  We have performed a series of three-dimensional hydrodynamic calculations of
binary coalescence using the smoothed particle hydrodynamics (SPH) method. The
initial conditions are exact polytropic equilibrium configurations with $\gam >
5/3$, on the verge of dynamical instability. We calculate the emission of
gravitational radiation in the quadrupole approximation. The fully nonlinear
development of the instability is followed until a new equilibrium
configuration is reached. We find that the properties of this final
configuration depend sensitively on both the compressibility and mass ratio. An
{\em axisymmetric} merged configuration is always produced when $\gam\lo2.3$.
As a consequence, the emission of gravitational radiation shuts off abruptly
right after the onset of dynamical instability. In contrast, {\em triaxial\/}
merged configurations are obtained when $\gam\go2.3$, and the system continues
to emit gravitational waves after the final coalescence. Systems with mass
ratios $q\ne1$ typically become dynamically unstable before the onset of mass
transfer. Stable mass transfer from one neutron star to another in a close
binary is therefore probably ruled out. The maximum amplitude $h_{max}$ and
peak luminosity $L_{max}$ of the gravitational waves emitted during the final
coalescence are nearly independent of $\gam$, but depend very sensitively on
the mass ratio $q$.
