  The gravitational instability of a filamentary molecular cloud in non-ideal
magnetohydrodynamics is investigated. The filament is assumed to be in
hydrostatic equilibrium. We add the effect of ambipolar diffusion to the
filament which is threaded by an initial uniform axial magnetic field along its
axis. We write down the fluid equations in cylindrical coordinates and perform
linear perturbation analysis. We integrate the resultant differential equations
and then derive the numerical dispersion relation. We find that, a more
efficient ambipolar diffusion leads to an enhancement of the growth of the most
unstable mode, and to increase of the fragmentation scale of the filament.
