  (shortened for babbage) We describe (1) a new test for dark matter and
alternate theories of gravitation based on the relative geometries of the X-ray
and optical surface brightness distributions and an assumed form for the
potential of the optical light, (2) a technique to measure the shapes of the
total gravitating matter and dark matter of an ellipsoidal system which is
insensitive to the precise value of the temperature of the gas and to modest
temperature gradients, and (3) a method to determine the ratio of dark mass to
stellar mass that is dependent on the functional forms for the visible star,
gas and dark matter distributions, but independent of the distance to the
galaxy or the gas temperature. We apply these techniques to X-ray data from the
ROSAT Position Sensitive Proportional Counter (PSPC) of the optically-flattened
elliptical galaxy NGC 720. The X-ray isophotes are significantly elongated,
$\epsilon = 0.20 - 0.30$ (90% confidence) for semi-major axis $a\sim
100\arcsec$. The major axes of the optical and X-ray isophotes are misaligned
by $\sim 30\deg \pm 15\deg$ (90% confidence). We conclude that matter
distributed like the optical light cannot produce the observed ellipticities of
the X-ray isophotes independent of the gas pressure, the gas temperature, and
the value of the stellar mass.
