We present several simple geometrical methods for analyzing the Cosmic velocity field using a sample of cataloged galaxies. These methods combined have the merit of allowing us to distinguish an attractor velocity field from a velocity field that does not converge within the confines of the sample, that is which is effectively 'constant'. We do not model the velocity field but rather work directly with the data so that our tests are parameter-free. The key idea is to transform the search for a 'great attractor' into a search for the associated geometric quantity, the Zero Radial Velocity Sphere. We have tested our methods on simulations, and we have applied them to the elliptical galaxy catalog of Faber et al. (1989). We conclude that a dominant attractor region is present, largely extended around a center at galactic coordinates (280 deg, 10 deg) and at a distance of 3800 km/s. Moreover, we conclude that the velocity field contains also a constant component in a direction different from that of the attractor region.