The problem of axisymmetric diffusion from a line source under constant flux in a soil is discussed. Earlier results are greatly simplified and made more accurate as well. An exact solution for power law diffusivities agrees remarkably well with a general analytical approximation for powers that cover the range from clay to sand. The latter could be used to predict the saturated front position, thereby simplifying the numerical prediction of the profile, or to predict the whole profile with a lesser accuracy