A quantitative model of the external magnetospheric field has been derived by making least squares fits to magnetic field measurements from four Imp satellites. The data set consists of 12,616 vector field averages over half-earth radii intervals between 4 and 17 RE, taken from 451 satellite orbits between 1966 and 1972. The data were fit to a power series expansion in the solar magnetic coordinates and the solar wind-dipole tilt angle, and thus the model contains the effects of seasonal north-south asymmetries. The expansion is divergence free, but unlike the usual scalar potential expansion, the model contains a non-zero curl representing currents distributed within the magnetosphere. The model includes four sets of coefficients, representing different degrees of magnetic disturbance as determined by the range of Kp values. The latitude at the earth separating open polar cap field lines from field lines closing on the day side is about 5¿ lower than that determined by previous theoretically derived models. At times of high Kp, additional high-latitude field lines extended back into the tail. Near solstice, the separation latitude can be as low as 75¿ in the winter hemisphere. The average northward component of the external field is much smaller than that predicted by theoretical models; this finding indicates the important effects of distributed currents in the magnetosphere. Current densities implied by the model are of the order of 10-9 A/m2 across the magnetotail.