  An exact solution of Einstein's field equations for a point mass surrounded
by a static, spherically symmetric fluid of strings is presented. The solution
is singular at the origin. Near the string cloud limit there is a $1/r$
correction to Newton's force law. It is noted that at large distances and small
accelerations, this law coincides with the phenomenological force law invented
by Milgrom in order to explain the flat rotation curves of galaxies without
introducing dark matter. When interpreted in the context of a cosmological
model with a string fluid, the new solution naturally explains why the critical
acceleration of Milgrom is of the same order of magnitude as the Hubble
parameter.
