On the Distribution Ofmass in Galaxies. I. The Large-Scale Structure of Ordinary Spirals with Applications to M 31.

The theory for the analysis of galactic rotation-curves to determine the mass distribution is given for the special case of a highly flattened system. This is done by compressing a sequence of spheroidal homoeoids into a surface distribution of matter. Then the appropriate integral equation can be solved, and the mass distribution can be obtained as an explicit integral of the rotational velocity-curve. The use of analytic expressions to represent the rotation-curves is also discussed, and the results are applied to M31. The determinations of the mass of M31 by Babcock (1939), Wyse and Mayall (1942), Schwarzschild (1954), Lohman (1954), Schmidt (1957), and this investigation can be shown to be mutually consistent with all the adjusted values lying between 3.5 and 4.0 X 1011 M0 for an adopted distance of 600 kpc.