On the Distribution of Matter Within Highly Flattened Galaxies.

This paper presents a new mathematical method for deducing, from an arbitrary law of rotation, the equilibrium distribution of mass within a highly flattened, axisymmetric, self-gravitating system, such as a spiral galaxy. An exact and an approximate single integral are developed, each of which gives the required surface mass density explicitly in terms of the rotation function In addition, certain conveniently expressible mass distributions are shown to correspond accurately to some fairly realistic functions describing the rotation velocity. The properties of some of these mathematically exact galaxy models are also discussed and intercompared.