  We examine the linear stability of an isothermal filamentary cloud permeated
by a perpendicular magnetic field. Our model cloud is assumed to be supported
by gas pressure against the self-gravity in the unperturbed state. For
simplicity, the density distribution is assumed to be symmetric around the
axis. Also for simplicity, the initial magnetic field is assumed to be uniform
and turbulence is not taken into account. The perturbation equation is
formulated to be an eigenvalue problem. The growth rate is obtained as a
function of the wavenumber for fragmentation along the axis and the magnetic
field strength. The growth rate depends critically on the outer boundary. If
the displacement vanishes in the region very far from the cloud axis (fixed
boundary), cloud fragmentation is suppressed by a moderate magnetic field,
which means the plasma beta is below 1.67 on the cloud axis. If the
displacement is constant along the magnetic field in the region very far from
the cloud, the cloud is unstable even when the magnetic field is infinitely
strong. The cloud is deformed by circulation in the plane perpendicular to the
magnetic field. The unstable mode is not likely to induce dynamical collapse,
since it is excited even when the whole cloud is magnetically subcritical. For
both the boundary conditions the magnetic field increases the wavelength of the
most unstable mode. We find that the magnetic force suppresses compression
perpendicular to the magnetic field especially in the region of low density.
