  When the gas of a magnetized filamentary cloud obeys a polytropic equation of
state, gravitational collapse of the cloud is studied using a simplified model.
We concentrate on the radial distribution and restrict ourselves to the purely
toroidal magnetic field. If the axial motions and poloidal magnetic fields are
sufficiently weak, we could reasonably expect our solutions to be a good
approximation. We show that while the filament experiences gravitational
condensation and the density at the center increases, the toroidal flux-to-mass
ratio remains constant. A series of spatial profiles of density, velocity and
magnetic field for several values of the toroidal flux-to-mass ratio and the
polytropic index, is obtained numerically and discussed.
