  Modified Newtonian dynamics (Mond) has had considerable success in describing
motions in galaxies. It uses a single force which falls off inversely with the
distance at large distances and inversely with the square of the distance at
smaller distances. We present an alternative theory with two forces, one the
traditional Newtonian inverse-square, and the other that falls off inversely
with distance at large distances. This obvious possibility has been avoided
because of fear that the second force would be incompatible with observed
planetary motions. However, the non-linear field equation that governs this
force is shown to reduce its strength near stars. The theory is derived from a
Lagrangian density with two scalar potentials. It is non-relativistic, but
nevertheless agrees with the classical tests of relativistic gravity and can be
used to calculate the bending of light in gravitational fields. Possible
applications to interactions in galactic clusters and to anomalous planetary
motions are noted.
