We prcscnt a theoretical model of quiescent prominences in the form of an infinite vertical sheet. Self-consistent solutions arc obtained by integrating simultaneousl~ thc set of nonlinear equations of magnctostatic equilibrium and thermal balancc. The basic features of the models arc:
(1) The prominence matter is confined to a sheet and supported against gravity by a bowed magnetic field. (2) Thc thermal flux is channellcd along magnetic field lines. (3) -I'he thermal flux is evcrywhere balanced by Low's (1975b) hypothetical beat sink which is proportional to the Iocal density. (4) A constant component of the magnetic field along the length of the prominence shields the cool plasma from the hot surrounding. We assumc that the prominence plasma emits more radiation than it absorbs from the radiation ficlds of the photosphere, chromosphcrc and corona, and we interpret the aboxc hypothetical heat sink to represent the amount of radiative loss that must be balanced by a nonradiative encrgy input. Using a central density and temperature of 10 a~ particles cm -3 and 5000 K respectively, a magnetic field strength between 2 to 10 gauss and a thermal conductivity that varies linearly with temperature, we discuss the physical properties implied bv the model. Thc analytic treatment can also be carried out for a class of more complex thermal conductivities. Thcse models provide a useful starting point for investigating the combined requirements of magnetostalic equilibrium and thermal balance in the quicscent prominence.