The radial component of the magnetic field in the southern hemisphere has been measured at Ulysses as it traveled from the equator to -80.2¿ latitude and returned. The radial component multiplied by the square of the radial distance, i.e., BRr2, averaged over 77 day intervals (three solar rotations) is approximately constant at -3.5 nT and shows no evidence of a dependence on heliographic latitude. To discriminate against possible time variations, the measurements have been compared with simultaneous observations in the ecliptic by IMP-8. The two sets of observations agree very well confirming the absence of a significant latitude gradient. Since the sun's dipolar magnetic field component is strong at this phase of the sunspot cycle, it is inferred that magnetic flux from the polar cap is transported to lower latitudes in the solar wind source region to produce a uniform radial field. Such a configuration would be expected if magnetic stresses are influencing the solar wind flow near the sun and are contributing to a non-radial deflection. Estimates of the flux of open field lines (3¿1014 webers), of the non-radial solar wind expansion (~3) and the polar cap magnetic field strength (~5 Gauss) are derived. ¿ American Geophysical Union 1995