Neutron monitor data recorded at Thule, Greenland, and McMurdo, Antarctica, are used to determine the cosmic-ray north-south anisotropy over the period 1961-1988. This anisotropy shows an 11 yr sunspot cycle variation, but it does not exhibit a dependence upon the direction of the Sun's magnetic dipole. The north-south anisotropy together with the two components of the diurnal anisotropy comprise a three-dimensional anisotropy, from which we extract detailed new information on the radial and latitudinal gradients of cosmic-ray density and the cosmic-ray scattering mean free path near Earth. We find that the bidirectional latitude gradient reverses sign with the solar magnetic polarity reversal, in accord with the predictions of drift theory, and its magnitude is generally larger during negative solar polarity than during positive polarity