The geomagnetic field, suitably scaled down and parameterized, is shown to give a very good fit to the magnetic field measurements taken on the first and third passes of the Mariner 10 space probe past Mercury. The excellence of the fit to a reliable planetary magnetospheric model is good evidence that the Mercury magnetosphere is formed by a simple, permanent, intrinsic planetary magnetic field distorted by the effects of the solar wind. The parameters used for a best fit to all the data are (depending slightly on the choice of data) 2.44--2.55 for the ratio of Mercury's magnetic field strength at the subsolar point to that of the earth's subsolar point field (this results in a dipole moment of 170 &ggr;RM3 (RM is Mercury Radius), i.e., 2.41¿1022G cm3 in the same direction as the earth's dipole), ~-113 &ggr;RM4 for the planetary quadrupole moment parallel to the dipole moment, 10¿--17¿ for the tilt of the planet dipole toward the sun, 4.5¿ for the tilt of the dipole toward dawn, and 2.5¿--7.6¿ aberration angle for the shift in the tail axis from the planet-sun direction because of the planet's orbital velocity. The rms deviation overall for the entire data set compared with the theoretical fitted model for the magnetic field strength was 17 &ggr; (~4% of the maximum field measured). If the data from the first pass that show presumed strong time variations are excluded, the overall rms deviation for the field magnitude is only 10 &ggr; (~2.5% of the maximum field measured).