  The Sagittarius galaxy (Sgr), the closest satellite galaxy of the Milky Way,
has survived for many orbits about the Galaxy. Extant numerical calculations
modeled this galaxy as a system with a centrally-concentrated mass profile,
following the light, and found that it should lose more than one-half of its
mass every 2--4 orbits and be completely disrupted long before now. Apparently
Sgr, and by implication other dSph galaxies, do not have a
centrally-concentrated profile for their dark matter. We develop a model in
which the stars of the Sgr dwarf are embedded in a constant-density dark matter
halo, representing the core of a tidally-limited system, and show that this is
consistent with its survival. We present new photometric and kinematic
observations of Sgr and show these data are consistent with this explanation
for the continued existence of this galaxy. Sgr is being tidally distorted and
is tidally limited, but is not disrupted as yet. The corresponding minimum
total mass is $10^9 \msun$, while the central mass to visual light ratio $\sim
50$ in Solar units.
  Our new photographic photometry allows the detection of main-sequence stars
of Sgr over an area of $22\deg \times 8\deg$. Sgr is prolate, with axis ratios
$\sim$~3:1:1. For an adopted distance of $16 \pm 2 \kpc$ from the Galactic
center on the opposite side of the Galaxy to the Sun, the major axis is $\gta 9
\kpc$ long and is aligned approximately normal to the plane of the Milky Way
Galaxy, roughly following the coordinate line $\ell=5^\circ$.
  The central velocity dispersion of giant stars which are members of Sgr is
$11.4 \pm 0.7 \kms$ and is consistent with being constant over the face of the
galaxy. The gradient in mean line-of-sight velocity with position along the
