Measurements of the rotational velocity in NGC 3115 show that the random stellar velocities in this elliptical galaxy are of the order of 200 km/sec; other elliptical systems with masses of 1O'° MO will also contain stars with the same velocity dispersion. The random velocities of interstellar atoms and dust particles in equilibrium, however, are less than 20 km/sec. Analysis of electron captures and free-free transitions, taking into account the variation of the g-factors with energy, shows that atoñ~is of appreciable abundance will, in fact, reach such a low-velocity equilibrium within 107_108 years; coffisions between dust particles will similarly reduce dust velocities within 105_106 years. Unless interstellar particles are subject to unknown forces, the velocities of these particles in the more massive elliptical and spherical galaxies must be much less than those of the stars. It follows that any interstellar matter in such stellar systems must be highly concentrated to the center or to the equatorial plane. For a rigorously spherical system the total mass of such matter cannot exceed 4X 1Q~ times the mass of all the stars. In an effiptical system the mass is unrestricted, but if the mass of interstellar matter exceeds that of the stars, then half of such matter must lie within 3 parsecs from the equatorial plane. In any case the light observed from spherical and effiptical systems of large mass must be direct starlight, not diffuse or scattered light. The equatorial layer of interstellar matter in an elliptical galaxy may in theory contain as much or more matter than the stars in the system. The determination by Oort of the stellar density distribution in the elliptical nebula NGC 3115, and in particular the high-luminosity gradient which he found close to the equatorial plane, suggest that a large fraction of the mass of this system may be in the form of dark matter in the equatorial plane. Matter in so dense a layer would presumably be quite different in its physical state from interstellar matter in our own Galaxy and would perhaps condense into faint stars of low random velocity. Further observations are necessary to decide whether a rotating massive disk of dark matter may play an important part in the structure of some effiptical systems