We describe a model for the formation of the cool condensed material t
hat comprises a coronal filament or prominence. Numerical calculations
are presented which demonstrate that large condensations form in a co
ronal loop if the loop satisfies two key requirements: (1) the loop he
ating must be localized near the chromospheric footpoints, and (2) the
loop must have a dipped geometry in order to support the prominence c
ondensation against gravity. We calculate one-dimensional equilibrium
solutions for the equations of force and energy balance assuming optic
ally thin radiative losses and a parameterized form for the coronal he
ating. This physical situation is modeled as a boundary value problem,
which we solve numerically using a B-spline collocation scheme. The r
elation of our solutions to the well-known loop scaling laws is discus
sed, and the implications of our model for active region and quiescent
prominences are discussed.