THE solar wind is a supersonic outflow of coronal plasma into interplanetary space, and is the agent that carries solar disturbances to the Earth. Direct measurements of the wind speed over a range of distances-from the orbit of Mercury(1) to beyond the outermost planets(2) and now over the solar poles(3)-show that the acceleration is largely complete by 70 solar radii (R(.)). But there are no direct measurements nearer the Sun with which to constrain theoretical models of the acceleration. In principle, the speed of the solar wind in the acceleration region can be inferred by indirect methods such as radio scattering, but this is not straightforward as these data provide a measure of the wind properties integrated along the lines of sight. Here we report radio-scattering measurements of the speed of the south polar stream which have been corrected for this path integration, and also for the potential bias due to the presence of plasma waves. Our results indicate that the acceleration of the polar wind is almost complete by 10 R(.), much closer to the Sun than had been expected(4). This suggests that the acceleration of the sofar wind and the heating of the solar corona occur in essentially the same region, and thus that the underlying mechanisms may be strongly linked(5).