Two‐dimensional numerical models of steady state convection show that convection cells of aspect ratio as large as 8.6 are possible for variable viscosity convection in the upper mantle. Our models include the effects of variable viscosity, viscous dissipation, internal heating, heat flow through the bottom, and the adiabatic gradient. The large aspect ratio of the convection cells is primarily due to the large viscosity contrast between the lithosphere and the asthenosphere. It appears possible for multiple convection cells to occur in a low‐viscosity zone while the surface velocities give the appearance of a single cell. The details of the viscosity law relevant to mantle materials and conditions are presently uncertain but are of crucial importance; temperature, viscosity, and flow patterns are inextricably entwined. Convection decreases the overall temperature gradient; consequently, generally accepted temperatures for most of the mantle are too high. The controversies over plate‐mantle decoupling and passive versus active plates are probably due to oversimplifications that disregard hydrodynamic concepts.

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The boundary conditions on the faces of compressional fractures are not known a priori since these faces may or may not be in contact, but the product of the normal stress and the normal relative displacement is necessarily null; similar but more complex conditions may be written for the shear stress and displacement. These conditions can be expressed in the form of a mixed linear complementarity problem. We use the Displacement Discontinuity Method and the PATH algorithm to solve them. This scheme is faster and more accurate than the methods previously used. The shear stresses on two parallel cracks depend on their separation, their inclination with respect to the imposed maximum compressional stress, and their geometry. The shear stress on two horizontal cracks separated by a small upward or downward step Ð considering the imposed direction of motion Ð drops to zero very near the step; in the case of a downward step this region is surrounded by a small region where the stress increases by a factor of about 10. Many more cases must be investigated before general conclusions can be drawn. 7

The methods of two dimensional model seismology were used to investigate the phenomena occurring when a Rayleigh wave is incident upon a corner whose angle is comprised between 0° and 180°. The wave bends its path only for angles between 130° and 180°. For smaller angles large and abrupt variations in reflection and transmission occur; the wave travels to the extremity of the corner and never “cuts corners”; only about 50 percent of the energy of the indicent surface wave is preserved as such, the rest goes into body waves; for a 90° corner the proportion is about 23 percent in P and 26 percent in S, with sharply preferential angles of incidence. The percentages given were found for a “plate Poisson’s ratio” of 0.17.

All the epicenters determined in the central part of the West African Rift Valley up to the middle of 1958 have been plotted on a map. Most of them are on the faults which border the Rift; a few are on faults which crosscut it. The eastern Virunga ‘extinct’ volcanoes show a fairly strong seismic activity. The most important discovery is that of a transverse zone stretching west from Lake Kivu to the Congo River (450 km); extinct or active volcanoes are located at the intersection of this zone with the Rift Valley. Diagrams show the amount of seismic energy liberated per year within 500 km of Lwiro. The mean value is 3.5×1020 ergs/year, which is about 0.03 per cent of that of the earth as a whole.