A source of a quasi--spherical space--time: The case for the M--Q solution

We present a physically reasonable source for an static, axially–symmetric solution to the Einstein equations. Arguments are provided, supporting our belief that the exterior space–time produced by such source, describing a quadrupole correction to the Schwarzschild metric, is particularly suitable (among known solutions of the Weyl family) for discussing the properties of quasi–spherical gravitational fields.