Regarding new bipolar magnetic regions as sources of flux, we have computed the evolution of the photospheric magnetic field during 1976 1984 and derived the corresponding evolution of the mean line-of-sight field as seen from Earth. We obtained a good, but imperfect, agreement between the observed mean field and the field computed for a nominal choice of flux transport parameters. Also, we determined the response of the computed mean field to variations in the transport parameters and the source properties. The results lead us to regard the mean-field evolution as a random-walk process with dissipation. New eruptions of flux produce the random walk, and together differential rotation, meridional flow (if present), and diffusion provide the dissipation. The net effect of each new source depends on its strength and orientation (relative to the strength and orientation of the mean field) and on the time elapsed before the next eruption (relative to the decay time of the field). Thus the mean field evolves principally due to the contributions of the larger sources, which produce a strong, gradually evolving field near sunspot maximum but a weak, sporadically evolving field near sunspot minimum.