to background extragalactic
reference frame. Our current result is: mu_l,*=[-6.18+/-0.19] mas/y and
mu_b,*=[-0.65+/-0.17] mas/y. The observations were obtained with the NRAO Very
Large Array at 4.9 GHz over sixteen years. The proper motion of Sgr A* provides
an estimate of its mass based on equipartition of kinetic energy between the
hole and the surrounding stars. The measured motion is largest in galactic
longitude. This component of the motion is consistent with the secular parallax
that results from the rotation of the solar system about the center, which is a
global measure of Oort's constants (A-B), with no additional peculiar motion of
Sgr A*. The current uncertainty in Oort's galactic rotation constants limits
the use of this component of the proper motion for a mass inference. In
latitude we find a small, and weakly significant, peculiar motion of Sgr A*,
-19+/-7 km/s after correction for the motion of the solar system with respect
to the local standard of rest.
