The low Reynolds number dynamics of a thin layer of fluid bounded below by a flat horizontal boundary and above by a fluid of another viscosity and greater density is reported. Three distinct stages of growth were observed. The first stage is a Rayleigh-Taylor instability, in which disturbances of one specific wave number grow most rapidly. If &egr; is the ratio of the viscosity of the thick layer to the viscosity of the thin layer, fastest growth is for wave number &egr;-1/3. In the second stage, distortion of the interface is large, and it is found experimentally that the fluid moves out of the thick layer as circular columns surrounded by relatively broad regions of descending material. In the third stage, fully matured structures are formed. If the upwelling material has less viscosity than the surrounding material, the structure develops a rim syncline and a pronounced overhang and eventually ascends as a sperical pocket of fluid fed by a conduit. Two applications to geophysics are given: The first application follows from the fact that a melt source must exist in the mantle below mid-ocean ridges. This source can be approximated as a cylindrical body with lower viscosity and density compared to the overlying mantle. If the cylinder develops a gravitational instability, it will develop regularly spaced vertical protrusions. Estimates of the spacing are compared to high-resolution segmentation data, and some constraints on viscosity of the mantle below spreading centers are made. These are that viscosity of the mantle is 1018¿1 P, and the ratio of this viscosity to the viscosity of the cylinder is less than 100. In the second application, the upwelling conduits are measured experimentally and solitary waves are observed. A recently found analog with magma rising up through the pores of a viscous crystalline matrix is discussed.