This paper considers the quasi-steady evolution of solar magnetic fields in response to gradual photospheric changes. Special interest is taken in the threshold of a sudden eruption in the solar atmosphere. The formal model of an evolving, force-free field dependent on two Cartesian coordinates has been treated previously, and we extend it to a field which is not force free but in static equilibrium with plasma pressure and gravity. The basic physics is illustrated by the evolution of a loop-shaped electric current sheet enclosing a potential bipolar field with footpoints rooted in the photosphere. A free-boundary problem is posed and solved for the equilibrium configuration of the current sheet in a hydrostatically supported isothermal atmosphere. As the footpoints move appart to spread a constant photospheric magnetic flux over a larger region, the equilibria available extend the field to increasingly great heights. Two basic behaviors are possible, depending on the ratio of the total magnetic flux to an equivalent flux constructed dimensionally from the pressure difference across the current sheet and the density scale height. For a small, total magnetic flux, nonequilibrium can set in with the appearance of a marginally stable equilibriu, as demonstrated previously for the frece-free fields. Formore » a total magnetic flux exceeding a certain critical value, the field lines rise high enough for gravity to play a significant role. The sequence of equilibria in this case suggests that nonequilibrium can set in with the opening of the field lines by magnetic buoyancy. This eruption can also take place with a prominence filament and may be the origin of the white light coronal transient.« less