Murnaghan’s theory of finite strain has been applied in an approximate form to a study of the density and velocity variations in a simplified model of the earth outside the core; the model consists of two homogeneous layers each at a uniform temperature. Following Jeffreys, the layers are separated by a first-order discontinuity at a depth of 474 kilometers. Above 474 kilometers the variations of the velocities in this model are shown to be practically identical with Jeffrey’s “observed” values. The main features of the velocity-depth curves are represented with fair precision down to the core. This is of course no longer true if the velocities are supposed to vary continuously through the 474-kilometer level. In either case, in order to reproduce closely the rate of change of velocity immediately below 474 kilometers a gradual change of composition must be introduced. The variation of density in the two-layer case is . . .