Filaments and prominences are classical examples of condensations of nongravitational origin, their formation being due to the thermal instability. The physics of this instability in a uniform plasma at coronal temperatures, which exhibits increasing radiative output as it cools, is well known (Field, 1965). Filaments, however, form in regions of sheared magnetic fields, as evidenced by their location above photospheric polarity-inversion lines and their occurrence after a period of increasing fibril inclination (Tandberg-Hanssen, 1974). Physically, the importance of the field structure is readily understood if one recalls the capability of magnetic field of strongly collimating the local heat conduction. Thus, the preferred locations for the development of the thermal instability will be those where the field configuration inhibits the stabilizing effects of thermal conduction on the growing temperature perturbation.